AERONAUTICAL
VESTPOCKET
HANDBOOK
Part No. P&W 79500
Twenty-Fourth Edition - First Printing
July 2006 Printed in the U.S.A
Table of Contents
Introduction
Soaring Through Time
.. 1
Pratt & Whitney Contact Information
.... 12
Technical Data
Conversion Factors . . . . . . . . . . . . .
. . . . . . . . . . . . .
. .... 15
Miscellaneous Conversions Weights and Measures
......... 28
Weights of Gases . . . . . . . . . . . . . . . . . . .
. .30
Heat and Temperature . . . . . . . . . . . . . . . . . . . . .
.
..... 31
Standard Atmosphere . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . .
.32
Compressible Flow Functions ............................. .44
General Properties of Air ................................. 71
General Properties of Gases . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .. 73
Atmospheric Viscosity ................................... 75
Specific Heats of Air at Low Pressures ...................... 76
Specific Heats of Products of Combustion .................... 77
Properties of Materials ................................... 80
Properties of Elements ................................... 88
Physical Constants ...................................... 94
Metric System (SI)
- SI Base and Supplementary Units . . . . . . . . . . .
. .......... 98
- SI Derived Units .................................... 99
- Standards . . . . . . . . . .
. . . . . . . . . . . . . . . ............... 102
- Metric Equivalents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .103
SI Prefixes
Multiples and Subdivisions ................... 104
Aircraft Information
Aerodynamic Terms ....................... .
Aerodynamic Relationships . . . .
. ... .
Airspeed Relationships . .
. . .
. ... .
Aircraft Noise Regulations and Restlictions
Absolute World Records .
Airlines and Airports
Two Letter Designation Codes of Selected Airlines
Major International Airport
. ....... 108
. . .. .
. .. 109
. .110
17
.120
125
Aviation Fuels and Lubricants
Jet Fuels . . . . . . . . . . . .
. .
Aviation Fuel and Lubricant Specifications
Gas Turbine Engines
. ... 130
... 131
Engine Types
Descriptions . . . .
. . . . .
. . .
. ....... 134
Engine Types
Station Designations
. . . . . . . . . .
.138
Turbojet and Turbofan Engine Noise . . . . . . . . . . . . . . . .
. ... 141
Gas Turbine Engine Symbols Used by Pratt & Whitney . . ..... 145
Gas Turbine
Subscripts . . . . . . . . . . .
. ............... 147
Pratt & Whitney Engine Characteristics ..................... 148
Pratt & Whitney Canada (PWC) Engine Characteristics ........ 156
Gas Turbine Parameter Correction Procedures . . . . . . . . . . . . .... 161
Theta Tables . . . . ...................................... 162
Compressor Inlet Pressure Recovery ....................... 170
Compressor Inlet Pressures and Temperatures ................ 171
Rocket Engines
Other Reaction Engines . . . . . . . . . . . . . . . . . . . . ............ 190
Liquid Rocket Engine Cycles ............................. 192
Theoretical Rocket Engine Propellant Summary . . ............ 196
Vapor Pressure of Liquid Propellants ....................... 198
Specific Gravities of Liquid Propellants ..................... 199
Liquid Rocket Engine Symbols ........................... 200
Rocket Engine Equations ................................ 203
Rocket Engine Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .204
Cryogenic Liquid Rocket Fuels . . . .
. . . . . . . . . . . .......... 206
U.S. Military
U.S. Military Aircraft Designations . . . . . . . .
. . . . . . . . . . . . .208
Standardized MDS Designator Symbols and
Descriptions for Guided Missiles, Rockets,
Probes, Boosters and Satellites . . . . . .
. . . .
The United States Military Enlisted Rand Insignia
The United States Military Officer Rank Insignia
HSo and World Maps
World Time Zones
U.S. Time Zones
ii
. .210
.211
INTRODUCTION
Soaring Through Time
Frederick Brant Rentschler founded Pratt & Whitney Aircraft in 1925
dming the early years of powered flight. With a small group of selected
engineers, he set out to develop a new, lightweight air-cooled engine with
a thrust-to-weight ratio unheard of at a time when heavier liquid-cooled
engines were the standard.
On Christmas Eve of 1925, the company's first engine was completed. It
was an air-cooled radial piston with 1340 cubic inches of displacement
that featured a revolutionary design for the crankshaft and master rod, and
weighed only 650 pounds. Called the Wasp, it was an immediate success,
shattering one record after another for speed, climb, performance at
altitude and reliability.
From the mid-1920s through the mid-1940s, Pratt & Whitney designed
eight different air-cooled radial models and produced hundreds of
thousands of engines for military and commercial applications.
R-1340 Wasp was in production from 1926 to 1960, with almost
35,000 engines manufactured. Charles Lindbergh shattered the
transcontinental speed record in 1930 and Amelia Earhart made
history with their Wasp-powered aircraft. Some major installations
included
Amphiblions N-2-C
Atlantic C-5
Boeing Model 40A
Lockheed C-17 Vega
Vought 02U Corsair
R-1690 Hornet was
power plant during the early growth years of
commercial air transportation. Initially rated at 525 horsepower, later
models developed more than 875 horsepower. Some popular
installations included
American Airplane &
l 00A Pilgram
BoeingYB-9
Boeing Model 40-B
Keystone LB-7, 8, lOA, 12,
03U-2 Corsair
R-985 Wasp Jr. was a smaller, 300 horsepower radial engine designed
for sport aircraft, helicopters and light transports. More than 39,000
hornet engines were produced with some popular installations as:
Airspeed Oxford V
Beech F-2 Kansas
Beech l 8S Series
Bell Model 42
Sikorsky S-51
Spartan UC-71 Executive
R-1535 Twin Wasp Jr. was Pratt & Whitney's first air-cooled piston
engine designed in a twin-row configuration. It produced 825
horsepower with some popular installations as
Boeing Model 247 A
Douglas 0-46A
Fokker G-1
Northrop A-17, 17A Nomad
Northrop BT-I
R-1830 Twin Wasp was a twin-row engine that displaced 1830 cubic
inches and delivered up to 1350 horsepower. A popular engine during
World War II, 173,618 Twin Wasp engines were built - more than any
other aircraft engine in history. Some popular installations included
Consolidated Vultee B-24 (PB4Y-1) Liberator
Douglas DC3A (C-41)
Douglas C-47 (R4D) Dakota Skytrain
Ford C-109 Flying Tanker
Grumman F4F Wildcat
R-2000 Twin Wasp was a derivative of the R-1830 built specifically
for Douglas' DC-4 aircraft. It delivered 1300 horsepower on 90 octane
fuel, with later models producing up to 1450 horsepower. Some
popular installations included
Cancargo CBY-3 Loadrnaster
Douglas DC-4 (C-54, R5D) 'CLnc;,n"l<>C't;:,,r
de Havilland DH C-4 Caribou
R-2800 Double Wasp was an 18-cylinder, twin-row engine that
provided up to 2,500 horsepower with improved water injection and
turbo-supercharging systems. Some popular installations included
Grumman F6F Hellcat
Grumman F7F Tigercat
Grumman F8F Bearcat
Republic P-4 7 Thunderbolt
Sikorsky S-56 (H-37, HR2S)
R-4360 Wasp Major was the largest and last piston engine built by Pratt
& Whitney. This powerful spiraling four-row, 28-cylinder configuration
delivered up to 4,300 horsepower. Some popular installations included
Boeing B-50
Boeing C-97, Model 377 Stratocruiser
Boeing B-377PG Pregnant Guppy
Douglas C-74 Globemaster I
Douglas C-124 Globemaster II
Pratt & Whitney was the revered king of piston engine power. However,
technology was moving aviation toward the faster and higher-performing
jet engine, an area unfamiliar to Pratt & Whitney at the time. The start was
slow. But, soon, in the early 50s, the company leapfrogged the industry
with the J57 jet engine -
a design that was as popular as the Wasp.
The 1950s were also a time of growth and diversification for the company.
Pratt & Whitney Canada, an overhaul affiliate founded in 1928, started
designing and manufacturing small aircraft engines and the company also
entered the field of liquid-fueled rocket propulsion. In addition, during the
next decade the company directed its business interests towards new
markets in marine and industrial electric power generating applications.
J42 Turbo Wasp was a centrifugal-flow turbojet
developing 5,000 pounds of thrust.
Grumman F9F-2 Panther
capable of
J48 Turbo Wasp was a centrifugal-How turbojet engine that developed
7,250 pounds of thrust and up to 8,750 pounds of thrust with
Grumman F9F-5 Panther
Grumman F9F-6, 8 Cougar
Lockheed F-94C Starfire
4
T34 was an axial-flow turbojet producing up to 7,200 horsepower. It
was featured on the
Douglas C-133 Cargomaster
Boeing B-377SG Super Guppy
Boeing C-97 J
Lockheed C-121F Constellation
J57 (JT3 Commercial) turbojet was aviation's first axial-flow, dual-
spool engine configuration. Producing up to 19,600 pounds with
afterbuming, more than 21,000 engines were built. Some popular
installations included
McDonnell F-101 Voodoo
General Dynamics F-102 Delta Dagger
Boeing B-52 Stratofortress
Lockheed C-135A Stratolifter
Ling-Temco Vought F-8 Crusader
Douglas A3D Skywarrior
Douglas F4D, F5D Skyray
Boeing 707-120
J75 (JT4 Commercial) was a dual-spool turbojet capable of
producing up to 26,500 pounds of thrust with afterbuming. The
engine's core was also used for industrial and marine applications.
Popular installations included
Republic F-105 Thunderchief
General Dynamics F-106 Delta Dart
Boeing 707-220, -320
McDonnell Douglas DC-8-20, -30
North American F-107 A
J52 was an axial-flow non-afterbuming turbojet in the 8,500 to 11,200
pound thrust class.
McDonnell Douglas A-4 series Skyhawk
Grumman A-6 series Intruder
North American Rockwell Missile AGM-28 Hound
J60 (JT12 Commercial) is the company's smallest turbojet.)
spool configuration that produced 3,300 pounds of thmst.
Rockwell International T-2B Buckeve
Rockwell International T-39A Sabe;liner
Lockheed Cl40 Jetstar
5
J58 was the company's most powerful turbojet. Producing 30,000
pounds of thrust, it powered Lockheed's SR-17 Blackbird at speeds as
high as Mach no. 3 and altitudes in excess of 80,000 feet.
Lockheed SR-71 Blackbird
Lockheed YF-12A
JFTD12 was a higher thmst, turboshaft version of the sm1sie-snnrn
JT12 engine. It produced 4,800 shaft horsepower.
Sikorsky S-64 Skyplane
Sikorsky CH-54A
TF33 (JT3D Commercial) was a low-bypass ratio turbofan derivative
of the JT3 turbojet. It is capable of 23,000 pounds of thrust. Some
popular models included
Boeing 707-120B, 320B, & C, 323C
McDonnell Douglas DC-8-50, 60
Boeing B-52H Stratofortress
Boeing KC-135B Stratotanker
Lockheed C-141A Starlifter
Boeing V C-13 7B, C Presidential Plane
RLlO was the first liquid-fueled engine to operate successfully in
space. A regenerative-cooled, pressure-fed, expanding-cycle engine, it
was used to help launch a number of spacecraft such as the Voyager,
Viking and Pioneer.
JT8D family, a low-bypass ratio and axial-flow series of turbofan
engines, was considered commercial aviation's workhorse from the
1960s through the 1980s as well as the benchmark for low
maintenance cost. The engine's core was also used for industrial
applications. The engine family covered the 14,000 to 17,400 pound
thrust range. Installations included
Boeing 727
Boeing 737
McDonnell Douglas DC-9
Saab 37 Series Viggin
Japan C-1
McDonnell Douglas MD-80 Series
6
TF30 was a low-bypass ratio turbofan
of producing more than
25,000 pounds thrust with its unique ea!m-zor1e afterburning system.
General Dynamics F-111
LTV A-7 A, B, C Corsair II
Grumman F-14A Tomcat
PT6, the first
developed by Pratt & Whitney Canada, covered
the 580 to 2000
horsepower range and was used in more than 100
applications. Some popular installations included
Raytheon Beech C90
Raytheon Beech Super King Air 200
de Havilland Canada Twin Otter
de Havilland Canada Dash 7
Piper Cheyenne
Bell UH-IN Twin Huey
Bell AN- IJ Sea Cobra
Sikorsky S-58T
Sikorsky S-76
The 1970s at Pratt & Whitney saw additional technological achievements,
a range of new products and business expansions that would carry the
company through the early 1990s. Commercial aviation entered a new era
with the high-bypass ratio engine and jumbo jetliner, while military
aircraft started a wave of power supremacy with the Fl 00 series engine
family. Both Pratt & Whitney's small engine and large commercial engine
businesses flourished with a number of new turbofan products.
JT9D family, covering a thrust range from 46,300 to 56,000 pounds,
was the first high-bypass ratio turbofan engine to serve commercial
aviation on a new generation of wide-bodied aircraft, starting with
Boeing's 747 aircraft. Some popular installations included
Boeing 747
Boeing 767
McDonnell Douglas DC-10-40
Airbus A310
Airbus A300-600
7
JTlSD, Pratt & Whitney Canada's first small turbofan, covered the
2,200 to 2,900 pound thrust range. It powered such
aviation
aircraft as
Aerospatiale Augusta S2 l 1, S211A Corvette
Beech T-lA Jayhawk
Cessna Citation I, II, SII
Cessna Citation V, Ultra
Peregrine by Gulfstream Aerospace
FlOO family is a high-performance, low-bypass ratio turbofan in the
25,000 pound thrust range with full afterbuming and an 8-to-l thrust-
to-weight ratio.
McDonnell Douglas F-15 Eagle
General Dynamics F-16 Fighting Falcon
Fl19 is a turbofan in the 35,000 pound thrust class capable of
supersonic cruise without an afterburner and thrust vectoring with a
two-dimensional, convergent-divergent exhaust nozzle.
Lockheed Martin F-22 Raptor
PWl00 series is a centrifugal turboprop engine that covers the 1800 to
2750 range of shaft horsepower. Its 25 different models powers
regional transports as well as utility and corporate aircraft.
Aerospatiale-Alenia ATR42-300/400/500/3200
Aerospatiale-Alenia ATR-72-210/500
Conadiar CL-215T/CL-415
Bombardier Aerospace QlO0, Q200, Q300
Ilysuhin IL-114-100
Bombardier Aerospace Q400
PW200 is a centrifugal flow turboshaft configuration produced by
Pratt & Whitney Canada and designed for light helicopters requiring
500 to 900 shaft horsepower.
Augusta Al09
Bell 427
Eurocopter EC 135
Kaman Ansat
McDonnell Douglas MD "-'AfJn.Hvt
8
PW2000 is a modem high-bypass ratio engine in the 37 ,000- to
41,700-pound thrust class. It introduced the full-authority
electronic control (FADEC) to commercial aviation.
Boeing 757
Fll7, a military version of the PW2000 commercial engine, is rated at
41,700 pounds of thrust.
McDonnell Douglas C-17 Globemaster III
V2500, which covers the 18,000- to 33,000-pound thrust range, is a
two-spool turbofan developed by a five nation consortium, called
International Aero Engines, in which Pratt & Whitney is a major
shareholder.
Airbus A319
Airbus A320
Airbus A321
Boeing MD-90
PW300 is a dual-spool, axial-flow turbofan in the 4,600- to 7,000-
pound thrust range designed to power business aircraft for
intercontinental and transcontinental missions. Installations include
Fairchild Dornier 328 Jet Envoy 3
IAI Galaxy
Learjet Model 60
Raytheon Hawker 1000
Raytheon Hawker Horizon
Gulfstream G200
Cessna Citation Sovereign
Dassault 2000 EX Falcon
PW4000 94-inch fan engine is the first in a family of high-thrust
models, covering the 52,000- to 62,000-pound thrust range, for wide-
bodied aircraft. A prominent feature is a large core for anticipated
thrust growth.
Boeing 747
Boeing 767
Airbus A300
Airbus A310-300
Boeing MD-11
9
PWS00 is a turbofan engine in the 3,000- to 4,500-pound thrust class
featuring advanced technologies to lower noise and emissions. Some
installations are
Cessna Bravo
Cessna Excel
Cessna Ultra Encore
Cessna UC-35C/D
PW4000 100-inch fan engine, the first growth model in the PW4000
high thrust family, covers the 64,000- to 68,000-pound thrust range
and was designed specifically for the A330 wide-bodied aircraft. It
was the first derivative engine approved for early ETOPS ( extended-
range twin-engine operations).
Airbus A330
Through the 1990s and into the next of the century, Pratt & Whitney
power dominated the military market as well as maintained a strong
presence in small and large commercial aircraft business segments.
Parallel with developing new technologies and products, the company
focused on significantly expanding its maintenance services capabilities.
Through acquisitions, joint ventures and partnerships, the company
quickly strategically positioned itself as a premier provider of overhaul,
repair and customer-tailored maintenance programs not only for Pratt &
Whitney models, but also for competitor engines.
Also, in 2004, Pratt & Whitney acquired Rocketdyne, a world leader in the
manufacture of solid and liquid rocket engines since the early 1950s.
Complementing its liquid engine products, Pratt & Whitney Rocketdyne
was the clear leader in space propulsion.
PW4000 112-inch fan engine is the highest thrust turbofan built by the
company, covering the 74,000 to 98,000 pound thrust range. A dual-
spool, I 0-foot diameter fan design with many technological
advancements, it was aviation's first aircraft engine to receive 180-
minute ETOPS before
revenue service.
Boeing 777 se1ies
P135 Joint Strike Fighter
rated in the 35,000 pound thrust
class, combines a derivative of the Fl 19's core with several
technological enhancements in electronics, lift-fan orcmu1s1cm and
aerothermodynantics.
Lockheed Martin F-35
10
PW6000 turbofan, with 18,000 to 24,000 pounds thrust, is designed
with advanced aerodynamics for fewer compressor and turbine stages,
..,._,,.u . "'h in a substantial reduction in maintenance and operating costs.
Airbus A318
Airbus A3 l 8 Elite
RLlOB-2 produces 24,750 pounds
specific thrust and features a
carbon-carbon extendible nozzle that enables a remarkable 465.6
seconds of
impulse.
PW600 is a 2,400-pound thrust dual-spool turbofan used for business
and
aviation aircraft.
Eclipse 500
Cessna Mustang
GP7000 is a high-thrust, dual spool turbofan in the 72,000- to 81,000-
pound thrust range developed by the Engine Alliance, a partnership
between Pratt & Whitney and General Electric.
AirbusA380
RL60 is an advanced liquid-hydrogen upper stage power plant in the
50,000 to 65,000 pound thrust range.
Pratt & Whitney Rocketdyne offers a range of products that
power installations such as the Space Shuttle, Atlas rockets, and the
Delta II/III/IV launch vehicles.
For decades, Pratt & Whitney has brought leadership in technical
innovation to aviation. Going into the future, it remains clear that" ... only
the best airplane can be built around the best engine," as profoundly stated
by Frederick Rentschler. It's been that way at Pratt & Whitney since 1925.
I,
Pratt & Whitney Contact Information
Corporate Headquarters
Pratt & Whitney
400 Main Street
East Hartford, CT 06108
United States: 860.565.4321
24 Hour Customer Help Desk
Airline Support
United States: 800.565.0140
International: 860.565.0140
help24@pw.utc.com
Military Customer Technical Support
United States: 800.526.1159
Support Equipment Operations Technical Support
United States: 800.233.1849
Power Systems Customer Support
United States: 866.769.3725 (866.POWER-ALL)
info@pw.utc.com
Pratt & Whitney Canada Main Switchboard
450.677.9411
Pratt & Whitney Rocketdyne
Jeff Kincaid, V.P. Engineering
818.586.4469/jeffrey.kincaid@pwr.utc.eom
Web site
ww\v.pw.utc.com
12
TECHNICAL DATA
14
Conversion Factors
Multiply
By
To obtain
acre
4.3560 X 104
square feet
4.0469 X }0-1
hectares
4.0469 X }03
square meters
1.5625 X 10-3
square miles
4.8400 X }03
square yards
atmosphere
7.6000 X 10
centimeters of mercury
(atm) (1962)
2.9921 X 10
inches of mercury
1.0332 X 104
kilograms/ square meter
1.0133 X 105
newtons/ square meter
1.4696 X 10
pounds/ square inch
bar
9.8962 X 10-1
atmospheres
1.0000 X 106
dynes/ square
centimeter
7.5006 X 102
millimeters of mercury
1.0000 X 1()5
newtons/ square meter
1.4504 X 10
pounds/ square inch
barn
1.0000 X 10-24
square centimeters
(nuclear cross-section)
barrel, liquid
3.1500 X 10
gallons
{U.S.)
1.1924 X lQ-1
cubic meters
British thermal
2.5180 X JQ2
calories (post-1956 1ST)
unit (Btu)
7.7817 X }()2
foot-pounds
1.0551 X 1010
ergs
3.9301 X 10-4
horsepower-hours
1.0551 X 103
joules
1.0551 X 103
newton-meters
2.9302 X IQ-4
kilowatt-hours
1.0551 X 103
watt-seconds
British thermal
4.1999
calories/ second
unit/minute
1.7548 X 108
ergs/ second
(Btu/min)
1.2970 X 10
foot-pounds/ second
2.3581 X 10- 2
horsepower
1.7548 X 10
joules/ second
1.7931
kilogram-meters/ second
1.7548 X 10
watts
' ~-~--=--"""'""-~"=-
15
Conversion Factors ( continued)
Multiply
By
To obtain
calorie
3.9683 X lQ-3
British thermal units
(cal)
3.0880
foot-pounds
4.1868 X 1Q7
ergs
4.1868
joules
1.1630 X 10-6
kilowatt-hours
4.1868
watt-seconds
calorie/ second
2.3810 X 10-1
British thermal
(cal/sec)
units/minute
4.1868 X 101
ergs/ second
3.0880
foot-pounds/ second
4.1868
joules/ second
centimeter
3.2808 X lQ-2
feet
(cm)
3.9370 X }0-1
inches
1.0000 X 1Q-S
kilometers
1.0000 X lQ-2
meters
1.0936 X tQ-2
yards
centimeter/
3.2808 X J0-2
feet/second
second
3.9370 X lQ-1
inches/ second
(cm/sec)
1.0000 X 10- 2
meters/ second
centipoise
6.7197 X }0-4
pounds (mass)/ second-foot
3.6000
kilograms/ hour-meter
chain
].0000 X 1Q2
links
(surveyor)
2.2000 X 10
yards
6.6000 X 10
feet
2.0117 X 10
meters
cord
1.2800 X 102
cubic feet
cubic centimeter 1.0000 X I0-3
cubic decimeters
(cm3)
3.5315 X 10-5
cubic feet
6.1024 X 10-2
cubic inches
1.0000 X }Q-6
cubic meters
1.3080 X 10-6
cubic yards
cubic decimeter 1.0000 X 103
cubic centimeters
(liter)
3.5315 X lQ-2
cubic feet
(dm3)
6.1024 X 10
cubic inches
1.0000 X 10-3
cubic meters
1.3080 X lQ-3
cubic yards
16
Multiply
By
To obtain
cubic foot
2.8317 X 104
cubic centimeters
(ft3)
2.8317 X 10
cubic decimeters
1.7280 X 103
cubic inches
2.8317 X lQ-2
cubic meters
3.7037 X 10-2
cubic yards
cubic foot H2O
(60F)
6.2366 X 10
pounds
cubic inch
1.6387 X 10
cubic centimeters
(in3)
1.6387 X 10-2
cubic decimeters
5.7870 X 10-4
cubic feet
1.6387 X to-5
cubic meters
2.1433 X }0-5
cubic yards
cubic meter
1.0000 X 1()6
cubic centimeters
(m3)
1.0000 X 103
cubic decimeters
3.5315 X 10
cubic feet
6.1024 X 104
cubic inches
1.3080
cubic yards
cubic yard
7.6455 X 1Q5
cubic centimeters
(yd3)
1.6455 X 102
cubic decimeters
2.7000 X 10
cubic feet
4.6656 X 104
cubic inches
7.6455 X 10-1
cubic meters
curie
3.7000 X 1010
disintegrations/ second
degree
6.0000 X 10
minutes
(deg)
1.7453 X JQ-2
radians
2.7778 X 10- 3
revolutions
3.6000 X J03
seconds
dyne
1.0197 X }Q-3
grams
1.0197 X 10- 6
kilograms
1.0000 X lQ-5
newtons
3.5970 X lQ-5
ounces
2.2481 X }0-6
pounds
dyne/ square
2.9530 X 10-5
inches of mercury
centimeter
1.0197 X lQ-2
kilograms/ square meter
7 .5006 X 10-4
millimeters of mercury
1. 0000 X 10
newtons/ square meter
1.4504 X lQ~ 5
pounds/ square inch
17
Conversion Factors ( continued)
Multiply
By
To obtain
electron volt
3.8268 X 10-20
calories
(eV)
1.6022 X 10-12
ergs
1.0000 X 10-6
MeV(mega electron volts)
erg
9.4782 X 10-11
British thermal units
2.3885 X 10-8
calories
1.0000
dyne-centimeters
7 .3756 X lQ-8
foot-pounds
1.0000 X 10- 7
joules
erg/second
5.6869 X lQ-9
British thermal units/minute
2.3885 X lQ-8
calories/ second
7.3756 X lQ-8
foot-pounds/ second
1.0000 X 10- 7
joules/ second
1.0000 X 10- 7
watts
flow rate, fuel
4.5359 X }Q-1
kilograms/ hour
(lb/hr)
foot
3.0480 X 10
centimeters
(ft)
1.2000 X 10
inches
3.0480 X 10-4
kilometers
3.0480 X lQ-1
meters
1.8939 X lQ-4
miles
3.3333 X lQ- l
yards
foot-pound
1.2851 X 10-3
British thermal units
(ft-lb)
J.3558 X }07
ergs
5.0505 X }0-7
horsepower-hours
1.3558
joules
3.7662 X 10-1
kilowatt-hours
1.3558
newton-meters
foot-pound/
7.7104 X 10-2
British thermal units/minute
second
3.2383 X lQ-1
calories/ second
(ft-lb/ sec)
1.8182 X lQ-3
horsepower
1.3558
joules/second
1.3826 X 10-1
kilogram-meters/ second
1.3558
watts
foot/ second
3.0480 X IO
centimeters/ second
(fps)
1.0973
kilometers/ hour
5.9248 X
lQ-
knots
3.0480 X 10
meters/ second
6.8182 X 10-
miles/hour
18
Multiply
By
To obtain
furlong
1.0000 X 10
chains
2.2000 X 1()2
yards
2.0117 X 102
meters
gallon (lJ. S.)
1.3368 X 10-1
cubic feet
(gal)
3.7854
liters
3.7854 X 10-3
cubic meters
8.0000
pints
4.0000
quarts
gram
1.0000 X 10-3
kilograms
(gm)
3.5274 X lQ-2
ounces
2.2046 X 10-3
pounds
9.8067 X }()2
dynes
9.8067 X }Q-3
newtons
hectare
2.4711
acres
1.0000 X 102
ares
1.0000 X 1 ()4
square meters
3.8610 X 10-3
square miles
horsepower
4.2436 X 10
British thermal
(hp)
units/minute
5.5000 X 102
foot-pounds/ second
3.3000 X 104
foot-pounds/ minute
7 .4570 X 102
joules/ second
7.6040 X 10
kilogram-meters/ second
7.4570 X }()2
watts
horsepower-hour 2.5461 X }03
British thermal units
(hp hr)
1.9800 X f ()6
foot-pounds
2.6845 X IQ6
joules
7.4570 X }Q-1
kilowatt-hours
hour
6.0000 X 10
minutes
(hr)
3.6000 X 1Q3
seconds
4.1781 X 10-2
sidereal days
4.1667 X 10-2
solar days
1.1416 X 10-4
solar years
imperial gallon 2.7742 X 1Q2
cubic inches
1.2009
gallons (U.S.)
4.5460
liters
--"''""'""=-~--~_,____,_,
19
Conversion Factors (continued)
----------------------~----
Multiply
inch
(in)
inch of mercury
at 0C
(in Hg)
inch/second
{ips)
inch of water
at 4C
(in H20)
joule
(J)
kilogram
(kg)
kilogram/
square meter
(kg/m2)
By
2.5400
8.3333 X J0-2
2.5400 X lQ-2
2.7778 X IQ-2
3.3421 X lQ-2
3.3864 X lQ-2
3.3864 X }()4
1.3595 X 10
2.5400 X 10
3.3864 X 103
7.0727 X 10
4.9116 X lQ-1
8.3333 X lQ-2
2.5400
2.5400 X lQ-2
2.4584 X 10-3
7 .3556 X I0-2
1.8683
2.4910 X 102
3.6128 X 10-2
9.4771 X lQ-4
2.3889 X lQ-1
1.0000 X 107
1.0000 X 107
7.3756 X I0-1
1.0000
1.0000
1.0000 X 103
3.5274 X 10
2.2046
6.8521 X 1Q-2
9.8067
7.9290 X 10
9.6783 X lQ-5
9.8067 X lQ-5
2.8959 X 10-3
9.8067
20
To obtain
centimeters
feet
meters
yards
atmospheres
bars
dynes/ square centimeter
inches of water
millimeters of mercury
newtons/ square meter
pounds/ square feet
pounds/square inch
feet/ second
centimeters/ second
meters/ second
atmospheres
inches of mercury
millimeters of mercury
newtons/ square meter
pounds/ square inch
British thermal units
calories
dyne-centimeters
ergs
foot-pounds
newton-meters
watt-seconds
grams
ounces
pounds
slugs
newtons
poundals
atmospheres
bars
inches of mercurv
newtons/ square ineter
Multiply
kilogram/
square meter
(kg/m2)
kilogram-meter
{kgm)
kilogram-meter/
second
(kgm/sec)
kilometer
(km)
By
6.5895
2.0482 X I0-1
1.4223 X tQ-3
9.2938 X 10-3
7.2330
9.8067
9.8067
2.7232 X I0-6
3.3458 X 10
2.3423
7.2330
9.8067
1.3151 X I0-2
9.8067 X 10-3
3.2808 X ]03
3.9370 X JCJ4
1.0000 X loJ
6.2137 X JO- I
1.0936 X JoJ
kilometer/ hour 9 .1130 x 10 - 1
(km/hr)
5.3960 x 10-1
6.2137 X IO- 1
2.7778 X J0-1
kilonewton
(kN)
kilowatt hour
(kWh)
knot
(kt}
league (U .S,)
2.2481 X 1()2
3.4128 X 1Q3
2.6560 X 1()6
1.3414
3.6000 X J()6
3.6721 X 1Q5
3.6000 X }()6
1.6878
1.1516
1.8532
5.1480 X 10-
3.0000
To obtain
poundals / square foot
pounds I square foot
pounds/ square inch
British thermal units
foot-pounds
joules
newton-meters
kilowatt-hours
British thermal units/hour
calories/ second
foot-pounds/ second
joules/second
horsepower
kilowatts
feet
inches
meters
miles
yards
feet/second
knots
miles/hour
meters/ second
pounds
British thermal units
foot-pounds
horsepower-hours
joules
kilogram-meters
watt-seconds
feet/ second
miles/hour
kilometers/ hour
meters/ second
nautical miles
---------
~ s.-...... ,. .. -----~-- ..- .. ,
.... ,,, ...
Conversion Factors ( continued)
-""'""'~-~
Multiply
By
To obtain
light year
3.1040 X 1016
feet
5.8786 X 1012
miles
9.4608 X 101s
meters
liter
6.1024 X 10
cubic inches
{l)
3.5315 X 10- 2
cubic feet
2.6417 X I0-1
gallons {U.S. liquid)
1.0000 X to-3
cubic meters
2.1134
pints {U.S. liquid)
1.0567
quarts (U.S. liquid)
meter
1.0000 X 102
centimeters
(m)
3.2808
feet
3.9370 X 10
inches
1.0000 X 10- 3
kilometers
6.2137 X }0- 4
miles
1.0936
yards
meter/ second
3.2808
feet/ second
{m/sec)
3.6000
kilometers/ hour
1.9438
knots
2.2369
miles/hour
metric
9.8632 X J0-1
horsepower
horsepower
7.3550 X 10-1
kilowatts
mile
5.2800 X 103
feet
(mi)
6.3360 X 104
inches
1.6093
kilometers
1.6093 X 1Q3
meters
3.2000 X 102
rods
1.7600 X IQ3
yards
mile/hour
1.4667
feet/second
(mph)
1.6093
kilometers/hour
8.6898 X 10-1
knots
4.4704 X 10-1
meters/ second
millimeter of
1.3332 X }03
dynes/ square centimeter
mercury at
3.9370 X 10-2
inches of mercury (0C)
0C (torr)
5.3526 X 10-1
inches of water (4C)
(mm Hg)
1.3332 X 102
newtons/ square meter
1.9337 X 10-
pounds/ square inch
~""~.....-,=............_~ ...
22
Multiply
By
To obtain
minute {angle)
1.6667 X 10-2
degrees
(min)
2.9089 X lQ-4
radians
4.6296 X 10-s
revolutions
6.0000 X 10
seconds
minute (time)
1.6667 X 10- 2
hours
(min)
6.0000 X 10
seconds
6.9444 X 10- 4
solar days
1.9026 X 10-6
solar years
nautical mile
6.0761 X 103
feet
(international)
1.8520 X 103
meters
(n mi)
newton
1.0000 X 105
dynes
(N)
1.0197 X 102
grams
1.0197 X lQ-1
kilograms
2.2481 X lQ-1
pounds
7.2330
poundals
newton/
9.8692 X 10-6
atmospheres
square meter
1.0000 X 10
dynes / square centimeter
(pascal (Pa))
2.9530 X 10-4
inches of mercury (0C)
(N/m2)
1.0197 X 10-1
kilograms/ square meter
6.7200 X 10-1
poundals / square foot
2.0885 X 10-2
pounds/ square foot
1.4504 X 10-4
pounds/ square inch
ounce
2.8349 X 10
grams
(oz)
2.8349 X JQ-2
kilograms
6.2500 X l0-2
pounds
1.9428 X tQ- 3
slugs
2.7801 X }Q4
dynes
parsec
1.9163 X J013
miles
3.0857 X 1016
meters
pieze
1.0000 X 103
newtons/ square meter
pint (US.)
1.6710 X 10-2
cubic feet
(pt)
1.2500 X 10-
gallons
4.7317 X 10-1
liters
4.7317 X 10-4
cubic meters
5.0000 X 10-- 1
quarts
23
Conversion Factors ( continued)
Multiply
By
To obtain
pound (mass)
4.5359 X 102
grams
(lb)
4.5359 X 10-1
kilograms
1.6000 X 10
ounces
3.1081 X 10-2
slugs
pound (force)
4.4482
newtons
(lbf)
4.4482 X 10-1
dekanewtons
4.4482 X lQ-3
kilo newtons
3.2174 X 10
poundals
pound/
4.7254 X 10-4
atmospheres
square foot
4.7880 X }0-4
bars
(psf)
4.7880 X 1()2
dynes / square centimeter
1.4139 X 10-2
inches of mercury (0C)
4.8824
kilograms/ square meter
4.7880 X 10
newtons I square meter
3.2174 X 10
poundals/ square foot
6.9444 X I0-3
pounds/square inch
pound/
6.8046 X 10-2
atmospheres
square inch
6.8948 X 1()4
dynes / square centimeter
(psi)
2.0360
inches of mercury (0C)
2.7681 X 10
inches of water {4C)
7 .0307 X 1()2
kilograms/ square meter
6.8948 X 1Q3
newtons/ square meter
4.6333 X 1Q3
poundals / square foot
1.4400 X 1Q2
pounds/ square foot
poundal
1.4098 X 10-2
kilograms
1.3825 X 10-1
newtons
3.1081 X 10- 2
pounds
poundal/
1.5174 X 10- 1
kilograms/ square meter
square foot
1.4882 X 10-1
newtons/square meter
3.1081 X 10-2
pounds/ square foot
2.1583 X 10- 4
pounds/ square inch
quart (U.S.)
3.3421 X 10-2
cubic feet
liquid (qt)
2.5000 X 10-1
gallons
9.4635 X 10-1
liters
9.4635 X 10-4
cubic meters
2.0000
pints
=., ~-,--~-~-<.,co-,,,_..,--r=.~-
radian
5.7296 X 10
degrees
{rad)
3.4378 X }03
minutes
1.5916 X 10-- j
revolutions
2,0626 X 105
seconds
24
Multiply
By
To obtain
revolution
3.6000 X 102
degrees
(rev)
2.1600 X 104
minutes
6.2832
radians
1.2960 X 106
seconds
second (angle)
2.7778 X }0-4
degrees
(sec)
1.6667 X lQ-2
minutes
4.8481 X lQ-6
radians
7.7160 X 10-7
revolutions
second (time)
2.7778 X 10-4
hours
(sec)
1.6667 X 10-2
minutes
1.1574 X }0-5
solar days
slug
1.4594 X 104
grams
1.4594 X 10
kilograms
5.1478 X 102
ounces
3.2174 X 10
pounds
solar day
2.4000 X 10
hours
1.4400 X 103
minutes
8.6400 X 104
seconds
1.0027
sidereal days
2.7379 X 10-3
solar years
solar year
8.7658 X 103
hours
3.6624 X 102
sidereal days
3.6524 X 102
solar days
square
1.0764 X 10-3
square feet
centimeter
1.5500 X 10-1
square inches
(cm2)
1.0000 X 10-4
square meters
1.0000 X 102
square millimeters
square foot
2.2957 X 10-5
acres
(ft2)
9.2903 X 102
square centimeters
1.4400 X 102
square inches
9.2903 X 10-2
square meters
3.5870 X }Q-8
square miles
1.1111 X JQ-l
square yards
Conversion Factors (continued)
Multiply
By
To obtain
.~.....,,.,..,-,..,,,,_,_,_~.="'
square inch
1.2732 X 106
circular mils
(in2)
6.4516
square centimeters
6.9444 X 10-3
square feet
6.4516 X 10-4
square meters
6.4516 X 102
square millimeters
1. 0000 X 106
square mils
7 .7160 X }0-4
square yards
--------~~
---~--- "-'<
square
2.4711 X 1Q2
acres
kilometers
1.0764 X 107
square feet
(km2)
1.0000 X 106
square meters
3.8610 X I0-1
square miles
square meter
2.4711 X lQ-4
acres
(m2)
1.0000 X 10- 4
hectares
1.0000 X 1 ()4
square centimeters
1.0764 X 10
square feet
1.5500 X 103
square inches
3.8610 X 10-7
square miles
1.1960
square yards
square mile
6.4000 X 102
acres
(mi2)
2.5900 X 102
hectares
2.7878 X 107
square feet
2.5900
square kilometers
2.5900 X 106
square meters
3.0976 X 106
square yards
square yard
2.0661 X I0-4
acres
(yd2)
9.0000
square feet
1.2960 X 103
square inches
8.3613 X 10-1
square meters
3.2283 X 10-7
square miles
thermie
4.1868 X 106
joules
thrust specific
1.0197
kilograms/hour/
fuel consumption
dekanewton
(TSFC)
L0197 X 102
kilograms/ hour/
(lb/hr /lb Fn)
kilonewton
Multiply
By
To obtain
watt (joule/
3.4121
British thermal units/hour
second)
5.6869 X 10-2
British thermal units/minute
(W)
2.3900 X 10- 1
calories/ second
1.0000 X 107
ergs/ second
7.3756 X lQ-1
foot-pounds/ second
1.3410 X }Q-3
horsepower
1.0197 X lQ-l
kilogram-meters/ second
watt second
9.4782 X lQ-4
British thermal units
(Wsec)
7.3756 X lQ-1
foot-pounds
1.0000
joule
2.7778 X 10-1
kilowatt-hours
yard
9.)440 X 10
centimeters
(yd)
3.0000
feet
3.6000 X 10
inches
9.1440 X 10-4
kilometers
9.1440 X }0-1
meters
5.6818 X }0-4
miles
1.8182 X lQ-1
rods
27
Miscellaneous Conversions
Weights and Measures
Liquid
Measure:
Dry
Measure:
Long
Measure:
Cubic
Measure:
Mariner's
Measure:
A po thecaries
Measure:
Shipping
Measure~
4 gills = 1 pint
2 pints - 1 quart
4 quarts = 1 gallon
31 gallons 1 barrel
2 barrels - 1 hogshead
1 U.S. gallon == 0.833 imperial gallon
1 imperial gallon = l.201 U.S. gallon
2 pint = 1 quart
8 quarts - 1 peck
4 pecks 1 bushel
36 bushels - 1 chaldron
12 inches = 1 foot
3 feet 1 yard
5 yards = 1 rod
40 rods 1 furlong
8 furlongs = 1 statute mile
1,728 cubic inches - 1 cubic foot
27 cubic feet 1 cubic yard
128 cubic feet = 1 cord (wood)
231 cubic inches 1 U.S. gallon
6 feet = 1 fathom
120 fathoms - 1 cable length
7 cable lengths = 1 mile
5,280 feet = 1 statute mile
6,080.2 feet = 1 nautical mile
60 minim ""' 1 liquid dram
8 drams = 1 liquid ounce
16 ounces ==- 1 pint
100 cubic feet = 1 register ton
40 cubic feet = U.S. shipping ton
42 cubic feet
1 British shipping ton
28
Weight:
Avoirdupois:
Precious Stones:
Troy:
Apothecaries:
16 drams .. 437.S grains "" 1 oz
16 oz 7000 grains - 1 lb
112 lb = 1 hundredweight
20 hundredweight -
1 long ton
2000 lb "" 1 short ton
2240 lb - 1 long ton
2204.60 lb 1 metric ton
1 carat 200 milligrams
24 grains -
1 pennyweight
20 pennyweights 1 oz
12 oz 5760 grains - 1 lb
20 grains 1 scruple
3 scruples 1 dram
8 drams =- 1 ounce
12 oz - 5760 grains - 1 lb
29
Weights of Gases
Gas
Air
Air
Carbon dioxide
Carbon monoxide
Helium
Hydrogen
Nitrogen
Oxygen
*At atmospheric pressure and 0C
Specific Wt *lb/cu ft
30
0.07651 (at 59.0F)
0.08071
0.12341
0.07806
0.01114
0.005611
0.07807
0.089212
Heat and Temperature
The two basic units of heat are the British thermal unit (Btu) and the
French thermal unit (kilogram calorie). A British thermal unit is the
quantity of heat necessary to raise the temperature of one pound of pure
water one degree Fahrenheit (F). A French thermal unit is the quantity of
heat necessary to raise the temperature of one kilogram of pure water one
degree Celsius (C) or Centigrade. One kilogram calorie
3.968 British
thermal units = 1,000 gram calories.
Absolute Temperature and Absolute Zero
A point has been theoretically detennined on the temperature measurement
scale that is called absolute zero, beyond which a further decrease in
temperature is inconceivable. That point is -459.67F or -273.15C. A
temperature measured from that point is called absolute temperature.
Absolute temperature in C is known as degrees Kelvin (K), and absolute
temperature in Fis known as degrees Rankine (R).
K = C + 273.15
R = F + 459.67
Pure water freezes at 32F/0C and boils at 212F/100C at standard sea-
level atmospheric pressure. The following formulas may be used to
convert temperatures from one scale to the other:
F = 9/5 (0 C) + 32
C 5/9 (F - 32)
Fahrenheit - Celsius (Centigrade) Conversion
-40
110
100
90
80
70
60
50
-30
10
Degree Celsius
31
20
30
40
Standard Atmosphere
In 1953, the United States Committee on Extension to the Standard
Atmosphere (COESA) was formed to assemble information on
atmospheric parameters at altitudes traversed by suborbital rockets. One
result of this effort was a midlatitude (45 N) mean atmospheric profile
published in U.S. Standard Atmosphere, 1962. The 1962 U.S. standard
atmosphere model was updated when the United States National Oceanic
and Atmospheric Administration (NOAA) released U.S. Standard
Atmosphere, 1976. The 1976 U.S. standard atmosphere is identical to the
1962 U.S. standard atmosphere for altitudes below 50 km (or
approximately 164,000 feet) but differs for the higher altitudes.
The internationally accepted standard atmosphere is called the
IntemationaJ Civil Aviation Organization (!CAO) or the International
Standard Atmosphere (ISA). The U.S. Standard Atmosphere, 1976 is
identical with the International Standard Atmosphere (ISA) for altitudes
below 32 km (approximately 105,000 feet).
ISA and U.S. Standard Atmospheres -
Values at Sea Level
Pressuret P 0
Temperatur~ _T0
Acceleration due to
gravity, g0
British Units
2116.22 lb/ft2
29.92 in. Hg
518.67R
59.0F
32.1741 ft/sec2
Specific weight, g0e0 0.076474 lb/ft3
Metric Units
1.013250 x 10s N/m2
760 mm Hg
288.15K
15.0C
9.80665 m/sec2
1.2250 kg/m3
Density, Qo
Kinematic
viscosity,
0.0023769 lb-sec2/ft4 0.12492 kg sec2/m4
Absolute
viscosity, 0
L5723 xto=4
ft2/sec
1.2024 X 10
lb/ft sec
1 A607 x 10 ~, ;lj
m2/sec
L7894 x 10
kg/m sec
Standard Values at Altitude
British Units
Isothermal
altitude, Z;
Isothermal
temperature, t
Temperature lapse
rate (sea level
to isothermal)
-69.7F
-3.57F/
1,000 ft
Geopotential Altitude
Metric Units
11,000 m
56.5C
-6.SC/km
The ISA is now established as the recognized basis for all aircraft analysis.
In the standard, height above sea level is measured as the true (tape-line)
distance (the geometric altitude), assuming constant gravitational
acceleration (g) with the height (i.e., a mean sea-level value g0 = 9.80665
rn/sec2). This height definition is known as the geopotential altitude. The
physical length of geopotential units is not constant but increases with
higher elevations because the acceleration due to gravity decreases as
elevation increases. Thus, at 100,000 feet geometric altitude (as measured
by a yardstick), an aircraft altimeter calibrated in geopotential units would
indicate 99,523 feet.
The following equation is used to relate geopotential to geometric altitude:
where
H - geopotential altitude
Z
geometric altitude
g0 - acceleration due to gravity at sea level
g = accelertion due to gravity at altitude Z
U.S. Standard Atmosphere, 1976
(Geopotential Altitude)
British Units
Altitude
Temperature
Pressure
feet
op
OR
oc
psia
in. Hg
2000
66.l
525.8
19.0
15.79
32.15
-1000
62.5
522.2
17.0
15.23
31.02
0
59.0
518.7
15.0
14.70
29.92
1000
55.4
515.1
13.0
14.17
28.86
2000
51.9
511.6
11.0
13.66
27.82
3000
48.3
508.0
9.1
13.17
26.82
4000
44.7
504.4
7.1
12.69
25.84
5000
41.2
500.9
5.1
12.23
24.90
6000
37.6
497.3
3.1
11.78
23.98
7000
34.0
493.7
1.1
11.34
23.09
8000
30.5
490.2
-0.8
10.92
22.23
9000
26.9
486.6
-2.8
10.50
21.39
10000
23.3
483.0
-4.8
10.11
20.58
11000
19.8
479.5
-6.8
9.720
19.79
12000
16.2
475.9
-8.8
9.346
19.03
13000
12.6
472.3
-10.7
8.984
18.29
14000
9.1
468.8
-12.7
8.633
17.58
15000
s.s
465.2
-14.7
8.294
16.89
16000
1.9
461.6
-16.7
7.965
16.22
17000
-1.6
458.1
-18.7
7.647
15.57
18000
-5.2
454.S
-20.7
7.339
14.94
19000
-8.8
450.9
-22.6
7.041
14.34
20000
-12.3
447.4
-24.6
6.754
13.75
21000
-15.9
443.8
-26.6
6.475
13.18
22000
-19.5
440.2
-28.6
6.207
12.64
23000
-23.0
436.7
-30.6
5.947
12.11
24000
-26.6
433.1
-32.5
5.696
11.60
25000
-30.2
429.5
-34.5
5.454
11.10
26000
-33.7
426.0
-36.5
S.220
10.63
27000
-37.3
422.4
-38.5
4.994
10.17
28000
-40.9
418.8
-40.5
4.777
9.725
29000
-44.4
415.3
-42.4
4.567
9.298
30000
-48.0
411.7
-44.4
4.364
8.886
Note: The ISA atmosphere is identical to the U.S Standard Atmosphere
for altitudes below 32 km (104,987 feet).
34
q/Ml
Sonic Velocity
0
y0
d
0
lb/ft2
ft/sec
kts
1.0138
1.0069
1.074
1.060
1592.
1124.1
666.0
1.0069
1.0034
1.037
1.030
1536.
1120.2
663.7
1.0000
1.0000
1.000
1.000
1481.
1116.4
661.5
.9932
.9966
.9644
. 9710
1429 .
1112.6
659.2
.9863
.9931
.9298
.9427
1377.
1108.7
656.9
.9794
. 9897
.8962
.9151
1328 .
1104.9
654.6
.9725
.9862
.8637
.8881
1279.
1101.0
652.3
.9657
.9827
.8321
. 8616
1233 .
1097.1
650.0
.9588
.9792
.8014
.8358
1187.
1093.2
647.7
.9519
.9757
.7716
. 8106
1143 .
1089.2
645.4
.9450
. 9721
.7428
.7860
1100 .
1085.3
643.0
.9382
.9686
.7148
. 7619
1059 .
1081.3
640.7
.9313
.9650
.6877
7385
1019 .
1077.4
638.3
.9244
.9615
.6614
.7155
979.8
1073.4
636.0
.9175
.9579
.6360
.6932
942.1
1069.4
633.6
.9107
.9543
.6113
.6713
905.6
1065.4
631.2
.9038
.9507
.5875
.6500
870.2
1061.3
628.8
.8969
.9470
.5644
.6292
836.0
1057.3
626.4
.8900
.9434
.5420
.6089
802.9
1053.2
624.0
.8831
.9398
.5203
.5892
770.8
1049.2
621.6
.8763
.9361
.4994
.5699
739.8
1045.1
619.2
.8694
.9324
.4791
.5511
709.8
1041.0
616.7
.8625
.9287
.4596
.5328
680.8
1036.8
614.3
.8556
.9250
.4406
.5150
652.7
1032.7
611.9
.8488
.9213
.4223
.4976
625.6
1028.5
609.4
.8419
.9175
.4047
.4806
599.4
1024.4
606.9
.8350
.9138
.3876
.4642
574.1
1020.2
604.4
.8281
.9100
.3711
.4481
549.7
1016.0
601.9
.8213
.9062
.3552
.4325
526.2
1011.7
599.4
.8144
.9024
.3398
.4173
503.4
1007.5
596.9
.8075
.8986
.3250
,4025
481.5
1003.2
594.4
.8006
.8948
.3107
.3881
460.3
988.9
591.9
.7938
.8909
.2970
.3741
439.9
994.6
589.3
35
U.S. Standard Atmosphere, 1976
(Geopotential Altitude) ( continued)
British Units
Altitude
Temperature
Pressure
feet
op
OR
oc
psia
in. Hg
31000
-51.6
408.1
-46.4
4.169
8.489
32000
-55.1
404.6
-48.4
3.981
8.106
33000
-58.7
401.0
-50.4
3.800
7.737
34000
62.3
397.4
-52.4
3.626
7.383
35000
-65.8
393.9
-54.3
3.458
7.041
36000
-69.4
390.3
56.3
3.297
6.712
*36089
-69.7
390.0
-56 . .5
3.282
6.683
37000
-69.7
390.0
56.5
3.142
6.397
38000
-69.7
390.0
-56.5
2.994
6.097
39000
-69.7
390.0
-56.5
2.854
5.811
40000
-69.7
390.0
-56.5
2.720
5.538
41000
-69.7
390.0
-56.5
2.592
5.278
42000
-69.7
390.0
-56.5
2.471
5.030
43000
-69.7
390.0
-56.5
2.355
4.794
44000
-69.7
390.0
-56.5
2.244
4.569
45000
-69.7
390.0
-56.5
2.139
4.355
46000
-69.7
390.0
-56.5
2.039
4.151
47000
-69.7
390.0
-56.5
1.943
3.956
48000
-69.7
390.0
-56.5
1.852
3.770
49000
-69.7
390.0
-56.5
1.765
3.593
50000
-69.7
390.0
-56.5
1.682
3.425
51000
-69.7
390.0
-56.5
1.603
3.264
52000
-69.7
390.0
-56.5
1.528
3.111
53000
-69.7
390.0
56.5
1.456
2.965
54000
-69.7
390.0
-56.5
1.388
2.826
55000
69.7
390.0
-56.5
1.323
2.693
56000
-69.7
390.0
-56.5
1.261
2.567
57000
-69.7
390.0
56.5
1.201
2.446
58000
-69.7
390.0
-56.5
1.145
2.321
59000
-69.7
390.0
-56.5
1.091
2.222
60000
-69.7
390.0
-56.5
1.040
2.118
61000
-69.7
390.0
-56.5
.9913
2.018
62000
69.7
390.0
56.5
,9448
1.924
63000
--69.7
390.0
-56.5
,9005
1.833
64000
69.7
390.0
56.5
.8582
L747
65000
69.7
390.0
- 56.5
.8179
1.665
"""''"''--
,-----.0,k
36
q/M2
Sonic Velocity
0
ve
d
a
lb/ft2
ft/sec
kts
,7869
.8871
.2837
.3605
420.3
990.3
586.8
.7800
.8832
.2709
.3473
401.3
986.0
584.2
.7731
.8793
.2586
.3345
383.1
981.6
581.6
.7663
.8754
.2467
.3220
365.5
977.3
579.0
.7594
.8714
.2353
.3099
348.6
972.9
576.4
.7525
.8675
.2243
.2981
332.3
968.5
573.8
.7519
.8671
.2234
.2971
330.9
968.1
573.6
.7519
.8671
.2138
.2843
316.7
968.1
573.6
.7519
.8671
.2038
.2710
301.8
968.1
573.6
.7519
.8671
.1942
.2583
287.7
968.1
573.6
.7519
.8671
.1851
.2462
274.2
968.1
573.6
.7519
.8671
.1764
.2346
261.3
968.1
573.6
.7519
.8671
.1681
.2236
249.0
968.1
573.6
.7519
.8671
.1602
.2131
237.4
968.1
573.6
.7519
.8671
.1527
.2031
226.2
968.1
573.6
.7519
.8671
.1455
.1936
215.6
968.1
573.6
.7519
.8671
.1387
.1845
205.5
968.l
573.6
.7519
.8671
.1322
.1758
195.8
968.1
573.6
.7519
.8671
.1260
.1676
186.7
968.1
573.6
.7519
.8671
.1201
.1597
177.9
968.1
573.6
.7519
.8671
.1145
.1522
169.5
968.1
573.6
.7519
.8671
.1091
.1451
161.6
968.1
573.6
.7519
.8671
.1040
.1383
154.0
968.1
573.6
.7519
.8671
.09909
. 1318
146.8
968.1
573.6
.7519
.8671
.09444
.1256
139.9
968.1
573.6
.7519
.8671
.09000
.1197
133.3
968.1
573.6
.7519
.8671
.08578
.1141
127.1
968.1
573.6
.7519
.8671
.08175
.1087
121.1
968.1
573.6
.7519
.8671
.07792
.1036
115.4
968.1
573.6
.7519
.8671
.07426
.09877
110.0
968.1
573.6
-~---~--=--- , .
.7519
.8671
. 07078
.09413
104.8
968.1
573.6
.7519
.8671
.06746
.08971
99.93
968.1
573.6
,7519
.8671
.06429
.08550
95.24
968.1
573.6
,7519
.8671
.06127
.08149
90.77
968.1
573.6
,7519
.8671
.05840 m161
86.51
968.l
573.6
.7519
.8671
.05566
.07402
82.45
968.1
573.6
37
U.S. Standard Atmosphere, 1976
( Geo potential Altitude) (continued)
British Units
Altitude
Temperature
Pressure
feet
OF
OR
oc
psia
in. Hg
* 65617
-69.7
390.0
-56.5
.7941
1.617
70000
-67.3
392.4
-55.2
.6437
1.311
75000
-64.6
395.1
-53.6
.5073
1.0333
80000
-61.8
397.9
-52.1
.4005
.8155
85000
-59.1
400.6
-50.6
.3167
.6449
90000
-56.3
403.4
49.1
.2509
.5108
95000
-53.6
406.1
-47.5
.1990
.4052
100000
-50.8
408.9
-46.0
.1581
.3220
*104987
-48.1
411.6
-44.5
.1259
.2563
150000
21.0
480.7
- 6.1
.01893
.03854
*154199
27.5
487.2
-
2.5
.01609
.03275
*170604
27.5
487.2
- 2.5
.00557
.01742
200000
-22.7
437.0
-30.4
.002576
.005245
*200131
-22.9
436.8
-30.5
.002578
.005249
*Boundary between atmosphere layers of constant thermal gradient
NOTE:
For intermediate altitudes up to and including 36,089 feet, ambient
pressure and temperature can be calculated as follows:
.
[
(Altitude {ft) x 1 o- 3) ] 5 2561
Pressure (ps1a) = 14.7 1 -
145
.4
5
Temperature (degrees R)
518. 7 - [3. 5662 x (Altitude (ft) x 10-3)]
38
q/W
Sonic Velocity
e
ve
d
a
lb/ft2
ft/sec
kts
.7519
.8671
.05403
.07186
80.04
968.1
573.6
.7565
.8698
.04380
.05789
64.88
971.0
575.3
.7618
.8728
.03452
.04532
51.14
974.4
577.3
.7671
.8759
.02726
.03553
40.37
977.8
579.3
.7724
.8789
.02155
.02790
31.93
981.2
581.3
.7777
.8819
.01707
.02195
25.29
984.5
583.3
.7830
.8849
.01354
.01730
20.06
987.9
585.3
.7883
.8878
.01076
.01365
15.94
991.2
587.3
.7935
.8908
.008567
.010800
12.69
994.5
589.2
.9269
.9627
.001288
.001390
1.908
1074.8
636.8
.9393
.9692
.0001095 .001165
1.622
1082.0
641.1
.9393
.9692
.0005823 .0006199
.8626 1082.0
641.1
.8771
.9365
.0001807 .0002060
.2677 1045.5
619.5
.8768
.9364
.0001797 .0002050
.2662 1045.4
619.4
39
U.S. Standard Atmosphere, 1976
(Geopotential Altitude) (continued)
Metric Units
Altitude
Temperature
Press.
meters
feet
op
OK
oc
N/m2
-500
-1640
64.8
291.4
16.3
107477
0
0
59.0
288.2
15.0
101325
500
1640
53.1
284.9
11.8
95461
1000
3281
47.3
281.7
8.5
89874
1500
4921
41.4
278.4
5.3
84556
2000
6562
35.6
275.2
2.0
79495
2500
8202
29.7
271.9
-1.2
74683
3000
9843
23.9
268.7
-4.5
70109
3500
11483
18.0
265.4
-7.7
65765
4000
13123
12.2
262.2
-11.0
61641
4500
14764
6.3
258.9
-14.2
57729
5000
16404
0.5
255.7
-17.5
54021
5500
18045
-5.4
252.4
-20.7
50508
6000
19685
-11.2
249.2
-24.0
47182
6500
21325
-17.l
245.9
-27.2
44036
7000
22966
-22.9
242.7
30.5
41062
7500
24606
-28.8
239.4
-33.7
38252
8000
26247
-34.6
236.2
-37.0
35601
8500
27887
-40.5
232.9
-40.2
33100
9000
29528
-46.3
229.7
-43.5
30744
9500
31168
-52.2
226.4
-46.7
28525
10000
32808
-58.0
223.2
-50.0
26437
10500
34449
-63.9
219.9
-53.2
24475
*11000
36089
-69.7
216.7
-56.5
22632
11500
37730
69.7
216.7
-56.5
20916
12000
39370
-69.7
216.7
-56.5
19330
12500
41011
-69.7
216.7
-56.5
17865
13000
42651
-69.7
216.7
-56.5
16510
13.500
44291
69.7
216.7
56.5
15258
14000
45932
69.7
216.7
56.5
14102
14500
47572
-69.7
216.7
-56.5
13032
~-"'----
15000
49213
69.7
216.7
56.5
12044
15500
50853
-69.7
216.7
56.5
11131
16000
52493
69.7
216.7
56.5
10287
16500
54134
-69.7
216.7
_,56,5
9507
17000
55774
69.7
216.7
56.5
8786
40
q/Ml Sonic Vet.
0
y0
d
0
Nlm2
m/sec
1.0113
1.0056
1.061
1.049
75234
342.2
1.0000
1.0000
1.0000
1.0000
70927
340.3
.9888
.9944
.9421
.9528
66822
338.4
.9775
.9887
.8870
.9074
62912
336.4
.9662
.9830
.8345
.8637
59189
334.5
.9549
.9772
.7846
.8216
55647
332.5
.9436
.9714
.7371
.7811
52278
330.6
.9324
.9656
.6919
.7421
49076
328.6
.9211
.9597
.6490
.7047
46035
326.6
.9098
.9538
.6084
.6687
43149
324.6
.8985
.9479
.5697
.6341
40410
322.6
.8872
.9419
.5331
.6009
37815
320.5
.8760
.9359
.4985
.5691
35355
318.5
.8647
.9299
.4657
.5385
33027
316.4
.8534
.9238
.4346
.5093
30825
314.4
.8421
.9177
.4052
.4812
28743
312.3
.8309
.9115
.3775
.4544
26777
310.2
.8196
.9053
.3514
.4287
24921
308.1
.8083
.8991
.3267
.4042
23170
305.9
.7970
.8928
.3034
.3807
21520
303.8
.7857
.8864
.2815
.3583
19967
301.6
.7745
.8800
.2609
.3369
18506
299.5
.7632
.8736
.2416
.3165
17133
297.3
.7519
.8671
.2234
.2971
15842
295.1
.7519
.8671
.2064
.2745
14641
295.1
.7519
.8671
.1908
.2537
13531
295.1
.7519
.8671
.1763
.2345
12505
295.1
.7519
.8671
.1629
.2167
11557
295.1
.7519
.8671
.1506
.2003
10681
295.1
,7519
.8671
.1392
.1851
9871
295.1
.7519
.8671
.1286
.1711
9123
295.1
.7519
.8671
.1189
,1581
8431
295.1
.7519
.8671
J099
,1461
7792
295.l
.,7519
.8671
.1015
.1350
7201
295.1
.7519
.8671
.09383
1248
6655
295.1
.7519
.8671
.08672
1153
6151
295.1
41
U.S. Standard Atmosphere, 1976
( Geopotential Altitude)
Metric Units
Altitude
Temperature
Press.
meters
feet
OF
OK
oc
Nlm2
17500
57415
-69.7
216.7
-56.5
8120
18000
59055
-69.7
216.7
-56.5
1505
18500
60696
69.7
216.7
-56.5
6936
19000
62336
-69.7
216.7
-56.5
6410
19500
63976
-69.7
216.7
56.5
5924
*20000
65617
-69.7
216.7
-56.5
5475
25000
82021
60.7
221.7
-51.5
2511
30000
98425
-51.7
226.7
-46.5
1172
*32000
104987
-48.1
228.7
-44.5
868
35000
114829
-33.0
237.1
-36.1
559
40000
131234
-7.8
251.1
-22.1
278
45000
147638
17.4
265.1
-8.1
143
*47000
154199
27.5
270.7
-2.5
111
50000
164042
27.5
270.6
-2.5
76
*52000
170604
27.5
270.6
-2.5
59
55000
180446
16.7
264.6
-8.5
40
60000
196850
-1.3
254.6
-18.5
21
*61000
200131
-4.9
252.6
-20.5
18
* Boundary between atmosphere layers of constant thermal gradient.
NOTE: The ICAO atmosphere is identical to the U.S. Standard
Atmosphere for altitudes below 20 km.
42
ql!vf2
Sonic Vel.
0
ve
d
a
Nlm2
m/sec
.7519
.8671
.08014
.1066
5684
295.1
.7519
.8671
.07407
.09850
5253
295.1
.7519
.8671
.06645
.09104
4655
295.1
.7519
.8671
.06326
.08413
4487
295.l
.7519
.8671
.05846
.07776
4147
295.1
.7519
.8671
.05403
.07186
3832
295.1
.7693
.8771
.02478
.03222
1758
298.5
.7866
.8869
.01157
.01470
820
301.8
.7935
.8908
.008567
.001080
608
303.1
.8227
.9070
.005516
.006705
391
308.6
.8713
.9334
.002739
.003144
194
317.6
.9199
.9591
.001413
.001536
100
326.4
.9393
.9692
.001095
.001165
78
329.8
.9393
.9692
.0007495
.0007980
53
329.8
.9393
.9692
.000S823
.0006199
41
329.8
.9184
.9584
.0003970
.0004323
28
326.l
.8837
.9401
.0002056 .. 0002327
15
319.9
.8768
.9364
.0001797
.0002050
13
318.6
43
Compressible Flow Functions
(For Perfect Gas, Constant Molecular Weight9
Constant Pressure Specific Heat, cp, and
Constant Specific Heat Ratio, 'Y)
Symbols
A
F
M
M*
p
q
R
T
w
WTAP
y
Q
Stream tube cross-sectional area
Impulse function
Mach number
(Velocity)/(Acoustic velocity at state where M = 1.0)
Pressure
Dynamic pressure
Gas constant
Temperature
Mass flow rate
Flow parameter
Specific heat ratio
Fluid density
Subscripts/Superscripts
s
Static (stream) condition
t
Total (isentropic stagnation) condition
x
Condition at front of normal shock
y
Condition behind normal shock
*
Condition where M = 1.0
44
Formulas
Isentropic
y
2
1.w)y-1
3. T1/T5 = (1 + y.w)
4. (,?tlQS = (1 +
[
1 + L=-!w]
5. A/A*= _I_
2
M
y+l
2
y+l
2(y-1)
6. qlPt = _!_ yM2 ( 1 + y- l w) - y-
2
2
7. FI F* =
l + Y M2
M ~ 2 ( 1 + Y - l M2) (l+ y)
2
J;i_M
8, WTAP
R
45
Formulas
9. My
Normal Shock
J
2 + {y - 1) Mi
2yMx2 -y + 1
10. Ps/Psx = (yM/ + 1)/(yM/ + 1)
(yMi + 1)
11. P1yl Ptx = (yM,2 + 1)
(yM/ + 1)
12. P5/Ptx = (yM/ + l)
(1 + s1Mx2)
(1 + r; I Mi)
( 1 + y; 1 M}) - I
(yMi + 1) (1 + y
2
l M/)
15. Ps/Psx =
(yMi + 1) (1 + r; l M/)
46
Greek Alphabet
A, a Alpha
N, v Nu
8, (3 Beta
='.,~Xi
r, y Gamma
0, o Omicron
A, d Delta
n. n Pi
E, t Epsilon
P, Q Rho
Z, l Zeta
L, a,i; Sigma
H, r, Eta
T, T Tau
0, 8 Theta
Y, u Upsilon
I, 1 Iota
4>, + Phi
K. x Kappa
X, X Chi
A. l. Lambda
'-V, 14> Psi
M, Mu
Q, w Omega
One Dimensional Isentropic Compressible Flow Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp),
and Constant Specific Heat Ratio (y) = 1.4)
M
M*
PrfPs
T/Ts
e1IQs
A/A*
q/Pt
FIF*
WTAP
0.0
0.0
1.000
1.000
1.000
00
0.0
00
.0
0,01
0.011
1.000
1.000
1.000
57.874
0.000
45.649
.0092
0.02
0.022
1.000
1.000
1.000
28.942
0.000
22.834
.0184
0.03
0.033
1.001
1.000
1.000
19.300
0.001
15.232
.0276
0.04
0.044
1.001
1.000
1.001
14.481
0.001
11.435
.0367
0.05
0.055
1.002
1.000
1.001
11.591
0.002
9.158
.0459
.j:,.
0.06
0.066
1.003
1.001
1.002
9.666
0.003
7.643
.0550
QC
0.07
0.077
1.003
1.001
1.002
8.292
0.003
6.562
.0641
0.08
0.088
1.004
1.001
1.003
7.262
0.004
5.753
.0732
0.09
0.099
1.006
1.002
1.004
6.461
0.006
5.125
.0823
0.10
0.109
1.007
1.002
1.005
5.822
0.007
4.624
.0913
0.120
1.008
1.002
1.006
5.299
0.008
4.215
.1003
0.
0.131
1.010
1.003
1.007
4.864
0.010
3.875
.1093
0.142
1.012
1.003
1.008
4.497
0.012
3.588
.. 1182
0.14
0.153
1.014
1.004
1.010
4.182
0.014
3.343
.1271
0.15
0.164
1.016
1.004
1.011
3.910
0.016
3.132
.1360
0.16
0.175
1.018
1.005
1.013
3.673
0.018
2.947
.1448
0.186
1.020
1.006
1.015
3.464
0.020
2.786
.1535
0.18
0.197
1.023
1.006
1.016
3.278
0.022
2.642
.1622
0.19
0.207
1.025
1.007
1.018
3.112
0.025
2.515
.1709
0.20
0.218
1.028
1.008
1.020
2.964
0.027
2.400
1794
0.21
0.229
1.031
1.009
1.022
2.829
0.030
2.298
.1879
0.22
0.240
1.034
1.010
1.024
2.708
0.033
2.205
.1964
0.23
0.251
1.038
1.011
1.027
2.597
0.036
2.120
.2048
0.24
0.261
1.041
1.012
1.029
2.496
0.039
2.043
.2131
0.25
0.272
1.044
1.012
1.032
2.403
0.042
1.973
.2213
0.26
0.283
1.048
1.014
1.034
2.317
0.045
1.909
.2295
0.27
0.294
1.052
1.015
1.037
2.238
0.049
1.850
.2375
0.28
0.304
1.056
1.016
1.040
2.166
0.052
1.795
.2455
0.29
0.315
1.060
1.017
1.043
2.098
0.056
1.745
.2535
0.30
0.326
1.064
1.018
1.046
2.035
0.059
1.698
.2613
0.31
0.336
1.069
1.019
1.049
1.977
0.063
1.655
.2690
+"-
0.32
0.347
1.074
1.020
1.052
1.922
0.067
1.614
.2767
ID
0.33
0.358
1.078
1.022
1.055
1.871
0.071
1.577
.2842
0.34
0.368
1.083
1.023
1.059
1.823
O.o?S
1.542
.2917
0.35
0.379
1.088
1.024
1.062
1.778
0.079
1.509
.2991
0.36
0.389
1.094
1.026
1.066
1.736
0.083
1.479
.3063
0.37
0.400
1.099
1.027
1.070
1.696
0.087
1.450
.3135
0.38
0.410
1.105
1.029
1.074
1.659
0.091
1.424
.3206
0.39
0.421
1.111
1.030
1.078
1.623
0.096
1.398
.3275
0.40
0.431
1.117
1.032
1.082
1.590
0.100
1.375
.3344
0.41
0.442
1.123
1.034
1.086
1.559
0.105
1.353
.3412
0.42
0.452
1.129
1.035
1.091
1.529
0.109
1.332
.3478
0.43
0.463
1.136
1.037
1.095
1.501
0.114
1.312
.3543
0.44
0.473
1.142
1.039
1.100
1.474
0.119
1.294
.3608
One Dimensional Isentropic Compressible Flow Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat ( cp),
and Constant Specific Heat Ratio (-y) = 1.4) (continued)
-
M
M*
P/Ps
T/T5
Qr/es
A/A*
q!Pi
FIF*
WTAP
0.45
0.483
1.149
1.040
1.104
1.449
0.123
1.276
.367]
0.46
0.494
1.156
1.042
1.109
1.425
0.128
1.260
.3733
0.47
0.504
1.163
1.044
1.114
1.402
0.133
1.244
.3793
0.48
0.514
1.171
1.046
1.119
1.380
0.138
1.230
.3853
0.49
0.524
1.178
1.048
1.124
1.359
0.143
1.216
.3911
0.50
0.535
1.186
1.050
1.130
1.340
0.148
1.203
.3969
0.51
0.545
1.194
1.052
1.135
1.321
0.152
1.190
.4025
0.52
0.555
1.202
1.054
1.141
1.303
0.157
1.179
.4080
0.53
0.565
1.211
1.056
1.146
1.286
0.162
1.168
.4133
0.54
0.575
1.219
1.058
1.152
1.270
0.167
1.157
.4186
0.55
0.585
1.228
1.060
1.158
1.255
0.172
1.147
.4237
0.56
0.595
1.237
1.063
1.164
1.240
0.177
1.138
.4287
0.57
0.605
1.247
1.065
1.170
1.226
0.182
1.129
.4336
0.58
0.615
1.256
1.067
1.177
1.213
0.187
1.121
.4384
0.59
0.625
1.266
1.070
1.183
1.200
0.193
1.113
.4430
0.60
0.635
1.276
1.072
1.190
1.188
0.198
1.105
.4475
0.61
0.645
1.286
1.074
1.197
1.177
0.203
1.098
.4519
0.62
0.654
1.296
1.077
1.203
1.166
0.208
1.091
.4562
0.63
0.664
1.306
1.079
1.210
1.155
0.213
1.085
.4603
0.64
0.674
1.317
1.082
1.218
1.145
0.218
1.079
.4643
0.65
0.684
1.328
1.084
1.225
1.136
0.223
1.073
.4682
0.66
0.693
1.340
1.087
1.232
l.127
0.228
1.068
.4720
0.67
0.703
1.351
1.090
1.240
1.118
0.233
1.063
.4757
0.68
0.713
1.363
1.092
1.247
1.110
0.238
1.058
.4792
0.69
0.722
1.375
1.095
1.255
1.102
0.242
1.053
.4826
0.70
0.732
1.387
1.098
1.263
1.094
0.247
1.049
.4859
0.741
1.400
1.101
1.271
1.087
0.252
1.045
.4891
0.72
0.751
1.412
1.104
1.280
1.081
0.257
1.041
.4921
0.73
0.760
1.425
1.107
1.288
1.074
0.262
1.Q38
.4950
0.74
0.770
1.439
1.110
1.297
1.068
0.266
1.034
.4978
0.75
0.779
1.452
1.112
1.305
1.062
0.271
1.031
.5005
0.76
0.788
1.466
1.116
1.314
1.057
0.276
1.028
.5031
0.77
0.798
1.480
1.119
1.323
1.052
0.280
1.026
.5055
0.78
0.807
1.495
1.122
1.333
1.047
0.285
1.023
.5079
0.79
0.816
1.509
1.125
1.342
1.043
0.289
1.021
.5101
0.80
0.825
1.524
1.128
1.351
1.038
0.294
1.019
.5122
0.81
0.834
1.540
1.131
1.361
1.034
0.298
1.016
.5142
0.82
0.843
1.555
1.134
1.371
1.030
0.303
1.015
.5160
0.83
0.852
1.571
1.138
1.381
1.027
0.307
1.013
5178
0.84
0.861
1.587
1.141
1.391
1.024
0.311
1.011
.5194
0.85
0.870
1.604
1.144
1.401
1.021
0.315
1.010
.5210
0.86
0.879
1.621
1.148
1.412
1.018
0.319
1.008
.5224
0.87
0.888
1.638
1.151
1.422
1.015
0.323
1.007
.5237
0.88
0.897
1.655
1.155
1.433
1.013
0.327
1.006
.5250
0.89
0.906
1.673
1.158
1.444
1.011
0.331
1.005
.5261
One Dimensional Isentropic Compressible Flow Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat ( cp),
and Constant Specific Heat Ratio ('Y) = 1.4) (continued)
M
M*
P/Ps
T1/T5
er!Qs
A/A*
qi Pt
FIF*
WTAP
0.90
0.915
1.691
1.162
1.456
1.009
0.335
1.004
.5271
0.91
0.923
1.710
1.166
1.467
1.007
0.339
1.003
.5280
0.92
0.932
1.729
1.169
1.478
l.006
0.343
1.002
.5288
0.93
0.941
1.748
1.173
1.490
1.004
0.346
1.002
.5295
0.94
0.949
1.767
1.177
1.502
1.003
0.350
1.001
.5301
0.95
0.958
1.787
1.180
1.514
1.002
0.353
1.001
.5306
0.96
0.966
1.808
1.184
1.526
1.001
0.357
1.001
.5310
0.97
0.975
1.828
1.188
1.539
1.001
0.360
1.000
.5313
0.98
0.983
1.850
1.192
1.552
1.000
0.363
1.000
.5316
0.99
0.992
1.871
1.196
1.564
1.000
0.367
1.000
.5317
LOO
1.000
1.893
1.200
1.577
1.000
0.370
1.000
.5317
LOI
1.008
1.915
1.204
1.591
1.000
0.373
1.000
.5317
1.02
1.017
1.938
1.208
1.604
1.000
0.376
1.000
.5316
1.03
1.025
1.961
1.212
1.618
1.001
0.379
1.000
.5314
1.04
1.033
1.985
1.216
1.632
1.001
0.382
1.001
.5311
LOS
1.041
2.009
1.220
1.646
1.002
0.384
1.001
.5307
1.06
1.049
2.033
1.225
1.660
1.003
0.387
1.001
.5302
1.07
1.057
2.058
1.229
1.674
1.004
0.389
1.002
.5297
1.08
1.065
2.083
1.233
1.689
LOOS
0.392
1.002
.5290
l.09
1.073
2.109
1.238
1.704
1.006
0.394
1.003
.5283
1.081
2.135
1.242
1.719
1.008
0.397
1.003
,5276
1.089
2.162
1.246
1.734
1.010
0.399
1.004
.5267
1.097
2.189
1.251
1.750
1.011
0.401
1.004
.5258
1.105
2.217
1.255
1.766
1.013
0.403
1.005
.5248
1.14
1.113
2.245
1.260
1.782
1.015
0.405
1.006
.5238
1.15
1.120
2.274
1.264
1.798
1.017
0.407
1.006
.5226
L16
1.128
2.303
1.269
1.814
1.020
0.409
1.007
.5214
,17
.136
2.333
1.274
1.831
1.022
0.411
1.008
.5202
,18
.143
2.363
1.278
1.848
1.025
0.413
1.009
.5189
1.19
1.151
2.394
1.283
1.865
1.028
0.414
1.010
.5175
1.20
1.158
2.425
1.288
1.883
1.030
0.416
1.011
.5160
L21
1.166
2.457
1.293
1.900
1.033
0.417
1.012
.5145
L22
U73
2.489
1.298
1.918
1.037
0.419
1.013
.5130
1.23
1.181
2.522
1.303
1.936
1.040
0.420
1.014
.5114
.24
1.188
2.556
1.308
1.955
1.043
0.421
1.015
.5097
.25
.195
2.590
l.312
1.974
1.047
0.422
1.016
.5080
L26
1.202
2.625
1.318
1.992
1.050
0.423
1.017
.5062
.27
1.210
2.661
1.323
2.012
1.054
0.424
1.018
.5044
L28
1.217
2.697
1.328
2.031
1.058
0.425
1.019
.5026
1.29
1.224
2.733
1.333
2.051
1.062
0.426
1.021
.5006
L30
1.231
2.771
l.338
2.071
1.066
0.427
1.022
.4987
1.238
2.809
1.343
2.091
1.071
0.428
1.023
.4967
L32
1.245
2.847
1.348
2.112
1.075
0.428
1.024
.4946
.33
l.252
2.887
1.354
2.132
1.080
0.429
l.025
.4926
.34
1.259
2.927
1.359
2.153
l.084
0.429
1.027
.4904
One Dimensional Isentropic Compressible Flow Functions
(Por Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat ( cp),
and Constant Specific Heat Ratio (-y) = 1.4) (continued)
M
M*
P/Ps
T/Ts
e1les
AIA*
q/P1
FIF*
WTAP
1.35
1.266
2.967
1.364
2.175
1.089
0.430
1.028
.4883
L36
1.273
3.009
1.370
2.196
1.094
0.430
1.029
.4861
1.37
1.280
3.051
1.375
2.218
1.099
0.431
1.031
.4838
L38
1.286
3.094
1.381
2.241
1.104
0.431
1.032
.4816
1.39
1.293
3.138
1.386
2.263
1.109
0.431
1.033
.4793
1.40
1.300
3.182
1.392
2.286
1.115
0.431
1.035
.4769
1.41
.306
3.227
1.398
2.309
1.120
0.431
1.036
.4746
1.42
1.313
3.273
1.403
2.333
1.126
0.431
1.037
.4722
1.43
1.320
3.320
1.409
2.356
1.132
0.431
1.039
.4698
l.44
1.326
3.368
1.415
2.380
1.138
0.431
1.040
.4673
1.45
1.333
3.416
1.420
2.405
1.144
0.431
1.042
.4648
.46
1.339
3.465
1.426
2.430
1.150
0.431
1.043
.4623
L47
1.346
3.515
1.432
2.455
1.156
0.430
1.044
.4598
1.48
1.352
3.566
1.438
2.480
1.163
0.430
1.046
.4573
1.49
1.358
3.618
1.444
2.506
1.169
0.430
1.047
.4547
1.50
1.365
3.671
1.450
2.532
1.176
0.429
1.049
.4521
.51
1.371
3.724
1.456
2.558
1.183
0.429
1.050
.4495
.52
1.377
3.779
1.462
2.585
1.190
0.428
1.052
.4469
1.53
1.383
3.834
1.468
2.612
1.197
0.427
1.053
.4442
1.54
l.389
3.891
1.474
2.639
1.204
0.427
1.055
.4416
.55
1.395
3.943
1.480
2.667
1.212
0.426
1.056
.4389
L56
1.401
4.007
1.487
2.695
1.219
0.425
1.058
.4362
L57
1.408
4.066
1.493
2.723
1.227
0.424
1.059
.4335
1.58
1.414
4.126
1.499
2.752
1.234
0.423
1.060
.4308
1.59
1.419
4.188
1.506
2.781
1.242
0.423
1.062
.4281
1.60
1.425
4.250
1.512
2.811
1.250
0.422
1.063
.4253
1.61
1.431
4.314
1.518
2.841
1.258
0.421
1.065
.4226
1.62
1.437
4.378
1.525
2.871
1.267
0.420
1.066
.4198
.63
1.443
4.444
1.531
2.902
1.275
0.418
1.068
.4171
1.64
1.449
4.511
1.538
2.933
1.284
0.417
1.069
.4143
1.65
1.454
4.579
1.544
2.964
1.292
0.416
1.071
.4115
1.66
1.460
4.648
1.551
2.996
1.301
0.415
1.072
.4087
1.67
1.466
4.718
1.558
3.029
1.310
0.414
1.074
.4059
1.68
1.471
4.789
1.564
3.061
1.319
0.413
1.075
.4031
1.69
1.477
4.862
1.571
3.094
1.328
0.411
1.077
.4004
1.70
1.482
4.936
1.578
3.128
1.338
0.410
1.079
.3976
L71
1.488
5.011
1.585
3.162
1.347
0.408
1.080
.3948
L72
1.493
5.087
1.592
3.196
1.357
0.407
1.082
.3919
:l.73
1.499
5.165
1.599
3.231
1.366
0.406
1.083
.3891
1.74
1.504
5.243
1.605
3.266
1.376
0.404
1.085
.3863
.75
1.510
5.324
1.612
3.302
1.386
0.403
1.086
.3835
,76
1.515
5.405
1.619
3.338
1.397
0.401
1.088
.3807
L77
1.520
5.488
1.627
3.374
1.407
0.400
1.089
,3779
L78
1.526
5.572
1.634
3.411
1.417
0.398
1.091
.3751
L79
1.531
5.658
1.641
3.448
1.428
0.396
1.092
.3723
One Dimensional Isentropic Compressible Flow Functions
(.For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp),
and Constant Specific Heat Ratio {-y) = 1.4) (continued)
M
M*
P/Ps
TtfTs
Qi/Qs
A/A*
q/Pt
F/F*
WTAP
1.80
1.536
5.745
1.648
3.486
1.439
0.395
1.094
.3695
L81
l.541
5.834
1.655
3.525
1.450
0.393
1.095
3668
1.82
1.546
5.924
1.662
3.563
1.461
0.391
1.096
.3640
L83
1.551
6.015
1.670
3.603
1.472
0.390
1.098
.3612
1.84
1.556
6.108
1.677
3.642
1.484
0.388
1.099
.3584
1.85
1.561
6.203
1.684
3.683
1.495
0.386
1.101
.3557
1.86
1.566
6.299
1.692
3.723
1.507
0.384
1.102
.3529
L87
1.571
6.397
1.699
3.764
1.519
0.383
1.104
.3501
1.88
1.576
6.496
1.707
3.806
1.531
0.381
1.105
.3474
l.89
1.581
6.597
1.714
3.848
1.543
0.379
1.107
.3447
L90
1.586
6.700
1.722
3.891
1.555
0.377
1.108
.3419
L91
1.591
6.804
1.730
3.934
l.568
0.375
1.110
.3392
L92
1.596
6.910
1.737
3.978
1.580
0.373
l.111
.3365
1.93
1.600
7.018
1.745
4.022
1.593
0.372
1.113
.3336
1.94
1.605
7.128
l.753
4.067
1.606
0.370
1.114
.3311
1.95
1.610
7.239
1.760
4.112
1.619
0.368
1.116
.3284
1.96
L615
7.352
1.768
4.158
1.633
0.366
1.117
.3257
L97
1.619
7.467
1.776
4.204
1.646
0.364
1.118
.3231
l.98
1.624
7.584
1.784
4.251
1.660
0.362
1.120
.3204
L99
1.628
7.703
1.792
4.299
1.673
0.360
1.121
.3178
2.00
1.633
7.824
1.800
4.347
1.687
0.358
1.123
.3151
2.05
.655
8.457
1.840
4.595
1.760
0.348
1.130
.3022
2.10
1.677
9.144
1.882
4.859
1.837
0.338
1.137
.2895
2.15
1.698
9.887
1.924
5.138
1.918
0.327
1.143
.2772
2.20
1.718
10.691
1.968
5.433
2.005
0.317
l.150
.2652
2.25
1.737
11.562
2.012
5.745
2.096
0.306
1.156
.2537
2.30
1.756
12.503
2.058
6.075
2.193
0.296
1.163
.2425
2.35
.775
13.520
2.104
6.424
2.295
0.286
1.169
.2317
2.40
1.792
14.613
2.152
6.793
2.403
0.276
1.175
.2213
2.45
1.809
15.804
2.200
7.182
2.517
0.266
1.181
.2113
2.50
1.826
17.084
2.250
7.593
2.637
0.256
1.187
.2017
2.55
1.842
18.464
2.300
8.026
2.763
0.247
1.192
.1925
Vi
2.60
1.857
19.951
2.352
8.483
2.896
0.237
1.198
.1836
--l
2.65
1.872
21.554
2.404
8.964
3.036
0.228
1.203
.1752
2.70
1.887
23.280
2.458
9.471
3.183
0.219
1.208
.1671
2.75
1.900
25.137
2.512
10.005
3.337
0.211
1.213
.1593
2.80
1.914
27.135
2.568
10.567
3.500
0.202
1.218
.1519
2.85
1.927
29.282
2.624
11.158
3.670
0.194
1.223
1449
2.90
L940
31.590
2.682
11.779
3.849
0.186
1.228
. 1381
2.95
1.952
34.068
2.740
12.432
4.037
0.179
1.232
.1317
3.00
1.964
36.728
2.800
13.118
4.234
0.172
1.237
.1256
3.10
1.987
42.641
2.922
14.593
4.657
0.158
1.245
.1142
3.20
2.008
49.430
3.048
16.218
5.121
0.145
1.253
.1038
3.30
2.028
57.211
3.178
18.003
5.628
0.133
1.260
.0945
3.40
2.047
66.109
3.312
19.961
6.183
0.122
1.268
.0860
3.50
2.064
76.262
3.450
22.106
6.789
0.112
1.274
.0783
One Dimensional Isentropic Compressible Flow Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp),
and Constant Specific Heat Ratio (,y) = 1.4) (continued)
M
M*
P/Ps
T/Ts
etfes
A/A*
q/Pt
F/F*
WTAP
3.60
2.081
87.825
3.592
24.451
7.449
0.103
1.281
.0714
3.70
2.096
100.967
3.738
27.012
8.168
0.095
1.287
.0651
3.80
2.111
115.874
3.888
29.804
8.950
0.087
1.292
.0594
3.90
2.125
132.749
4.042
32.844
9.798
0.080
1.298
.0543
4.00
2.138
151.816
4.200
36.148
10.718
0.074
1.303
.0496
4.10
2.150
173.318
4.362
39.735
11.714
0.068
.308
.0454
Vt
4.20
2.162
197.523
4.528
43.624
12.791
0.063
1.312
.0416
00
4.30
2.173
224.720
4.698
47.835
13.954
0.058
1.317
.0381
4.40
184
255.224
4.872
52.388
15.209
0.053
1.321
.0350
4.50
2.194
289.379
5.050
57.305
16.561
0.049
.325
.0321
4.60
2.203
327 .555
5.232
62.608
18.016
0.045
1.328
.0295
4.70
2.212
370.156
5.418
68.322
19.581
0.042
1.332
.0272
4.80
2.220
417.615
5.608
74.470
21.262
0.039
1.335
.0250
4.90
2.228
470.404
5.802
81.079
23.065
0.036
1.339
.0231
5.00
2.236
529.028
6.000
88.174
24.998
0.033
1.342
.0213
5.20
2.250
666.005
6.408
103.937
29.281
0.028
1.347
.0182
5.40
2.263
833.428
6.832
121.993
34.172
0.024
1.352
.0156
5.60
2.275
1036.907
7.272
142.594
39.737
0.021
1.357
.0134
.5.80
2.286
1282.884
7.728
166.010
46.046
0.018
1.362
.0115
6.00
2.295
1578.712
8.200
192.532
53.176
0.016
I .365
.0100
6.50
2.316
2593.995
9.450
274.505
75.129
O.Qll
1.374
.0071
7.00
2.333
4139.453
10.800
383.293
104.136
0.008
1.381
.0051
750
2.347
6433.371
12.250
525.187
141.833
0.006
1.387
.0037
8.00
2.359
9762.039
13.800
707.412
190.098
0.005
1.391
.0028
9.00
2.377
21101.633
17.200
1226.868
327.171
0.003
1.399
.0016
10.00
2.390
42436.316
21.000
2020.820
535.911
0.002
1.404
.0010
LOO
2.400
80329.500
25.200
3187.739
841.370
0.001
1.408
.0006
One Dimensional Normal Shock Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp),
and Constant Specific Heat Ratio (,y) = 1.4)
Mx
My
P5ylPsx
P,/Ptx
Ps/Ptx
Ts/Tsx
Ts/Ttx
'1s/'2sx
LOO
1.0000
1.0000
1.0000
0.5283
1.0000
0.8333
1.0000
,01
0.9901
1.0234
1.0000
0.5344
1.0066
0.8361
1.0167
.02
0.9805
1.0471
1.0000
0.5403
1.0132
0.8387
1.0334
.03
0.9712
1.0710
1.0000
0.5462
1.0198
0.8413
1.0502
1.04
0.9620
1.0952
0.9999
0.5519
1.0263
0.8438
1.0671
.05
0.9531
1.1196
0.9999
0.5574
1.0328
0.8462
1.0840
O'\
.06
0.9444
1.1442
0.9998
0.5628
1.0393
0.8486
1.1009
C
L07
0.9360
1.1690
0.9996
0.5681
1.0457
0.8509
1.1179
.08
0.9277
1.1941
0.9994
0.5732
1.0522
0.8531
1349
L09
0.9197
1.2194
0.9992
0.5782
1.0586
0.8553
1.1520
.10
0.9118
1.2450
0.9989
0.5831
1.0649
0.8574
1.1691
0.9041
1.2708
0.9986
0,5878
1.0713
0.8595
1.1862
U2
0.8966
1.2968
0.9982
0.5924
1.0776
0.8615
1.2034
.13
0.8892
1.3230
0.9978
0.5968
1.0840
0.8635
1.2206
14
0.8820
1.3495
0.9973
0.6011
1.0903
0.8654
1.2378
.15
0.8750
1.3762
0.9967
0.6053
1.0966
0.8672
1.2550
U6
0.8632
1.4032
0.9961
0.6093
1.1029
0.8690
1.2723
0.8615
1.4303
0.9953
0.6132
1.1092
0.8708
1.2896
0.8549
1.4578
0.9946
0.6170
1.1154
0.8725
1.3069
0.8485
1.4854
0.9937
0.6206
1.1217
0.8741
1.3242
1.20
0.8422
1.5133
0.9928
0.6241
1.1280
0.8758
1.3416
L21
0.8360
1.5414
0.9918
0.6274
1.1343
0.8774
1.3590
.22
0.8300
1.5698
0.9907
0.6306
1.1405
0.8789
1.3763
1.23
0.8241
1.5983
0.9896
0.6337
1.1468
0.8804
1.3937
1.24
0.8183
1.6271
0.9884
0.6366
1.1531
0.8819
1.4111
1.25
0.8126
1.6562
0.9871
0.6394
1.1594
0.8833
1.4285
.26
0.8071
1.6855
0.9857
0.6421
1.1656
0.8847
1.4460
1,27
0.8017
1.7150
0.9842
0.6446
1.1719
0.8861
1.4634
1.28
0.7963
1.7447
0.9827
0.6470
1.1782
0.8874
1.4808
.29
0.7911
1.7747
0.9811
0.6493
1.1845
0.8888
1.4982
uo
0.7860
1.8049
0.9794
0.6514
1.1909
0.8900
1.5157
Ul
0.7809
1.8354
0.9776
0.6535
1.1972
0.8913
1.5331
0,
L32
0.7760
1.8661
0.9758
0.6554
1.2035
0.8925
1.5505
,_,
1.33
0.7712
1.8970
0.9738
0.6571
1.2099
0.8937
1.5679
.34
0.7664
1.9281
0.9718
0.6588
1.2162
0.8949
1.5853
1.35
0.7618
1.9595
0.9697
0.6603
1.2226
0.8960
1.6027
L36
0.7572
1.9911
0.9676
0.6617
1.2290
0.8971
1.6201
.37
0.7527
2.0230
0.9653
0.6630
1.2354
0.8982
1.6375
1.38
0.7483
2.0550
0.9630
0.6642
1.2418
0.8993
1.6549
1.39
0.7440
2.0874
0.9607
0.6652
1.2482
0.9003
1.6723
1.40
0.7397
2.1199
0.9582
0.6662
1.2547
0.9014
1.6896
0.7355
2.1527
0.9557
0.6670
1.2611
0.9024
1.7069
1.42
0.7314
2.1857
0.9S31
0.6677
1.2676
0.9033
1.7243
1.43
0.7274
2.2189
0.9504
0.6683
1.2741
0.9043
1. 7415
1.44
0.7235
2.2524
0.9477
0.6688
1.2806
0.9052
l. 7588
One Dimensional Normal Shock Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat (cp),
and Constant Specific Heat Ratio (-y) = 1.4) (continued)
Mx
My
Ps/Psx
P1ylP1x
P5ylP1x
Ts/Tsx
Ts/Ttx
es/esx
.45
0.7196
2.2861
0.9448
0.6692
1.2872
0.9062
1. 7761
L46
0.7158
2.3201
0.9420
0.6695
1.2937
0.9071
1.7933
L47
0.7120
2.3543
0.9390
0.6697
1.3003
0.9079
1.8105
.48
0.7083
2.3887
0.9360
0.6698
1.3069
0.9088
1.8277
1.49
0.7047
2.4233
0.9329
0.6698
1.3135
0.9097
1.8449
1.50
0.7011
2.4582
0.9298
0.6697
1.3202
0.9105
1.8620
.51
0.6976
2.4933
0.9266
0.6694
1.3269
0.9113
1.8791
L52
0.6941
2.5287
0.9233
0.6691
1.3335
0.9121
1.8962
0.6907
2.5642
0.9200
0.6687
1.3403
0.9129
1.9132
.54
0.6874
2.6001
0.9166
0.6682
1.3470
0.9137
1.9303
L55
0.6841
2.6361
0.9132
0.6677
1.3538
0.9144
1.9472
.56
0.6809
2.6724
0.9097
0.6670
l.3605
0.9151
1.9642
L57
0.6777
2.7089
0.9062
0.6662
1.3674
0.9159
1.9811
.58
0.6746
2.7456
0.9026
0.6654
1.3742
0.9166
1.9980
1.59
0.6715
2.7826
0.8989
0.6645
1.3811
0.9173
2.0149
L60
0.6685
2.8198
0.8952
0.6635
1.3879
0.9180
2.0317
L61
0.6655
2.8573
0.8915
0.6624
1.3949
0.9186
2.0484
.62
0.6625
2.8950
0.8877
0.6612
1.4018
0.9193
2.0652
1.63
0.6596
2.9329
0.8838
0.6600
1.4088
0.9199
2.0819
l.64
0.6568
2.9710
0.8799
0.6587
1.4157
0.9206
2.0985
1.65
0.6540
3.0094
0.8760
0.6573
1.4228
0.9212
2.1152
1.66
0.6512
3.0480
0.8720
0.6558
1.4298
0.9218
2.1317
L67
0.6485
3.0869
0.8680
0.6543
1.4369
0.9224
2.1483
1.68
0.6458
3.12S9
0.8640
0.6527
1.4440
0.9230
2.1648
1.69
0.6432
3.1653
0.8599
0.6S10
1.4511
0.9236
2.1812
L70
0.6406
3.2048
0.8557
0.6493
1.4583
0.9242
2.1976
0.6380
3.2446
0.8516
0.6475
1.4655
0.9247
2.2140
1.72
0.6355
3.2846
0.8474
0.6457
1.4727
0.9253
2.2303
1.73
0.6330
3.3248
0.8431
0.6438
1.4800
0.9258
2.2466
1.74
0.6305
3.3653
0.8389
0.6418
1.4872
0.9263
2.2628
L75
0.6281
3.4060
0.8346
0.6398
1.4945
0.9269
2.2790
L76
0.6257
3.4470
0,8303
0.6377
1.5019
0.9274
2.2951
0\
L77
0.6234
3.4882
0.8259
0.6356
1.5092
0.9279
2.3112
u:.
L78
0.6211
3.5296
0.8215
0.6334
1.5166
0.9284
2.3272
1.79
0.6188
3.5712
0.8171
0.6312
1.5241
0.9289
2.3432
1.80
0.6165
3.6131
0.8127
0.6289
1.5315
0.9294
2.3591
1.81
0.6143
3.6552
0.8033
0.6266
1.5390
0.9298
2.3750
1.82
0.6121
3.6975
0.8038
0.6242
1.5465
0.9303
2.3908
l.83
0.6099
3.7401
0.7993
0.6218
1.5541
0.9307
2.4066
1.84
0.6078
3.7829
0.7948
0.6193
1.5617
0.9312
2.4223
1.85
0.6057
3.8260
0.7903
0.6168
1.5693
0.9316
2.4380
1.86
0.6036
3.8693
0.7857
0.6142
1.5770
0.9321
2.4536
1.87
0.6016
3.9128
0.7812
0.6117
1.5846
0.9325
2.4692
1.88
0.5996
3.9565
0.7766
0.6090
1.5923
0.9329
2.4847
1.89
0.5976
4.0005
0.7720
0.6064
1.6001
0.9333
2.5002
One Dimensional Normal Shock Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat ( cp),
and Constant Specific Heat Ratio (,y) = 1.4) (continued)
-
Mx
My
Ps/Psx
Pr/Pix
PsylP1x
T5ylTsx
Ts/Ttx
'1sylQs,x
1.90
0.5956
4.0447
0.7674
0.6037
1.6079
0.9337
2.5156
.91
0.5937
4.0892
0.7628
0.6010
1.6157
0.9341
2.5309
1.92
0.5918
4.1338
0.7582
0.5982
1.6235
0.9345
2.5462
.93
0.5899
4.1787
0.7535
0.5954
1.6314
0.9349
2.5615
1.94
0.5880
4.2239
0.7489
0.5926
1.6393
0.9353
2.5766
L95
0.5862
4.2693
0.7442
0.5898
1.6472
0.9357
2.5918
C\
1.96
0.5844
4.3149
0.7396
0.5869
1.6552
0.9361
2.6068
+"
L97
0.5826
4.3607
0.7349
0.5840
1.6632
0.9364
2.6219
L98
0.5808
4.4068
0.7302
0.5811
1.6713
0.9368
2.6368
1.99
0.5791
4.4531
0.7256
0.5781
1.6793
0.9371
2.6517
2.00
0.5774
4.4997
0.7209
0.5751
1.6874
0.9375
2.6666
2.01
0.5757
4.5464
0.7162
0.5722
1.6956
0.9378
2.6813
2.02
0.5740
4.5935
0.7116
0.5691
1.7038
0.9382
2.6961
2.03
0.5723
4.6407
0.7069
0.5661
1.7120
0.9385
2. 7107
2.04
0.5707
4.6882
0.7022
0.5631
1.7202
0.9388
2.7254
2.05
0.5691
4.7359
0.6975
0.5600
1.7285
0.9392
2.7399
2.06
0.5675
4.7838
0.6929
0.5569
1.7368
0.9395
2.7544
2.07
0.5659
4.8320
0.6882
0.5538
1.7451
0.9398
2.7688
2.08
0.5643
4.8804
0.6835
O.S507
1.7535
0.9401
2.7832
2.09
0.5628
4.9291
0.6789
O.S476
1.7619
0.9404
2.7975
2.10
0.5613
4.9779
0.6742
0.5444
1.7704
0.9407
2.8118
2.11
0.5598
5.0271
0.6696
0.5413
1.7789
0.9410
2.8260
2.12
0.5583
5.0764
0.6650
0.5381
1.7874
0.9413
2.8401
2.13
0.5568
5.1260
0.6603
0.5349
1.7959
0.9416
2.8542
2.14
0.5554
5.1758
0.6557
0.5318
1.8045
0.9419
2.8682
2.15
0.5540
5.2258
0.6511
0.5286
1.8131
0.9422
2.8822
2.16
0.5526
5.2761
0.6465
0.5254
1.8218
0.9425
2.8961
2.17
0.5512
5.3266
0.6419
0.5222
1.8305
0.9427
2.9099
2.18
0.5498
5.3774
0.6373
0.5190
1.8392
0.9430
2.9237
2.19
0.5484
5.4283
0.6327
0.5157
1.8480
0.9433
2.9374
:2.20
0.5471
5.4796
0.6282
0.5125
1.8568
0.9435
2.9511
2.21
0.5457
5.5310
0.6236
0.5093
1.8656
0.9438
2.9647
O'\
2.22
0.5444
5.5827
0.6191
0.5061
1.8745
0.9440
2.9782
u,
2.23
0.5431
5.6346
0.6146
0.5029
1.8834
0.9443
2.9917
2.24
0.5418
5.6867
0.6101
0.4996
1.8923
0.9445
3.0051
2.25
0.5406
5.7391
0.6056
0.4964
1.9013
0.9448
3.0185
2.26
0.5393
5.7917
0.6011
0.4932
1.9103
0.9450
3.0318
2.27
0.5381
S.8446
0.5966
0.4899
1.9194
0.9453
3.0451
2.28
0.5368
5.8976
0.5922
0.4867
1.9284
0.9455
3.0582
2.29
0.5356
5.9510
0.5878
0.4835
1.9376
0.9457
3.0714
2.30
0.5344
6.0045
0.5833
0.4803
1.9467
0.9460
3.0844
2.3l
0.5332
6.0583
0.5789
0.4770
1.9559
0.9462
3.0974
2.32
0.5321
6.1123
0.5746
0.4738
1.9651
0.9464
3.1104
2.33
0.5309
6.1665
O.S702
0.4706
1.9744
0.9466
3.1233
2.34
0.5298
6.2210
0.5659
0.4674
1.9837
0.9469
3.1361
One Dimensional Normal Shock Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat ( cp),
and Constant Specific Heat Ratio (-y) = 1.4) (continued)
Mx
My
PsylPsx
P1ylP1x
Ps/P,x
T5ylTsx
Ts/Ttx
Qs/Cls.x
2.35
0.5286
6.2757
0.5615
0.4642
1.9930
0.9471
3.1488
2.36
0.5275
6.3307
0.5572
0.4610
2.0024
0.9473
3.1615
2.37
0.5264
6.3858
0.5529
0.4578
2.0118
0.9475
3.1742
2.38
0.5253
6.4412
0.5487
0.4546
2.0212
0.9477
3.1868
2.39
0.5242
6.4969
0.5444
0.4514
2.0307
0.9479
3.1993
2.40
0.5231
6.5528
0.5402
0.4483
2.0402
0.9481
3.2118
2.41
0.5221
6.6089
0.5360
0.4451
2.0498
0.9483
3.2242
2.42
0.5210
6.6652
0.5318
0.4420
2.0594
0.9485
3.2365
2.43
0.5200
6.7218
0.5276
0.4388
2.0690
0.9487
3.2488
2.44
0.5189
6.7786
0.5235
0.4357
2.0787
0.9489
3.2610
2.45
0.5179
6.8356
0.5194
0.4325
2.0884
0.9491
3.2732
2.46
0.5169
6.8929
0.5153
0.4294
2.0981
0.9493
3.2853
2.47
0.5159
6.9504
0.5112
0.4263
2.1079
0.9495
3.2974
2.48
0.5149
7.0082
0.5071
0.4232
2.1177
0.9496
3.3094
2.49
0.5140
7.0662
0.5031
0.4201
2.1275
0.9498
3.3213
2.50
0.5130
7.1244
0.4991
0.4170
2.1374
0.9500
3.3332
2.51
0.5120
7.1828
0.4951
0.4140
2.1473
0.9502
3.3450
2.52
0.5111
7.2415
0.4911
0.4109
2.1573
0.9503
3.3568
2.53
0.5102
7.3004
0.4871
0.4079
2.1673
0.9505
3.3685
2.54
0.5092
7.3595
0.4832
0.4048
2.1773
0.9507
3.3802
2.55
0.5083
7.4189
0.4793
0.4018
2.1873
0.9509
3.3917
2.56
0.5074
7.4785
0.4754
0.3988
2.1974
0.9510
3.4033
2.57
0.5065
7.5384
0.4716
0.3958
2.2076
0.9512
3.4148
2.58
0.5056
7.5984
0.4678
0.3928
2.2178
0.9514
3.4262
2.59
0.5048
7.6588
0.4640
0.3899
2.2280
0.9515
3.4375
2.60
0.5039
7.7193
0.4602
0.3869
2.2382
0.9517
3.4488
2.61
0.5030
7.7801
0.4564
0.3840
2.2485
0.9518
3.4601
2.62
0.5022
7.8411
0.4527
0.3811
2.2588
0.9520
3.4713
2.63
0.5013
7.9023
0.4490
0.3781
2.2692
0.9521
3.4824
2.64
0.5005
7.9638
0.4453
0.3752
2.2796
0.9523
3.4935
2.65
0.4997
8.0255
0.4416
0.3724
2.2900
0.9524
3.5045
2.66
0.4988
8.0875
0.4380
0.3695
2.3005
0.9526
3.5155
""
2.67
0.4980
8.1496
0.4343
0.3666
2.3110
0.9527
3.5264
-..1
2.68
0.4972
8.2120
0.4307
0.3638
2.3216
0.9529
3.5373
2.69
0.4964
8.2747
0.4272
0.3610
2.3321
0.9530
3.5481
2.70
0.4956
8.3376
0.4236
0.3582
2.3428
0.9532
3.5589
2.71
0.4949
8.4007
0.4201
0.3554
2.3534
0.9533
3.5696
2.72
0.4941
8.4640
0.4166
0.3526
2.3641
0.9534
3.5802
2.73
0.4933
8.5276
0.4131
0.3498
2.3748
0.9536
3.5908
2.74
0.4926
8.5914
0.4097
0.3471
2.3856
0.9537
3.6013
2.75
0.4918
8.6554
0.4063
0.3444
2.3964
0.9539
3.6118
2.76
0.4911
8.7197
0.4029
0.3416
2.4073
0.9540
3.6222
2.77
0.4903
8.7842
0.3995
0.3389
2.4182
0.9541
3.6326
2.78
0.4896
8.8490
0.3961
0.3363
2.4291
0.9542
3.6429
2.79
0.4889
8.9139
0.3928
0.3336
2.4400
0.9544
3.6532
One Dimensional Normal Shock Functions
(For Perfect Gas, Constant Molecular Weight, Constant Pressure Specific Heat ( cp),
and Constant Specific Heat Ratio (-y) = 1.4) (continued)
Mx
My
PsylPsx
P1/Ptx
PsylPrx
TsylTsx
Ts/Ttx
Qs/'2sx
2.80
0.4882
8.9791
0.3895
0.3309
2.4510
0.9545
3.6634
2.81
0.4875
9.0446
0.3862
0.3283
2.4621
0.9546
3.6736
2.82
0.4868
9.1103
0.3830
0.3257
2.4731
0.9548
3.6837
2.83
0.4861
9.1762
0.3797
0.3231
2.4842
0.9549
3.6938
2.84
0.4854
9.2423
0.3765
0.3205
2.4954
0.9550
3.7038
2.85
0.4847
9.3087
0.3733
0.3179
2.5066
0.9551
3. 7137
2.86
0.4840
9.3753
0.3702
0.3154
2.5178
0.9552
3.7236
2.87
0.4834
9.4421
0.3670
0.3128
2.5290
0.9554
3.7335
2.88
0.4827
9.5092
0.3639
0.3103
2.5403
0.9555
3.7433
2.89
0.4820
9.5765
0.3608
0.3078
2.5517
0.9556
3.7530
2.90
0.4814
9.6441
0.3578
0.3053
2.5630
0.9557
3.7627
2.91
0.4807
9.7118
0.3547
0.3028
2.5745
0.9558
3.7724
2.92
0.4801
9.7799
0.3517
0.3004
2.5859
0.9559
3.7820
2.93
0.4795
9.8481
0.3487
0.2979
2.5974
0.9560
3. 7915
2.94
0.4788
9.9166
0.34S7
0.2955
2.6089
0.9562
3.8010
2.95
0.4782
9.9853
0.3428
0.2931
2.6205
0.9563
3.8105
2.96
0.4776
10.0542
0.3399
0.2907
2.6321
0.9564
3.8199
2.97
0.4770
10.1234
0.3370
0.2884
2.6437
0.9565
3.8292
2.98
0.4764
10.1928
0.3341
0.2860
2.6554
0.9566
3.8385
2.99
0.4758
10.2624
0.3312
0.2837
2.6671
0.9567
3.8478
3.00
0.4752
10.3323
0.3284
0.2813
2.6788
0.9568
3.8570
3.20
0.4643
11.7800
0.2762
0.2383
2.9220
0.9587
4.0315
3.40
0.4552
13.3200
0.2322
0.2015
3.1802
0.9602
4.1884
3.60
0.4474
14.9S33
0.1953
0.1702
3.4537
0.9615
4.3296
3.80
0.4407
16.6800
0.1645
0.1439
3.7426
0.9626
4.4568
4.00
0.4350
18.5000
0.1388
0.1218
4.0469
0.9635
4.5714
5.00
0.4152
29.0000
0.0617
0.0548
5.8000
0.9667
5.0000
6.00
0.4042
41.8333
0.0297
0.0265
7.9406
0.9684
5.2683
7.00
0.3974
57.0000
0.0154
0.0138
10.4694
0.9694
5.4444
8.00
0.3929
74.5000
0.0085
0.0076
13.3867
0.9701
5.5652
Q\
''
General Properties of Air
Speed of Sound in Air at Atmospheric Temperature
CJps = 49.02 \[T0R
Cmph = 33.42 \[T0R
Ckts = 29.04 \[T0R
Cm/sec = 20.0S \[T OR
Specific Weight of Air in lb/ft3
ge = .07647 (~)(~) = 1.326 (p i;;RHg)
Density of Air in lb sec2/ft4 or slug/ft3
Q = .002377(~)(~) = .041206 (~~RHg)
Air Density Ratio
o = __g_ =(~)('Ifl) = 17.336 (Pin. Hg)
Qo
Po
T
ToR
Coefficient of Viscosity in lb/ft sec
fJ (T )312
c =
OR
TOR+ s
where: S = 198.72 R
{J = 7.3025 x 10- 7 ft/sec y 0R
Kinematic Viscosity in ft2/sec
V =_&_
gp
Absolute Viscosity for Air in lb-sec/ft2
IJ = pv
r0.3170 (ToR) 3/2(
734.7
).1 X 10 10
r
T0 R + 216 LJ
Specific Heat (Heat Capacity) of Air at 59F
BTU
J
at constant pressure cp = 0.240 --- = 1004.76 --
lb ()R
kg K
at constant volume
= 0, 1715 BTU = 717,986
1
lb 0R
kg K
Specific heat ratio,
Gas Constant for Air
R = 53.35
ft lb
0R lbm
A
287.074-
1
-
kg K
Normal Composition of Clean, Dry
Atmospheric Air Near Sea Level
Constituent Gas
and Formula
Nitrogen (N2)
Oxygen (02)
Argon (A)
Carbon dioxide (CO2)
Neon (Ne)
Helium (He)
Krypton (Kr)
Xenon (Xe)
Hydrogen (Hi)
Methane (CH4)
Nitrous oxide Ozone (03)
Content, Percent
by Volume
78.084
20.9476
0.934
0.0314
0.001818
0.000524
0.000114
0.0000087
0.00005
0.0002
Molecular
Weight*
28.0134
31.9988
39.948
44.00995
20.183
4.0026
83.80
131.30
2.01594
16.04303
0.00005
44.0128
Summer: 0 to 0.000007
47 .9982
Winter: 0 to 0.000002
47 .9982
Sulfur dioxide (SO2)
0 to 0.0001
64.0628
Nitrogen dioxide (N02)
0 to 0.000002
46.0055
Ammonia (NH3)
Oto trace
17.03061
Carbon monoxide (CO)
0 to trace
28.01055
Iodine (12)
0 to 0.000001
253.8088
*On basis of carbon-12 isotope scale for which en
12.
Molecular
of ah
28,9644
lb
(.
kg
;)
lb mo!
, kg mol 1
General Properties of Gases
Perfect Gas Law
at constant temperature
at constant pressure
at constant volume
Reversible adiabatic process
Polytropic process
Steady-flow energy equation
PV = mRT
P1IP2 = V2IV1
V1IV2
T1IT2
P1IP2 = T1IT2
P1 = ( V2) Y
P2
V1
( ~~)
P1 =( QJ )y
P2
Q2
P1V1n == P2V2n
!J. = ( fl) 1-n
T2
V2
T1 = ( P1) n;;l
T2
P2
v2
1\2
q + h1 + _1 + Z1 = h2 + -
+ Z2 + W
2g
2g
Bernoulli equation (W = 0)
I
v22 - v12
(P2
P1) + _____ __._ + (Z2 - Z1) = 0
Qg
where Z
altitude
Flow per unit area
; = f1 ~;T
y-lM,,,-~-
J fl
2
Velocity of sound in a perfect gas
\!ygRT
PSYCHROMETRIC CHART
FOR
SEA LEVEL BAROMETRIC PRESS.
TO FIND VpAT Br ADD A VpTO S.L, Vp
AV p = (29.9 -
{td -
tw)
2800 - 1.3 tw
SPECIFIC HUMIDITY W/A = 0.622 (
Vp
)
.06
BT - Vp
2.5
Vp = VAPOR PRESS. IN. HG
By = TRUE BAR. PRESS. IN. HG
2.3
td = DRY TEMP. DEG F
tw = WET BULB TEMP. DEG F
.05
ENTER CHART WITH DRY AND
a:
2.1
WET BULB TEMP. AT INTER"
<
SECTION READ RELATIVE
>-a:
HUMIDITY, READ LEFT FOR
0
1.9
DEW POINT, READ RIGHT FOR
al
SPECIFIC HUMIDITY AND
.04 ,::::!
(!'j
VAPOR PRESS
w
1.7 :r:
a:
:::::,
~
I-
~
en
w
5
1.5 a:
~ Ii
::?!
:::::,
~
en
.03 al
en
:
....I
1.3 w
I.;;:,
t
a:
!if
a.
a
1.1
a:
J
~
0
1.,.'a.
:::::,
<
i:'
.02 I
0.9 >
a
(.)
l
~
~
(.)
0.7
w
'b'
a.
~
en
0.5
:S'
A..(l;j
.01
~""
0.3
t,.~
,?f)
O.'!
20
30 40 50
60 70 80 90 100 110 120
DRY BULB TEMPERATURE DEG F
74
Atmospheric Viscosity
(U.S. Standard Atmosphere)
( Geo potential)
Pressure
Kinematic Viscosity, Absolute Viscosity,
Altitude, ft
ft2/sec
lb sec/ft2
0
1.572 X lQ-4
3.737 X 10-7
5,000
1.776
3.638
10,000
2.013
3.538
15,000
2.293
3.435
20,000
2.625
3.330
25,000
3.019
3.224
30,000
3.493
3.115
35,000
4.065
3.004
40,000
5.074
2.981
45,000
6.453
2.982
50,000
8.206
2.983
55,000
10.44
2.985
60,000
13.27
2.986
70,000
21.69
3.005
80,000
35.15
3.043
90,000
58.53
3.080
100,000
95.19
3.118
150,000
1066.00
3.572
200,000
6880.00
3.435
Specific Heats of Air at Low Pressures
T
Cp
Cv
y
OR
Btu/lb F
Btu/lb F
Cplcv
350
.2394
.1708
1.401
400
.2394
.1709
1.401
450
.2395
.1710
1.401
500
.2397
.1711
1.401
550
.2400
.1714
1.400
600
.2404
.1719
1.399
650
.2410
,1724
1.398
700
.2417
.1731
1.396
750
.2425
.1739
1.394
800
.2435
.1749
1.392
900
.2458
.1773
1.387
1000
.2486
.1800
1.381
1100
.2516
.1830
1.375
1200
.2547
.1862
1.368
1300
.2579
.1894
1.362
1400
.2611
.1925
1.356
1500
.2641
.1956
1.351
1600
.2670
.1985
1.345
1700
.2698
.2012
1.341
1800
.2724
.2038
1.336
1900
.2748
.2063
1.332
2000
.2771
.2085
1.329
2100
.2792
.2106
1.325
2200
.2811
.2126
1.323
2300
.2829
.2144
1.320
2400
.2846
.2161
1.317
Gas Tables (1980), Keenan, Chao & Kaye, Copyright 1980, Estate of J.H. Keenan
and J. Chao. Reprinted by permission of John Wiley & Sons, Inc.
16
Specific Heats of Products of Combustion
1 OOo/o Theoretical Air
Fuel (CH~n
T
Cp
Cy
y
OR
Btu/lb 0P
Btu/lb 0P
CpfCv
800
.2618
.1932
1.355
850
.2636
.1951
1.351
900
.2656
.1970
1.348
950
.2675
.1990
1.345
1000
.2695
.2016
1.341
1100
.2737
.2051
1.334
1200
.2779
.2093
1.328
1300
.2820
.2135
1.321
1400
.2862
.2176
l.315
1500
.2902
.2216
1.309
1600
.2941
.2255
1.304
1700
.2978
.2292
1.299
1800
.3012
.2327
1.295
1900
.3046
.2360
1.290
2000
.3077
.2391
1.287
2100
.3106
.2421
1.283
2200
.3134
.2448
1.280
2300
.3160
.2474
1.277
2400
.3184
.2498
1.274
.2500
.3207
.2521
1.272
2600
.3228
.2542
1.270
2700
.3248
.2S62
1.268
2800
.3266
.2581
1.266
2900
.3284
.2598
1.264
3000
.3301
.2615
1.262
3200
.3330
.2645
1.259
3400
.3357
.2672
1.257
3600
.3381
.2695
1.254
3800
.3402
.2716
1.252
4000
.3420
.2735
1.251
Gas Tables (1980), Keenan, Chao & Kaye, Copyright 1980, Estate of J .H. Keenan
and J, Chao. Reprinted by permission of John Wiley & Sons, Inc,.
Specific Heats of Products of Combustion
( continued)
2000Jo Theoretical Air
Fuel (CHz)n
T
Cp
Cv
y
OR
Btu/lb F
Btu/lb F
Cplcv
800
.2529
.1844
1.372
850
.2544
.1859
1.369
900
.2560
.1875
1.366
950
.2577
.1891
1.363
1000
.2594
.1908
1.359
1100
.2630
.1944
1.353
1200
.2667
.1981
1.346
1300
.2704
.2019
1.340
1400
.2740
.2055
1.334
1500
.2776
.2090
1.328
1600
.2810
.2124
1.323
1700
.2843
.2157
1.318
1800
.2873
.2187
1.313
1900
.2902
.2216
1.309
2000
.2929
.2243
1.306
2100
.2954
.2269
1.302
2200
.2978
.2293
1.299
2300
.3000
.2315
1.296
2400
.3021
.2335
1.294
2500
.3040
.2355
1.291
2600
.3058
.2373
1.289
2700
.3075
.2390
1.287
2800
.3091
.2406
1.285
2900
.3106
.2420
1.283
3000
.3120
.2435
1.282
3200
.3146
.2460
1.279
3400
.3168
.2483
1.276
3600
.3188
.2503
1.274
3800
.3207
.2521
1.272
4000
.3223
.2538
1.270
Gas Tables (1980), Keenan, Chao & Kaye, Copyright 1980, Estate of J .H. Keenar
and L Chao. Reprinted by permission of John Wiley & Sons, Inc
/8
400% Theoretical Air
Fuel (CH~)n
T
Cp
Cv
y
oR
Btu/lb F
Btu/lb F
CplCv
800
.2483
.1797
1.381
850
.2496
.1810
1.379
900
.2510
.1824
1.376
950
.2525
.1839
1.373
1000
.2541
.1855
1.370
1100
.2574
.1888
1.363
1200
.2608
.1923
1.357
1300
.2643
.1957
1.350
1400
.2677
.1991
1.344
1500
.2710
.2024
1.339
1600
.2741
.2056
1.333
1700
.2771
.2086
l.329
1800
.2798
.2114
1.324
1900
.2826
.2141
1.320
2000
.2851
.2166
1.317
2100
.2874
.2189
1.313
2200
.2896
.2216
1.310
2300
.2916
.2231
1.307
2400
.2935
.2249
1.305
2500
.2953
.2267
1.302
2600
.2969
.2284
1.300
2700
.2984
.2299
1.298
2800
.2999
.2313
1.296
2900
.3012
.2327
1.295
3000
.3025
.2340
1.293
3200
.3048
.2363
1.290
3400
.3069
.2383
1.288
3600
.3087
2402
1.285
3800
.3104
.2419
1.283
4000
.3119
.2434
1.282
Gas Tables (1980), Keenan, Chao & Kaye, Copyright 1980, Estate of J.H. Keenan
and J. Chao. Reprinted by permission of .John Wiley & Sons, Inc,
79
Properties of Materials
Nonmetallics
Classification/
Temp
AMS or
Common
Limit Density2
PWA*
Designation
"Fl
lb/cu in.
Usage
Spec
Plastics
Polyester
250
0.049
Molded
635*
Epoxy
300
0.043
409*, 411 *, 460*,
36418, 36419,
36422
Molded Composite
635*
Adhesive
455*,457*,
464*,603*
Nylon
300
0.041
Molded Composites
479*
Polyetherimide
300
Molded Composites
36426
Bismaleimide
350
Adhesive
36484
Laminated Composite 36443
Phenolic
350
0.051
Adhesive
593* IND
Flange Sealant
36033* IND
Nonmetallic
412* IND
Honeycomb Matrix
Paint
3108, 3122,
3132
Polyamideimide
480
Molded Composites
36415
Teflon
500
0.Q78
Clamp Cushion Matrix 484*
Coating
2515, 2516,
36038*
Polyurethane
597
0.041
Adhesive
597
Erosion Coating
36013
Polymide
600
0.055
Laminated
414*, 36425,
36407,36433
Adhesive
36435
449*
80
Classification/
Temp
Common
Limit
Designation
Fl
Synthetic Rubbers
Poly sulfide
180
Chloroprene
250
Nitrile
250
Fluorosilicone
400
Flurocarbon
450
Silicone
500
1. Approximate
Density2
lb/cu in.
0.053
0.045
O.o35
0.050
0.061
0.048
Usage
Adhesive/Sealant
Erosion Resistant
Coating
Adhesive
Seals
AMS or
PWA*
Spec
416* IND
580*
36027*
3207-3209,
3240-3242
0-Rings Resisting Jet
7260, 7270,
Fuel and Synthetic Oil
Gasket Matrix
475*
0-Rings Resisting Jet
7273
Fuel Clamp Cushions 36081 * IND
Molded Parts, Gaskets 36076* IND
0-Rings Resisting
7276
Synthetic Oil
Adhesive
Damper
Sealant
Abradable
616*,36003*
404*
617*, 36003*,
36029*, 36751*
407,36447
2. Density values are for the base polymer.
'~ Identifies PWA spec.
Properties of Materals
Metals and Alloys
Common
AMS or
Designation
PWA* Specl
Condition2
Al Alloys
AA 2014
4029, 4133
T6
AA 2024
4037,4120
T3,T4
AA 2219
4143
T62
AA 2618
4132
T61
AA 6061
4027,4127
T6
AA 355.0
4212
T6
AA C355.0
4215
T6
AA 356.0
4217
T6
AAA356.0
4218
T6
RR-350
4225
T6
A-357
4219,4215
T61
F-357
4289
T6
Co Alloys
L-605
5537,5759
s
Haynes Alloy
5608, 5772,
No. 188
1042*
s
WI-52
653*,654*
AC
MAR-M-509
647*
AC
MAR-M-302
657*
AC
Haynes Alloy
No. 31
5382
AC
Stellite
No. 31
5382
AC
Stellite 6B
5894
FHT
MP159
5841,5842, 5843 FHT
MP35N
l 15*
FHT
Mg Alloys
AZ61A
4350
I:"'
QE22A
4418
'T6
AZ92A
4434
i. * Identifies PWA Spec
/ Temper designations given iff
and Mg
s solution heat-treated
A.pproximate
81.
Max,
Recommended Hardness
Use Temp, F3
HB
300
120 min
300
100 min
600
110 min
600
115 min
300
80min
300
65-95
300
75-110
300
65-95
300
70-105
550
80min
300
80-120
300
80-120
1900
248-302 max
2000
293-302 max
1800
353 max
1800
1800
2000
319 max
1500
319 max
1600
38 (HRC)
1100
44 (HRC)
700
44 (HRC)
300
50min
600
62-85
300
70-95
Coefficient
Thermal Expansion
Elastic
Typical
from 70F to Ind.
Thermal
Modulus
UTS
Temp F
Conductivity
70F
70F
Density
in/in/F x 10-6
Btu-in/sq ft/hr('F
psi X 106
ksi
lb/cu in
600F 1200F
70F 600F l200F'
10.6
70
0.101
13.7
[070
1240
10.5
69
0.100
13.7
840
1295
10.6
60
0.102
13.7
960
1220
10.8
64
0.100
13.5
1070
1240
10.0
45
0.098
14.2
1070
1240
10.3
35
0.098
13.8
985
1150
10.3
42
0.098
13.8
985
1150
10.3
33
0.097
13.0
1044
10.3
40
0.097
13.0
1044
10.5
38
0.102
13.7
1075
1170
10.4
41 (-3s)
0.097
13
10.4
41 (min)
34.3
130 min
0.329
7.55
8.25
105.2 149
33.5
130 min
0.324
7.4
8.7
112
165
32.5
96.1 min
0.323
7.51
8.25
145
197.6
33.5
95.4 min
0.317
7.01
8.0
145
197.6
35.l
135
0.333
7.14
7.8
145
197.6
32.7
108
0.311
7.7
8.5
120
160
32.8
95
0.311
7.74
8.50
118.7 161.6
30.4
154
0.303
7.6
8.5
75
115
160
35.2
279
0.302
7.9
8.15
9.5
X
33
260
0.304
8.2
530
740
710
Properties of Materals
Metals and Alloys (continued)
Max.
Common
AMS or
Recommended
Designation
PWA* Specl
Condition2
Mg Alloys ( continued)
EZ33A
4442
T5
WE43A
4427
T6
Ni and Ni Alloys
A Nickel IND
6000*, 6005* IND A
Alloy 455
1480*
s
Astroloy
1013* IND
FHT
B-1900,
663*IND
FHT
B-1900 +Hf
1455*
C-263
5872
s
Hastelloy N
5607,5771
s
Hastelloy W
5755
s
Hastelloy X
5536,5754
s
IN 100
658*
FHT
IN 100 IMP
1100*
FHT
Incoloy 901
5661, 1003*
FHT
Inconel 600
5540,5665
A
Inconel 625
5599,5666
s
Inconel 706
5606,5702
s
1025*
Inconel 713
655*
AC
Inconel 718
1085*, 1010*
FHT
Inconel X-7 50
5598,5671
FHT
MAR-M-200
1422*
FHT
DS4
MAR-M-247
1447*
FHT
SC2000
1484*
s
TD Nickel
5865
S-R
U-700
689 IND
FHT
Waspaloy
1007*, 1016*
FHT
1.
Identifies PWA Spec.
A= annealed; AC as-cast; FHT =
S = solution heat-treated; S-R
solidified
84
Hardness
Use Temp, F3
HB
600
48-60
570
75-95
600
75-140
2000
1400
313-403
1900
1500
1400
255 max
1400
170-241
2000
241-277
1900
319-409
1250
388
1300
302-388
1800
187 max
1800
287 max
1200
285-321
1600
1200
331 min
1350
298-302
1900
1900
2000
2100
1600
1400
321-415
Coefficient
Thermal Expansion
Elastic
Typical
from 70F to Ind.
Thermal
Modulus
UTS
Temp F
Conductivity
70F
70F
Density
in/in/F x 10-6
Btu-in/sq ft/hr/F
psi X 106
ksi
lb/cu in
600F 1200F
70F 600F 1200F
6.5
23
0.066
15.5
690
6.5
37
0.066
30.0
63
0.321
8.3
8.9
460
340
380
18.2
150
0.314
6.77
7.42
79.l
112.l
31.5
205
0.290
7.5
8.0
73
102
140
29.5
141
0.296
7.0
7.6
70
95
127
32.3
120 min
0.302
7.08
8.20
82.0
114.0
153.3
31.6
122
0.317
6.9
7.4
95
132
158
30.6
123
0.325
6.9
7.4
30.0
120
0.298
7.9
8.6
60
105
150
29.5
147
0.280
7.2
7.8
100
130
31.0
227
0.284
7.16
7.78
78
100
131
28.0
175
0.294
8.15
8.7
90
112
135
31.0
96
0.305
7.8
8.4
104
133
172
29.8
140
0.305
7.4
8.2
65
97
130
30.5
165 min
0.292
8.42
8.96
87.7
124.4
30.2
123
0.286
7.3
8.0
62
95
137
29.8
208
0.297
7.9
8.4
84
117
153
31.0
174
0.298
7.5
8.3
82
110
142
18.6
145
0.309
6.8
7.5
60
90
122
29.6
140
0.311
7.1
7.6
60
88
120
18.2
147
0.323
6.77
7.42
79.1
112.l
18.4
65
0.322
7.4
8.0
570
350
300
32.0
204
0.288
8.0
73
102
140
30.8
194
0.298
I
72
96
131
85
Properties of Materals
Metals and Alloys ( continued)
Max.
Common
AMS or
Recommended
Designation
PWA* Specl
Condition2
Steel - Carbon and Low-Alloy
Low Carbon
5042, 5062
Steel
AISI 4340
6414,6415
FHT
AISI 9310
6260,6265
FHT
17-22A
6304, 733*, 7459
FHT
Pyrowewar 53 6308
FHT
Steel - Stainless
AISI 301
5519,5518, 5517
AISI 304
5910, 5911, 5913
AISI316
5524,5648
s
AISI 321
5510,5645
s
AISI 347
5512,5646
s
AISI 410
5504, 5613
FHT
AISI 440C
5630
FHT
Greek Ascoloy
5616, 7470
FHT
17-4PH
5643
FHT
A-286
5525,5732
FHT
H-11
6488
FHT
M-50
6490, 6491,
FHT
725*, 793*
52100
6440,6444, 723*
FHT
Ti and Ti Alloys
Ti-75A
4901,4921
A
AllOAT,
4910, 4926
A
Ti-5Al-2.5Sn
Ti-6Al-4V
4911, 4928, 1228*
A
Ti-8Al-1Mo-1 V 1202*
FHT
Ti-6Al-2Sn-
1214*) !224.
FHT
4Zr-2Mo
1225
Ii-6Al-2Sn-
1227
FHT
4Zr-6Mo
15-3
4914
Beta 21S
1233'''
Hardness
Use Temp, F3
HB
700
90-110
700
336-370
350
35-40 (HRC)
1000
336-370
450
35-42 (HRC)
700
176
700
176
800
140-255
1500
140-255
1500
140-255
850
285-352
300
58 (HRC)
1000
285-352
600
336-400
1300
248-341
500
53 (HRC)
600
62 (HRC)
400
58 (HRC)
400
800
600
900
max
1000
800
400 max
550
Coefficient
Thermal Expansion
Elastic
Typical
from 70F to Ind.
Thermal
Modulus
UTS
Temp F
Conductivity
70F
70F
Density
in/in/F x 10-6
Btu-in/sq ft/hr/F
psi X 106
ksi
lb/cu in
600F 1200F
70F 600F 1200F
31.0
44
0.283
7.3
8.3
386
324
240
31.0
168
0.283
7.1
8.2
278
220
30.l
175
0.283
7.3
X
278
220
30.7
166
0.283
7.3
8.0
308
278
220
30
177
0.283
6.8
7.4
28
75
0.286
9.8
10.6
28
75
0.286
9.6
10.5
28.5
85
0.286
9.6
10.3
126
158
29.0
85
0.285
9.7
10.3
133
165
29.0
85
0.286
9.7
10.3
130
164
31.8
150
0.279
6.2
6.7
187
200
29.0
143 (-3s) 0.275
6.25
31.8
150
0.285
5.9
6.5
187
200
29.8
175
0.283
6.5
29.0
146
0.287
9.5
9.95
90
127
174
30.0
280
0.282
6.8
29.0
412
0.284
6.6
7.8
30.0
292
0.283
7.2
X
15.6
96
0.163
5.3
5.6
121
118
133
15.5
125
0.161
5.3
5.5
53
76
107
16.6
143
0.160
5.1
5.5
46
102
l7.2
140
0.158
5.0
5.7
41
95
17.4
150
0.164
5.4
!'/j
188
0.168
14.'/
i45
0.172
'5.l
60
14.9
87
Properties of Elements
Melting
Boiling
Solid
Atomic
Atomic
Point
Point
Densit~
Element
Number
Weight
oc
oc
g/cm3
Actinium,
89
227.028
1050 50
3200 300
10.07
Aluminum,
13
26.9815
660
2467
2.70
95
243.
9944
2607
13.67
51
121.75
630.74
1750
6.62
Argon,Ar
18
39.948
-189.2
-185.7
1.62 (at TP)
Arsenic,
33
74.9216
817 (28 atm)
613 (sub)
5.76
Astatine, At
85
210.
302
337
00
Barium, Ba
56
137.33
725
1640
00
Berkelium,
97
247.
14.78
Ber~11lium, Be
4
9.0122
1278 5
2970 (5mm)
1.85
Bismuth, Bi
83
208.980
271.3
1560 5
9.80
Bohrium, Bh
107
264
Boron,
5
10.81
2079
2550
Bromine,
35
79.904
-7.2
58.78
Cadmium, Cd
48
112.41
320.9
765
Calcium,
20
40.08
839 2
1484
Calfornium,
98
(251).
::~arbon (Diamond),
6
12.011
3652 (sub)
t
~~erium,
58
140.12
798 2
3257
6.77
Cesium,
55
132.905
28.40 .01
669.3
.90
Melting
Boiling
Solid
Atomic
Atomic
Point
Point
Density*
Element
Number
Weight
oc
oc
g/cm3
Chlorine, Cl
17
35.453
-100.98
-34.6
Chromium,
24
51.996
1857 20
2672
7.19
:::obalt, Co
27
51.9332
1495
2870
8.82
Copper, Cu
29
63.546
1083.4
2567
8.94
Curium, Cm
96
(247)
1340 40
13.51
Darmstadtium, Ds
110
281
Dubrium, Db
I05
262
Dysprosium, Dy
66
162.50
1409
2335
8.56
00
Einsteinium, Es
99
(25 X 2)
7.0
\0
Erbium, Er
68
167.26
1522
2510
9.05
Europium, Eu
63
151.96
8225
1597
5.25
Fennium, Fm
100
(257)
Plourine, F
9
18.9984
-219.62
-188.14
Francium, Fr
87
223
27 (est.)
677 (est.)
1.108
Gadolinium, Gd
64
157.25
1311 1
3223
7.90
Gallium, Ga
31
69.72
29.78
2403
5.91
Germanium, Ge
32
72.59
937.4
2830
5.32
Gold, Au
79
196.967
1064.434
3080
19.3]
Hafnium, Hf
72
178.49
2227 20
4602
13.29
Hassium, Hs
108
277
Properties of Elements ( continued)
Melting
Boiling
Solid
Atomic
Atomic
Point
Point
Density*
Element
Number
Weight
oc
oc
g/cm3
Helium, He
2
4.00260
-272.226 (atm)
-268.934
Holmium, Ho
67
164.930
1470
2720
8.79
1
1.00794
-259.14
-252.87
Indium, In
49
114.82
156.61
2080
7.30
Iodine, l
53
126.905
113.5
184.35
4.93
Iridium,
77
192.2
2410
4130
22.65
Iron,
26
55.847
1535
2750
7.87
'-0 Krypton,
36
83.30
-156.6
-152.30 10
2.83 (at TP)
0
Lanthanum,
57
138.91
9205
3454
16
Lawrencium, Lw
103
(260)
Lead, Ph
82
207.19
357.502
1740
11.34
Lithium, Li
3
6.941
180.54
1342
Lutetium,
71
174.967
1656 5
3315
9.84
Magnesium,
12
24.312
684.8 0.5
1090
.74
Manganese, Mn
25
54.9380
1244 3
1962
7.44
Meitneriurn, Mt
109
268
Mendelevium, Md
101
(258)
80
200.59
-38.87
356.58
13.546
(liquid)
Molybdenum,
42
95.94
2617
4612
10.22
Neodymium, Nd
60
144.24
1010
3127
7.01
Melting
Boiling
Solid
Atomic
Atomic
Point
Point
Element
Number
Weight
oc
oc
g/cm3
1\lcon, Ne
10
20.179
-248.67
-246.048
l.44 (at TP)
93
237.048
640 1
3902
20.35
28
58.71
1453
2732
8.91
Niobium, Nb
41
92.9064
2468 10
4742
8.57
.Nitrogen, N
7
14.0067
-209.86
-195.8
0.88
Nobelium, No
102
(259)
Osmium,
76
190.2
3045 30
5027 100
22.59
8
15.9994
-218.4
-182.962
. ~
Palladium, Pd
46
106.42
1554
3140
12.02
Phos:ehoms, P
15
30.9738
44.1 (white)
280 (white)
1.83 (white)
Platinum, Pt
78
195.08
1772
3827 100
21.45
Plutonium, Pu
94
(244)
641
3232
19.85
Polonium,
84
(209)
254
962
9.40
Potassium, K
19
39.09
63.25
759.9
0.86
Praseodymium, Pr
59
140.908
931 4
3212
6.78
Promethium, Pm
61
(145)
1080
2460
7.30
Protactinium, Pa
91
231.0359
1600
15.37
Radium, Ra
88
226.025
700
1140
5.00
Radon, Rn
86
(222)
-71
-61.8
Rhenium. Re
75
186.207
3180
5627 (est)
21.03
Properties of Elements (continued)
Melting
Boiling
Solid
Atomic
Atomic
Point
Point
Densit)
Elemenl
Number
Weight
oc
oc
glcm3
Rhodium, Rh
45
102.906
1965 3
3727 100
12.41
111
272
-
Rubidium, Rb
37
85.4678
38.89
686
Ruthenium, Ru
44
101.07
2310
3900
12.45
Rutherfordium, R{
104
261
Samarium, Sm
62
150.36
1072 5
1778
7.53
Scandium, Sc
21
44.9559
1539
2832
2.99
106
266
Selenium,
34
78.96
217
684.9 10
4.80
Silicon, Si
14
28.0855
1410
2355
2.33
Silver ..
47
107.868
961.93
2212
10.50
Sodium, Na
11
22.9898
97.81 .03
882.9
0.97
Strontium,
38
87.62
769
l384
Sulfur,
16
32.06
112.8
444.674
2.07
Tantalum, Ta
73
180.9479
2996
5425 100
16.6
Technetium, Tc
43
99.
2172
4877
11.49
Tellurium, Te
52
127.60
449.5 .03
989.8 3.8
6.24
Terbium, Tb
65
158.925
1360 4
3041
8.25
Thalliurn,
81
204.383
303.5
1457 10
11.86
Thorium, Th
90
232.038
1750
4790~.)
11.72
Melting
Boiling
Solid
Atomic
Atomic
Point
Point
Element
Number
Weight
oc
oc
g/cm3
Thulium, Tm
69
168.934
1545 15
1727
9.32
Tin,
50
118.71
231.9681
2270
7.23 (white)
Titanium, Ti
22
47.88
1660 10
3287
4.51
w
22
183.85
3410 20
5660
19.25
Unnihexium
106
(263)
Unnilpentium
105
(262)
104
(261)
107
(262)
Uranium,
92
238.029
1132 0.8
3818
19.04
' Vanadium, V
23
50.9415
1890 10
3380
6.11
(J.)
Wolfram (see Tungsten)
Xenon,Xe
54
131.29
-111.9
-1071.1 3
3.54
TP)
Ytterbium, Yb
70
173.04
8245
1193
6.94
Yttrium,
39
88.9059
1523 8
3337
4.47
Zinc, Zn
30
65.39
419.58
907
Zirconium, Zr
40
91.224
1852 2
4377
6.48
(TP) = Triple Point
(SP) Sublimination Point at atmospheric pressure
'''Room Temperature unless stated otherwise
triple point; (graphite -
liquid
3627 50C at a pressure of 10.1 MPa and
(graphite diamond -
liquid), 3830 to 3930C at a pressure of 12 to 13 0Pa.
Data in this table has been assembled by Pratt & Whitney from a variety of reputable sources.
Physical Constants
Constant
Value
Electron charge, e
1.602 X 10-19
coulomb
Electron mass, me
9.109 X lQ-31
kg
Unified atomic mass
constant, mu
1.660 X lQ-27
kg
Proton mass, mp
1.672 X to-27
kg
Neutron mass, mn
1.674 X lQ-27
kg
Planck constant, h
6.625 X 10- 34
J sec
Boltzmann constant, k
1.380 X IQ-23
J/OK
Avogadros number, N 0
6.022169 X }023
molecules/
mole
Gas constant, R
8.31434
J/K mole
Velocity of light
in a vacuum, c0
2.998 X 108
m/sec
Volume of ideal gas
(at std. temp. and press.)
2.241 X 10
m3/mol
Acceleration of gravity, g
9.8066
m/sec2
Mass of hydrogen atom, m8
1.673 X lQ-27
kg
Gravitational constant, G
6.673 X 10- 11
Nm2/kg2
94
0.88
U")
0.84
l.t)
~
cc 0.80
w
r-
<(
s:
~
0.76
(J)
z
w
0.72~
a
w
>
o~f
~
--I
w
a::
0.64
-40
Average Relative Density-Temperature
Variation of Aviation Fuels
I
I
I
I
!
I
I
-20
0
20
40
60
80
100
TEMPERATURE, C
I
120
0
0
I.O
LO
""""
~
cc
UJ
I-
~
~'
ci5
z
w
Cl
w
>
i='.
Average Relative Density-Temperature
Variation of Aviation Fuels
:3
W 0.68
tr.
0.64,___ _
....__ _ _.__ _ _.__ _____________ _.__ _
-40
-20
0
20
40
60
80
100
120
TEMPERATURE, C
METRIC SYSTEM (SI)
97
Metric System
International System (SI) of Units
SI Base and Supplementary Units
Quantity
Mass ..
Time.
Name
SI Base Units
.. meter
second
Symbol
Electric current . . .
. ........ ampere
...... A
Them1odynamic temperature l . Kelvin ................. K
Amount of substance ......... mole . . . . . . . . . . . . . . . . mol
Luminous intensity.... . . . . . . candela ................ cd
SI Supplementary Units
Plane angle ................. radian ................. rad
Solid angle . . . . . . . . . . . . . . . . . steradian ............... sr
1 It is acceptable to use the Celsius temperature (symbol t) defined by
t
T - To where T is the thermodynamic temperature, expressed in
degrees Kelvin, and T0 = 273.15 degrees Kelvin, by definition. The unit
"degree Celsius" is thus equal to the unit "Kelvin" when used as an
interval or difference of temperature. Celsius temperature is expressed in
degrees Celsius (symbol 0 C).
SI Derived Units with Special Names
Quantity
Name
Symbol
SI Derived Unit'i
... Hertz ........ Hz
Force ................... Newton
. . ... N
Pressure, stress . . . . . . . . . . . Pascal
Pa
Energy, work,
quantity of heat ......... joule . . . . .
. ... J
Power, radiant flux ........ Watt ........... W
Quantity of electricity,
electric charge .......... coulomb ....... C
Electric potential,
potential difference,
electromotive force ...... volt ........... V
Capacitance . . . . . . . . . ... farad .......... F
Electric resistance ........ ohm ........... fl
Conductance ............. siemens ........ S
Magnetic flux ............ weber ......... Wb
Magnetic flux density ..... tesla ........... T
Inductance . . . . . . .
. ..... henry .......... H
Luminous flux . . ........ lumen
..... lm
Illurninance . . . . ........ lux . . . . . .
. lx
Activity (radioactive)
. becquerel . .
Bq
Absorbed dose
gray
Gy
Expression
in Terms of
Other Unit'-.
m-kg/s2
N/m2
N-m
J/s
A-s
W/A
C/V
V/A
A/V
V-s
Wb/m2
Wb/A
cd-sr
lm/m2
s-1
Metric System ( continued)
Examples of SI Derived Units Expressed in Terms of Base Units
Quantity
SI Unit
Unit Symbol
Area
Volume ..... .
square meter
. cubic meter ...
meter per second
Speed, velocity
Acceleration
..
. . ... meter per second squared
. m2
.m3
mis
.. m/s2
..m-I
Wave number
. 1 per meter . . . . ..
Density, mass density ...
. kilogram per cubic meter . . . .
Ctment density . . . . . . . . . ampere per square meter ..... A/m2
Magnetic field strength . . . ampere per meter ........... Alm
Concentration ( of amount
of substance) ........... mole per cubic meter ........ mol/m3
Specific volume .......... cubic meter per kilogram ..... m3/kg
Luminance .............. candela per square meter ..... cd/m2
lOO
Examples of SI Derived Units Expressed by
Means of Special Names
Quantity
SI Unit
Unit Symbol
Dynamic viscosity
....... Pascal second
. . . . . . . ..... Pa- s
Moment of force
.. meter Newton.
.Nm
Surface tension.
Newton per meter. .
. Nim
Heat flux density,
irradiance . . . . . . . . .
. . Watt per square meter
.. W /m2
Heat capacity, entropy ..... joule per Ke] vin . . . . . . . . . . J/K
Specific heat capacity,
specific entropy . . . . . . . . joule per kilogram Kelvin .... J/(kg-K)
Specific energy . . . . . . . . .. joule per kilogram . . . . . . . . . J/kg
Thermal conductivity ...... Watt per meter Kelvin ....... W/(mK)
Energy density ........... joule per cubic meter ........ J/m3
Electric field strength ...... volt per meter . . . . . . . . ..... V /m
Electric charge density ..... coulomb per cubic meter ..... C/m3
Electric flux density ....... coulomb per square meter .... C/m2
Permittivity .............. farad per meter ............. F/m
Permeability ............. henry per meter ............ Him
Molar energy ............ joule per mole ............. J/mol
Molar entropy, molar
heat capacity ........... joule per mole Kelvin ....... J/(mol-K)
101
Metric System ( continued)
Unit
absolute zero
ampere
candela
coulomb
Kelvin
kilogram
(unit of mass)
meter
mole
radian
second
Standards
Reference/Specification/Description
The temperature at which all parts of a system are at
the lowest energy level permitted by the laws of
quantum mechanics
The flow of one coulomb per second that passes a
given point
The luminous intensity of a black body of surface area
1/60 cm2 at the temperature of
platinum
(1,769C) and at atmospheric pressure
The measure of electrical charge equivalent to that
carried by 6.281 x 1018 electrons
Temperature scale with O point at absolute zero and a
degree being equal to a degree Celsius
The mass of a particular cylinder of platinum-iridium
alloy, called the international prototype kilogram, that
is preserved in a vault at Sevres, France, by the
International Bureau of Weights and Measures
1,650,763.73 wavelengths of the orange-red radiation
of krypton 86 under specified conditions
The amount of substance containing the same number
of entities (atoms, ions, etc.) as the number of atoms
in 0.012 kilograms of carbon-12. The mass of 1 mole
of a compound is its gram molecular weight.
The angle subtended at the center of a circle by an arc
of length equal to that of the radius of the circle
The time of 9,192,631,770 periods of the
electromagnetic radiation corresponding to a transition
in the cesium-133 atom
-------------------------
102
Squares
Volume
Dry measure
Liquid measure
Metric Equivalents
l centimeter 0.394 inch
1 inch 2.540 centimeters
1 meter= 3.281 feet
1 foot= 0.35 meter
1 meter
1.0936 yards
1 yard 0.9144 meter
1 kilometer= 0.6214 mile
1 mile= 1.6094 kilometers
1 sq. centimeter= 0.1550 sq. inch
1 sq. inch = 6.452 sq. centimeters
1 sq. meter= 10.764 sq. feet
1 sq. foot
0.09290 sq. meter
1 sq. meter= I. 196 sq. yards
1 sq. yard= 0.8361 sq. meter
1 sq. kilometer 0.386 sq. mile
1 sg. mile = 2.59 sg. kilometers
1 cubic centimeter 0.061 cubic inch
1 cubic inch= 16.39 cubic centimeters
1 cubic meter 35.314 cubic feet
1 cubic foot
0.02832 cubic meter
1 cubic meter = 1.308 cubic yards
1 cubic yard= 0.7646 cubic meter
I liter= 0.908 quart
1 quart= 1.101 liters
1 peck 8.8098 liters
1 bushel
35.239 liters
1 liter = 1.0567 quarts
1 quart = 0.9463 liter
1 U.S. gallon= 3.785 liters
1 imperial gallon = 4.546 liters
1 liter= 0.264 U.S. gallon
l liter= 0.220 imperial gallon
1 gram 0.03527 ounce
1 ounce 28.35 grams
kilogram= 2.2046
I
= 0.4536 kilogram
l metric ton= 0.98421 English tor,
1 Ene:lish ton= 1.016 metric tons
103
... ,
0
~
SI Prefix - Multiples and Subdivisions
J\.n SI prefix is a prefix that can be applied to an SI unit to form a decimal multiple or submultiple. Many SI prefixes
the introduction of the SI in 1960. They can be applied correctly to many non-SI units. As part of the Sl system,
determined by the International Bureau of Weights and Measures.
SI Prefixes
10n
Prefix
Simbol
Short Scale
Lo!!_g Scale
Decimal Eguivalent
Q24
yotta
y
Septillion
Quadrillion
I 000 000 000 000 000 000 000 000
1021
zetta
z
Sextillion
Trillard (thousand trillion)
1 000 000 000 000 000 000 000
)_018
exLt
E
Quintillion
Trillion
1 000 000 000 000 000 000
iOVi
peta
p
Quadrillion
Billard (thousand billion)
1 000 000 000 000 000
on
t.cra
T
Trillion
Billion
1 000 000 000 000
rnCJ
giga
G
Billion
Milliard (thousand million) 1000000 000
H)E
mega
M
Million
1000000
1<::i1c
k
Thousand
1 000
~()2
hecto
h
Hundred
100
iOi
deca,dcka
da
Ten
IO
oc
none
none
One
1
J.0
dee
d
Tenth
0.1
t ()- ~!
centl
C
Hundreth
0.01
Q.,
rnilic
m
Thousandth
0.001
10-t
micro
g(u)
Millionth
0.000 001
0
IJl.
SI Prefixes ( continued)
JOil
Prefix
Symbol
Short Scale
10-9
nano
n
Billionth
pico
p
Trillionth
femtc
Quadrillionth
alto
a
Quintillionth
zepto
z
Sextillionth
10-24
yocto
y
Septillionth
Source: Wikipedia, the.free encyclopedia
Prefixes for Binary Multiples
Long Scale
Milliardth
Billionth
Billiardth
Trillionth
Trilliardth
Quadrillionth
Decimal E_quivalent
0.000 000 001
0.000 000 000 001
0.000 000 000 000 001
0.000 000 000 000 000 001
0.000 000 000 000 000 000 001
0.000 000 000 000 000 000 000 001
In December 1998 the International Electrotechnical Commission (IEC), the leading international organization for
worldwide standardization in electrotechnology, approved as an IEC International Standard names and
for
for
multiples for use in the fields of data processing and data transmission. The prefixes are as follows:
Factor Name Symbol
Origin
Derivation
Examples and Comparisons with SI Prefixes
210
kibi
Ki
kilobinary (21 O) l
kilo (103)1
one kibibit
1 Ki bit= 210bit = 1024 bit
2,20
meb1
Mi
megabinary
mega (103)2
one kilobit
1 kbit
1Q3bil= 1000 bit
Gi
gigabinary
giga (103)3
one mebibyte 1 MiB = 220B
1048 576 B
rnbi
terabinary (210)4
tera (103)4
one megabyte l MB = 106B = 1 000 000 B
pebi
Pi
petabinary (210)5
peta (103)5
one gibibyte 1 GiB
230B = 1073741 824 B
760
exbi
Ei
exabinary (210)6
exa (103)6
one gigabyte I GB
JQ9B
1 000 000 000 B
106
AIRCRAFr INFORMATION
i(rI
Aerodynamic Terms
Aerodynamics is a branch of fluid dynamics concerned with the study
gas flows. It requires the understanding of the prope11ies of the flow
velocity, pressure, density, and temperature
as a function of space and
time. Understanding the flow pattern makes it possible to calculate or
approximate the forces acting on objects in the flow. Aerodynamics is the
scientific basis for heavier-than-air flight.
One of the major goals of aerodynamics is to predict the aerodynamic
forces on aircraft. The four basic forces that act on a powered aircraft are
lift, weight, ( or gravity), thrust, and drag. Weight is the force due to gravity
and thrust is the force generated by the engine. Lift and drag are forces due
to the motion of the vehicle through the air. Lift is defined as the
aerodynamic force acting perpendicular to the relative airflow and drag is
defined as the aerodynamic force acting parallel to the relative airflow.
Lift is positive upwards and drag is positive rearwards.
External aerodynamics is the study of flow around solid objects of various
shapes. Evaluating the lift and drag on an airplane, the shockwaves that form
in front of the nose of a rocket are examples of external aerodynamics.
Internal aerodynamics is the study of flow through passages in solid objects.
For instance, internal aerodynamics encompasses the study of the airflow
through a jet engine.
The flow speed relative to the speed of sound comprises a second
classification of aerodynamics. Speed is called subsonic if all the speeds
are less than the speed of sound, transonic if speeds both below and above
the speed of sound are present, supersonic when the characteristic flow
speed is greater than the speed of sound, and hypersonic when the flow
speed is much greater than the speed of sound.
The speed of sound in air at sea level is approximately 341 mis, 1,087
ftls, 761 mph or 1,235 km/h.
Subsonic speed is slower than the speed of sound in air. The speed of
sound in air varies with atmospheric conditions, primarily on the altitude,
temerature and pressure and less on humidity. Sound travels slower with
increased altitude. Transonic
refers to a range of velocities just
below and above the speed of sound (about Mach 0.8 - 1 Most modem
jet powered aircraft spend a considerable amount of time in the transonic
Supersonic
is any speed over the
of sound. And if the
is exceeds the
of sound in air
more than
times,
refeITed
as Hypersonic
108
Aerodynamic Relationships
b = Wing Span
ft
c = Wing Chord - ft
D = Drag-lb
L = Lift
lb
l = Rolling Moment - lb-ft
m Pitching Moment
lb- ft
n Yawing Moment - lb
q = Dynamic Pressure
lb/sq ft
S = Wing Area sq ft
b2
AR = Aspect Ratio =
( or
s
Life Coefficient, CL = _L_
qS
Where q = l/2 e v2
b
C
e = Angle of Down Wash deg
a = Angle of Attack - deg
'Y Flight-path Angle - deg
e = Density - lb sec2/ft4
, = Absolute Viscosity
v Kinematic Viscosity
L = Length - ft
V = Velocity
ft/sec
for rectangular \Ving)
Drag coefficient, CD = _!}_
qS
.hi
ffi.
C
m
P1tc ng moment coe c1ent, m = --
qcS
.
rn
C
l
Rollmg moment coe cient, z =
qbS
J: c2 db
Mean aerodynamic chord = ----
J: cdb
n
Yawing moment coefficient, C11 =
qbS
Reynolds mrmbei, N.,q &
VL
fJ,
VL
i09
Airspeed Relationships
---------------------------------
Indicated airspeed (read from cockpit instrumentation,
includes cockpit instrument error correction)
Calibrated airspeed (indicated airspeed cmrected for
airspeed instmmentation position error)
Equivalent airspeed (calibrated airspeed corrected for
compressibility effects)
True airspeed (equivalent airspeed c01Tected for change
in atmospheric density)
VrAs=
~
= .JifjL. where ~o = !~J , or air density correction
where
P = air pressure at flight condition
Po = air pressure at sea level
T
air temperature at flight condition
To = air temperature at sea level
Airspeed Correction
G]
aV1
l9
AVp
~
AVc
~
Vo
~
I
I
I
I
,,
i
I
I
i
fl
I
!
I
I
I
I
I
I
I
I
I
I
I
I
Cockpit
Instrument
Reading
Instrument
Error
Correction
Indicated
Airspeed
Airspeed
V;
Sensor
Position
Error
Correction Calibrated
+ LlVp
Airspeed Compress-
ibility
VpAs = VcAS
Correction Equivalent __
1
Airspeed Air Density
VEAS
Ve
Correction
True
-~ V'l'A I.' -
Airspeed
-/7
Airspeed Relationships ( continued)
Mach number M
where
V
trueFrspeed
C = sonic velocity
specjfic-heat ratio
g = gravitational constant
R gas constant
T= an1bienttemperature
Change in velocity with change in air density at constant THP,
y2 = VJ 1*-
(approximate)
Change in velocity with change in power at constant air density,
y2 =VJ~ (approximate)
Reynolds Number Effects
When air in motion (or the movement of a body through air) is studied,
three principal factors must be considered: the velocity, the density and the
viscosity of the air. The effect of the changing viscosity does not become
pronounced until the air density drops to a relatively low value. At the
airspeeds normal for a turbojet aircraft, the effect of low air density is
usually encountered at altitudes of approximately 35,000 feet and above.
At these high altitudes, the cohesive force between the individual air
molecules (called viscosity) and the inertial (ram) force of a cubic inch of
molecules in motion are both reduced below the normal sea-level value for
any
airspeed. However, the inertial force is reduced more, in
proportion, than the ""'""'''"" The term that is used to describe these
effects is "Reynolds number." Reynolds number is a dimensionless
parameter that relates airflow inertia to the "'"''"C"h' of the air. At low
Reynolds number, airi1ow is predominantly laminar, or
and
smooth. At high Reynolds number. the airflow
turbulent
Above the critical Reynolds number, the trans1t1on from laminar to
turbulent flow takes place soon enough to provide a relatively thick,
turbulent boundary layer that transfers considerable energy from the free
stream and successfully follows the airfoil contour down to the trailing
edge. However, below the critical Reynolds number, the viscous forces
predominate and make the boundary-layer air incapable of making the
transition from laminar to turbulent flow, with the result that the .low-
energy laminar layer slows down and begins to separate from the airfoil
surface, helped along by the pressure gradients existing at the upper
surface of the airfoil. Consequently, the drag and friction losses of the
wing or compressor blade begin to increase and the lift to decrease
noticeably above an altitude of roughly 35,000 feet. This, in tum, reduces
the operating efficiency of the aircraft or engine involved. The effect
becomes greater as altitude is increased. This effect is expressed by a
factor called Reynolds number index, which is applied to the performance
values obtained at or near sea level to correct the sea level performance to
that which actually will be obtained at high altitudes.
Mach Number
A characteristic of gases makes it very difficult for a certain velocity to be
exceeded, either when the gas itself is in motion or when an object is
moving through the gas. A few examples of this restricting effect would be
the flow of a gas through a nozzle, an aircraft in flight, and the movement
of a sound wave through air or some other medium. All of these reach a
velocity above which it is difficult or impossible to accelerate further.
In case of sound, this gas characteristic actually determines the maximum
speed at which a pressure wave or a warning signal can be transmitted
upstream. Because the speed of sound is the most common evidence of
this characteristic, as well as the most easily measured, it is used as the
basis for detennining Mach number, which is the ratio of the speed of an
object to the speed of sound in the same medium and at the same
temperature. The restricting tendency is dependent only on the
temperature of the air, not its density. Mach number also varies with
different gases, liquids and solids. It has been found to he a
convenient parameter in studying high-velocity flow and as a measure
for high-perfon11ance aircraft,
13
AIRSPEED CONVERSION
45000 FT
40000 FT
1 1
35000 FT
.
30000 FT
25000 FT
1.0
20000 FT
15000 FT
10000 FT
0.9
5000 FT
a:
w 0.8
aJ
~
~ 0.7
::r:
(.)
< 0.6
~
0.5
0.4
0.3
SEA LEVEL
1 EAS
M=~ 661.5
FOR ALL TAM'S
0.2-..c;.;-........ __ ____..._._ ____ ,_.a___
100 150 200 250 300 350 400
VEAS KNOTS
.20
1.10
a:
w
aJ
21.00
::::)
z
I
0
<(
.90
2
.80
AIRSPEED CONVERSION
PRESSURE ALTITUDE, 1000 FEET
50
40
30
20
10
(J)
I-
0 z
~
s:-
<(
0
SL Cl
I-
~
0 w
w
a..
en
700 a:
<(
w
::::)
a:
I-
600
L,_L_---L.::~--L-..3oL.L.--L---L...a........_,j~---L.JL----.-~500
300
400
500
600
CALIBRATED AIRSPEED, KNOTS
15
AIRSPEED CONVERSION
PRESSURE ALTITUDE, 1000 FEET
60 50 40
30
20
10
0.?r-----:r---.--.--r"""l'r"-r--,-r:::--r-~-..::-i,--"T"""""I
0.5
SL
a:
1-----,...._,_,_.....,
w
aJ
:a
:::,
z 0.4
I
..... ~......._
(.)
<(
~
0.3
A. CAS
""215 KTS 200
0.2
B. ALT
15000 FT
C. MN
.429
D. TAS
== 268 KTS
(ICAO STD DAY)
E. TAMB
:: 30 C
F.TAS
"'290 KTS
0 J ....._____
A
---------~===---' 100
50
150
250
350
450
CALIBRATED AIRSPEED, KNOTS
Aircraft Noise Regulations and Restrictions
Annex 16 - Environmental Protection is one of the technical annexes to
the Convention on International Civil Aviation ( Chicago, 1944) that
established ICAO as the worldwide governing civil aviation body. Volume
1 of Annex 16 evolved in 1968 and contains standards and recommended
practices for the limitation of aircraft noise. This document has since been
updated several times.
The standards of Annex 16 are embodied in national legislation by the
nations subscribing to ICAO. In the U.S., these fall into Federal Aviation
Regulation, Part 36, administered by the FAA (Federal Aviation
Administration). In Europe, the European Aviation Safety Agency
(EASA) administers certification limits on aircraft noise through CS 36
that supercedes JAA (Joint Aviation Authorities) JAR 36. The
requirements, and much of the language, of FAR 36 and CS 36 mirror
those of ICAO Annex 16 so that all standards are closely harmonized.
The latest FAA Stage 4 standard, adopted as Amendment 26 of the noise
certification rule, became effective August 4, 2005, and applies to all
applications for airworthiness of new airplane-type designs submitted on
and after January 1, 2006. Stage 3 airplanes can continue to be produced
and operated.
In the certification scheme, noise limits are set at three points; two for
takeoff ( one underneath the flight path called Flyover or Cutback,
referring to thrust cutback, and one to the side at full power called Sideline
or Lateral) and one for Approach or Landing (underneath the flight path).
Noise-measuring locations for each of these conditions are shown in
Figure 1. Noise limits at each of these conditions are established in terms
of EPNdB as a function of maximum takeoff weight. ICAO Chapter 3 and
Chapter 4 limits (FAA
3 and Stage 4 limits) are shown in Figures 2
and 3, respectively. Please note that for Cutback, 2E, 3E, and 4E denote
2-, 3- and 4-engine aircraft, respectively. The difference between an
aircraft noise level and the rule limit at a given condition both expressed
in EPNdB - is referred to
the margin at that condition.
In addition to the ce1tification limits imposed by government agt:mc11es
airport-specific local restrictions or rules have proliferated. As an
example, the quota count (QC) system was developed in 1995 by the UK
government to help manage the noise generated
aircraft night
operations at the three designated London airports Gatwick, Heathrow
and Stansted. In this scheme, aircraft arc grouped into QC bands.
depending on their measured noise p:e1t:rn:.rn:111c:e dming certification. Fm
l 17
departure, these bands are based on an average of flyover and sideline
noise levels -
the noisier aircraft falling into the higher QC bands.
similar scheme exists for determining the QC bands for arrivals. The value
of the bands, as shown in Table 1, double every three decibels to reflect
the nature of noise perception - i.e., a doubling in noise energy for every
three decfoel increase. In addition, movement and noise quota (QC) limits
are set for each summer and winter season, and air traffic is managed
accordingly.
Table 1: Quota Count EPNdB Bands
Certificated Noise Level
(EPNdB)
Quota Count
Less than 90
0.5
90 to 92.9
1
93 to 95.9
2
96 to 98.9
4
99 to 101.9
8
Greater than 101. 9
16
Figure 1: Noise Certification Measurement Points
Approach
mfe~QflCf!
point
Sldiline
tefefe:n~
Hne
As of 2002, night-
time departures are
not permitted to be
scheduled
fa~;$ oli
tef 1,ite,nt'.:'
po!rit
Figure 2: Noise Limits at Chapter 3 Certification Measurement Points
iii'
'C
~ 100 +------------~-------,<-~------,,'"------~
~
(3~ ~ -~P_P!e
::J
(I)
95 -j--f--ltrt,o,111~-t--11rrn1r-----:-~--r------r-------r-------------------j
II)
'5
z
90 +------:r-----:r------:7"'------,.n:-a-=-p=-tr:e:":'.r:--:4.-r..-:-1m=1t-=-s----------1
Margin to any Chapter 3 condition > O EPNdB
Sum of margins to any two Chapter 3 conditions > 2 EPNdB
Sum of margins to all three Chapter 3 conditions > 1 O EPNdB
85 +-------------~-------------------<
10
100
MTOW (1000 kg)
Figure 3: Cumulative Noise Limit for Chapter 4 Certification
1,000
320 _ ................................................................................................................ ----------.
4ELimit
i 310 +--------------------.,,.:-'_--_-":_._~_:-;)2-E~:-11diimffi_
-lt-i1_:_:_,--
~
Chapter 3 Cum Limits,' ,
~
>
;
~---=c~---,--:
I 300 t-------------~-;-"----;+-77"-:;=====~~~
::J
(I)
II)
5
Z 290 +------
(I)
>
~
:i
E
:s
0
iO
100
MTOW (1000 kg)
119
[,000
Absolute World Records
Speed Around the world, Nonstop, Nonrefueled
Speed (mph)
Date
Plane
Pilots
115.65
Dec.14-23, Voyager
Dick Rutan &
1986
Jeana Yeager (U.S.)
Place
Edwards AFB,
Calif.
Distance, Great Circle Without Landing, also Distance5
Closed Circuit Without Landing
Distance (mi)
Date
Plane
Pilots
Place
24,986.727
Dec.14-23, Voyager
Dick Rutan &
Edwards AFB,
1986
Jeana Yeager (U.S.)
Calif.
Speed over a Straight Course
Speed (mph)
Date
Plane Type
2,193.16
July 28,
Lockheed
1976
SR-71A
Speed over a Closed Circuit
Pilot
Capt. Eldon W.
Joersz (USAF)
Speed (mph) Date
Plane Type
Pilot
2,092.294
July 27,
Lockheed Maj. Adolphus H.
1976
SR-71A Bledsoe, Jr. (USAF)
Altitude
Height (ft)
123,523.58
Date
Aug. 31,
1977
Plane Type
MIG-25,
E-266M
Pilot
Alexander
Fedotov (USSR)
Altitude in Horizontal Flight
Height (ft)
Date
85,068.997
July 28,
1976
Pilot
Capt. Robert C. Helt
(USAF)
Altitude, Aircraft Launched from a Carrier Airplane
Height (ft)
Date
Plane Type
Pilot
314,750.00
July 17.
N. American
Maj. Robert
120
Place
Beale AFB,
Calif.
Place
Beale AFB,
Calif.
Place
USSR
Place
Beale AFB.
Calif.
~---
Place
Edwards AFB.
AIRLINES AND AIRPORTS
Two Letter Designation Codes
of Selected Air lines
Code
Airline
Code
Airline
AA
American Airlines
CM Copa Airlines
AB Air Berlin
co Continental Airlines
AC
Air Canada
CT
Midcontinent Airlines
AE Mandarin Airlines
cc
Linea Aerea Cuban a
AF
Air France
ex Cathay Pacific
AH
Air Algerie
CY
Cyprus Airways
AI
Air India
CZ
China Southern Airlines
AK
Air Asia
DJ
Virgin Blue
AM Aero Mexico
DL
Delta Air Lines
AQ Aloha Airlines
DM MaerskAir
AR Aerolineas Argentinas
DS Air Senegal
AS
Alaska Airlines
EF
Far Eastern Air Transport
AT
Royal Air Maroc
EI
Aer Lingus
AV Avianca
EK
Emirates Airlines
AY
Finnair
EL
Air Nippon Co., Ltd.
AZ Alitalia
EQ
Tame
BA
British Airways
ET
Ethiopian Airlines
BD British Midland
EV
Atlantic Southeast Airlines
BG
Biman Bangladesh
EW Eurowings
Airlines
FG
Ariana Afghan Airlines
BI
Royal Brunei Airlines
FI
Icelandair
BP
Air Botswana
FJ
Air Pacific
BR
EVA Air
FL
Airtran Airway
BT Air Baltic
FR
Ryanair
BW BWJA West Indian
FY
Pulkovo Aviation
Airways
F9
Frontier Airlines
B6
Jet Blue Airway:::
GE
TNA
Air China
GF
Gulf Air
Alliane Air
GH
Ghana IntemationaJ
China Airlines:
Airlines
China Northern
Guiner
Code
Airline
Code
Airline
GL
Air Greenland
LX
Swiss International Air
HA
Hawaiian Airlines
Lines
HK
Yangon Airways
LY
El Al Israel Airlines
HM Air Seychelles
LZ
Balkan Airlines
HP
America West Airlines
MA Malev
HY
Uzbekistan Airways
MD Air Madagascar
IA
Iraqi Airways
ME Middle East Airlines
IB
Iberia
MH Malaysia Airlines
IC
Indian Airlines
MI
Silk Air
IR
Iran Air
MK Air Mauritius
IT
Kingfisher Airlines
MP Martinair
IY
Yemenia Yemen Airways
MS
Egypt Air
JL
Japan Airlines
MU China Eastern Airlines
JM
Air Jamaica
MX Mexicana Airlines
JP
Adria Airways
NE
Sky Europe
JU
JAT
NG
LaudaAir
KA
Dragonair
NH All Nippon Airways
KB DrnkAir
NK
Spirit Airlines
KE
Korean Air
NW Northwest Airlines
KL KLM
Royal Dutch
NX
Air Macau
Airlines
NZ
Air New Zealand
KM Air Malta
OA
Olympic Airlines
KQ
Kenya Airways
OK
Czech Airlines
KU
Kuwait Airways
ON
Air Nauru
KX
Cayman
00
SkyWest
LA
LA.'\J Airlines
OS
Aust1ian Airlines
LB
Lloyd Aereo Bolivianu
OU
Croatia Airlines
Luxair
0\/
Estonian Air
LH
Lufthansa
oz
Asiana Airlines
LK
PC
LOT
PG
LACSA
PH
Two Letter Designation Codes
of Selected Airlines (continued)
Code
Airline
Code
Airline
PK
Pakistan International
TK
Turkish Airlines
Airlines
TM
LAM - Linhas Aereas de
PR
Philippine Airlines
Mocambique
PU
Pluna
TO
President Airlines
PX
Air Niugini
TP
TAP Air Portugal
PY
Sminam Airways
TU
Tunis Air
QF
Qantas Airways
TW Trans World Airlines
QP
Airkenya Aviation
UA
United Airlines
QR Qatar Airways
UB Myanmar Airlines
QV
Lao Airlines
UL
Sri Lankan Airlines
QW Blue Wings
UM Air Zimbabwe
RA Royal Nepal Airlines
UN
Transaero
RB
Syrian Airlines
us US Airways
RC
Atlantic Airways
UY Cameroon Airlines
RG Varig Brazil
U2
EasyJet
RJ
Royal Jordanian
VA
Volare Airlines
RO
Tarom - Romanian Air
VE Avensa
Transport
VH Aeropostal
SA
South African Airways
VN Vietnam Airlines
SB
Air Calin
vs
Virgin Atlantic Airways
SD
Sudan Airways
VT
Air Tahiti
SG
Jetsgo
WN
Southwest Airlines
SK
SAS - Scandinavian
WR Royal Tongan Airlines
Airlines System
XR
Skywest Airlines
SQ
Singapore Airlines
(Australia)
SU
Aeroflot
YK KTWY
sv
Saudi Arabian Airljnes
Mesa Airlines
SW Air:\lambia
Midwest Airlines
S2
Air Sahara
ZB Monarch Airlines
Taca (Group
JX
Air Commuter
TC
Air Tanzania
Jet Airways
re
Thai
Major International Airports
3-Letter Elevation
Longest
City
Airport
Code
(ft)
Runway (ft)
Abidjan
Abidjan Port Bonet
ABJ
20
9,843
Addis-Ababa
Bole Intl.
ADD
7,625
12,139
Algiers
Houari Boumediennc
ALG
54
11,483
Amman
Queen Alia Intl.
AMM
2,539
12,007
Amsterdam
Schiphol
AMS
-ll
12,487
Anchorage
Ted Stevens
ANC
152
l 1 .584
Anchorage Intl.
Athens
Eleftherios Venizelos Intl. ATH
308
13,123
Atlanta
Hartsfield Atlanta Intl.
ATL
1,026
11,889
Auckland
Auckland Intl.
AKL
23
11,926
Azores
Santa Maria
SMA
305
10,004
Baghdad
Baghdad Intl.
SDA
113
10,827
Bahrain
Bahrain Intl.
BAH
6
12,995
Bangkok
DonMuang
BKK
9
12,139
Beijing
Beijing Capital Intl.
PEK
105
12,467
Beirut
Rafic Hariri Intl.
BEY
87
12,467
Belgrade
Belgrade Nikola Tesia Intl. BEG
335
11,155
Berlin
Tegel Intl.
TXL
121
9,918
Berlin
Tempelhof Intl.
THF
167
6,870
Bogota
El Dorado Intl.
BOG
8,361
12,467
Boston
Logan Intl.
BOS
19
10,083
Brisbane
Brisbane
BNE
13
11,709
Bucharest
All Airports
BUH
312
11,483
Budapest
Budapest Ferihegy Intl. BUD
495
12,162
Buenos Aires
Ezieza
BUE
66
10,827
Cairo
Cairo Intl.
CAl
381
13,120
Calcutta
Netaji Subhash Chandra
11,900
Bose IntL
Calgary Intl.
YYC:
12,675
Intl.
CPT
10,483
Caracas
Simon Bolivar
ccs
!1.483
r:asablancc:
Mohamed V Inti
CMN
125
Major International Airports ( continued)
3-Letter Elevation
Longest
City
Airport
Code
(ft)
Runway (ft)
Chicago
0' Hare Intl.
ORD
667
13,001
Copenhagen
Copenhagen
CPH
17
10.833
Dakar
Dakar-Yoff Intl.
DKR
89
11,450
Dallas
Dallas/Ft. Worth IntL
DFW
607
13,401
Damascus
Damascus Intl.
DAM
2,020
11,811
Darwin
Darwin
DRW
102
11,004
Delhi
Indira Ghandi Intl.
DEL
744
12,500
Denver
Denver Intl.
DEN
5,431
16,000
Douala
Douala Airport
DLA
33
9,350
Dublin
Dublin Intl.
DUB
242
8,650
Edmonton
Edmonton Intl.
YEG
2,373
11,000
Fairbanks
Fairbanks Intl.
PAI
434
11,800
Frankfurt
Frankfurt Intl.
FRA
365
13,123
Geneva
Cointrin Intl.
GVA
1,411
12,795
Glasgow
Glasgow Prestwick Intl. PIK
66
9,800
Guam
Antonio B. Won Pat Intl. GUM
298
10,000
Halifax
Halifax Intl.
YHZ
477
8,800
Hamburg
Hamburg
HAM
22
12,024
Hamilton
Bermuda Intl.
BDA
12
9,713
Hartford
Bradley Intl.
BDL
173
9,502
Helsinki
Helsinki-Vantaa Intl.
HEL
179
11,286
Hong Kong
Hong Kong Intl.
HKG
19
12,467
Honolulu
Honolulu Intl.
HNL
13
12,300
Houston
George Bush
IAH
98
12,000
Intercontinental
Istanbul
Ataturk IntL
IST
10
9,843
Jakarta
Halim
HLP
86
9,843
Jeddah
King Abdul Aziz Intl
JED
69
10,499
Johannesburg Inti
JNB
S,512
14,495
Kano
Kano lntL
KAM
i,565
10,827
Kansas
MCI
1,025
10,801
Karachi
fnti
KHI
100
10,500
3-Letter Elevation
Longest
City
Airport
Code
(ft)
Runway (ft)
Khartoum
Khartoum
KRT
1,261
8,366
Kinshasa
Ndjili
FIH
1,027
15,420
Kuwait
Kuwait IntL
KWI
656
11,482
LaPaz
El Alto Intl.
LPB
13,310
13,124
Murtala Muhammed Intl. LOS
135
12,796
Lima
Jorge Chavez Intl.
LIM
112
11,506
Lisbon
Portela
LIS
374
12,484
London
London Heathrow Intl. LHR
80
12,802
Los Angeles
Los Angeles
LAX
126
12,090
Madrid
Barajas Intl.
MAD
2,000
14,895
Manila
Ninoy Aquino Intl.
MNL
74
12,261
Melbourne
Melbourne
MEL
434
12,000
Mexico City
Benito Juarez Intl.
MEX
7,341
12,966
Miami
Miami Intl.
MIA
8
13,002
Minn.-St. Paul
Minn. -St. Paul Intl.
MSP
841
11,006
Montreal
Montreal-Pierre Elliot Intl. YUL
117
11,000
Montreal
Montreal (Mirabel) Intl. YMX
270
12,000
Moscow
Sheremetyevo Intl.
svo
623
12,140
Moscow
Vnukovo
VKO
676
10,039
Mubai
Chatrapati Shiraji Intl. BOM
36
11,447
Myanmar
Yangon Intl.
RGN
109
8,100
Nairobi
Jomo Kenyatta Intl.
NBO
5,327
13,507
Nadi
Nadi Intl.
NAN
59
10,739
New Orleans
Louis Armstrong
MSY
4
10,104
New Orleans Intl.
New York
Kennedy Intl.
JFK
l'
,::.,
14,574
Osaka
Osaka IntL
OSA
39
Oslo
Oslo
OSl
68',
1,811
Panama
focumen Intl.
PTY
10,007
Paris
B DeGaullf;
387
11,861
Major International Airports ( continued)
3-Letter Elevation
Longest
City
Airport
Code
(ft)
Runway (ft)
Paris
Le Bourget
LBG
217
9,843
Paris
Orly Intl.
ORY
292
11,975
Perth
Perth
PER
67
11,299
Port
Jacksons Intl.
POM
125
9,022
Quito
Mariscal Sucre Intl.
UIO
9,226
10,240
Recife
Guararapes
REC
36
10,171
Reykjavik
Keflavik NAS
KES
169
10,000
Rio de Janeiro
Galeao
GIG
30
13,124
Riyadh
King Khaled Intl.
RUH
2,049
13,796
Rome
Leonardo da Vinci Intl.
FCO
14
12,796
San Francisco
San Francisco Intl.
SFO
13
11,870
Santiago
Arturo Merino Benitez Intl. SCL
1,554
10,499
Seattle
Seattle-Tacoma Intl.
SEA
429
11,900
Seoul
Incheon Intl.
ICN
23
12,303
Shanghai
Hong Qiao Intl.
SHA
10
11,154
Shannon
Shannon Intl.
SNN
47
10,500
Sharjah
Sharjah Intl.
SHJ
109
12,336
Singapore
Singapore Changi Intl.
SIN
21
13,123
Stockholm
Arlanda
ARN
123
10,827
Sydney
Kingsford-Smith Intl.
SYD
21
13,018
Taipei
Chiang Kai-shek Intl.
TPE
73
12,008
Tananarive
I vato Airport
TNR
4,196
10,170
Tehran
Mehrabad
THR
3,963
13,123
Tel Aviv
Ben Gurion Intl.
TLV
135
12,000
Tokyo
Tokyo Intl. (Narita)
1'.'RT
141
13,124
Toronto
Toronto Intl.
YYZ
569
11,050
Tunis
Tunis-Carthage Int:1
TUN
20
10,500
Vancouver
Vancouver Tntl.
YVR
11,500
Warsaw
Frederic Chopin Intl
WAW
361
12,107
Washington
Dulles Intl.
IAD
11,500
Zurich
Zurich Intl.
ZRH
AVIATION FUELS
AND LUBRICANTS
Jet Fuels
Jet A is the standard jet fuel type used in the U.S. since the 1950s. Jet A
has a fairly high :flashpoint of -38C, with an autoignition temperature of
over 425C Jct A can be identified in trucks and storage facilities by the
fuel code 1863. Jet A trucks, storage tanks and pipes that carry Jet A will
be marked with a black sticker with a white "JET A" written over it next
to another black stripe. Jet A will have a clear to straw color if it is clean
and free of contamination. Water is heavier that Jet A and will collect at
the bottom of a tank. Jet A storage tanks must be sumped regularly to
check for water contamination. It is possible for water particles to become
suspended in Jet A, which can be found
performing a clear-and-bright
test. A hazy appearance can indicate water contamination beyond the
acceptable limit of 30 ppm (parts per million).
Jet Al is a version of Jet A with freezing point of -47C instead of -40C.
U.S. commercial fuels are not required by law to contain antistatic
additives and generally do not contain them.
In the 1990s the U.S. Air Force switched from JP-4 (a wide-cut fuel) to
JP-8 (kerosene-based) that, among other characteristics, has a higher
flashpoint and is less carcinogenic, although it has a strong odor and an
oily touch and is relatively unpleasant to handle. Its NATO code is F-34.
It is specified by MIL-DTL-83133 and British Defence Standard 91-87. It
is similar to the commercial Jet A 1.
JP-8+ 100 is a version of JP-8 with an additive that increases its thermal
stability by 100F (56C). The additive is a combination of a surfactant, a
metal deactivator and an antioxidant.
Source: Wikipedia.org
Densities and Weights of Fuels
Ji'uels
JP-4 (max.)
(min.)
JP-5 (max.)
(min.)
JP-8 (max.)
(min.)
Jet A and Jet AJ.
Density
kg/l@ 15C
0.802
0.751
0.845
0.788
0.840
130
Density
lb/U.S. gal
6.69
6.27
7.05
6.58
7.01
Density
lb/cu ft
50.07
46.88
52.75
49.19
52.44
Aviation Fuel and Lubricant Specifications
Document
Issued
Civilian
ASTM D 1655-06
2006
ASTM D 661
2006
Defence Standard 91-91 lssue 5
8 Feb 05
Military
MIL-DTL-5624
5 Jan 04
MIL-DTL-38219 D
21 Aug 98
MlL-DTL-83133 E
1 Apr 99
I-'
MIL-DTL-25524 E
20 Nov 97
'J.l
MIL-DTL-46162 E
2002
MIL-F-81912 (3)
9 Oct 96
MIL-F-53080
13 Jul 00
MlL-P-25576C
19 Jun 03
MIL-PRF-16884 K
14 Nov 02
MTL-PRF-7808 L
2 May 97
MIL-PRF-23699
21 May 97
SAEJl899
1 Nov 95
MIL-L-6082E)
.11966
1 Nov 95
(formerly MIL-L-22851D)
Descrip_tion
The Standard Specification for Aviation Turbine Fuels Jet A, Jet A-1
The Standard Specification for Aviation Turbine Fuel Jet B
The United Kingdom Ministry of Defence (JetA-1), used for most civilian
fuels outside the U.S.; also NATO F-35, Joint Service Designation: AVTUR
Turbine Fuel, Aviation Grades JP-4, JP-5
Turbine Fuel, Low Volatility JP-7
Turbine Fuels, Aviation, Kerosene
NATO F-34, JP-8, JP-8+100
Turbine Fuel, Aviation, Thermally Stable
Fuel, Diesel, Referee Grade
Fuel, Expendable Turbine Engine
Fuel,
Design, Referee Grade, Types l & II
Propellant Kerosene
Fuel Naval Distillate
Lubricating Oil, Aircraft Turbine Engine, Synthetic Base
Lubricating Oil, Aircraft Turbine
Synthetic Base
Straight (Nondispersant) Mineral Oil, SAE 40, 50 60
Ashless Dispersant Additive Mineral Oils SAE 40, 50, 60, 20W 150,
25W/60
Military documents available at http://assist.daps.dla.miVquicksearch/
GAS TURBINE ENGINES
Engine Types - Descriptions
Turbojet
A turbojet is an aircraft gas-turbine engine that uses only the thrust
developed within the engine to produce its propulsive force. Because
turbojets have no added features such as a fan, propeller or free turbine,
they are sometimes referred to as straight jets. The two kinds of turbojets
-- the centrifugal-flow compressor type and the axial-flow compressor
type - may have one or more compressors, and some engines use both a
cent1ifugal compressor and an axial-flow compressor.
Large, high-performance turbojets (and turbofans) require greater efficiency
and higher compression ratios that can be obtained only with an axial-flow
compressor. These have the added advantage of enabling an engine to have
a small frontal area. The dual-compressor type results in very high
compressor efficiency, compression ratio and thrust. The dual-compressor
configuration is often called a two-spool, or twin-spool, engine. The single-
compressor turbojet is often called a single-spool engine.
Because the efficiency of a turbojet is sustained at high altitude and
airspeed, these engines are well suited for high-flying, high-speed aircraft
that operate over a sufficient range to make the climb to their best
operating altitude worth while.
Pratt & Whitney's most famous turbojet engine was the J57. It powered
numerous military aircraft; was the first dual-spool, axial-flow turbojet;
and was the first turbojet to achieve aircraft speed greater than 1,000 mph.
Due to the results achieved by the J57, Pratt & Whitney received the
Collier Trophy for the best aeronautical achievement in 1956. The success
of the J57 led to the development of the higher thrust (34,500-pound) J58
engine that powered the SR-71 Blackbird.
Turboprop and Turboshaft Engines
When the exhaust gases from the basic part of a turbojet (often called a
gas generator) are used to rotate an additional turbine that drives a
propeller through a speed-reducing gear system, the engine becomes a
turboprop (sometimes called a propjet).
In some turboprops, an extra turbine stage is incorporated in lhe turbine
assembly that rotates the compressor. The additional power that is
produced drives the propeller reduction gearing directly from tht:
:::ompressor drive shaft. Engines of this type are known as direct-chive
;_34
turboprops. A free turbine is incorporated in most modern turboprops.
This turbine is independent of the compressor-drive turbines and is free to
rotate by itself in the engine exhaust gas stream. The shaft on which the
free turbine is mounted drives the propeller through the propeller
reduction gear system.
Another configuration of the free-turbine turboprop has a rather
unconventional rear-to-front air- and gas-flow direction. This configuration
provides great flexibility in the design of nacelle installations; the space
behind the engine is not used for an exhaust duct and can be used for wheel
wells or fuel tanks. The compressor is a combination axial/centrifugal-flow
design. An example of such engine is the PT6 manufactured by Pratt &
Whitney Canada.
Turbofan
In principle, a turbofan is much like a turboprop except that the ratio of
secondary airflow (the airflow through the fan or propeller) to the primary
airflow through the basic engine is less. This is called the bypass ratio.
Also, in the turbofan, the gear-driven propeller is replaced by an axial-
flow fan with rotating blades and stationary vanes that are considerably
larger but are otherwise similar to the blades and vanes of an axial-flow
compressor. The fan is enclosed in a duct
In a turbofan, the fan makes a substantial contribution to the total thrust.
Over and above the thrust developed by the basic engine, the fan
accelerates the air passing through it, similar to the function of the
propeller of a turboprop. The fans of turbofan engines produce between 30
and 75 percent of the total thrust, the actual amount depending principally
upon the bypass ratio.
After the secondary air leaves the fan, it does not pass through the basic
engine for burning with fuel. In turbofan engines, the fan-discharged air
may be exhausted into the outside air through a fan-jet nozzle soon after
it leaves the fan, or it may be carried rearward by an annular fan-discharge
duct that surrounds the basic engine for its full length. The Pratt &
Whitney JT9D, PW2000 and PW 4000-series turbofans are examples of
with short ducts. The JT8D-series engines have the full-length
annular duct, or long duct, as it is sometimes called, and have a nonmixed
exhaust, that is, although the fan-discharged air is carried to the rear of the
engine, it is not mixed with the exhaust gases from the basic engine before
being delivered to the outside air. Some long-duct engines have a mixed
exhaust. The fan discharge
carried to the
tailpipe where mixes
135
with the exhaust from the basic engine. The air from the fan and the
exhaust gases are then discharged together through the engine
One fundamental difference between a turbofan and turboprop is that the
airflow through the fan is controlled by the design of the engine air-inlet
duct in such a manner that the velocity of the air through the fan blades is
not greatly affected by the speed of the aircraft.
When compared with a turbojet of equal thrust, the turbofan has the
advantage of a lower noise level for the engine exhaust, an important
feature at all commercial airports. The lower level of noise occurs because
a turbofan engine has at least one additional turbine stage to drive the fan.
Extraction of more power from the engine exhaust gases as they pass
through the additional turbine (or turbines) reduces the velocity of the
engine exhaust. Less velocity through the
nozzle results in less noise.
The turbofan combines the good operating efficiency and high-thrust
capability of a turboprop and the high-speed, high-altitude capability of a
turbojet. A turbofan is not only lighter than a turboprop but is less
complex.
For those and other reasons, including lower fuel consumption, the
modern turbofan has become the most widely used power plant for all
conventional large aircraft, both military and commercial.
Jet Engines with Afterburners
When a particular type of aircraft, such as a military fighter, needs extra
bursts of speed during takeoff and climb or for an intercept mission, each
of its power plants is usually provided with an afterburner. Such an engine
can develop 50 percent or more additional thrust when the afterburner is
operating.
Both turbojet and low-bypass-ratio turbofan engines can be equipped with
an afterburner, no matter what type of compressor they use. The afterburner,
\Vhen added to a turbofan engine, is sometimes called an augmentor.
Essentially, an afterburner is a pipe attached to the rear of an
instead of a tailpipe and jet nozzle. Afterbuming is possible because only
about 25 percent of the air (oxygen) entering the basic engine at the
compressor is used to support combustion there. The remaining
through the engine is used for
136
Aircraft Engines for Short TakeoffNertical Takeoff
and Landing
Special engine configurations allow fixed-wing aircraft to take off from
short runways, make tighter maneuvers while in flight or to take off and
land vertically. The engines are gas turbines that operate according to the
fundamentals already discussed, but their placement in the aircraft, their
exhaust duct and nozzle
and, at times, their configuration differ
from the conventional jct
Short takeoff and landing (STOL) capability is partly dependent on the
design of an airplane's wing, which can be optimized for high lift at low
runway speeds. After the wing and fuselage design, the engine is the
deciding factor. Engines can provide STOL ability with a variable-angle
exhaust nozzle, that is, the exhaust nozzle is flexible and can deflect the
exhaust gases to help "roll" the nose of the aircraft upward and then push
the plane upward at a steep angle of climb. The U.S. Air Force's new
C-17 A airlifter uses an alternative method. The exhaust gases from the
turbofans mounted on the wings are deflected through special "slats"
themselves small wings -
that extend from the trailing edges of the
wings. The slats tum the exhaust over the back edge of the wings,
accelerating the airflow over the wings and creating greater lift than would
be possible by the wings themselves.
The vertical takeoff and landing (VTOL) engine can allow STOL as well
as VTOL. Depending on the need, the exhaust of the jet nozzle -
or of
both the jet nozzle and the fan exhaust nozzle on turbofans
can be
deflected at an angle to push the aircraft at a steep climb, or the exhaust
can be deflected perpendicularly to the ground to allow the airplane to take
off straight upward like a helicopter. For vertical takeoff and hovering, the
vectored thrust of the engines must be greater than the aircraft weight;
more than 25,000 pounds of thrust would be necessary to allow a 25,000-
pound aircraft to take off vertically. By contrast, a conventional aircraft
taking off from a conventional airfield requires about one quarter to one
third of its weight in engine thrust.
An alternative to deflecting a jet exhaust
to tilt the entire engine in the
direction of takeoff. In this case the
can be a turbojet, turbofan or
a turboprop with large-diameter prc,peuers, the turboprop ... L.',;,_',:'"
.. 1v~..,.,u-u"i'F,n
most directly like a helicopter when
propeller tlm1st
directed
toward the
Engine Types - Station Designations
Numelical station designations are assigned to the various sections of gas
turbine engines to enable specific locations within the engine to be easily
and accurately identified. The station number coincides with the position,
front to rear, of the engine components, and are used as subscripts when
designating different temperatures and pressures at the front, rear, or
inside of an engine. The sketches which follow show the standard station
aeing11ar10rts for various types of jct
AM
4
5
INLET
COMPRESSOR
BURNER TURBINE EXHAUST EXHAUST
DIFFUSER
DUCT
NOZZLE
& DUCT
Single-Compressor Turbojet without an Afterburner, JT12, J60
4
5
COMPRESSOR
BURNER TURBINE DIFFUSER AFTERBURNER
COMBUSTION
CHAMBER
Single~Compressor Turbojet with an Afterburner
LOW PRESSUFI::
COMPRSSOR
Dual-Compressor Turbojet without an Afterburner, JT3, J52
,--
I .. -~ I
I
~ I ii I ~
... ;:g.::~
;~Q~;
ii
-alll
COMPRESSOR
BURNER
~
~
AM
I
0:
2
. 5
1
Single-Compressor Turboprop
Dual-Compressor Low Bypass Turbofan, JTSD-200
DualQCompressor Low Bypass Turbofan with an Afterburner, TF30
139
Engine Types - Station Designations ( continued)
I ~OWl'fltSSLMU:
COMPAES$0f\
2
2.5
Dual-Compressor ffigh Bypass Turbofan, PW2000, PW 4000
140
Turbojet and Turbofan Engine Noise
Noise Sources
The noise generated by turbojet and turbofan
dominated by two sources: the fan/compressor and the
is normally
exhaust.
Fan/Compressor: Noise from this source is generated primarily by flow
interactions between rotating airfoils and stationary objects in the flow
stream such as stators and struts. These flow interactions produce both
tone and broadband noise. Tone noise appears at discrete frequencies in
the noise spectrum (Figure 1) with the acoustic
concentrated at
multiples of blade-passing frequency. For broadband
the acoustic
energy
is distributed broadly over
the
frequency spectrum.
Fan/compressor noise propagates forward from turbojet engines and both
forward and rearward from turbofan engines.
Jet Exhaust Noise: Noise from this source is generated in the turbulent
mixing region behind the engine where high-velocity exhaust gases mix
with ambient air. This noise is broadband in nature with the acoustic
energy distributed broadly over the frequency spectrum.
Secondary Sources: Other sources, such as the turbine and combustor, can
also contribute to the total engine noise, becoming more significant as the
two primary noise sources are reduced in level.
Turbojet and Turbofan Engine Noise
( continued)
FAN
DISCRETE NOISE
I (TONES!
FUNDAMEHT Al.
FAN
BROADBAND NOi
RMONIC
TYPICAL TURBOFAN ENGINE FREQUENCY SPECTRUM
COMMON OCTAVE BANDS
f---1 ~2--+-,-3~4 ........ 5-+-&-----+--1......,_,--i
MIDDLE
r
""'la------PIANOKEYBOARD
I
I
-
TYPICAL LIMITS OF HUMAN EAR SENSITIVITY
20
50
100
200
500
1000 2000
5000
10,000
20,000
FREQUENCY IN CYCLES PER SECONDS
Figure 1
Noise Measurement Units
Measurements of aircraft/engine noise can be categ(Jn,~eo into two basic
types of units: physical and subjective.
The physical quantity normally measured when dealing with noise is the
Root-mean-square (RMS) sound pressure. Typically, the audible range
varies from 0.0002 dynes/cm2, the threshold of hearing, to about 1,000
dynes/cm2, the threshhold of pain. Because of the very large range of
sound pressures encountered in our acoustic environment and because the
human ear normally responds to the relative loudness of two sounds by the
ratio of their intensities rather than in an absolute way, a logarithmic scale,
sound pressure level, is used.
Sound pressure level, expressed in deciBels (dB), equals:
20 log =
P
sound pressure measured
PO
referrence pressure of 0.0002 dynes/cm2
Figure 2 displays the relationship between the sound pressure and sound-
pressure-level scales for various common noises covering the audible
range of interest.
Aircraft noise measurements generally are presented in terms of a
subjective rather than a physical unit to provide an indication of the level
of annoyance. Subjective units utilize different weighting factors that are
a function of frequency to approximate perceived annoyance. ln general,
higher frequency noises are assigned greater weightings.
Commonly used subjective units are dBA and Perceived Noise deciBels
(PNdB). Another subjective unit used in the noise certification process for
transport airplanes, Effective Perceived Noise deciBel (EPNdB),
"-,,.-, .. ~-, PNdD with additional corrections for
duration of the
the presence of tones,
Turbojet and Turbofan Engine Noise
( continued)
Relation Between Sound Pressure
and Sound-Pressure Level
200
100
50
10
5
0.5
0.1
0.05
0.01
0.005
0.001
0.0005
0.0002
Sound
Pressure
120 Automobile Hom (3 Feet)
110
100
90
80
70
60
50
40
30
20
10
0
Alarm Clock and
Washing Machine
Gasoline Powered
Lawn Mower
Quiet Residential Area
Soft Whisper
Sound
Pressure
Level db
Referenced to
0.0002
Figure 2
144
Gas Turbine Engine Symbols Used
by Pratt & Whitney
A
a
C
CLB
CON
CRZ
D
EGT
e
F
f
g
hp
H
h
l
LHV
m
M
M
MCL
MCR
MCT
N
n
cross-sectional area
linear acceleration
of sound
specific heat
coefficient, factor of proportionality, correction factor
maximum climb rating
maximum continuous rating
maximum cruise rating
diameter
exhaust gas temperature
2.718281828459045 (the base of the natural system
of logarithms)
thrust, force
frequency
acceleration due to gravity
horsepower
enthalpy
specific enthalpy
length
lower heating value of fuel
mass
moment
Mach number
maximum climb rating
maximum cruise rating
maximum continuous rating
rotational speed
polytropic exponent
pressure (absolute)
pressure (gauge)
Prandtl number
volume rate of flow
quantity of heat
pressure
gas constam
145
Gas Turbine Engine Symbols Used
by Pratt & Whitney (continued)
Re
r
s
s
SFC
TSFC
T
T
Reynolds number
radius
entropy
specific entropy
specific fuel consumption (esfc, bsfc, equiv., brake)
thrust-specific fuel consumption
torque
temperature (absolute)
temperature
t
time
TO
takeoff rating
TOD
dry takeoff rating
TOW
wet takeoff rating
u
internal energy (specific)
u
linear gas velocity
V
velocity
V
volume
v
specific volume
W
weight
w
weight rate of flow
a
angle of attack
a
angular acceleration
'Y
ratio of specific heats, cpfcv
a
relative pressure ratio, P/P0
Ll
finite difference
lJ
efficiency
0
relative temperature ratio, T/T0
,
absolute viscosity
kinematic viscosity
1,
3.141592653589793 (ratio ()T circumferenu
of a circle to its diameter)
i;
density
relative density ratio el ec
gross thrust paramete1
angular velocity
Gas Turbine Engine Subscripts
1, 2, 3, etc. engine station designations
air (Va); added
AIB
afterburner
am
ambient
av
average
ax
axial
b
burner, combustion chamber
bl
bleed
c
compressor (11c); compressible (qc)
er
critical (Per)
d
diffuser; duct; discharge
e
exhaust; exit
ej
ejector cPej)
f
fuel (wj); fluid (hj); fan
g
gas (wg); gross (Fg)
H
hub (DH)
h
heat exchanger; intercooler
inlet (r,i); indicated()
j
jet (Aj)
m
mixed (Ptm)
n
nozzle (11n); net (Fn)
o
standard sea level value; free stream condition
p
propeller (r,p); propulsion; airplane;
constant pressure (cp); primary
px
r
power extraction
ram (1Jr); radial CV,.); rejected
s
static (Ps); shaft; secondary
tip (Dy)
total
turbine (11t)
lh
thennal (11th)
constant volume
wall (Tw ); work
147
reverse
.j:::,.
00
P&W Engine Characteristics
Rotating Stages
Max. Std. Day S.L.
Engine Model
FAN LPC
lWC HPT LPT
Thrust(lbs)
Jl3C-6
11,200
9
7
1
2
12,000
JT3C-12
13,000
JT3D-l/IA
17,000
17,000
JT3D-l/1A-MC8
6
1
3
17,000
JT3D-3B/3C
18,000
JT3D-7l7A
19,000
JT4A-1 l/12
17,500
JT4A-3!/5
8
7
1
2
15,800
JT4A-9/10
I
16,800
JTSD-1/1 A/lB
!
14,000
14,000
14,500
JT8D-l l
15,000
JTSD-15
4
3
15,500
7
1
15,500
JTSD-17
16,000
r18D-l7/I
16,000
JT8D-17AR
17,400
JT8D-17R
I
17,400
JT8D-209
!
19,250
JTSD-217/217 A
j
6
7
1
3
20,850
JT8D-217C
i
20,850
TSFC
Engine Dimensions (in)
(lbm/hr/lbr)
Applications
D
L
0.775
707-120. DC-8-10
0.785
38.8
136.8
720
0.82
720
0.52
136.3
707-120B/720B, DC-8-50
0.52
145.5
720B
0.52
53.l
145.5
707-120B, 720B, DC-8-50
0.535
136.3
720, 707,DC-8-50/F/61/F/62
0.55
136.3
707-320B/C/F, DC-8-63/F
0.84
707-320, DC-8-20/30
0.78
43
144.1
707-320, DC-8-20
0.81
707-320, DC-8-20
0.585
727-100, DC-9-10-30, Caravclle
0.585
727-100, 737-IO0. DC-9
0.595
727-100, 737-200, Caravelle, DC-9
0.62
DC-9-20/30/40
0.63
39.9
120
727-200, 737-200, DC-9, Mercure
0.599
727-200, 737-200, DC-9, Mercure
0.645
727-200, 737-200, DC-9-30/50
0.613
727-200, 737-200, DC-9-30/50
0.622
727-200
0.655
727-200
0.501
MD-82
0.51
49.2
154.1
MD-82/87
0.5
MD-82/83/87 /88, Super 27
+'-
\0
Engine Model
JTSD-219
,JT9D-59A
IJT9D-70A
i .TT9D-20
JT9D-7
I .JT9D-7A
.JT9D-7F
JT9D-7J
JT9D-7Q/7Q3
JT9D-7R4D
JT9D-7R4D1
JT9D-7R4E
.IT9D-7R4El
JT9D-7R4E3
JT9D-7R4E4
I JT9D-7R4G2
JT9D-7R4Hl
PW2037
PW2040
PW2043
PW4050
PW4052
PW4056
P\V4060
FAN
1
I
l
I
t
Rotating Stages
LPC HPC HPT LPT
6
7
1
3
4
11
2
4
3
11
2
4
4
11
4
4
12
2
5
4
11
4
Max. Std. Day S.L.
TSFC
Engine Dimensions (in)
Applications
Thrust(lbs)
(Ibm/hrllbr)
D
L
21,700
0.519
49.2
154.1
MD-82/83/87 /88, Super 27
53,000
0.375
97
132.2
DC-10-40, A300
53,000
0.375
97
132.2
747-200
46,300
0.349
95.6
128.2
DC-10-40
45,600
0.374
95.6
128.2
747-100/200, 747SR
46,250
0.364
95.6
128.2
747-J00/200, 747SR/SP
48,000
0.367
95.6
128.2
747-100/200, 747SR/SP
50,000
0.37
95.6
128.2
747-100/200, 747SR/SP
53,000
0.375
97
132.2
747-200B/C/F
48,000
0.34
767-200
48,000
0.34
A310-200
50,000
0.343
767-200
50,000
0.343
97
132.7
J\310-200
50,000
0.346
767-200
50,000
0.346
A310-200
54,750
0.36
747-200, 300
I
56,000
0.364
A300-600
38,250
0.342
757-200
1
41,700
0.352
757-200, 200F
84.8
146.8
43,000
0.362
757-200/300
50,000
0.348
7 67-200/200ER/300
52,200
0.351
767-200/200ER
97
132.7
56,750
0.359
767-300/300ER, 747-400
60,000
0.365
767-300ER/400, 747-400
P&W Engine Characteristics (continued)
Rotatin2 Stares
Max. Std. Day S.L.
TSFC
Engine Dimensions (in)
Engine Model
Applications
FAN LPC HPC HPT LPT
Thrust (lbs)
(lbnJhr/lbr)
D
L
PW4062/62A
62,000
0.365
767-300ER/400, 747-400
PW4152
52,000
0.339
A310-300
PW4156A
l
4
11
2
4
56,000
0.35
97
132.7
A300-600
PW4158
58,000
0.355
A300-600R
PW4460/62
60/62,000
0.371
MD-11
PW4164
64,000
0.35
A330
1
5
11
2
5
107
163
PW4168/68A
68,600
0.348
A330
PW4077
78,040
0.313
777-200/200ER
PW4077D
[
6
11
2
7
78,040
0.319
119
191.6
777-200/200ER
PW4090
91,790
0.355
777-200/200ER/300
PW4098
1
7
11
2
7
98,000
0.358
120
194.7
777-300
PW6122A
6
22,100
0.383
A318
PW6124A
1
4
1
3
23,800
0.374
56.5
108.2
A318
V2500-Al
I
3
10
2
5
25,000
0.355
63.0
126
A320-200
V2522-A5
23,000
0.355
A319
V2524-A5
24,500
0.355
A319
V2525-D5
25,600
0.347
MD-90-30/30ER
1
4
10
2
5
26,600
0.355
63.5
126
A319CJ, A320-200
28,600
0.347
MD-90-30/50
V2530-A5
30,400
0.355
A321-100
V2533-A5
32,000
0.355
A321-200
GP7270
70,000
A380
1
5
9
6
117
187
GP7277
76,500
i\380-F
FlO0-PW-100
3
JO
2
2
23,450
2.1
46.5
191.2
F-151\/B, CID
Fl00-PW-200
23,770
F-16A/B, CID
Rotatini Stages
Max. Std. Day S.L.
TSFC
Engine Dimensions (in)
1
I
Engine Model
Applications
FAN LPC HPC HPT LPT
Tbrust(lbs)
(Ibn/hrflbr)
D
L
I FlO0-PW-220
23,830
2.1
191.2
F-15C/D/E, F-16A/B/C/D
!
j F100-PW-220E
23,770
2.1
191.2
F-15C/D. F-16A/B/C/D
! FlO0-PW-229
10
2
2
29,100
1.94
46.5
191.2
F-15E/l/S, F-16C/D
FlO0-PW-232
32,500
1.91
190.7
FIO0-PW-229 Upgrade
I
Fl 17-PW-100
l
4
12
2
5
40,900
0.34
84.5
146.8
C-17A
Fll9-PW-100
3
6
1
2
35,000
F-22
F135-PW-l00
40,000
CTOLF-35A
Fl35-PW-400
1
2
40,000
CTOLF-35C
Fl35-PW-600
40,000
STOVL f<-35B
TF30-P-3/103
18,500
2.5
49
F-lllA/C/E
TF30-P-6
42
128.!
TF30-P-7/7A/I07
20,360
2.62
50.7
241.4
FB-11
6
7
I
3
TF30-P-9/9A/109
20,840
2.62
49
241.6
F-IllD
i TF30-P-100/l l l
25,100
2.45
48.9
241.7
F-1 llF
I TF30-P-414/414t
20,900
2.78
50.7
235.7
F-14A
'
I J52-P-6A/B
8,500
0.82
31.7
116.9
I
5
7
1
1
9,300
0.86
32
116.9
A-4F/A-6E/EA-6A
J52-P-408
11,200
0.89
32
118.9
A-4M,EA-6B
17,000
0.52
136.3
B-52H
TF33-P-5
6
7
1
3
18,000
0.515
53.1
EC-135B
TF33-P-9
18,000
0.515
137.4
C-1358
TF33-P-7/7A
21,000
0.56
C-141
7
7
1
3
0.56
54
142.2
E-3A
i
TF33-P- l 00A
21,000
TF33-PW-102
2
6
7
1
3
18,000
0.54
53.1
136.3
C-18A, C/KC-135E, E-4C
!
P&W Engine Characteristics (continued)
i
Rotatinl! Starres
Max. Std. Day S.L.
TSFC
Engine Dimensions (in)
!
Engine Model
Applications
FAN LPC HPC HPT LPT
Thrust (lbs)
(Ihm/hr llbr)
D
L
ffl3-PW- !02B
18,000
0.515
!
Tr33-PW-102
2
6
7
1
3
19,000
0.525
53.1
136.3
E-8C
TF33-PW-102
17,000
0.505
B-5211
.175-P-BB
-
146.5
ER-2, TR-1
J75-P-l7
8
7
1
24,500
2.15
43
237.6
F-106A
J75-P-19W
i
26,500
2.2
259.3
F-105D, F, G
.157-P-4/A/22
I
16,000
2.2
39.8
267.6
F-8A. F-813
.157-P-10
10,500
0.795
40.5
157.5
A-3B
l
15,000
2.25
40.1
216.1
FIOIA. C
.157-P-lG
16,900
2.3
39.6
266.9
F-8C
J57-P-19W
12,100
0.85
40.5
157.5
B52,B. D,E
J57-P-20.
18,000
2.35
40
266.9
F-8E
J57-P-2J, A, B
7
1
2
16,000
2.1
40.5
246.5
F-IOOA, B,
D .
.157-P-23.
B
16,000
2.1
40.5
246.5
FI02A
J57-P-29W/W;\
12,100
0.85
40.5
157.5
B52B, C,
E
J57-P-43W/WA
13,750
0.95
38.8
167.3
B52F, G, KC-l35A
J57-P-55/55A
16,900
2.3
39.9
252.9
F-1018
J57-P-59W
13,750
0.95
38.8
167.3
KC-135A
J57-P-420
I
19,600
2.3
40
266.9
F-8J
J58
9
2
34,500
2.174
55.5
211.7
SR-71
JG0-P-3, 5, 6
9
2
21.9
70.5
C-140, T-39, T-28
Take-off Rating
Dimensions
Thrboshafts ThermoESHP MechSHP Shaft RPM
L
Willia
H
Applications
PT6B-37A
1002
900
4373
64.4
19.5
35.2
Agusta All9 Koala
PT6C-67A
1940
1940
30,032
59.3
22.5
-
Bell Agusta BA609
PT6C-67C
1679
1100
21,000
59.3
22.5
PT6C-67D
1692
1183
21,200
59.3
22.5
PT6T-3B
1800
1800
6600
65.8
43.5
32.6
!
PT6T-3D
1920
1800
6600
65.8
43.5
32.6
PT6T-3DF
1920
1800
6600
65.8
43.5
32.6
PT6T-6B
1970
1875
6600
65.8
43.5
32.6
PW206B2
621
431
5898
41
19.7
24.7 I Eurocoptcr EC135
PW206C
640
561
6100
35.9
19.7
22.3
PW207D
710
572
6000
35.9
19.7
22.3
Bcll 427
PW207E
l
710
646
6000
35.9
19.7
22.3 MD
PW207K
I
730
646
6000
35.9
19.7
22.3
Kazan Ansat
P&W Engine Characteristics (continued)
Take-off Ratin~
Dimensions
Turbofans
Thermo (lbt) Mech (lbt)
L W/Dia
H
Applications
JT15D-4
2500
2500
Acrospatiale Corvette
JTl5D-4C
2500
2500
Agusta S211/S2l 1A
JTl5D-5
3190
2965
60.4
27.3
-
Raytheon Beech Beech_jct 400A
.JT15D-5A
3190
2900
JT15D-5B
3190
2900
JT15D-5C
3190
3190
JT15D-5D
3350
3045
3190
2900
60.4
27
- I Raytheon Beech TCX
I
PW305A
5929
4679
65
34.3
43.8
PW306A
6718
6040
75.7
36.5
45.2 Gulfstream G200
PW306B
6976
6050
Fairchild Dornier 328 Jet
PW306C
6816
5770
75.7
36.5
-
Cessna Citation
PW307A
7500
6405
80.2
Dassault Falcon 7X
PW308A
8242
6904
93
39
-
Raytheon Hawker Horizon
PW308C
8349
7002
93
39
Dassault Falcon 2000EX
Take-off Rating
Dimensions
Turbofans
Thermo (lbt) Mech (lbt)
L
W/Dia
H
Applications
PW530A
3120
2887
60
27.6
34.4
Cessna Citation Bravo
PW535A
3841
3400
63.9
28.15
34.9
Cessna Citation Ultra Encore,
UC-35 CID
PW545A
4400
3804
68
32
38.4
Cessna Citation Excel
PW545B
4696
3991
Cessna Citation XLS
PW610F
-
900
41.7
18.7
-
Eclipse 500
PW615F
1350
49.3
21.9
-
Cessna Mustang
PW617F
1615
52.4
23.63
Phenom 100
Combined Load
'
MaxPneu
Generator
APUs
Load at I00F
Output
Applications
PW901A
585 lb/min at 57 psia
2 x 90 kva or 286 shp at 8000 rpm
Boeing 747-400
j
fi PW980A
706 lb/min at 57 psia
2 x 120 kva or 390 shp at 24,000 rpm
Airbus A380
I:
>-'
U1
'
P&W Canada (PWC) Engine Characteristics
Take-off Rating
Dimensions
Thermo Mech
Shaft
Turboprops
ESHP
SHP
RPM
L WIDia
H
PT6A-11AG
668
550
2200
62
19
, PT6A-l5AG
751
680
2200
62
19
i
PT6A-2J
663
550
2200
62
19
IT6A-25C
886
750
2200
62
19
751
680
2200
62
19
i
Applications
I
Air Tractor AT 402A/402B
I
Schweizer G-164B AG
Air Tractor 402A/402B/502B
Ayres Turbo Thrush T-15
Frakes Turbo Cat A/B/C
Schweizer G-164B AG
Raytheon Beech
Air C90A/B/SE
Turbine Air Bonanza
Embraer EMB-312 Tucano
Pilatus Turbo Trainer PC-7 /PC-7 MKIJ
PZL-Okecie PZL-130 TC-II
Turbo-Orlik
CATIC/HAIG Y-12
de Havilland DHC-6 Twin Otter
Series 300
Embraer Bandeirante EMB-110
LET L410
Pilatus Turbo Porter PC-6
Raytheon Beech 99A, B99
!
Take-off Ratin
I
Dimensions
Thermo Mech
Shaft
Turboprops
ESHP
SHP
RPM
L W/Dia H
Applications
PT6A-34/AG
886
750
2200
62
19
Air Tractor 502B
Turbo Thrush T-34
Embraer Bandeirante EMB-l 10,
EMB-111, Caraja
Frakes Mallard, Turbo Cat Model A/B/C
JetPROPDLX
Pacific Aero Cresco 750, 750XL
PZL-Okecie PZL-106 Turbo-Kruk
Schweizer G-l 64B AG-Cat, G-164D AG-Cat
Vazar Dash 3 Turbine Otter
PT6A-35
927
750
2190
62
19
JetPROPDLX
PT6A-l 14A
940
675
1900
62
19
Cessna 208/208B Caravan
PT6A-i35A
927
750
1900
62
19
Cessna Conquest I
Raytheon Beech King Air F90- l
Vazar Dash Turbine Otter
I 1089
I 850 I 2000
I 66.9 I 19 I
I Piper Cheyenne lII/llIA
Raytheon Beech King Air 200/B200
PT6A-4'2
l
1090 I 850 I 2000
166.9 I
19 I I
Beech Cl 2F, King Air 200/8200
PT6A-42A
1090
850
2000
67.9
19
P&W Canada (PWC) Engine Characteristics (continued)
Take-off Rating
I
Dimensions
Thermo Mech
Shaft
Turboprops
ESHP
SHP
RPM
L W/Dia H
Applications
PT6A-60A/AG
1218
1050
1700
72.5
19
Raytheon Beech King Air 300/350
Air Tractor AT 602
Ayres Model 660
PT6A-62
1365
950
2000
70.5
19
Pilatus Turbo Trainer PC-9
PT6A-64
1583
700
2000
70
19
Socata TBM 700
PT6A-65AG
1461
1300
1700
75
19
Air Tractor AT 602, 802/802A/802AF/802F
Ayres Turbo Thrush T-65
PT6A-65B
1548
I 1100 I 1700
I 14 I 19 I
I Polish Aviation Factory M28
Beech l 900/l 900C
PT6A-66
1572
850
2000
70
19
PIAGGIO Avanti P-180
PT6A-66A
1583
850
2000
70
19
Ibis Aerospace Ac 270 HP
PT6A-67A
1825
1200
1700
74
19
Raytheon Beech
PT6A-67AG
1634
1350
1700
76
19
Air Tractor 802/802A/802AF/802F
Model 660
Vi
...o
Turboprops
PT6A-67B
PT6A-67R
PT6A-67T
PT6A-68
PT6A-68B
PT6A-68C
PW1l8
PW12!
PWl23
PW123E
PW127E
PW127F
PWl27G
PW127H
PW127J
PW150A.
! PW150B
Take-off Rating
Thermo Mech
Shaft
ESHP
SHP
RPM
1703
1200
1700
1754
1424
1700
1807
1424
1700
1805
1250
2000
1927
1600
2000
1962
1600
2000
2286
1800
1300
2497
2150
1200
2950
2380
1200
3113
2380
1200
3295
2400
1200
3365
2750
1200
3546
2920
1200
3341
2750
1200
3365
2750
1200
6680
5071
1020
6576
5071
1020
Dimensions
I
L W/Dia H
Applications
74
19
Pilatus PC
76
19
Basler Turbo BT-67
Shorts 360/360-300
76
19
de Havilland DHC-4
72.2
19
Raytheon T-6A Texan II
72.2
19
Pilatus PC-21
72.2
19
Embraer EMB-314 Super Tucano
81
25
31
Embraer EMB- l 20
84
25
31
ATR42-320
Bombardier Q 100
84
26
33
Bombardier Q300
84
26
33
Bombardier Q300
I
84
26
33
ATR72
i
84
26
33
ATR 72-210/500
I
i
84
26
33
CASA 295
84
26
33
Ilyushin IL-114-1 00
84
26
33
XIANMA-60
95.4
30.2
43.5
Bombardier Q400
95.4
30.2
43.5
AVIC II Y8F600
Notes and Abbreviations
c V2500 engine models belong to JAE (International
Engines),
collaboration of Pratt & Whitney, R-R, MTU and JAEC
GP7000
models belong to EA (Engine Alliance), a
venture
GE & Pratt & Whitney.
Abbreviations
In Development
APU
Auxiliary Power Unit
D
Diameter
ESHP
Effective Shaft Horsepower
H
Height
HPC
High Pressure Compressor
HPT
High Pressure Turbine
L
Length
lbs
Pounds
lbt
Pound thrust
LPC
Low Pressure Compressor
LPT
Low Pressure Turbine
Max
Maximum
RPM
Revolutions Per Minute
SL
Sea Level
SHP
Shaft
Std
Standard
rsFc
Thrust
W/Di2. Width/Diameter
160
Gas Turbine Parameter Correction Procedures
The corrected (generalized) gas turbine performance parameters, defined
below, provide a basis for the comparison of the performance of engines
operated at different atmospheric and flight conditions. The Greek letters
o and O are factors representing the ratio of the pressure and temperature
of the air stream at the chosen reference station relative to sea-level
standard atmospheric conditions. With these factors, the observed
performance parameters of rotor speed(s), thrnst, fuel flow, airflow and
exhaust gas temperature are referenced to a common condition, either that
of ambient air or stagnation conditions at the engine inlet, whichever is
most appropriate. The values of 5 and 8 are detemlined by:
PX
TX
0x =
8x
Pa
To
where x denotes the reference condition, i.e., ambient or engine station 2
(stagnation).
Gas turbine parameters are corrected as follows:
Corrected net thrnst
Corrected fuel flow
Corrected fuel consumption
Corrected air flow
Cmrected exhaust
gas temperature
Corrected rotor speed
Fn (corr)
Wf(corr) =
Fn ( observed)
0
Wf ( observed)
oO 0.5*
TSFC ( corr) = Wf ( corr)
Fn (corr)
TSFC
00.5*
Wa ( observed) 0-5
Wa (corr)=
0
EGT (corr)= EGT (observed)
0*
N (corr)
N (observed)
0 0.5
'The exponent for theta, 0, is a function of the engine cycle and i:c;
developed from theoretical and empirical data. The exponent
approximately 0.5 for ctmecting fuel flow and TSFC and approximately
1.0 for c(mecting temperatures.
i6J
Theta (0) Tables
0 represents the ratio of the air stream temperature at a chosen reference
station relative to sea level standard atmosphe1ic conditions.
0 = TITO = [ ((
0F) + 459.67] = [ /( 0C) + 273,}5]
518.67
288.15
op
oc
0
9.5
9.62
9.67
9.91
80
-62.2
0.7320
0.8556
0.8241
0.8114
0.7529
-79
-61.7
0.7339
0.8567
0.8255
0.8128
0.7547
78
-61.1
0.7359
0.8578
0.8268
0.8142
0.7565
-77
-60.6
0.7378
0.8589
0.8282
0.8157
0.7583
-76
60.0
0.7397
0.8601
0.8295
0.8171
0.7601
-75
-59.4
0.7416
0.8612
0.8308
0.8185
0.7619
74
-58.9
0.7436
0.8623
0.8322
0.8200
0.7637
-73
-58.3
0.7455
0.8634
0.8335
0.8214
0.7655
-72
-57.8
0.7474
0.8645
0.8349
0.8228
0.7673
-71
-57.2
0.7494
0.8657
0.8362
0.8242
0.7691
-70
-56.7
0.7513
0.8668
0.8375
0.8256
0.7709
-69
-56.l
0.7532
0.8679
0.8389
0.8271
0.7727
-68
-55.6
0.7551
0.8690
0.8402
0.8285
0.7745
-67
55.0
0.7571
0.8701
0.8415
0.8299
0.7763
-66
-54.4
0.7590
0.8712
0.8428
0.8313
0.7781
65
-53.9
0.7609
0.8723
0.8442
0.8327
0.7799
-64
-53.3
0.7629
0.8734
0.8455
0.8341
0.7817
-63
-52.8
0.7648
0.8745
0.8468
0.8355
0.7835
-62
-52.2
0.7667
0.8756
0.8481
0.8370
0.7853
-61
-51.7
0.7686
0.8767
0.8495
0.8384
0.7871
-51.1
0.7706
0.8778
0.8508
0.8398
0.7889
-50.6
0.7725
0.8789
0.8521
0.8412
0.7907
50.0
0.7744
0.8800
0.8534
0.8426
0.7924
-49.4
0.7764
0.8811
0.8547
0.8440
0.7942
48.9
0.7783
0.8822
0.8561
0.8454
0.7960
-48.3
0.7802
0.8833
0.8574
0.8468
0.7978
47.8
0.7821
0.8844
0.8587
0.8482
0.7996
47.2
0.7841
0.8855
0.8600
0.8496
0.8014
46.7
0.7860
0.8866
0.8613
0.8510
0.8032
46.1
0.7879
0.8876
0.8626
0.8524
0.8050
162
op
oc
0
a.s
0 .62
0 .67
0 .91
-50
-45.6
0.7898
0.8887
0.8639
0.8538
0.8068
49
-45.0
0.7918
0.8898
0.8652
0.8552
0.8086
-48
-44.4
0.7937
0.8909
0.8665
0.8566
0.8104
-47
-43.9
0.7956
0.8920
0.8678
0.8580
0.8122
-46
43.3
0.7976
0.8931
0.8691
0.8594
0.8140
,,_ _____ ..,. _ ,
-45
-42.8
0.7995
0.8941
0.8704
0.8608
0.8158
-44
-42.2
0.8014
0.8952
0.8717
0.8622
0.8175
-43
-41.7
0.8033
0.8963
0.8730
0.8635
0.8193
-42
-41.l
0.8053
0.8974
0.8743
0.8649
0.8211
-41
-40.6
0.8072
0.8984
0.8756
0.8663
0.8229
-40
-40.0
0.8091
0.8995
0.8769
0.8677
0.8247
-39
-39.4
0.8111
0.9006
0.8782
0.8691
0.8265
-38
-38.9
0.8130
0.9017
0.8795
0.8705
0.8283
37
38.3
0.8149
0.9027
0.8808
0.8719
0.8301
-36
-37.8
0.8168
0.9038
0.8821
0.8732
0.8318
-35
-37.2
0.8188
0.9049
0.8834
0.8746
0.8336
-34
-36.7
0.8207
0.9059
0.8847
0.8760
0.8354
-33
-36.1
0.8226
0.9070
0.8860
0.8774
0.8372
-32
-35.6
0.8246
0.9080
0.8873
0.8788
0.8390
-31
-35.0
0.8265
0.9091
0.8886
0.8801
0.8408
-30
-34.4
0.8284
0.9102
0.8898
0.8815
0.8426
-29
-33.9
0.8303
0.9112
0.8911
0.8829
0.8443
-28
-33.3
0.8323
0.9123
0.8924
0.8842
0.8461
-27
-32.8
0.8342
0.9133
0.8937
0.8856
0.8479
-26
-32.2
0.8361
0.9144
0.8950
0.8870
0.8497
-25
31.7
0.8380
0.9154
0.8962
0.8884
0.8515
-24
-31.1
0.8400
0.9165
0.8975
0.8897
0.8533
-23
-30.6
0.8419
0.9176
0.8988
0.8911
0.8550
-22
-30.0
0.8438
0.9186
0.9001
0.8925
0.8568
-21
-29.4
0.8458
0.9197
0.9013
0.8938
0.8586
-20
-28.9
0.8477
0.9207
0.9026
0.8952
0.8604
-19
-28.3
0.8496
0~9217
0.9039
0.8966
0.8622
-18
-27.8
0.8515
0.9228
0.9052
0.8979
0.8639
17
-27.2
0.8535
0.9238
0.9064
0.8993
0.8657
16
26.7
0.8554
0.9249
0.9077
0.9006
0.8675
163
Theta (0) Tables (continued)
8 represents the ratio of the air stream temperature at a chosen
station relative to sea level standard atmospheric conditions.
0 = TIT~ = [ t(F) + 459.67 ] = [ f(C) + 273.15]
518.67
288.15
op
oc
0
05
0,62
0,67
0,91
-15
-26.1
0.8573
0.9259
0.9090
0.9020
0.8693
14
-25.6
0.8593
0.9270
0.9102
0.9034
0.8711
13
-25.0
0.8612
0.9280
0.9115
0.9047
0.8728
-12
-24.4
0.8631
0.9290
0.9128
0.9061
0.8746
-11
-23.9
0.8650
0.9301
0.9140
0.9074
0.8764
-10
-23.3
0.8670
0.9311
0.9153
0.9088
0.8782
-9
-22.8
0.8689
0.9321
0.9166
0.9101
0.8800
-8
-22.2
0.8708
0.9332
0.9178 0.9115
0.8817
-7
-21.7
0.8728
0.9342
0.9191
0.9128
0.8835
-6
-21.1
0.8747
0.9352
0.9203
0.9142
0.8853
-5
-20.6
0.8766
0.9363
0.9216
0.9155 0.8871
-4
-20.0 0.8785
0.9373
0.9228 0.9169
0.8888
-3
-19.4
0.8805
0.9383
0.9241
0.9182
0.8906
-2
-18.9
0.8824
0.9394
0.9254
0.9196
0.8924
-1
-18.3
0.8843
0.9404
0.9266
0.9209
0.8942
0
-17.8
0.8862
0.9414
0.9279
0.9223
0.8959
1
-17.2
0.8882
0.9424
0.9291
0.9236
0.8977
2
-16.7
0.8901
0.9435
0.9304
0.9250
0.8995
3
-16.1
0.8920
0.9445
0.9316
0.9263
0.9013
4
-15.6
0.8940
0.9455
0.9329
0.9276
0.9030
5
15.0
0.8959
0.9465
0.9341
0.9290
0.9048
6
-14.4
0.8978
0.9475
0.9354
0.9303
0.9066
7
-13.9
0.8997
0.9485
0.9366
0.9317
0.9083
8
-13.3
0.9017
0.9496
0.9378
0.9330
0.9101
9
12.8
0.9036
0.9506
0.9391
0.9343
0.9119
10
-12.2
0.9055
0.9516
0.9403
0.9357
0.9137
11
11.7
0.9075
0.9526
0.9416
0.9370
0.9154
12
, lLl
0.9094
0.9536
0.9428
0.9383
0.9172
13
10.6
0.9113
0.9546
0.9440
0.9397
0.9190
:!4
10.0
0.9132
0.9556
0.9453
0.9410
0.9207
Of
oc
0
9.5
9.62
9.67
9.91
15
-9.4
0.9152
0.9566
0.9465
0.9423
0.9225
16
-8.9
0.9171
0.9577
0.9478
0.9437
0.9243
17
-8.3
0.9190
0.9587
0.9490
0.9450
0.9260
18
-7.8
0.9210
0.9597
0.9502
0.9463
0.9278
19
-7.2
0.9229
0.9607
0.9515
0.9476
0.9296
20
-6.7
0.9248
0.9617
0.9527
0.9490
0.9313
21
-6.1
0.9267
0.9627
0.9539
0.9503
0.9331
22
-5.6 0.9287
0.9637
0.9552
0.9516
0.9349
23
-5.0
0.9306
0.9647
0.9564
0.9529
0.9366
24
-4.4
0.9325
0.9657
0.9576
0.9543
0.9384
25
-3.9
0.9344
0.9667
0.9588
0.9556
0.9402
26
-3.3
0.9364
0.9677
0.9601
0.9569
0.9419
27
-2.8
0.9383
0.9687
0.9613
0.9582
0.9437
28
-2.2
0.9402
0.9697
0.962S
0.9595
0.9455
29
-1.7
0.9422
0.9706
0.9637
0.9609
0.9472
30
-1.1
0.9441
0.9716
0.9650
0.9622
0.9490
31
-0.6
0.9460
0.9726
0.9662
0.9635
0.9508
32
0.0
0.9479
0.9736
0.9674
0.9648
0.9525
33
0.6
0.9499
0.9746
0.9686
0.9661
0.9543
34
1.1
0.9518
0.9756
0.9698
0.9674
0.9560
35
l.7
0.9537
0.9766
0.9711
0.9688
0.9578
36
2.2
0.9557
0.9776
0.9723
0.9701
0.9596
37
2.8
0.9576
0.9786
0.9735
0.9714
0.9613
38
3.3
0.9595
0.9795
0.9747
0.9727
0.9631
39
3.9
0.9614
0.9805
0.9759
0.9740
0.9648
40
4.4
0.9634
0.9815
0.9771
0.9753
0.9666
41
5.0
0.9653
0.9825
0.9783
0.9766
0.9684
42
5.6
0.9672
0.9835
0.9796
0.9779
0.9701
43
6.1
0.9692
0.9845
0.9808
0.9792
0.9719
44
6.7
0.9711
0.9854
0.9820
0.9805
0.9736
45
7.2
0.9730
0.9864
0.9832
0.9818
0.9754
46
7.8
0.9749
0.9874
0.9844
0.9831
0.9772
47
8.3
0.9769
0.9884
0.9856
0.9844
0.9789
48
8.9
0.9788
0.9893
0.9868
0.9857
0.9807
49
9.4
0.9807
0.9903
0.9880
0.9870
0.9824
165
Theta ( 0) Tables ( continued)
8 represents the ratio of the air stream temperature at a chosen reference
station relative to sea level standard atmospheric conditions.
0 = TITO = [ t{F) + 459.67 ] = [ t{C) + 273.15]
518.67
288.15
op
oc
8
9.5
9.62
9.67
9.91
50
10.0
0.9826
0.9913
0.9892
0.9883
0.9842
51
10.6
0.9846
0.9923
0.9904 0.9896
0.9860
52
11.1
0.9865
0.9932
0.9916
0.9909
0.9877
53
11.7
0.9884
0.9942 0.9928
0.9922
0.9895
54
12.2
0.9904
0.9952
0.9940
0.9935
0.9912
55
12.8
0.9923
0.9961
0.9952
0.9948
0.9930
56
13.3
0.9942 0.9971
0.9964
0.9961
0.9947
57
13.9
0.9961
0.9981
0.9976 0.9974
0.9965
58
14.4
0.9981
0.9990
0.9988
0.9987
0.9982
59
15.0
1.0000
1.0000 1.0000
1.0000
1.0000
60
15.6
1.0019
1.0010 1.0012
1.0013
1.0018
61
16.1
1.0039
1.0019
1.0024
1.0026
1.0035
62
16.7
1.0058
1.0029
1.0036
1.0039
1.0053
63
17.2
1.0077
1.0038
1.0048
1.0052
1.0070
64
17.8
1.0096
1.0048
1.0060 1.0064
1.0088
65
18.3
1.0116
1.0058
1.0072
1.0077
1.0105
66
18.9
1.0135
1.0067
1.0083
1.0090
1.0123
67
19.4
1.0154
1.0077
1.0095
1.0103
1.0140
68
20.0
1.0174
1.0086
1.0107
1.0116
1.0158
69
20.6
1.0193
1 .0096
1.0119
1.0129
1.0175
70
21.1
1.0212
1.0105
1.0131
1.0142
1.0193
71
21.7
1.0231
1.0115
1.0143
1.0154
1.0210
72
22.2
1.0251
1.0125
1.0155
1.0167
1.0228
73
22.8
1.0270
1.0134
1.0167
1.0180
1.0245
74
23.3
1.0289
1.0144
1.0178
1.0193
1.0263
75
23.9
1.Q308
1.0153
1.0190
1.0206
1.0280
76
24.4
1.0328
1.0163
1.0202
1.0218
1.0298
77
25.0
1.0347
1.0172
1.0214
1.0231
1.0315
78
25.6
1.0366
1.0182
1.0226
1.0244
1.0333
79
26.1
1.0386
1.0191
1.0237
1.0257
1.0350
--=~----
166
, __ ""'-~
op
oc
8
9.5
9.62
9.67
9.91
80
26.7
1.0405
1.0200
1.0249
1.0269
1.0368
81
27.2
1.0424
1.0210
1.0261
1.0282
1.0385
82
27.8
1.0443
1.0219
1.0273
1.0295
1.0403
83
28.3
1.0463
1.0229
1.0284
1.0308
1.0420
84
28.9
1.0482
1.0238
1.0296
1.0320
1.0438
~ ------~
85
29.4
1.0501
1.0248
1.0308
1.0333
1.0455
86
30.0
1.0521
1.0257
1.0320
1.0346
1.0473
87
30.6
1.0540
1.0266
1.0331
1.0359
1.0490
88
31.1
1.0559
1.0276
1.0343
1.0371
1.0508
89
31.7
1.0578
1.0285
1.0355
1.0384
1.0525
90
32.2
1.0598
1.0295
1.0366
1.0397
1.0542
91
32.8
1.0617
1.0304
1.0378
1.0409
1.0560
92
33.3
1.0636
1.0313
1.0390
1.0422
1.0577
93
33.9
1.0656
J.0323
1.0402
1.0435
1.0595
94
34.4
1.0675
1.0332
1.0413
1.0447
1.0612
95
35.0
1.0694
1.0341
1.0425
1.0460
1.0630
96
35.6
l.0713
1.0351
1.0436 1.0472
1.0647
97
36.1
1.0733
1.0360
1.0448
1.0485
1.0665
98
36.7
1.0752
1.0369
1.0460
1.0498
1.0682
99
37.2
1.0771
1.0378
1.0471
1.0510
1.0699
100
37.8
1.0790
1.0388
1.0483
1.0523
1.0717
101
38.3
1.0810
1.0397
1.0495
1.0536
1.0734
102
38.9
1.0829
1.0406
1.0506
1.0548
1.0752
103
39.4
1.0848
1.0416
1.0518
1.0561
1.0769
104
40.0
1.0868
1.0425
1.0529
1.0573
1.0787
105
40.6
1.0887
1.0434
1.0541
1.0586
1.0804
106
41.1
1.0906
1.0443
1.0553
1.0598
1.0821
107
41.7
1.0925
1.0452
1.0564
1.0611
1.0839
108
42.2
1.0945
1.0462
1.0576
1.0623
1.0856
109
42.8
1.0964
1.0471
1.0587
1.0636
1.0874
110
43.3
1.0983
1.0480
1.0599
1.0649
1.0891
111
43.9
1.1003
1.0489
1.0610
1.0661
1.0908
112
44.4
1.1022
1.0498
1.0622
1.0674
1.0926
113
45.0
L1041
1.0508
1.0633
1.0686
1.0943
114
45.6
L1060
1.0517
1.0645
1.0699
1.0961
-=----
---~.~
l6'/
Theta (0) Tables ( continued)
0 represents the ratio of the air stream temperature at a chosen reference
station relative to sea level standard atmospheric conditions.
0 = TIT0 =
[ /(
0f) + 459.67 ] = [ t(C) + 273.15]
518.67
288.15
op
oc
0
0.s
0,62
0,67
0,91
115
46.1
1.1080
1.0526
1.0656
1.0711
1.0978
116
46.7
1.1099
1.0535
1.0668
1.0724
1.0995
117
47.2
1.1118
1.0544
1.0679
1.0736
1.1013
118
47.8
1.1138
1.0553
1.0691
1.0749
1.1030
119
48.3
1.1157
1.0563
1.0702
1.0761
1.1047
120
48.9
1.1176
1.0572
1.0714
1.0773
1.1065
121
49.4
1.1195
1.0581
1.0725
1.0786
1.1082
122
50.0
1.1215
1.0590
1.0737
1.0798
1.1100
123
50.6
1.1234
1.0599
1.0748
1.0811
1.1117
124
51.1
1.1253
1.0608
1.0759
1.0823
1.1134
125
51.7
1.1272
1.0617
1.0771
1.0836
1.1152
126
52.2
1.1292
1.0626
1.0782
1.0848
1.1169
127
52.8
1.1311
1.0635
1.0794
1.0860
1.1186
128
53.3
1.1330
1.0644
1.0805
1.0873
1.1204
129
53.9
1.1350
1.0653
1.0817
1.0885
1.1221
130
54.4
1.1369
1.0662
1.0828
1.0898
1.1238
131
55.0
1.1388
1.0672
1.0839
1.0910
1.1256
132
55.6
1.1407
1.0681
1.0851
1.0922
1.1273
133
56.1
1.1427
1.0690
1.0862
1.0935
1. 1290
134
56.7
1.1446
1.0699
1.0873
1.0947
1.1308
135
57.2
1.1465
1.0708
1.0885
1.0959
1.1325
136
57.8
1.1485
1.0717
1.0896
1.0972
1.1342
137
58.3
1.1504
1.0726
1.0907
1.0984
1.1360
138
58.9
1.1523
1.0735
1.0919
1.0996
1.1377
139
59.4
1.1542
1.0744
1.0930
1.1009
1.1394
140
60.0
1.1562
1.0753
1.0941
1.1021
1.1412
141
60.6
1.1581
1.0761
1.0953
l.1033
1 1429
142
61.1
1.1600
1.0770
1.0964
1.1046 L1446
143
61.7
1.1620
1.0779
1.0975
U058
1.1464
144
62.2
1.1639
1.0788
1.0987
L1070
L1481
---~-.---Cr---
168
op
oc
0
0.s
0.62
0.67
0.91
145
62.8
1.1658
1.0797
1.0998
1.1083
1.1498
146
63.3
1.1677
1.0806
1.1009
1.1095
1.1516
147
63.9
1.1697
1.0815
1.1020
1.1107
1.1533
148
64.4
1.1716
1.0824
1.1032
1.1119
1.1550
149
65.0
1.1735
1.0833
1.1043
1.1132
1.1567
150
65.6
1.1754
1.0842
1.1054
1.1144
1.1585
151
66.1
1.1774
1.0851
1.1065
1.1156
1.1602
152
66.7
1.1793
1.0860
1.1077
1.1168
1.1619
153
67.2
1.1812
1.0868
1.1088
1.1181
1.1637
154
67.8
1.1832
1.0877
1.1099
1.1193
1.1654
155
68.3
1.1851
1.0886
1.1110
1.1205
1.1671
156
68.9
1.1870
1.0895
1.1121
1.1217
1.1688
157
69.4
1.1889
1.0904
1.1133
1.1229
1.1706
158
70.0
1.1909
1.0913
1.1144
1.1242
1.1723
159
70.6
1.1928
1.0922
1.1155
1.1254
1.1740
160
71.1
1.1947
1.0930
1.1166
1.1266
1.1758
161
71.7
1.1966
1.0939
1.1177
1.1278
1.1774
162
72.2
1.1986
1.0948
1.1188. 1.1290
1.1792
163
72.8
1.2005
1.0957
1.1200
1.1302
1.1809
164
73.3
1.2024
1.0965
1.1211
1.1314
1.1826
l69
Compressor Inlet Pressure Recovery
The internationally accepted standard atmosphere
the ICAO, also known
the ISA. The ISA and the U.S. Standard Atmosphere, 1976 are a function
of altitude and are identical up to 32 km (approximately 105,000
The
equations that follow range from sea level to 75,000 feet.
1.00
M 0
1.0
I
1.00 0.076 (M - 1)1.35
from M > 1.0
5.0
800
!Pu =
forM > 5.0
M4 + 935
where
P 12 =
total pressure at compressor inlet
Pu
free-stream total pressure
M
flight Mach number
Compressor Inlet Pressures and Temperatures
U.S. Standard Atmosphere, 1976/ISA (Geopotential)
Inlet Pressure Recovery
Altitude = 0 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PT/Po
psia
dr2
op
0r2
0.0
0.0
1.000
1.000
14.70
1.00000
59.00
1.000
66.1
1.007
1.007
14.80
1.00702
60.03
1.002
132.3
1.028
1.028
15.11
1.02828
63.14
1.008
198.4
1.064
1.064
15.64
1.06443
68.32
1.018
J,4
264.5
1.117
1.117
16.41
1.11655
75.59
1.032
330.7
1.186
1.186
17.43
1.18621
84.92
1.050
396.8
1.276
1.276
18.74
1.27550
96.33
1.072
462.9
1.387
1.387
20.38
l.38710
109.82
1.098
0.8
529.1
1.524
1.524
22.40
1.52434
125.38
1.128
0,9
595.2
1.691
1.691
24.86
1.69130
143.02
1.162
661.4
1.893
1.893
27.82
1.89293
162.73
1.200
793.6
2.425
2.404
35.33
2.40425
208.37
1.288
.4
925.9
3.182
3.113
45.75
3.11299
262.31
1.392
1058.2
4.250
4.090
60.11
4.09045
324.56
1.512
1190.4
5.746
5.427
79.75
5.42693
395.10
1.648
1322.7
7.824
7.238
106.36
7.23761
473.94
1.800
1984.1
36.733
29.710
436.62
29.7099
992.63
2.800
Altitude = 5,000 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PT/Po
psia
dT2
op
0T2
0.0
0.0
L(K)()
1.000
12.23
0.83205
41.16
0.966
65.0
1.007
1.007
12.31
0.83789
42.16
0.968
130.0
1.028
1.028
12.57
0.85558
45.16
0.973
195.0
l.064
1.064
13.02
0.88565
50.17
0.983
260.0
1.117
1.117
13.65
0.92902
57.18
0.997
324.9
1.186
1.186
14.50
0.98698
66.20
1.014
389.9
1.276
1.276
15.60
1.06128
77.22
1.035
454.9
1.387
1.387
16.96
1.15413
90.24
l.060
0.8
519.9
1.524
1.524
18.64
1.26832
105.27
1.089
584.9
1.691
1.691
20.68
1.40724
122.30
1.122
649.9
1.893
1.893
23.15
1.57500
141.33
L159
779.9
2.425
2.404
29.40
2.(K)()45
185.40
1.244
909.8
3.182
3.113
38.06
2.59015
237.49
1.344
1039.8
4.250
4.090
50.02
3.40344
297.60
1.460
1169.8
5.746
5.427
66.36
4.51546
365.71
591
1299.8
7.824
7.238
88.50
6.02203
441.84
1.738
1949.7
36.733
29.710
363.29
24.7200
942.70
2.704
Altitude = 10,000 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PT/Po
psia
dT2
op
0T2
0.0
0.0
1.000
1.000
10.11
0.68770
23.33
0.931
63.8
1.007
1.007
10.18
0.69253
24.29
0.933
127.6
1.028
1.028
10.39
0.70715
27.19
0.939
191.5
1.064
1.064
10.76
0.73201
32.02
0.948
U.4
255.3
1.117
1.117
11.28
0.76785
38.78
0.961
319. l
1.186
1.186
11.99
0.81576
47.48
0.978
382.9
1.276
1.276
12.89
0.87717
58.10
0.998
446.7
1.387
1.387
14.02
0.95391
70.66
1.023
0.8
510.6
1.524
1.524
15.41
1.04829
85.15
1.050
574.4
1.691
1.691
17.09
1.16311
101.58
1.082
638.2
1.893
1.893
19.13
1.30177
119.93
1.117
765.9
2.425
2.404
24.30
1.65341
162.44
1.199
893.5
3.182
3.113
31.46
2.14081
212.67
1.296
1021.l
4.250
4.090
41.34
2.81301
270.64
1.408
L8
1148.8
5.746
5.427
54.85
3.73211
336.33
1.535
2.0
1276.4
7.824
7.238
73.15
4.97732
409.75
1.676
3\ 0 0
1914.6
36.733
29.710
300.26
20.4316
892.77
2.607
Altitude = 15,000 Feet
Va
PT2
Mach
kts
PT/Po
PT/Po
psia
dT2
op
0T2
0.0
0.0
1.000
1.000
8.29
0.56434
5.50
0.897
62.6
1.007
1.007
8.35
0.56830
6.43
0.899
:\25.3
1.028
1.028
8.53
0.58030
9.22
0.904
187.9
1.064
1.064
8.83
0.60070
13.87
0.913
250.5
1.117
1.117
9.26
0.63011
20.38
0.926
313.2
1.186
1.186
9.84
0.66943
28.75
0.942
375.8
1.276
1.276
10.58
0.71982
38.99
0.961
438.4
1.387
1.387
11.50
0.78280
51.08
0.985
501.1
1.524
1.524
12.64
0.86024
65.04
1.012
563.7
1.691
1.691
14.03
0.95447
80.86
1.042
626.3
1.893
1.893
15.70
1.06826
98.53
l.076
751.6
2.425
2.404
19.94
1.35681
139.47
1.155
876.8
3.182
3.113
25.82
1.75678
187.85
1.248
1002.l
4.250
4.090
33.92
2.30840
243.68
1.356
1127.4
5.746
5.427
45.01
3.06263
306.94
1.478
1252.6
7.824
7.238
60.03
4.08447
377.65
1.614
1879.0
36.733
29.710
246.40
16.7665
842.85
2.511
Altitude = 20,000 Feet
Va
Pr2
Tr2
Mach
kts
PylPo
PTlPo
psia
dT2
op
0r2
0.0
1.000
1.000
6.75
0.45954
12.34
0.862
61.4
1.007
1.007
6.80
0.46277
-11.44
0.864
122.8
1.028
1.028
6.94
0.47254
-8.76
0.869
184.3
1.064
1.064
7.19
0.48915
4.28
0.878
OA
245.7
1.117
1.117
7.54
0.51310
1.98
0.890
307.1
1.186
1.186
8.01
0.54511
10.03
0.906
368.5
1.276
1.276
8.61
0.58615
19.87
0.925
429.9
1.387
1.387
9.37
0.63743
31.51
0.947
,_,
0.8
491.4
1.524
1.524
10.29
0.70050
44.93
0.973
--1
Lil
552.8
1.691
1.691
11.42
0.77722
60.14
1.002
614.2
1.893
1.893
12.78
0.86988
77.14
1.035
737.0
2.425
2.404
16.24
1.10485
116.51
1.11
859.9
3.182
3.113
21.02
1.43055
163.03
1.201
982.7
4.250
4.090
27.62
1.87973
216.72
1.304
i.8
1105.6
5.746
5.427
36.65
2.49390
277.56
1.421
1228.4
7.824
7.238
48.88
3.32598
345.56
1.552
1842.6
36.733
29.710
200.64
13.6529
792.92
2.415
Altitude = 25,000 Feet
Va
PT2
Ty2
Mach
kts
Pr/Po
PT/Po
psia
dT2
op
0T2
0.0
0.0
1.000
1.000
5.45
0.37109
30.17
0.828
60.2
1.007
1.007
5.49
0.37369
-29.31
0.830
120.4
1.028
1.028
5.61
0.38158
-26.73
0.835
180.6
1.064
1.064
5.80
0.39500
-22.43
0.843
OA
240.7
1.117
1.117
6.09
0.41434
16.42
0.855
05
300.9
1.186
1.186
6.47
0.44019
-8.69
0.870
0,.6
361
1.276
l.276
6.96
0.47333
0.76
0.888
421.3
1.387
1.387
7.56
0.51474
11.93
0.909
'.::i
0.8
481.5
1.524
1.524
8.31
0.56567
24.81
0.934
0\
0.9
541.7
1.691
1.691
9.22
0.62763
39.42
0.962
601.8
1.893
1.893
10.32
0.70245
55.74
0.994
722.2
2.425
2.404
13.11
0.89219
93.54
1.067
842.6
3.182
3.113
16.98
1.15520
138.21
1.153
962.9
4.250
4.090
22.31
1.51792
189.75
1.252
1083.3
5.746
5.427
29.60
2.01388
248.17
1.365
1203.7
7.824
7.238
39.47
2.68581
313.46
1.491
1805.5
36.733
29.710
162.02
11.0251
742.99
2.319
Altitude = 30,000 Feet
Va
PT2
TT2
Mach
kts
PTlPo
PT/Po
psia
dT2
op
0T2
0.0
0.0
1.000
1.000
4.36
0.29696
-48.00
0.794
58.9
1.007
1.007
4.39
0.29904
-47.17
0.795
17.8
1.028
1.028
4.49
0.30536
-44.70
0.800
176.8
1.064
1.064
4.65
0.31609
-40.59
0.808
0 .. 4
235.7
1.117
1.117
4.87
0.33157
34.82
0.819
294.6
1.186
1.186
5.18
0.35226
27.41
0.833
353.5
1.276
1.276
5.57
0.37877
-18.35
0.851
412.4
1.387
1.387
6.05
0.41191
-7.65
0.872
0.8
471.4
1.524
1.524
6.65
0.45267
4.70
0.895
530.3
1.691
1.691
7.38
0.50225
18.70
0.922
589.2
1.893
1.893
8.26
0.56212
34.34
0.952
707.1
2.425
2.404
10.49
0.71397
70.57
1.022
824.9
3.182
3.113
13.59
0.92443
113.39
1.105
942.7
4.250
4.090
17.85
1.21470
162.79
1.200
LS
1060.6
5.746
5.427
23.68
1.61158
218.79
1.308
2.0
178.4
7.824
7.238
31.59
2.14928
281.37
1.429
:LO
1767.6
36.733
29.710
129.66
8.82265
693.07
2.222
Altitude = 35,000 Feet
-
Va
PT2
Mach
kts
PT1/Po
PT/Po
psia
oT2
OF
0T2
0,.0
0.0
1.000
1.000
3.46
0.23530
-65.83
0.759
57.6
1.007
1.007
3.48
0.23696
-65.04
0.761
15.3
1.028
1.028
3.56
0.24196
-62.68
0.765
172.9
1.064
1.064
3.68
0.25046
-58.74
0,773
230.5
1.117
1.117
3.86
0.26273
53.22
0.784
288.2
1.186
1.186
4.10
0.27912
-46.13
0.797
345.8
1.276
1.276
4.41
0.30013
37.47
0.814
403.4
1.387
1.387
4.80
0.32639
-27.23
0.834
461.0
1.524
1.524
5.27
0.35868
15.41
0.857
518.7
1.691
1.691
5.85
0.39797
~2.02
0.882
576.3
1.893
1.893
6.55
0.44541
12.95
0.911
691.6
2.425
2.404
8.31
0.56573
47.61
0.978
806.8
3.182
3.113
10.76
0.73250
88.57
l.057
922.l
4.250
4.090
14.14
0.96250
135.83
1.148
1037.4
5.746
5.427
18.77
1.27698
189.40
1.251
152.6
7.824
7.238
25.03
1.70304
249.27
1.367
1728.9
36.733
29.710
102.74
6.99086
643.14
2.126
Altitude = 36,089 Feet
Va
PT2
TT2
Mach
kts
Py/P0
PT/Po
psia
dT2
op
0y2
0.0
1.000
1.000
3.28
0.22336
69.71
0.752
57.3
1.007
1.007
3.31
0.22493
-68.93
0.753
114.7
1.028
1.028
3.38
0.22968
-66.59
0.758
172.0
1.064
1.064
3.49
0.23775
62.69
0.765
0.4
229.4
1.117
1.117
3.67
0.24939
57.23
0.776
286.7
1.186
1.186
3.89
0.26495
50.21
0.789
344.1
1.276
1.276
4.19
0.28490
-41.63
0.806
401.4
1.387
1.387
4.55
0.30982
-31.49
0.826
,-,
0.8
458.8
1.524
1.524
5.00
0.34048
19.79
0.848
~
516.l
1.691
1.691
5.55
0.37777
-6.53
0.874
573.5
1.893
1.893
6.21
0.42281
8.29
0.902
688.2
2.425
2.404
7.89
0.53701
42.60
0.968
802.8
3.182
3.ll3
10.22
0.69532
83.16
1.047
917.5
4.250
4.090
13.43
0.91364
129.96
l.137
L8
1032.2
5.746
S.421
17.81
1.21216
183.00
1.239
2.0
1146.9
7.824
7.238
23.76
1.61660
242.28
1.353
1720.4
36.733
29.710
97.52
6.63602
632.27
2.105
Altitude = 40,000 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PTlPo
psia
dr2
op
0T2
0.0
0.0
1.000
1.000
2.72
0.18508
69.71
0.752
57.3
1.007
1.007
2.74
0.18638
-68.92
0.753
114.7
l.028
1.028
2.80
0.19032
66.59
0.758
172.0
1.064
1.064
2.90
0.19701
-62.69
0.765
229.4
1.117
1.117
3.04
0.20666
57.23
0.776
286.7
1.186
1.186
3.23
0.21955
-50.21
0.789
0.6
344.l
1.276
1.276
3.47
0.23607
-41.63
0.806
401.4
1.387
1.387
3.77
0.25673
-31.49
0.826
>-'
458.8
1.524
1.524
4.15
0.28213
19.79
0.848
00
0.8
0
516.l
1.691
1.691
4.60
0.31303
-6.53
0.874
573.5
1.893
1.893
5.15
0.35035
8.29
0.902
"-t,
688.2
2.425
2.404
6.54
0.44499
42.60
0.968
i-'
802.8
3.182
3.113
8.47
0.57616
83.16
1.047
917.5
4.250
4.090
11.13
0.75708
129.96
1.137
.. 8
1032.2
5.746
5.427
14.76
1.00444
183.00
1.239
146.9
7.824
7.238
19.69
1.33956
242.28
1.353
1720.4
36.733
29.710
80.81
5.49883
632.27
2.105
Altitude = 45,000 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PT/Po
psia
dT2
OF
0r2
0.0
0.0
LOOO
1.000
2.14
0.14555
-69.71
0.752
57.3
1.007
1.007
2.15
0.14657
-68.93
0.753
114.7
1.028
1.028
2.20
0.14966
-66.59
0.758
172.0
1.064
1.064
2.28
0.15492
-62.69
0.765
0~4
229.4
1.117
1.117
2.39
0.16251
-57.23
0.776
286.7
1.186
1.186
2.54
0.17265
50.21
0.789
344.1
1.276
1.276
2.73
0.18564
-41.63
0.806
(U
401.4
1.387
1.387
2.97
0.20189
-31.49
0.826
,-,
00
,-
0.8
458.8
1.524
1.524
3.26
0.22186
19.79
0.848
516.1
1.691
1.691
3.62
0.24616
-6.53
0.874
573.5
1.893
1.893
4.05
0.27551
8.29
0.902
688.2
2.425
2.404
5.14
0.34993
42.60
0.968
802.8
3.182
3.113
6.66
0.45308
83.16
1.047
L6
917.5
4.250
4.090
8.75
0.59535
129.96
l.137
.8
1032.2
5.746
5.427
11.61
0.78987
183.00
1.239
146.9
7.824
7.238
15.48
1.05340
242.28
1.353
1720.4
36.733
29.710
63.SS
4.32415
632.27
2.105
Altitude = 50,000 Feet
Va
PT2
Mach
kts
PT/Po
PT/Po
psia
dT2
op
0T2
0.0
0.0
1.000
1.000
1.68
0.11445
-69.71
0.752
57.3
1.007
1.007
1.69
0.11526
-68.93
0.753
14.7
1.028
1.028
1.73
0.11769
66.59
0.758
172.0
1.064
1.064
1.79
0.12183
-62.69
0.765
229.4
1.117
1.117
1.88
0.12779
57.23
0.776
286.7
1.186
1.186
2.00
0.13577
-50.21
0.789
344.1
1.276
1.276
2.15
0.14599
-41.63
0.806
401.4
1.387
1.387
2.33
0.15876
-31.49
0.826
0,8
458.8
1.524
1.524
2.56
0.17447
19.79
0.848
516.1
1.691
1.691
2.84
0.19358
-6.53
0.874
573.5
1.893
1.893
3.18
0.21665
8.29
0.902
688.2
2.425
2.404
4.04
0.27518
42.60
0.968
802.8
3.182
3.113
5.24
0.35629
83.16
1.047
917.5
4.250
4.090
6.88
0.46817
129.96
1.137
1032.2
5.746
5.427
9.13
0.62113
183.00
1.239
146.9
7.824
7.238
12.17
0~82837
242.28
1.353
1720.4
36.733
29.710
49.97
3.40041
632.27
2.105
Altitude = 55,000 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PT/Po
psia
oT2
op
9T2
0.0
0.0
1.000
1.000
1.32
0.09000
-69.71
0.752
57.3
1.007
1.007
1.33
0.09064
-68.93
0.753
14.7
1.028
1.028
1.36
0.09255
-66.59
0.758
172.0
1.064
1.064
1.41
0.09580
-62.69
0.765
:;)A,
229.4
1.117
1.117
1.48
0.10049
-57.23
0.776
286.7
1.186
1.186
1.57
0.10676
50.21
0.789
344.l
1.276
1.276
1.69
0.11480
-41.63
0.806
401.4
1.387
1.387
1.83
0.12484
-31.49
0.826
}-'
0.8
458.8
1.524
1.524
2.02
0.13720
19.79
0.848
00
l,_,.j
516.l
1.691
1.691
2.24
0.15222
-6.53
0.874
,0
573.5
1.893
1.893
2.50
0.17037
8.29
0.902
688.2
2.425
2.404
3.18
0.21639
42.60
0.968
802.8
3.182
3.113
4.12
0.28018
83.16
1.047
917.5
4.250
4.090
5.41
0.36816
129.96
1.137
L8
1032.2
5.746
5.427
7.18
0.48844
183.00
1.239
1146.9
7.824
7.238
9.57
0.65141
242.28
1.353
1720.4
36.733
29.710
39.30
2.67401
632.27
2.105
Altitude = 60,000 Feet
-
Va
PT2
Mach
kts
Pr/Po
PT/Po
psia
or2
op
0T2
0.0
0.0
1.000
l.000
1.04
0.07078
-69.71
0.752
57.3
1.007
1.007
1.05
0.07127
-68.93
0.753
14.7
1.028
l.028
1.07
0.07278
-66.59
0.758
172.0
1.064
l.064
1.11
0.07534
-62.69
0.765
229.4
1.117
1.117
1.16
0.07903
57.23
0.776
286.7
1.186
1.186
1.23
0.08396
-50.21
0.789
344.1
1.276
1.276
1.33
0.09028
-41.63
0.806
401.4
1.387
1.387
1.44
0.09817
-31.49
0.826
458.8
1.524
1.524
1.59
0.10789
19.79
0.848
516.l
1.691
1.691
1.76
0.11971
--6.53
0.874
573.5
1.893
1.893
1.97
0.13398
8.29
0.902
688.2
2.425
2.404
2.50
0.17017
42.60
0.968
802.8
3.182
3.113
3.24
0.22033
83.16
1.047
917.5
4.250
4.090
4.25
0.28951
129.96
1.137
1032.2
5.746
5.427
5.64
0.38410
183.00
1.239
146.9
7.824
7.238
7.53
0.51226
242.28
1.353
]720.4
36.733
29.710
30.90
2.10278
632.27
2.105
Altitude = 65,000 Feet
Va
PT2
TT2
l\1ach
kts
PT/Po
PT/Po
psia
dT2
OF
0T2
0.0
0.0
1.000
1.000
0.82
0.05566
69.71
0.752
S7.3
1.007
1.007
0.82
0.05605
-68.93
0.753
114.7
1.028
1.028
0.84
0.05723
-66.59
0.758
172.0
1.064
1.064
0.87
0.05924
62.69
0.765
OA
229.4
l.117
1.117
0.91
0.06214
57.23
0.776
286.7
1.186
1.186
0.97
0.06602
-50.21
0.789
0.6
344.l
1.276
1.276
1.04
0.07099
-41.63
0.806
0,7
401.4
1.387
1.387
1.13
0.07720
-31.49
0.826
~
00
(1,8
458.8
1.524
1.524
1.25
0.08484
19.79
0.848
IJl
516.1
1.691
1.691
1.38
0.09413
-6.53
0.874
573.5
1.893
1.893
1.55
0.10536
8.29
0.902
688.2
2.425
2.404
1.97
0.13381
42.60
0.968
802.8
3.182
3.113
2.55
0.17326
83.16
1.047
917.5
4.250
4.090
3.35
0.22766
129.96
1.137
.8
103:'!.2
5.746
S.427
4.44
0.30205
183.00
1.239
2.0
1146.9
7.824
7.238
S.92
0.40283
242.28
1.353
:LO
!720.4
36.733
29.710
24.30
1.65358
632.27
2.105
Altitude = 70,000 Feet
Va
PT2
Mach
kts
PT/Po
PT/Po
psia
dT2
op
0T2
0.0
0.0
1.000
1.000
0.64
0.04380
-67.31
0.757
57.5
1.007
1.007
0.65
0.04411
-66.52
0.758
15.0
1.028
1.028
0.66
0.04504
-64.17
0.763
172.6
1.064
1.064
0.69
0.04662
-60.24
0.770
OA
230.1
1.117
1.117
0.72
0.04890
54.75
0.781
287.6
1.186
1.186
0.76
0.05195
-47.69
0.794
0.6
345.l
1.276
1.276
0.82
0.05587
-39.06
0.811
402.7
1.387
1.387
0.89
0.06075
-28.85
0.831
...-
0.8
460.2
1.524
1.524
0.98
0.06676
-17.08
0.853
00
0\
0.9
517,7
1.691
1.691
1.09
0.07408
-3.74
0.879
575.2
1.893
1.893
1.22
0.08291
11.17
0.908
690.3
2.425
2.404
1.55
0.10530
45.70
0.974
805.3
3.182
3.113
2.00
0.13634
86.51
1.053
920.4
4.250
4.090
2.63
0.17916
133.60
1.144
L8
1035.4
5.746
5.427
3.49
0.23769
186.96
1.247
150.5
7.824
7.238
4.66
0.31700
246.61
1.362
1725.7
36.733
29.710
19.12
1.30125
639.00
2.118
Altitude = 75,000 Feet
Va
PT2
TT2
Mach
kts
PT/Po
PT/Po
psia
"T2
op
0T2
0.0
0.0
1.000
1.000
0.51
0.03452
64.56
0.762
57.7
1.007
1.007
0.51
0.03477
-63.77
0.763
15.4
1.028
1.028
0.52
0.03550
-61.40
0.768
173.2
1.064
1.064
0.54
0.03675
57.45
0.776
OA
230.9
1.117
1.117
0.57
0.03855
51.92
0.786
288.6
1.186
1.186
0.60
0.04095
-44.81
0.800
346.3
1.276
1.276
0.65
0.04403
-36.11
0.817
404.l
1.387
1.387
0.70
0.04789
-25.84
0.836
,....._
0.8
461.8
1.524
1.524
0.77
0.05262
13.99
0.859
00
-J
519.5
1.691
1.691
0.86
0.05839
-0.55
0.885
577.2
1.893
1.893
0.96
0.06535
14.46
0.914
692.7
2.425
2.404
1.22
0.08300
49.23
0.981
808.l
3.182
3.113
1.58
0.10747
90.33
1.060
923.6
4.250
4.090
2.08
0.14121
137.74
1.152
L8
1039.0
5.146
5.427
2.75
0.18735
191.48
1.255
154.5
7.824
7.238
3.67
0.24986
251.54
1.371
l73L7
36.733
29.710
15.07
1.02567
646.68
2.133
188
ROCKET ENGINES
189
Other Reaction Engines
Ramjets, pulsejets and rocket motors are members of the reaction engine
family, even though they are not classified as gas turbine engines.
Ramjet
The most simple jet engine is the ramjet, which has no moving parts.
Essentially, a ramjet is only a large, open-ended pipe with a fuel-injection
and fuel-metering system. As its name implies, a ramjet relies entirely
upon ram effect to build up the pressure of the air entering the engine to
the amount that will enable the engine to operate. This is done by
accelerating the ramjet to a speed at which the shape of its air inlet can
help compress the air for efficient combustion. This is just as a gas turbine
on an airplane operates, but forward speed and ram effect supplant the
rotating compressor of the gas turbine. Hence, a ramjet must be carried
aloft and accelerated to operating speed by some means other than its own
thrust. It may ride "piggyback" on a rocket to operational altitude, or it
may be borne to the proper height and speed as a dropable external store
on a conventional airplane. Once they commence to operate by
themselves, ramjets function on the jet propulsion principle, just like any
other reaction engine.
Pulsejet
A pulsejet is a ramjet with an air inlet that has a set of shutters that are spring-
loaded to remain in the closed position. After a pulsejet engine is launched,
ram air pressure forces the shutters to open and fuel is injected into the
combustion chamber where it is burned. Ignition, however, is intermittent,
timed to go on and off as the shutters open and close. As soon as the pressure
in the combustion chamber equals the ram air pressure, the shutters close.
The gases produced by combustion are forced out the jet nozzle at the rear of
the engine by the pressure that has built up within the chan1ber. The
acceleration of the gases through the nozzle generates thrust. Then the
pressure drops in the combustion chamber, the shutters open again, admitting
more air, and the cycle repeats itself with great rapidity. Pulsejets can be
started and operated at considerably lower speed than ramjets, and it is
possible to design a pulsejet that does not need a high initial velocity to be
started. The V-1 "Buzz Bomb" of World War lI was powered by a pulsejet
Rocket Engine
A rocket engine operates on the jct-propulsion principle and canies ics
fuel and an oxidizer to bum with the fuel either in the rocket, itself, or
aboard the vehicle that the rocket propels. Therefore, unlike ramjets,
pulsejets and gas turbine engines, a rocket engine is not an air- breathing
190
engine and because of this, it can operate completely independently of the
outside atmosphere, as in the airlessness of outer space. The fuel for
rocket engine and the oxidizing agent required for combustion together
constitute the prope11ant. Solid-.fuel engines carry the propellant in the
combustion chamber. Fuel and oxidizer are mixed together in solid fonn
and remain packed together until they are burned. Liquid-fuel engines
carry the propellant separately in tanks. Liquid oxygen is stored in one
fuel tank, and a liquid fuel, usually kerosene or hydrogen, is stored in
another tank. The fuel and oxidizer are pumped to the combustion
chamber and are ignited. Both solid- and liquid-propellant engines consist
primarily of the combustion chamber and a jet nozzle through which the
gases of combustion are expelled at high velocity to develop thrust.
Hybrid Ram-Rocket Engines
Hybrid versions of ramjets and rocket engines are being considered by
aerospace scientists as potential power for supersonic or hypersonic
aircraft (both commercial and military). Another application for hybrid
engines is in "single-stage-to-orbit" space vehicles, spacecraft that take off
from conventional runways or from launch pads without using expendable
rocket stages that are jettisoned when out of fuel. Currently, spacecraft
must carry their own oxidizer, but a successful hybrid ramjet-rocket would
use air in the atmosphere until the vehicle reaches an altitude where the air
is too thin, whereupon the rocket engine would begin to operate by using
a store of liquid oxygen to attain orbit. Since the vehicle uses atmospheric
air for part of its flight, much weight in oxidizer is saved, making it
possible to design a vehicle that can take off and land horizontally like
conventional airplanes. Besides making flight operations more
convenient, such a design would also reduce expendable materials (such
as jettisoned rocket stages).
The supersonic-combustion ramjet
or simply "scramjet" -
is designed
to overcome the problems of internal heat and shock. The scramjet would
use hydrogen as a fuel. Since hydrogen can burn within a fast airstream,
the air would not have to be slowed as much as it would have to be if
conventional fuels were used. New materials, aerodynamic concepts and
variable-airflow geometry controlled by high-speed computers are other
factors that will go into the making of a scramjet.
Hybrid engines are neither
ramjet nor rocket engine but, instead, are
integrated designs meant to save aircraft weight and fuel load for hypersonic
flight. The physical realities of hypersonic flight will probably dictate
use of some version of these types of
engines in the future
191
Liquid Rocket Engine Cycles
There are three basic liquid rocket engine cycles: the expander cycle, the
gas generator cycle, and the staged combustion cycle. A simple flow
schematic is shown for each cycle in Figures 1, 2 and 3.
The Expander Cycle - A typical expander cycle rocket engine cools the
chamber/nozzle components with the fuel flow. The energy picked up by
the fuel then provides the power to drive the turbopumps. From the turbine
discharge, the fuel proceeds to the combustion chamber and combines
with the oxidizer and is expanded through the nozzle to produce thrust.
The expander cycle is a simple, efficient, and reliable process with a
relatively benign turbine environment. The cycle is capable of thrust levels
up to a million pounds but is limited to chamber pressure below 200 psia.
An example of an expander cycle engine is Pratt & Whitney's highly
successful RLIO.
The Gas Generator Cycle Like the expander, the gas generator cycle
engine typically uses its fuel to cool the hot gas components. However, a
small portion of the fuel and oxidizer are routed to a gas generator where
they are combusted. The resultant combustion products are used to drive
the turbopumps, exhausting to a low (ambient) pressure. The remaining
propellants are combined in the main chamber and expanded through the
nozzle to produce the engine's main thrust. The gas generator engine uses
the turbine's higher temperature and large pressure ratio, to attain high
chamber pressure and, because the turbine power in not dependent on
nozzle heat transfer, thrust above 2 million pounds is possible. However,
due to the inefficient use of the turbine exhaust products, cycle
performance of the gas generator is lower than the expander. The gas
generator cycle is the most common liquid rocket engine used with the
LR-87, LR-91 and MA-5 as examples.
The Staged Combustion Cycle - The typical staged combustion cycle
engine, like the gas generator, uses combustion products to power the
turbopumps. However, in this cycle the turbine exhaust gases are routed to
the main chamber requiring high flow and low pressure ratio turbines. The
cycle requires very high pressures and temperatures to make it capable of
high chamber pressure and high thrust levels demonstrated by the gas
generator
but, because it makes efficient use of its turbine exhaust
gases, it can match the expander cycle's performance efficiency level. The
only staged combustion
in today's U.S. inventory
the Space Shuttle Main
192
FUEL
IN
EXPANDER CYCLE
OXIDIZER IN
HEX
OXIDIZER
PUMP
RL 10 ... CENTAUR
SATURN 1, S-4
TITAN
DELTA
ATLAS
93
GAS GENERATOR CYCLE
FUEL
FUEL
IN
PUMP
RECT. GAS
GENERATOR
F-1, J-2 ... SATURN I8/V
MA-5, MA-3 ... ATLAS
H-1 ... SATURN 1
RS-27c .. THOR, DELTA
LR87, LR91 ,TITAN
RS-6R""DELTA IV
194
OXIDIZER
TURBINE
STAGED COMBUSTION CYCLE
FUEL
IN
SSME ... SPACE SHUTTLE
Theoretical Rocket Engine Propellant Summary
( Oxygen and Flourine Oxidizers vs. Various Fuels
at Pc = 1000 psia)
Oxidant
Fuel
0/F
dp
Tc
C*
02
H2
6.00
0.362
6296.0 7577.0
CH4
3.50
0.832
6419.0 6017.0
C2H6
2.95
0.898
6490.0 6025.0
C3H8
3.20
0.932
6584.0 5890.0
C2H2
1.60
0.857
7382.0 6522.0
C2H4
2.45
0.887
6795.0 6127.0
RP-1
2.90
1.022
6680.0 5811.0
N2H4
0.90
1.068
6122.0 6218.0
UMDH
1.67
0.978
6485.0 6104.0
NH3
1.41
0.890
5537.0 5840.0
F2
H2
8.00
0.463
7152.0 8380.0
B2H6
5.45
1.091
9264.0 7316.0
BsH9
4.60
1.198
9463.0 7047.0
CH4
4.35
1.019
7377.0 6746.0
N2H4
2.25
1.304
8498.0 7290.0
CN2H6
2.38
1.240
7834.0 6775.0
UDMH
2.45
1.188
7462.0 6590.0
N2H4-UDMH
2.50
1.260
8033.0 6870.0
NH3
3.30
1.171
8294.0 7199.0
196
o,0-=-.=co-
IvAc
Oxidant
Fuel
ARs:20
R ... 10
AR-150
02
H2
436.4
462.6
474.I
CH4
353.7
379.0
390.7
C2H6
351.4
374.8
385.4
C3Hs
347.3
373.7
386.1
C2H2
371.7
392.2
401.1
C2H4
356.6
379.9
390.6
RP-1
342.5
368.4
380.6
N2H4
336.8
377.3
386.1
UDMH
354.4
376.8
387.0
NH3
334.8
354.3
362.7
F2
H2
465.5
484.9
492.5
B2Ho
423.6
453.3
468.2
BsH9
408.6
437.5
451.9
CH4
397.5
423.8
435.2
N2H4
415.9
437.3
445.9
CN2H 6
398.6
424.7
435.7
UDMH
391.7
418.9
430.6
N2H4-UDMH
401.1
427.0
438.2
NH3
409.7
430.2
438,3
\0
00
Vapor Pressure of Liquid Propellants
:: f tUitiltb$ I I II II I uounnm i 11111111 :~~ rr
u.f -200
a:
:::J
i
w
a..
~
w
.....
-100
0
+100
+200 I
+300 t-- --+-+--+--
--+----1---+-l-+-++H +360
___ ......... +660
... ""'NJ~ I I 11111 +760
+400
rvnrunr.L l'\Lvvvnv1.., 1--ia,,IF-+H.....;=--ia:1:--+-+-H--f'"'lll~t-----i~~ttt +860
87% HYDROGEN PEROXIDE
+500 L...-..L-...&,._.......i..1.1..,U..-.l-.,j,,_j,,.,,j, __ .._.__---i.._._..;;a.i.....1-1,.-J,_......._,.i......... ......... .....i.1 +960
0.01
0.1
1.0
10
100
VAPOR PRESSURE, ATM
0
w
a:
:::J
~
a:
UJ
a..
~
UJ
t-
I-'
\C
\,0
Specific Gravities of Liquid Propellants
TEMPERATURE, 0 R
60
160
,6
.4 I FLUORINE
260
360
460
RED FUMING NITRIC ACID
WHITE FUMING NITRIC ACID
N 2 0 4 ~__,,,,,
560
>-
87% HYDROGEN PEROXIDE __..,.,..- NITROMETNANE
660
r-
'L2
>
~1 ~i,-----,~<~I-
FURFURALALCOHOL~ -r-----1
<(
.o
a:
HYDRAZINE HYDRATE -
CJ
0
0.8
LL 0.6
-
0
LU -
CL 0.4
(f)
0.2 i--+---t--------+--.......... --+----+
LIQUID HYDROGEN
o-----------------------
-400
-300
-200
-100
0
+ 100
+200
TEMPERATURE, F
Liquid Rocket Engine Symbols
Ao
Design Area Ratio
Ae
Nozzle Exit Area
in)
At
Throat Area
in.2
Effective Exhaust Velocity
ft/sec
Cp
Thrust Coefficient
CpID
Ideal Thrust Coefficient
(for an optimum expansion
ratio nozzle)
Cs
Stream Thrust Coefficient
(ratio of actual to theoretical
vacuum thrust coefficient)
Cv
Velocity Coefficient
(ratio of actual to ideal thrust
coefficient at constant chamber
to ambient pressure ratio, area
ratio not necessarily constant)
c*
Characteristic Exhaust Velocity
ft/sec
'le*
Characteristic Exhaust Velocity
Efficiency
De
Nozzle Exit Diameter
in.
Dt
Nozzle Throat Diameter
in.
dr
Fuel Specific Gravity
do
Oxidizer Specific Gravity
Propellant Bulk Specific
Gravity
_...., _____ ~-s-.. ~
200
Ee
Nozzle Exit to Throat
Area Ratio - A.el A1
F
Thrust
lbf
go
Gravitational Constant 32,174
lbm ft/lbr-sec2
Ah
Turbopump Head Rise
fL
hsv
Pump Suction Head
ft.
Above Vapor Pressure
Is
Specific Impulse
lb1 sec/lbm
(instantaneous)
!s
Time-Averaged Specific
lb1 sec/lbm
Impulse (when operating in
changing ambient pressure)
Isl
Sea Level Specific Impulse
lbr-sec/lbm
Ivac
Specific Impulse at Pa = 0
lb1 sec/lbm
k or y
Ratio of Specific Heats
L*
Characteristic Chamber Length
in.
M
Mach Number
M
Molecular Weight of
lbm
Exhaust Products
lb mole
N
Rotational Speed
rpm
Ns
Pump Specific Speed
(rpm) (gpm)
Parameter
ft
Chamber Pressure
psia
(throat total}
Liquid Rocket Engine Symbols (continued)
Pa
Ambient Pressure
psia
Pse
Nozzle Exit Pressure (static)
psia