Aeronautical Engineer Data Book Episode 14 ppt

 �







2Ss

�s

2Ss 2

due to roll rate

D



 da 2dy

(i) wing contribution – CL – cyy

y

�Fa1

F

Many contributions, but often

�s

Ss 2

1

due to yaw rate

2dy

y

0

h V

�F F



b

l

� – Lv(fin)

b

F (ii) fin contribution a1

F

�s

Ss

2

approximately CD/6

V

�F F



b

F

Table A3.3 Longitudinal aerodynamic control derivatives Small perturbation derivatives referred to aircraft wind axes

due to

elevator

– 2  S S T

 kTCL

T a2

Usually insignificantly small

force due

to elevator

–  S S T

 a2

M Pitching – V �Ta2 Principal

Compressible flow tables

o

/ = Ratio of local flow density to stagnation densityo

T/To = Ratio of static temperature to total temperature

 = (1 – M2) = Compressibility factor

V/a* = Local velocity/speed of sound at sonic point

A/A* = Local flow area/flow area at sonic point

M P/P o / o T/T o  q/P o A/A* V/a*

0.00 1.0000 1.0000 1.0000 1.0000 0.0000 – 0.0000 0.01 0.9999 1.0000 1.0000 0.9999 7.000e–5 57.8738 0.0110 0.02 0.9997 0.9998 0.9999 0.9998 2.799e–4 28.9421 0.0219 0.03 0.9994 0.9996 0.9998 0.9995 6.296e–4 19.3005 0.0329 0.04 0.9989 0.9992 0.9997 0.9992 1.119e–3 14.4815 0.0438 0.05 0.9983 0.9988 0.9995 0.9987 1.747e–3 11.5914 0.0548 0.06 0.9975 0.9982 0.9993 0.9982 2.514e–3 9.6659 0.0657 0.07 0.9966 0.9976 0.9990 0.9975 3.418e–3 8.2915 0.0766 0.08 0.9955 0.9968 0.9987 0.9968 4.460e–3 7.2616 0.0876 0.09 0.9944 0.9960 0.9984 0.9959 5.638e–3 6.4613 0.0985 0.10 0.9930 0.9950 0.9980 0.9950 6.951e–3 5.8218 0.1094 0.11 0.9916 0.9940 0.9976 0.9939 8.399e–3 5.2992 0.1204 0.12 0.9900 0.9928 0.9971 0.9928 9.979e–3 4.8643 0.1313 0.13 0.9883 0.9916 0.9966 0.9915 1.169e–2 4.4969 0.1422 0.14 0.9864 0.9903 0.9961 0.9902 1.353e–2 4.1824 0.1531 0.15 0.9844 0.9888 0.9955 0.9887 1.550e–2 3.9103 0.1639 0.16 0.9823 0.9873 0.9949 0.9871 1.760e–2 3.6727 0.1748 0.17 0.9800 0.9857 0.9943 0.9854 1.983e–2 3.4635 0.1857 0.18 0.9776 0.9840 0.9936 0.9837 2.217e–2 3.2779 0.1965 0.19 0.9751 0.9822 0.9928 0.9818 2.464e–2 3.1123 0.2074 0.20 0.9725 0.9803 0.9921 0.9798 2.723e–2 2.9635 0.2182 0.21 0.9697 0.9783 0.9913 0.9777 2.994e–2 2.8293 0.2290 0.22 0.9668 0.9762 0.9904 0.9755 3.276e–2 2.7076 0.2398 0.23 0.9638 0.9740 0.9895 0.9732 3.569e–2 2.5968 0.2506 0.24 0.9607 0.9718 0.9886 0.9708 3.874e–2 2.4956 0.2614 0.25 0.9575 0.9694 0.9877 0.9682 4.189e–2 2.4027 0.2722 0.26 0.9541 0.9670 0.9867 0.9656 4.515e–2 2.3173 0.2829 0.27 0.9506 0.9645 0.9856 0.9629 4.851e–2 2.2385 0.2936 0.28 0.9470 0.9619 0.9846 0.9600 5.197e–2 2.1656 0.3043 0.29 0.9433 0.9592 0.9835 0.9570 5.553e–2 2.0979 0.3150

Table A4.1 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

0.31 0.9355 0.9535 0.9811 0.9507 6.293e–2 1.9765 0.3364 0.32 0.9315 0.9506 0.9799 0.9474 6.677e–2 1.9219 0.3470 0.33 0.9274 0.9476 0.9787 0.9440 7.069e–2 1.8707 0.3576 0.34 0.9231 0.9445 0.9774 0.9404 7.470e–2 1.8229 0.3682 0.35 0.9188 0.9413 0.9761 0.9367 7.878e–2 1.7780 0.3788 0.36 0.9143 0.9380 0.9747 0.9330 8.295e–2 1.7358 0.3893 0.37 0.9098 0.9347 0.9733 0.9290 8.719e–2 1.6961 0.3999 0.38 0.9052 0.9313 0.9719 0.9250 9.149e–2 1.6587 0.4104 0.39 0.9004 0.9278 0.9705 0.9208 9.587e–2 1.6234 0.4209 0.40 0.8956 0.9243 0.9690 0.9165 0.1003 1.5901 0.4313 0.41 0.8907 0.9207 0.9675 0.9121 0.1048 1.5587 0.4418 0.42 0.8857 0.9170 0.9659 0.9075 0.1094 1.5289 0.4522 0.43 0.8807 0.9132 0.9643 0.9028 0.1140 1.5007 0.4626 0.44 0.8755 0.9094 0.9627 0.8980 0.1186 1.4740 0.4729 0.45 0.8703 0.9055 0.9611 0.8930 0.1234 1.4487 0.4833 0.46 0.8650 0.9016 0.9594 0.8879 0.1281 1.4246 0.4936 0.47 0.8596 0.8976 0.9577 0.8827 0.1329 1.4018 0.5038 0.48 0.8541 0.8935 0.9559 0.8773 0.1378 1.3801 0.5141 0.49 0.8486 0.8894 0.9542 0.8717 0.1426 1.3595 0.5243 0.50 0.8430 0.8852 0.9524 0.8660 0.1475 1.3398 0.5345 0.51 0.8374 0.8809 0.9506 0.8602 0.1525 1.3212 0.5447 0.52 0.8317 0.8766 0.9487 0.8542 0.1574 1.3034 0.5548 0.53 0.8259 0.8723 0.9468 0.8480 0.1624 1.2865 0.5649 0.54 0.8201 0.8679 0.9449 0.8417 0.1674 1.2703 0.5750 0.55 0.8142 0.8634 0.9430 0.8352 0.1724 1.2549 0.5851 0.56 0.8082 0.8589 0.9410 0.8285 0.1774 1.2403 0.5951 0.57 0.8022 0.8544 0.9390 0.8216 0.1825 1.2263 0.6051 0.58 0.7962 0.8498 0.9370 0.8146 0.1875 1.2130 0.6150 0.59 0.7901 0.8451 0.9349 0.8074 0.1925 1.2003 0.6249 0.60 0.7840 0.8405 0.9328 0.8000 0.1976 1.1882 0.6348 0.61 0.7778 0.8357 0.9307 0.7924 0.2026 1.1767 0.6447 0.62 0.7716 0.8310 0.9286 0.7846 0.2076 1.1656 0.6545 0.63 0.7654 0.8262 0.9265 0.7766 0.2127 1.1552 0.6643 0.64 0.7591 0.8213 0.9243 0.7684 0.2177 1.1451 0.6740 0.65 0.7528 0.8164 0.9221 0.7599 0.2226 1.1356 0.6837 0.66 0.7465 0.8115 0.9199 0.7513 0.2276 1.1265 0.6934 0.67 0.7401 0.8066 0.9176 0.7424 0.2326 1.1179 0.7031 0.68 0.7338 0.8016 0.9153 0.7332 0.2375 1.1097 0.7127 0.69 0.7274 0.7966 0.9131 0.7238 0.2424 1.1018 0.7223 0.70 0.7209 0.7916 0.9107 0.7141 0.2473 1.0944 0.7318 0.71 0.7145 0.7865 0.9084 0.7042 0.2521 1.0873 0.7413 0.72 0.7080 0.7814 0.9061 0.6940 0.2569 1.0806 0.7508 0.73 0.7016 0.7763 0.9037 0.6834 0.2617 1.0742 0.7602 0.74 0.6951 0.7712 0.9013 0.6726 0.2664 1.0681 0.7696 0.75 0.6886 0.7660 0.8989 0.6614 0.2711 1.0624 0.7789 0.76 0.6821 0.7609 0.8964 0.6499 0.2758 1.0570 0.7883 0.77 0.6756 0.7557 0.8940 0.6380 0.2804 1.0519 0.7975 0.78 0.6691 0.7505 0.8915 0.6258 0.2849 1.0471 0.8068 0.79 0.6625 0.7452 0.8890 0.6131 0.2894 1.0425 0.8160 0.80 0.6560 0.7400 0.8865 0.6000 0.2939 1.0382 0.8251 0.81 0.6495 0.7347 0.8840 0.5864 0.2983 1.0342 0.8343 0.82 0.6430 0.7295 0.8815 0.5724 0.3026 1.0305 0.8433 0.83 0.6365 0.7242 0.8789 0.5578 0.3069 1.0270 0.8524 0.84 0.6300 0.7189 0.8763 0.5426 0.3112 1.0237 0.8614 0.85 0.6235 0.7136 0.8737 0.5268 0.3153 1.0207 0.8704

Table A4.1 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

0.87 0.6106 0.7030 0.8685 0.4931 0.3235 1.0153 0.8882 0.88 0.6041 0.6977 0.8659 0.4750 0.3275 1.0129 0.8970 0.89 0.5977 0.6924 0.8632 0.4560 0.3314 1.0108 0.9058 0.90 0.5913 0.6870 0.8606 0.4359 0.3352 1.0089 0.9146 0.91 0.5849 0.6817 0.8579 0.4146 0.3390 1.0071 0.9233 0.92 0.5785 0.6764 0.8552 0.3919 0.3427 1.0056 0.9320 0.93 0.5721 0.6711 0.8525 0.3676 0.3464 1.0043 0.9407 0.94 0.5658 0.6658 0.8498 0.3412 0.3499 1.0031 0.9493 0.95 0.5595 0.6604 0.8471 0.3122 0.3534 1.0021 0.9578 0.96 0.5532 0.6551 0.8444 0.2800 0.3569 1.0014 0.9663 0.97 0.5469 0.6498 0.8416 0.2431 0.3602 1.0008 0.9748 0.98 0.5407 0.6445 0.8389 0.1990 0.3635 1.0003 0.9833 0.99 0.5345 0.6392 0.8361 0.1411 0.3667 1.0001 0.9916

o

/o = Ratio of local flow density to stagnation density (r/ro)

T/To = Ratio of static temperature to total temperature

 =   1 – M2 = Compressibility factor

V/a* = Local velocity/speed of sound at sonic point q/Po = Dynamic pressure/total pressure

A/A* = Local flow area/flow area at sonic point

M P/P o / o T/T o  q/P o A/A* V/a*

1.00 0.5283 0.6339 0.8333 0.0000 0.3698 1.0000 1.0000 1.01 0.5221 0.6287 0.8306 0.1418 0.3728 1.0001 1.0083 1.02 0.5160 0.6234 0.8278 0.2010 0.3758 1.0003 1.0166 1.03 0.5099 0.6181 0.8250 0.2468 0.3787 1.000 1.0248 1.04 0.5039 0.6129 0.8222 0.2857 0.3815 1.0013 1.0330 1.05 0.4979 0.6077 0.8193 0.3202 0.3842 1.0020 1.0411 1.06 0.4919 0.6024 0.8165 0.3516 0.3869 1.0029 1.0492 1.07 0.4860 0.5972 0.8137 0.3807 0.3895 1.0039 1.0573 1.08 0.4800 0.5920 0.8108 0.4079 0.3919 1.0051 1.0653 1.09 0.4742 0.5869 0.8080 0.4337 0.3944 1.0064 1.0733 1.10 0.4684 0.5817 0.8052 0.4583 0.3967 1.0079 1.0812 1.11 0.4626 0.5766 0.8023 0.4818 0.3990 1.0095 1.0891 1.12 0.4568 0.5714 0.7994 0.5044 0.4011 1.0113 1.0970 1.13 0.4511 0.5663 0.7966 0.5262 0.4032 1.0132 1.1048 1.14 0.4455 0.5612 0.7937 0.5474 0.4052 1.0153 1.1126 1.15 0.4398 0.5562 0.7908 0.5679 0.4072 1.0175 1.1203 1.16 0.4343 0.5511 0.7879 0.5879 0.4090 1.0198 1.1280 1.17 0.4287 0.5461 0.7851 0.6074 0.4108 1.0222 1.1356 1.18 0.4232 0.5411 0.7822 0.6264 0.4125 1.0248 1.1432 1.19 0.4178 0.5361 0.7793 0.6451 0.4141 1.0276 1.1508 1.20 0.4124 0.5311 0.7764 0.6633 0.4157 1.0304 1.1583 1.21 0.4070 0.5262 0.7735 0.6812 0.4171 1.0334 1.1658

Table A4.2 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

1.23 0.3964 0.5164 0.7677 0.7162 0.4198 1.0398 1.1806 1.24 0.3912 0.5115 0.7648 0.7332 0.4211 1.0432 1.1879 1.25 0.3861 0.5067 0.7619 0.7500 0.4223 1.0468 1.1952 1.26 0.3809 0.5019 0.7590 0.7666 0.4233 1.0504 1.2025 1.27 0.3759 0.4971 0.7561 0.7829 0.4244 1.0542 1.2097 1.28 0.3708 0.4923 0.7532 0.7990 0.4253 1.0581 1.2169 1.29 0.3658 0.4876 0.7503 0.8149 0.4262 1.0621 1.2240 1.30 0.3609 0.4829 0.7474 0.8307 0.4270 1.0663 1.2311 1.31 0.3560 0.4782 0.7445 0.8462 0.4277 1.0706 1.2382 1.32 0.3512 0.4736 0.7416 0.8616 0.4283 1.0750 1.2452 1.33 0.3464 0.4690 0.7387 0.8769 0.4289 1.0796 1.2522 1.34 0.3417 0.4644 0.7358 0.8920 0.4294 1.0842 1.2591 1.35 0.3370 0.4598 0.7329 0.9069 0.4299 1.0890 1.2660 1.36 0.3323 0.4553 0.7300 0.9217 0.4303 1.0940 1.2729 1.37 0.3277 0.4508 0.7271 0.9364 0.4306 1.0990 1.2797 1.38 0.3232 0.4463 0.7242 0.9510 0.4308 1.1042 1.2864 1.39 0.3187 0.4418 0.7213 0.9655 0.4310 1.1095 1.2932 1.40 0.3142 0.4374 0.7184 0.9798 0.4311 1.1149 1.2999 1.41 0.3098 0.4330 0.7155 0.9940 0.4312 1.1205 1.3065 1.42 0.3055 0.4287 0.7126 1.0082 0.4312 1.1262 1.3131 1.43 0.3012 0.4244 0.7097 1.0222 0.4311 1.1320 1.3197 1.44 0.2969 0.4201 0.7069 1.0361 0.4310 1.1379 1.3262 1.45 0.2927 0.4158 0.7040 1.0500 0.4308 1.1440 1.3327 1.46 0.2886 0.4116 0.7011 1.0638 0.4306 1.1501 1.3392 1.47 0.2845 0.4074 0.6982 1.0775 0.4303 1.1565 1.3456 1.48 0.2804 0.4032 0.6954 1.0911 0.4299 1.1629 1.3520 1.49 0.2764 0.3991 0.6925 1.1046 0.4295 1.1695 1.3583 1.50 0.2724 0.3950 0.6897 1.1180 0.4290 1.1762 1.3646 1.51 0.2685 0.3909 0.6868 1.1314 0.4285 1.1830 1.3708 1.52 0.2646 0.3869 0.6840 1.1447 0.4279 1.1899 1.3770 1.53 0.2608 0.3829 0.6811 1.1580 0.4273 1.1970 1.3832 1.54 0.2570 0.3789 0.6783 1.1712 0.4266 1.2042 1.3894 1.55 0.2533 0.3750 0.6754 1.1843 0.4259 1.2116 1.3955 1.56 0.2496 0.3710 0.6726 1.1973 0.4252 1.2190 1.4015 1.57 0.2459 0.3672 0.6698 1.2103 0.4243 1.2266 1.4075 1.58 0.2423 0.3633 0.6670 1.2233 0.4235 1.2344 1.4135 1.59 0.2388 0.3595 0.6642 1.2362 0.4226 1.2422 1.4195 1.60 0.2353 0.3557 0.6614 1.2490 0.4216 1.2502 1.4254 1.61 0.2318 0.3520 0.6586 1.2618 0.4206 1.2584 1.4313 1.62 0.2284 0.3483 0.6558 1.2745 0.4196 1.2666 1.4371 1.63 0.2250 0.3446 0.6530 1.2872 0.4185 1.2750 1.4429 1.64 0.2217 0.3409 0.6502 1.2998 0.4174 1.2836 1.4487 1.65 0.2184 0.3373 0.6475 1.3124 0.4162 1.2922 1.4544 1.66 0.2151 0.3337 0.6447 1.3250 0.4150 1.3010 1.4601 1.67 0.2119 0.3302 0.6419 1.3375 0.4138 1.3100 1.4657 1.68 0.2088 0.3266 0.6392 1.3500 0.4125 1.3190 1.4713 1.69 0.2057 0.3232 0.6364 1.3624 0.4112 1.3283 1.4769 1.70 0.2026 0.3197 0.6337 1.3748 0.4098 1.3376 1.4825 1.71 0.1996 0.3163 0.6310 1.3871 0.4085 1.3471 1.4880 1.72 0.1966 0.3129 0.6283 1.3994 0.4071 1.3567 1.4935 1.73 0.1936 0.3095 0.6256 1.4117 0.4056 1.3665 1.4989 1.74 0.1907 0.3062 0.6229 1.4239 0.4041 1.3764 1.5043 1.75 0.1878 0.3029 0.6202 1.4361 0.4026 1.3865 1.5097 1.76 0.1850 0.2996 0.6175 1.4483 0.4011 1.3967 1.5150 1.77 0.1822 0.2964 0.6148 1.4604 0.3996 1.4070 1.5203

Table A4.2 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

1.79 0.1767 0.2900 0.6095 1.4846 0.3964 1.4282 1.5308 1.80 0.1740 0.2868 0.6068 1.4967 0.3947 1.4390 1.5360 1.81 0.1714 0.2837 0.6041 1.5087 0.3931 1.4499 1.5411 1.82 0.1688 0.2806 0.6015 1.5207 0.3914 1.4610 1.5463 1.83 0.1662 0.2776 0.5989 1.5326 0.3897 1.4723 1.5514 1.84 0.1637 0.2745 0.5963 1.5445 0.3879 1.4836 1.5564 1.85 0.1612 0.2715 0.5936 1.5564 0.3862 1.4952 1.5614 1.86 0.1587 0.2686 0.5910 1.5683 0.3844 1.5069 1.5664 1.87 0.1563 0.2656 0.5884 1.5802 0.3826 1.5187 1.5714 1.88 0.1539 0.2627 0.5859 1.5920 0.3808 1.5308 1.5763 1.89 0.1516 0.2598 0.5833 1.6038 0.3790 1.5429 1.5812 1.90 0.1492 0.2570 0.5807 1.6155 0.3771 1.5553 1.5861 1.91 0.1470 0.2542 0.5782 1.6273 0.3753 1.5677 1.5909 1.92 0.1447 0.2514 0.5756 1.6390 0.3734 1.5804 1.5957 1.93 0.1425 0.2486 0.5731 1.6507 0.3715 1.5932 1.6005 1.94 0.1403 0.2459 0.5705 1.6624 0.3696 1.6062 1.6052 1.95 0.1381 0.2432 0.5680 1.6741 0.3677 1.6193 1.6099 1.96 0.1360 0.2405 0.5655 1.6857 0.3657 1.6326 1.6146 1.97 0.1339 0.2378 0.5630 1.6973 0.3638 1.6461 1.6192 1.98 0.1318 0.2352 0.5605 1.7089 0.3618 1.6597 1.6239 1.99 0.1298 0.2326 0.5580 1.7205 0.3598 1.6735 1.6284 2.00 0.1278 0.2300 0.5556 1.7321 0.3579 1.6875 1.6330 2.01 0.1258 0.2275 0.5531 1.7436 0.3559 1.7016 1.6375 2.02 0.1239 0.2250 0.5506 1.7551 0.3539 1.7160 1.6420 2.03 0.1220 0.2225 0.5482 1.7666 0.3518 1.7305 1.6465 2.04 0.1201 0.2200 0.5458 1.7781 0.3498 1.7451 1.6509 2.05 0.1182 0.2176 0.5433 1.7896 0.3478 1.7600 1.6553 2.06 0.1164 0.2152 0.5409 1.8010 0.3458 1.7750 1.6597 2.07 0.1146 0.2128 0.5385 1.8124 0.3437 1.7902 1.6640 2.08 0.1128 0.2104 0.5361 1.8238 0.3417 1.8056 1.6683 2.09 0.1111 0.2081 0.5337 1.8352 0.3396 1.8212 1.6726 2.10 0.1094 0.2058 0.5313 1.8466 0.3376 1.8369 1.6769 2.11 0.1077 0.2035 0.5290 1.8580 0.3355 1.8529 1.6811 2.12 0.1060 0.2013 0.5266 1.8693 0.3334 1.8690 1.6853 2.13 0.1043 0.1990 0.5243 1.8807 0.3314 1.8853 1.6895 2.14 0.1027 0.1968 0.5219 1.8920 0.3293 1.9018 1.6936 2.15 0.1011 0.1946 0.5196 1.9033 0.3272 1.9185 1.6977 2.16 9.956e–2 0.1925 0.5173 1.9146 0.3252 1.9354 1.7018 2.17 9.802e–2 0.1903 0.5150 1.9259 0.3231 1.9525 1.7059 2.18 9.649e–2 0.1882 0.5127 1.9371 0.3210 1.9698 1.7099 2.19 9.500e–2 0.1861 0.5104 1.9484 0.3189 1.9873 1.7139 2.20 9.352e–2 0.1841 0.5081 1.9596 0.3169 2.0050 1.7179 2.21 9.207e–2 0.1820 0.5059 1.9708 0.3148 2.0229 1.7219 2.22 9.064e–2 0.1800 0.5036 1.9820 0.3127 2.0409 1.7258 2.23 8.923e–2 0.1780 0.5014 1.9932 0.3106 2.0592 1.7297 2.24 8.785e–2 0.1760 0.4991 2.0044 0.3085 2.0777 1.7336 2.25 8.648e–2 0.1740 0.4969 2.0156 0.3065 2.0964 1.7374 2.26 8.514e–2 0.1721 0.4947 2.0267 0.3044 2.1153 1.7412 2.27 8.382e–2 0.1702 0.4925 2.0379 0.3023 2.1345 1.7450 2.28 8.251e–2 0.1683 0.4903 2.0490 0.3003 2.1538 1.7488 2.29 8.123e–2 0.1664 0.4881 2.0601 0.2982 2.1734 1.7526 2.30 7.997e–2 0.1646 0.4859 2.0712 0.2961 2.1931 1.7563 2.31 7.873e–2 0.1628 0.4837 2.0823 0.2941 2.2131 1.7600 2.32 7.751e–2 0.1609 0.4816 2.0934 0.2920 2.2333 1.7637 2.33 7.631e–2 0.1592 0.4794 2.1045 0.2900 2.2538 1.7673

Table A4.2 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

2.35 7.396e–2 0.1556 0.4752 2.1266 0.2859 2.2953 1.7745 2.36 7.281e–2 0.1539 0.4731 2.1377 0.2839 2.3164 1.7781 2.37 7.168e–2 0.1522 0.4709 2.1487 0.2818 2.3377 1.7817 2.38 7.057e–2 0.1505 0.4688 2.1597 0.2798 2.3593 1.7852 2.39 6.948e–2 0.1488 0.4668 2.1707 0.2778 2.3811 1.7887 2.40 6.840e–2 0.1472 0.4647 2.1817 0.2758 2.4031 1.7922 2.41 6.734e–2 0.1456 0.4626 2.1927 0.2738 2.4254 1.7956 2.42 6.630e–2 0.1439 0.4606 2.2037 0.2718 2.4479 1.7991 2.43 6.527e–2 0.1424 0.4585 2.2147 0.2698 2.4706 1.8025 2.44 6.426e–2 0.1408 0.4565 2.2257 0.2678 2.4936 1.8059 2.45 6.327e–2 0.1392 0.4544 2.2366 0.2658 2.5168 1.8092 2.46 6.229e–2 0.1377 0.4524 2.2476 0.2639 2.5403 1.8126 2.47 6.133e–2 0.1362 0.4504 2.2585 0.2619 2.5640 1.8159 2.48 6.038e–2 0.1346 0.4484 2.2694 0.2599 2.5880 1.8192 2.49 5.945e–2 0.1332 0.4464 2.2804 0.2580 2.6122 1.8225 2.50 5.853e–2 0.1317 0.4444 2.2913 0.2561 2.6367 1.8257 2.51 5.762e–2 0.1302 0.4425 2.3022 0.2541 2.6615 1.8290 2.52 5.674e–2 0.1288 0.4405 2.3131 0.2522 2.6865 1.8322 2.53 5.586e–2 0.1274 0.4386 2.3240 0.2503 2.7117 1.8354 2.54 5.500e–2 0.1260 0.4366 2.3349 0.2484 2.7372 1.8386 2.55 5.415e–2 0.1246 0.4347 2.3457 0.2465 2.7630 1.8417 2.56 5.332e–2 0.1232 0.4328 2.3566 0.2446 2.7891 1.8448 2.57 5.250e–2 0.1218 0.4309 2.3675 0.2427 2.8154 1.8479 2.58 5.169e–2 0.1205 0.4289 2.3783 0.2409 2.8420 1.8510 2.59 5.090e–2 0.1192 0.4271 2.3892 0.2390 2.8688 1.8541 2.60 5.012e–2 0.1179 0.4252 2.4000 0.2371 2.8960 1.8571 2.61 4.935e–2 0.1166 0.4233 2.4108 0.2353 2.9234 1.8602 2.62 4.859e–2 0.1153 0.4214 2.4217 0.2335 2.9511 1.8632 2.63 4.784e–2 0.1140 0.4196 2.4325 0.2317 2.9791 1.8662 2.64 4.711e–2 0.1128 0.4177 2.4433 0.2298 3.0073 1.8691 2.65 4.639e–2 0.1115 0.4159 2.4541 0.2280 3.0359 1.8721 2.66 4.568e–2 0.1103 0.4141 2.4649 0.2262 3.0647 1.8750 2.67 4.498e–2 0.1091 0.4122 2.4757 0.2245 3.0938 1.8779 2.68 4.429e–2 0.1079 0.4104 2.4864 0.2227 3.1233 1.8808 2.69 4.362e–2 0.1067 0.4086 2.4972 0.2209 3.1530 1.8837 2.70 4.295e–2 0.1056 0.4068 2.5080 0.2192 3.1830 1.8865 2.71 4.229e–2 0.1044 0.4051 2.5187 0.2174 3.2133 1.8894 2.72 4.165e–2 0.1033 0.4033 2.5295 0.2157 3.2440 1.8922 2.73 4.102e–2 0.1022 0.4015 2.5403 0.2140 3.2749 1.8950 2.74 4.039e–2 0.1010 0.3998 2.5510 0.2123 3.3061 1.8978 2.75 3.978e–2 9.994e–2 0.3980 2.5617 0.2106 3.3377 1.9005 2.76 3.917e–2 9.885e–2 0.3963 2.5725 0.2089 3.3695 1.9033 2.77 3.858e–2 9.778e–2 0.3945 2.5832 0.2072 3.4017 1.9060 2.78 3.799e–2 9.671e–2 0.3928 2.5939 0.2055 3.4342 1.9087 2.79 3.742e–2 9.566e–2 0.3911 2.6046 0.2039 3.4670 1.9114 2.80 3.685e–2 9.463e–2 0.3894 2.6153 0.2022 3.5001 1.9140 2.81 3.629e–2 9.360e–2 0.3877 2.6260 0.2006 3.5336 1.9167 2.82 3.574e–2 9.259e–2 0.3860 2.6367 0.1990 3.5674 1.9193 2.83 3.520e–2 9.158e–2 0.3844 2.6474 0.1973 3.6015 1.9219 2.84 3.467e–2 9.059e–2 0.3827 2.6581 0.1957 3.6359 1.9246 2.85 3.415e–2 8.962e–2 0.3810 2.6688 0.1941 3.6707 1.9271 2.86 3.363e–2 8.865e–2 0.3794 2.6795 0.1926 3.7058 1.9297 2.87 3.312e–2 8.769e–2 0.3777 2.6901 0.1910 3.7413 1.9323 2.88 3.263e–2 8.675e–2 0.3761 2.7008 0.1894 3.7771 1.9348 2.89 3.213e–2 8.581e–2 0.3745 2.7115 0.1879 3.8133 1.9373

Table A4.2 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

2.91 3.118e–2 8.398e–2 0.3712 2.7328 0.1848

2.92 3.071e–2 8.307e–2 0.3696 2.7434 0.1833

2.93 3.025e–2 8.218e–2 0.3681 2.7541 0.1818

2.94 2.980e–2 8.130e–2 0.3665 2.7647 0.1803

2.95 2.935e–2 8.043e–2 0.3649 2.7753 0.1788

2.96 2.891e–2 7.957e–2 0.3633 2.7860 0.1773

2.97 2.848e–2 7.872e–2 0.3618 2.7966 0.1758

2.98 2.805e–2 7.788e–2 0.3602 2.8072 0.1744

2.99 2.764e–2 7.705e–2 0.3587 2.8178 0.1729

3.00 2.722e–2 7.623e–2 0.3571 2.8284 0.1715

3.02 2.642e–2 7.461e–2 0.3541 2.8496 0.1687

3.04 2.564e–2 7.303e–2 0.3511 2.8708 0.1659

3.06 2.489e–2 7.149e–2 0.3481 2.8920 0.1631

3.08 2.416e–2 6.999e–2 0.3452 2.9131 0.1604

3.10 2.345e–2 6.852e–2 0.3422 2.9343 0.1577

3.12 2.276e–2 6.708e–2 0.3393 2.9554 0.1551

3.14 2.210e–2 6.568e–2 0.3365 2.9765 0.1525

3.16 2.146e–2 6.430e–2 0.3337 2.9976 0.1500

3.18 2.083e–2 6.296e–2 0.3309 3.0187 0.1475

3.20 2.023e–2 6.165e–2 0.3281 3.0397 0.1450

3.22 1.964e–2 6.037e–2 0.3253 3.0608 0.1426

3.24 1.908e–2 5.912e–2 0.3226 3.0818 0.1402

3.26 1.853e–2 5.790e–2 0.3199 3.1028 0.1378

3.28 1.799e–2 5.671e–2 0.3173 3.1238 0.1355

3.30 1.748e–2 5.554e–2 0.3147 3.1448 0.1332

3.32 1.698e–2 5.440e–2 0.3121 3.1658 0.1310

3.34 1.649e–2 5.329e–2 0.3095 3.1868 0.1288

3.36 1.602e–2 5.220e–2 0.3069 3.2077 0.1266

3.38 1.557e–2 5.113e–2 0.3044 3.2287 0.1245

3.40 1.512e–2 5.009e–2 0.3019 3.2496 0.1224

3.42 1.470e–2 4.908e–2 0.2995 3.2705 0.1203

3.44 1.428e–2 4.808e–2 0.2970 3.2914 0.1183

3.46 1.388e–2 4.711e–2 0.2946 3.3123 0.1163

3.48 1.349e–2 4.616e–2 0.2922 3.3332 0.1144

3.50 1.311e–2 4.523e–2 0.2899 3.3541 0.1124

3.52 1.274e–2 4.433e–2 0.2875 3.3750 0.1105

3.54 1.239e–2 4.344e–2 0.2852 3.3958 0.1087

3.56 1.204e–2 4.257e–2 0.2829 3.4167 0.1068

3.58 1.171e–2 4.172e–2 0.2806 3.4375 0.1050

3.60 1.138e–2 4.089e–2 0.2784 3.4583 0.1033

3.62 1.107e–2 4.008e–2 0.2762 3.4791 0.1015

Table A4.2 Continued

M P/P o / o T/T o  q/P o A/A* V/a*

3.94 7.137e–3 2.929e–2 0.2436 3.8110 7.755e–2 10.158 2.1303 3.96 6.948e–3 2.874e–2 0.2418 3.8317 7.627e–2 10.342 2.1329 3.98 6.764e–3 2.819e–2 0.2399 3.8523 7.500e–2 10.528 2.1355 4.00 6.586e–3 2.766e–2 0.2381 3.8730 7.376e–2 10.718 2.1381 4.04 6.245e–3 2.663e–2 0.2345 3.9143 7.135e–2 11.107 2.1431 4.08 5.923e–3 2.564e–2 0.2310 3.9556 6.902e–2 11.509 2.1480 4.12 5.619e–3 2.470e–2 0.2275 3.9968 6.677e–2 11.923 2.1529 4.16 5.333e–3 2.379e–2 0.2242 4.0380 6.460e–2 12.350 2.1576 4.20 5.062e–3 2.292e–2 0.2208 4.0792 6.251e–2 12.791 2.1622 4.24 4.806e–3 2.209e–2 0.2176 4.1204 6.049e–2 13.246 2.1667 4.28 4.565e–3 2.129e–2 0.2144 4.1615 5.854e–2 13.715 2.1711 4.32 4.337e–3 2.052e–2 0.2113 4.2027 5.666e–2 14.198 2.1754 4.36 4.121e–3 1.979e–2 0.2083 4.2438 5.484e–2 14.696 2.1796 4.40 3.918e–3 1.909e–2 0.2053 4.2849 5.309e–2 15.209 2.1837 4.44 3.725e–3 1.841e–2 0.2023 4.3259 5.140e–2 15.738 2.1877 4.48 3.543e–3 1.776e–2 0.1994 4.3670 4.977e–2 16.283 2.1917 4.52 3.370e–3 1.714e–2 0.1966 4.4080 4.820e–2 16.844 2.1955 4.56 3.207e–3 1.654e–2 0.1938 4.4490 4.668e–2 17.422 2.1993 4.60 3.053e–3 1.597e–2 0.1911 4.4900 4.521e–2 18.017 2.2030 4.64 2.906e–3 1.542e–2 0.1885 4.5310 4.380e–2 18.630 2.2066 4.68 2.768e–3 1.489e–2 0.1859 4.5719 4.243e–2 19.260 2.2102 4.72 2.637e–3 1.438e–2 0.1833 4.6129 4.112e–2 19.909 2.2136 4.76 2.512e–3 1.390e–2 0.1808 4.6538 3.984e–2 20.577 2.2170 4.80 2.394e–3 1.343e–2 0.1783 4.6947 3.861e–2 21.263 2.2204 4.84 2.283e–3 1.298e–2 0.1759 4.7356 3.743e–2 21.970 2.2236 4.88 2.177e–3 1.254e–2 0.1735 4.7764 3.628e–2 22.696 2.2268 4.92 2.076e–3 1.213e–2 0.1712 4.8173 3.518e–2 23.443 2.2300 4.96 1.981e–3 1.173e–2 0.1689 4.8581 3.411e–2 24.210 2.2331 5.00 1.890e–3 1.134e–2 0.1667 4.8990 3.308e–2 25.000 2.2361 5.10 1.683e–3 1.044e–2 0.1612 5.0010 3.065e–2 27.069 2.2433 5.20 1.501e–3 9.620e–3 0.1561 5.1029 2.842e–2 29.283 2.2503 5.30 1.341e–3 8.875e–3 0.1511 5.2048 2.637e–2 31.649 2.2569 5.40 1.200e–3 8.197e–3 0.1464 5.3066 2.449e–2 34.174 2.2631 5.50 1.075e–3 7.578e–3 0.1418 5.4083 2.276e–2 36.869 2.2691 5.60 9.643e–4 7.012e–3 0.1375 5.5100 2.117e–2 39.740 2.2748 5.70 8.663e–4 6.496e–3 0.1334 5.6116 1.970e–2 42.797 2.2803 5.80 7.794e–4 6.023e–3 0.1294 5.7131 1.835e–2 46.050 2.2855 5.90 7.021e–4 5.590e–3 0.1256 5.8146 1.711e–2 49.507 2.2905 6.00 6.334e–4 5.194e–3 0.1220 5.9161 1.596e–2 53.179 2.2953