Mattingly J.D., Heiser W.H., Pratt D.T. Aircraft Engine Design
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Appendix A
Units and Conversion Factors
Table A.1 Basic definitions and constants
Constant Definition
Time 1 h = 3600 s
Length 1 in. = 2.540 cm
1 ft= 12in.
1 mile = 5280 ft
Mass 1 Ibm = 0.45359 kg
1 slug = 32.174 Ibm
Force 1 lbf = 32.174 lbm-ft/s 2
1 N = 1 kg-rn/s 2
Energy 1 Btu = 778.16 ft-lbf
1J=lN-m
Power 1 hp = 550 ft-lbf/s
lW= 1J/s
Pressure 1 atm = 14.696 lbf/in. 2 = 2116.2 lbf/ft 2
1 Pa = 1 N/m 2
Temperature The Farenheit scale is T(°F) = 1.8 T(°C) + 32
where T(°C) is the International Celsius scale.
The Rankine scale is
T(°R) = T(°F) + 459.69;
T(°R) = 1.8 {T(°C) + 273.16};
T(°R) = 1.8 T(K)
where T(K) is the Kelvin scale.
Acceleration of go = 9.8067 m/s 2 = 32.174 ft/s 2
standard gravity
Newton constant gc =
ma/F
= 32.174 lbm-ft/(lbf-s 2) for British Engineering
gc = 1 for SI
Table A.2 Scale factors
Number Prefix Symbol Example
10 6 mega M megawatt (MW)
103 kilo k kilometer (km)
10 -2 centi c centimeter (cm)
10 -3 milli m milliwatt (mW)
509
510
AIRCRAFT ENGINE DESIGN
Table A.3 Unit conversion factors
Conversion factor
British Engineering (Multiply British
System SI Engineering system
Quantity unit unit to get SI value)
Length ft m 0.3048
Mile 5280 ft 1.609 km
Nautical mile (NM) 6080 ft 1.853 km
Area ft 2 m 2 0.09290
Mass lbm kg 0.4536
slug kg 14.59
Force lbf N 4.448
Pressure and lbf/ft 2 (psf) N/m 2 (Pa) 47.88
Stress lbf/in. 2 (psi) kN/m 2 (kPa) 6.895
Den sity lbm/ft 3 kg/m 3 16.02
Temperature difference ° R K 1 / 1.8
Specific enthalpy and Btu/lbm kJ/kg 2.326
fuel heating value
Specific heat
(Cp, Cv)
Gas constant
(gc R)
Rotational speed
Specific thrust
(F/~n)
Thrust specific
fuel consumption (S)
Power
Power specific
fuel consumption
(Se)
Btu/(lbm-°R) kJ/(kg-K) 4.187
ft2[(S 2 _o
R)
m2/(s 2-K)
0.1672
rpm rad/s 2rr/60 = 0.1047
lbf/(lbm/s) N-s/kg = m/s 9.807
lbm fuel/h lbm mg fuel/s mg 28.33
lbf thrust lbf-h N thrust N-s
hp W 745.7
Btu/hr W 0.2931
Ibm fuel/h mg/s mg 0.1690
hp W W-s
Appendix B
Altitude Tables
British Engineering (BE) units
h
(kft)
8
( P / Pstd)
Standard day Cold day Hot day Tropic day
0 0 0 0 h
(T/Ts~) (T/Ts~) (T/Ts~) (T/Tstd)
(kft)
0 1.0000 1.0000 0.7708 1.0849 1.0594 0
1 0.9644 0.9931 0.7972 1.0774 1.0520 1
2 0.9298 0.9863 0.8237 1.0700 1.0446 2
3 0.8963 0.9794 0.8501 1.0626 1.0372 3
4 0.8637 0.9725 0.8575 1.0552 1.0298 4
5 0.8321 0.9656 0.8575 1.0478 1.0224 5
6 0.8014 0.9588 0.8575 1.0404 1.0150 6
7 0.7717 0.9519 0.8575 1.0330 1.0076 7
8 0.7429 0.9450 0.8575 1.0256 1.0002 8
9 0.7149 0.9381 0.8575 1.0182 0.9928 9
10 0.6878 0.9313 0.8565 1.0108 0.9854 10
11 0.6616 0.9244 0.8502 1.0034 0.9780 11
12 0.6362 0.9175 0.8438 0.9960 0.9706 12
13 0.6115 0.9107 0.8375 0.9886 0.9632 13
14 0.5877 0.9038 0.8312 0.9812 0.9558 14
15 0.5646 0.8969 0.8248 0.9738 0.9484 15
16 0.5422 0.8901 0.8185 0.9664 0.9410 16
17 0.5206 0.8832 0.8121 0.9590 0.9336 17
18 0.4997 0.8763 0.8058 0.9516 0.9262 18
19 0.4795 0.8695 0.7994 0.9442 0.9188 19
20 0.4599 0.8626 0.7931 0.9368 0.9114 20
21 0.4410 0.8558 0.7867 0.9294 0.9040 21
22 0.4227 0.8489 0.7804 0.9220 0.8965 22
23 0.4051 0.8420 0.7740 0.9145 0.8891 23
24 0.3880 0.8352 0.7677 0.9071 0.8817 24
25 0.3716 0.8283 0.7613 0.8997 0.8743 25
26 0.3557 0.8215 0.7550 0.8923 0.8669 26
27 0.3404 0.8146 0.7486 0.8849 0.8595 27
28 0.3256 0.8077 0.7423 0.8775 0.8521 28
29 0.3113 0.8009 0.7360 0.8701 0.8447 29
30 0.2975 0.7940 0.7296 0.8627 0.8373 30
31 0.2843 0.7872 0.7233 0.8553 0.8299 31
32 0.2715 0.7803 0.7222 0.8479 0.8225 32
(continued)
511
512 AIRCRAFT ENGINE DESIGN
British Engineering (BE) units (continued)
Standard day Cold day Hot day Tropic day
h 8 0 0 0 0 h
(kft)
(P/Pstd) (T/Tstd) (T/Tstd) (T/Tstd) (T/Tstd)
(kft)
33 0.2592 0.7735 0.7222 0.8405 0.8151 33
34 0.2474 0.7666 0,7222 0.8331 0.8077 34
35 0.2360 0.7598 0.7222 0.8257 0.8003 35
36 0.2250 0.7529 0.7222 0.8183 0.7929 36
37 0.2145 0.7519 0.7222 0.8109 0.7855 37
38 0.2044 0.7519 0.7222 0.8035 0.7781 38
39 0.1949 0.7519 0.7222 0.7961 0.7707 39
40 0.1858 0.7519 0.7222 0.7939 0.7633 40
42 0.1688 0.7519 0.7222 0.7956 0.7485 42
44 0.1534 0.7519 0.7095 0.7973 0.7337 44
46 0.1394 0.7519 0.6907 0.7989 0.7188 46
48 0.1267 0.7519 0.6719 0,8006 0,7040 48
50 0.1151 0.7519 0.6532 0.8023 0.6892 50
52 0.1046 0.7519 0.6452 0.8040 0.6744 52
54 0.09507 0.7519 0.6452 0.8057 0.6768 54
56 0.08640 0.7519 0.6452 0.8074 0.6849 56
58 0.07852 0.7519 0.6452 0.8091 0.6929 58
60 0.07137 0.7519 0.6452 0.8108 0.7009 60
62 0.06486 0.7519 0.6514 0.8125 0.7090 62
64 0.05895 0.7519 0.6609 0.8142 0.7170 64
66 0.05358 0.7521 0.6704 0.8159 0.7251 66
68 0,04871 0.7542 0.6799 0.8166 0.7331 68
70 0.04429 0.7563 0.6894 0.8196 0.7396 70
72 0.04028 0,7584 0.6990 0.8226 0.7448 72
74 0.03665 0.7605 0.7075 0.8255 0.7501 74
76 0.03336 0.7626 0.7058 0.8285 0.7553 76
78 0.03036 0.7647 0.7042 0.8315 0.7606 78
80 0.02765 0.7668 0.7026 0.8344 0.7658 80
82 0.02518 0.7689 0.7009 0.8374 0.7711 82
84 0.02294 0.7710 0.6993 0.8403 0.7763 84
86 0.02091 0.7731 0.6976 0.8433 0.7816 86
88 0.01906 0.7752 0.6960 0.8463 0.7868 88
90 0.01738 0.7772 0.6944 0.8492 0.7921 90
92 0.01585 0.7793 0.6927 0.8522 0.7973 92
94 0.01446 0.7814 0.6911 0.8552 0.8026 94
96 0.01320 0.7835 0.6894 0.8581 0.8078 96
98 0.01204 0.7856 0.6878 0.8611 0.8130 98
100 0.01100 0.7877 0.6862 0.8640 0.8183 100
Density: p =
Pstd r~ = Pstd (6/0).
Speed
of sound:
a =
astd~#O.
Reference values:
Pstd
=
2116.2
lbf/ft2;
Tst d
=
518.69°R;
Pstd
=
0.07647 lbm/ft3;
ast d
=
1116 ft/s.
APPENDIX B: ALTITUDE TABLES 513
System International (SI) units
Standard day Cold day Hot day Tropic day
h ~ 0 0 0 0 h
(km) ( P / Pstd) ( T / Tsul) ( T / Tstd) ( T / Tstd) ( T / Tstd)
(km)
0 1.0000 1.0000 0.7708 1.0849 1.0594 0
0.25 0.9707 0.9944 0.7925 1.0788 1.0534 0.25
0.50 0.9421 0.9887 0.8142 1.0727 1.0473 0.50
0.75 0.9142 0.9831 0.8358 1.0666 1.0412 0.75
1.00 0.8870 0.9774 0.8575 1.0606 1.0352 1.00
1.25 0.8604 0.9718 0.8575 1.0545 1.0291 1.25
1.50 0.8345 0.9662 0.8575 1.0484 1.0230 1.50
1.75 0.8093 0.9605 0.8575 1.0423 1.0169 1.75
2.00 0.7846 0.9549 0.8575 1.0363 1.0109 2.00
2.25 0.7606 0.9493 0.8575 1.0302 1.0048 2.25
2.50 0.7372 0.9436 0.8575 1.0241 0.9987 2.50
2.75 0.7143 0.9380 0.8575 1.0180 0.9926 2.75
3.00 0.6920 0.9324 0.8575 1.0120 0.9866 3.00
3.25 0.6703 0.9267 0.8523 1.0059 0.9805 3.25
3.50 0.6492 0.9211 0.8471 0.9998 0.9744 3.50
3.75 0.6286 0.9155 0.8419 0.9938 0.9683 3.75
4.00 0.6085 0.9098 0.8367 0.9877 0.9623 4.00
4.25 0.5890 0.9042 0.8315 0.9816 0.9562 4.25
4.50 0.5700 0.8986 0.8263 0.9755 0.9501 4.50
4.75 0.5514 0.8929 0.8211 0.9695 0.9441 4.75
5.00 0.5334 0.8873 0.8159 0.9634 0.9380 5.00
5.25 0.5159 0.8817 0.8107 0.9573 0.9319 5.25
5.50 0.4988 0.8760 0.8055 0.9512 0.9258 5.50
5.75 0.4822 0.8704 0.8003 0.9452 0.9198 5.75
6.00 0.4660 0.8648 0.7951 0.9391 0.9137 6.00
6.25 0.4503 0.8592 0.7899 0.9330 0.9076 6.25
6.50 0.4350 0.8535 0.7847 0.9269 0.9015 6.50
6.75 0.4201 0.8479 0.7795 0.9209 0.8955 6.75
7.00 0.4057 0.8423 0.7742 0.9148 0.8894 7.00
7.25 0.3916 0.8366 0.7690 0.9087 0.8833 7.25
7.50 0.3780 0.8310 0.7638 0.9027 0.8773 7.50
7.75 0.3647 0.8254 0.7586 0.8966 0.8712 7.75
8.00 0.3519 0.8198 0.7534 0.8905 0.8651 8.00
8.25 0.3393 0.8141 0.7482 0.8844 0.8590 8.25
8.50 0.3272 0.8085 0.7430 0.8784 0.8530 8.50
8.75 0.3154 0.8029 0.7378 0.8723 0.8469 8.75
9.00 0.3040 0.7973 0.7326 0.8662 0.8408 9.00
9.25 0.2929 0.7916 0.7274 0.8601 0.8347 9.25
9.50 0.2821 0.7860 0.7222 0.8541 0.8287 9.50
9.75 0.2717 0.7804 0.7222 0.8480 0.8226 9.75
(continued)
514 AIRCRAFT ENGINE DESIGN
System International (SI) units (continued)
Standard day Cold day Hot day Tropic day
h ~ 0 0 0 0 h
(km) (P/Pstd) (T/Tstd) (T/Tstd) (T/Tstd) (T/Tstd) (km)
10.00 0.2615 0.7748 0.7222 0.8419 0.8165 10.00
10.25 0.2517 0.7692 0.7222 0.8358 0.8104 10.25
10.50 0.2422 0.7635 0.7222 0.8298 0.8044 10.50
10.75 0.2330 0.7579 0.7222 0.8237 0.7983 10.75
11.00 0.2240 0.7523 0.7222 0.8176 0.7922 11.00
11.25 0.2154 0.7519 0.7222 0.8116 0.7862 11.25
11.50 0.2071 0.7519 0.7222 0.8055 0.7801 11.50
11.75 0.1991 0.7519 0.7222 0.7994 0.7740 11.75
12.00 0.1915 0.7519 0.7222 0.7933 0.7679 12.00
12.25 0.1841 0.7519 0.7222 0.7940 0.7619 12.25
12.50 0.1770 0.7519 0.7222 0.7947 0.7558 12.50
12.75 0.1702 0.7519 0.7222 0.7954 0.7497 12.75
13.00 0.1636 0.7519 0.7222 0.7961 0.7436 13.00
13.25 0.1573 0.7519 0.7145 0.7968 0.7376 13.25
13.50 0.1513 0.7519 0.7068 0.7975 0.7315 13.50
13.75 0.1454 0.7519 0.6991 0.7982 0.7254 13.75
14.00 0.1399 0.7519 0.6914 0.7989 0.7193 14.00
14.25 0.1345 0.7519 0.6837 0.7996 0.7133 14.25
14.50 0.1293 0.7519 0.6760 0.8003 0.7072 14.50
14.75 0.1243 0.7519 0.6683 0.8010 0.7011 14.75
15.00 0.1195 0.7519 0.6606 0.8017 0.6951 15.00
15.25 0.1149 0.7519 0.6529 0.8024 0.6890 15.25
15.50 0.1105 0.7519 0.6452 0.8031 0.6829 15.50
15.75 0.1063 0.7519 0.6452 0.8037 0.6768 15.75
16.0 0.1022 0.7519 0.6452 0.8044 0.6708 16.0
16.5 0.09447 0.7519 0.6452 0.8058 0.6774 16.5
17.0 0.08734 0.7519 0.6452 0.8072 0.6839 17.0
17.5 0.08075 0.7519 0.6452 0.8086 0.6905 17.5
18.0 0.07466 0.7519 0.6452 0.8100 0.6971 18.0
18.5 0.06903 0.7519 0.6452 0.8114 0.7037 18.5
19.0 0.06383 0.7519 0.6531 0.8128 0.7103 19.0
19.5 0.05902 0.7519 0.6611 0.8142 0.7169 19.5
20.0 0.05457 0.7519 0.6691 0.8155 0.7235 20.0
20.5 0.05046 0.7534 0.6771 0.8169 0.7301 20.5
21.0 0.04667 0.7551 0.6851 0.8180 0.7367 21.0
21.5 0.04317 0.7568 0.6930 0.8204 0.7410 21.5
22.0 0.03995 0.7585 0.7010 0.8228 0.7453 22.0
23 0.03422 0.7620 0.7063 0.8277 0.7539 23
(continued)
APPENDIX B: ALTITUDE TABLES
System International (SI) units (continued)
515
Standard day Cold day Hot day Tropic day
h 6 0 0 0 0 h
(km) ( P / Pstd) (T / Tsta) (T / Tstd) (T / Tstd) (T / Tstd)
(km)
24 0.02933 0.7654 0.7036 0.8326 0.7625 24
25 0.02516 0.7689 0.7009 0.8374 0.7711 25
26 0.02160 0.7723 0.6982 0.8423 0.7797 26
27 0.01855 0.7758 0.6955 0.8471 0.7883 27
28 0.01595 0.7792 0.6928 0.8520 0.7969 28
29 0.01372 0.7826 0.6901 0.8568 0.8056 29
30 0.01181 0.7861 0.6874 0.8617 0.8142 30
Density: p =
Pstd a = Pstd (3/0).
Speed of sound: a =
astd ~'0.
Reference
values:Pst d
= 101,325 N/m2;
Tst d
= 288.15 K;
Pstd
= 1.225 kg/m3;
ast d
= 340.3 m/s.
US Bureau of Standards, Standard Atmosphere 1976
A computer model (e.g., ATMOS program) of the standard day atmosphere can be written
from the following material extracted from Ref. 4 of Chapter 1. All of the following is
limited to geometric altitudes below 86 km--the original tables go higher, up to 1000 km.
In addition, the correction for variation in mean molecular weight with altitude is very small
below 86 km, so is neglected.
The geometric or actual altitude (h) is related to the geo-potential altitude (z), only used
for internal calculations (a correction for variation of acceleration of gravity, used only for
pressure and density calculations), by
z = roh/(ro + h)
where r0 = 6,356.577 km is the earth's radius.
The variation of temperature (T) with geo-potential altitude is represented by a contin-
uous, piecewise linear relation,
T = Ti + Li(z - zi),
i=0through7,
with fit coefficients
i zi (kin) Li
(K/km)
0 0 -6.5
1
11 0.0
2 20 +1.0
3 32 +2.8
4 47 0.0
5 51 -2.8
6 71 -2.0
7 84.852
516 AIRCRAFT ENGINE DESIGN
with To = 288.15 K given, the corresponding values of temperature ~ can be readily
generated from the given piecewise linear curve-fit. Note that z7 corresponds exactly to
h = 86km.
The corresponding pressure (P), also a piecewise continuous function, is given by
z,)
P=Pi LifO,
or
P=Piexp , Li=O
where go = 9.80665 m/s 2, R* = 8,314.32 J/krnol-K, W0 = 28.9644 kg/kmol, and the
pressure calculations start from P0 = 101,325.0 N/m 2.
The density (p) is given simply by the ideal gas law,
PWo
p--
R*T
Cold, Hot, and Tropic Day Temperature Profiles
A computer model (e.g., ATMOS program) of the temperature profiles for Cold, Hot,
and Tropic days can be written from the following material extracted from linear curve-fits
of the data in Ref. 5 and 6 of Chapter 1. The following is limited to pressure altitudes
below 30.5 km. The variation of temperature (T) with pressure altitude is represented by a
continuous, piecewise linear relation,
T = Ti + Li(h - hi),
i = 0 through 7,
with fit coefficients
Cold day Hot day Tropic day
i hi (kin) Li (K/km) hi (kin) Li (K]km) hi (kin) Li (K]km)
0 0 +25
1 1 0
2 3 -6.0
3 9.5 0
4 13 -8.88
5 15.5 0
6 18.5 +4.6
7 22.5 -0.775
0 -7.0 0 -7.0
12 +0.8 16 +3.8
20.5 +1.4 21 +2.48
With To given below for the respective temperature profile, the corresponding values of
temperature T/can be readily generated from the given piecewise linear curve-fit.
Sea level base temperature
Day Cold Hot Tropic
To (K) 222.10 312.60 305.27
APPENDIX B: ALTITUDE TABLES 517
30
25
20
h (kin)
15
10
5
)~
/'tropic
cold .~~ic
0.6 0.7 0.8 0.9 1.0 1.1
0 (T/Tst d)
Fig. B.1
-
90
8O
70
60
50 h (kft)
40
30
20
-
10
-0
Four atmospheric temperature profiles vs pressure altitude (h).
The pressure at the pressure altitude comes directly from the standard atmosphere cal-
culation for the geometric or actual altitude (h) equal to that pressure altitude. Figure B.1
shows the three non-standard day temperature profiles versus pressure altitude along with
that of a standard day.
X
C
C
ii
I-"
t,t}
L
m
<
o
r~.
,-?,
~ o <
.... ~l~l~ ~l- ~
Nd ~XM 2MdMdd dd ddd ddd~d
o
.=.
~5
.o
<
~<
ff
E~
519