# Normal shock tables

In aerodynamics, the normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a normal shock wave.[1] With a given upstream Mach number, the post-shock Mach number can be calculated along with the pressure, density, temperature, and stagnation pressure ratios. Such tables are useful since the equations used to calculate the properties after a normal shock are cumbersome.

The tables below have been calculated using a heat capacity ratio, $\gamma$, equal to 1.4. The upstream Mach number, $M_1$, begins at 1 and ends at 5. Although the tables could be extended over any range of Mach numbers, stopping at Mach 5 is typical since assuming $\gamma$ to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5.

## Normal shock table equations

Given an upstream Mach number, $M_1$, and the ratio of specific heats, $\gamma$, the post normal shock Mach number, $M_2$, can be calculated using the equation below.

$M_2 = \sqrt{\frac{M_1^2\left(\gamma - 1\right)+2}{2\gamma M_1^2 - \left(\gamma - 1\right)}}$

The next equation shows the relationship between the post normal shock pressure, $p_2$, and the upstream ambient pressure, $p_1$.

$\frac{p_2}{p_1} = \frac{2\gamma M_1^2}{\gamma + 1} - \frac{\gamma - 1}{\gamma + 1}$

The relationship between the post normal shock density, $\rho_2$, and the upstream ambient density, $\rho_1$ is shown next in the tables.

$\frac{\rho_2}{\rho_1} = \frac{\left(\gamma + 1\right)M_1^2}{\left(\gamma - 1\right)M_1^2 + 2}$

Next, the equation below shows the relationship between the post normal shock temperature, $T_2$, and the upstream ambient temperature, $T_1$.

$\frac{T_2}{T_1} = \frac{\left(1 + \frac{\gamma - 1}{2}M_1^2\right)\left(\frac{2\gamma}{\gamma - 1}M_1^2 - 1\right)}{M_1^2\left(\frac{2\gamma}{\gamma - 1} + \frac{\gamma - 1}{2}\right)}$

Finally, the ratio of stagnation pressures is shown below where $p_{01}$ is the upstream stagnation pressure and $p_{02}$ occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic.

$\frac{p_{02}}{p_{01}} = \left(\frac{\frac{\gamma + 1}{2}M_1^2}{1 + \frac{\gamma - 1}{2}M_1^2}\right)^\frac{\gamma}{\gamma - 1}\left(\frac{1}{\frac{2\gamma}{\gamma + 1}M_1^2 - \frac{\gamma - 1}{\gamma + 1}}\right)^\frac{1}{\gamma - 1}$

## The normal shock tables (for γ=1.4)

 M1 M2 p2/p1 ρ2/ρ1 T2/T1 p02/p01 D=DX 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0100 0.9901 1.0235 1.0167 1.0066 1.0000 1.0200 0.9805 1.0471 1.0334 1.0132 1.0000 1.0300 0.9712 1.0711 1.0502 1.0198 1.0000 1.0400 0.9620 1.0952 1.0671 1.0263 0.9999 1.0500 0.9531 1.1196 1.0840 1.0328 0.9999 1.0600 0.9444 1.1442 1.1009 1.0393 0.9998 1.0700 0.9360 1.1691 1.1179 1.0458 0.9996 1.0800 0.9277 1.1941 1.1349 1.0522 0.9994 1.0900 0.9196 1.2195 1.1520 1.0586 0.9992 1.1000 0.9118 1.2450 1.1691 1.0649 0.9989 1.1100 0.9041 1.2708 1.1862 1.0713 0.9986 1.1200 0.8966 1.2968 1.2034 1.0776 0.9982 1.1300 0.8892 1.3231 1.2206 1.0840 0.9978 1.1400 0.8820 1.3495 1.2378 1.0903 0.9973 1.1500 0.8750 1.3763 1.2550 1.0966 0.9967 1.1600 0.8682 1.4032 1.2723 1.1029 0.9961 1.1700 0.8615 1.4304 1.2896 1.1092 0.9953 1.1800 0.8549 1.4578 1.3069 1.1154 0.9946 1.1900 0.8485 1.4855 1.3243 1.1217 0.9937 1.2000 0.8422 1.5133 1.3416 1.1280 0.9928 1.2100 0.8360 1.5415 1.3590 1.1343 0.9918 1.2200 0.8300 1.5698 1.3764 1.1405 0.9907 1.2300 0.8241 1.5984 1.3938 1.1468 0.9896 1.2400 0.8183 1.6272 1.4112 1.1531 0.9884 1.2500 0.8126 1.6563 1.4286 1.1594 0.9871 1.2600 0.8071 1.6855 1.4460 1.1657 0.9857 1.2700 0.8016 1.7151 1.4634 1.1720 0.9842 1.2800 0.7963 1.7448 1.4808 1.1783 0.9827 1.2900 0.7911 1.7748 1.4983 1.1846 0.9811 1.3000 0.7860 1.8050 1.5157 1.1909 0.9794 1.3100 0.7809 1.8355 1.5331 1.1972 0.9776 1.3200 0.7760 1.8661 1.5505 1.2035 0.9758 1.3300 0.7712 1.8971 1.5680 1.2099 0.9738 1.3400 0.7664 1.9282 1.5854 1.2162 0.9718 1.3500 0.7618 1.9596 1.6028 1.2226 0.9697 1.3600 0.7572 1.9912 1.6202 1.2290 0.9676 1.3700 0.7527 2.0231 1.6376 1.2354 0.9653 1.3800 0.7483 2.0551 1.6549 1.2418 0.9630 1.3900 0.7440 2.0875 1.6723 1.2482 0.9607 1.4000 0.7397 2.1200 1.6897 1.2547 0.9582 1.4100 0.7355 2.1528 1.7070 1.2612 0.9557 1.4200 0.7314 2.1858 1.7243 1.2676 0.9531 1.4300 0.7274 2.2191 1.7416 1.2741 0.9504 1.4400 0.7235 2.2525 1.7589 1.2807 0.9476 1.4500 0.7196 2.2863 1.7761 1.2872 0.9448 1.4600 0.7157 2.3202 1.7934 1.2938 0.9420 1.4700 0.7120 2.3544 1.8106 1.3003 0.9390 1.4800 0.7083 2.3888 1.8278 1.3069 0.9360 1.4900 0.7047 2.4235 1.8449 1.3136 0.9329 1.5000 0.7011 2.4583 1.8621 1.3202 0.9298 1.5100 0.6976 2.4935 1.8792 1.3269 0.9266 1.5200 0.6941 2.5288 1.8963 1.3336 0.9233 1.5300 0.6907 2.5644 1.9133 1.3403 0.9200 1.5400 0.6874 2.6002 1.9303 1.3470 0.9166 1.5500 0.6841 2.6363 1.9473 1.3538 0.9132 1.5600 0.6809 2.6725 1.9643 1.3606 0.9097 1.5700 0.6777 2.7091 1.9812 1.3674 0.9062 1.5800 0.6746 2.7458 1.9981 1.3742 0.9026 1.5900 0.6715 2.7828 2.0149 1.3811 0.8989 1.6000 0.6684 2.8200 2.0317 1.3880 0.8952 1.6100 0.6655 2.8575 2.0485 1.3949 0.8915 1.6200 0.6625 2.8951 2.0653 1.4018 0.8877 1.6300 0.6596 2.9331 2.0820 1.4088 0.8838 1.6400 0.6568 2.9712 2.0986 1.4158 0.8799 1.6500 0.6540 3.0096 2.1152 1.4228 0.8760 1.6600 0.6512 3.0482 2.1318 1.4299 0.8720 1.6700 0.6485 3.0871 2.1484 1.4369 0.8680 1.6800 0.6458 3.1261 2.1649 1.4440 0.8639 1.6900 0.6431 3.1655 2.1813 1.4512 0.8599 1.7000 0.6405 3.2050 2.1977 1.4583 0.8557 1.7100 0.6380 3.2448 2.2141 1.4655 0.8516 1.7200 0.6355 3.2848 2.2304 1.4727 0.8474 1.7300 0.6330 3.3251 2.2467 1.4800 0.8431 1.7400 0.6305 3.3655 2.2629 1.4873 0.8389 1.7500 0.6281 3.4063 2.2791 1.4946 0.8346 1.7600 0.6257 3.4472 2.2952 1.5019 0.8302 1.7700 0.6234 3.4884 2.3113 1.5093 0.8259 1.7800 0.6210 3.5298 2.3273 1.5167 0.8215 1.7900 0.6188 3.5715 2.3433 1.5241 0.8171 1.8000 0.6165 3.6133 2.3592 1.5316 0.8127 1.8100 0.6143 3.6555 2.3751 1.5391 0.8082 1.8200 0.6121 3.6978 2.3909 1.5466 0.8038 1.8300 0.6099 3.7404 2.4067 1.5541 0.7993 1.8400 0.6078 3.7832 2.4224 1.5617 0.7948 1.8500 0.6057 3.8263 2.4381 1.5693 0.7902 1.8600 0.6036 3.8695 2.4537 1.5770 0.7857 1.8700 0.6016 3.9131 2.4693 1.5847 0.7811 1.8800 0.5996 3.9568 2.4848 1.5924 0.7765 1.8900 0.5976 4.0008 2.5003 1.6001 0.7720 1.9000 0.5956 4.0450 2.5157 1.6079 0.7674 1.9100 0.5937 4.0895 2.5310 1.6157 0.7627 1.9200 0.5918 4.1341 2.5463 1.6236 0.7581 1.9300 0.5899 4.1791 2.5616 1.6314 0.7535 1.9400 0.5880 4.2242 2.5767 1.6394 0.7488 1.9500 0.5862 4.2696 2.5919 1.6473 0.7442 1.9600 0.5844 4.3152 2.6069 1.6553 0.7395 1.9700 0.5826 4.3611 2.6220 1.6633 0.7349 1.9800 0.5808 4.4071 2.6369 1.6713 0.7302 1.9900 0.5791 4.4535 2.6518 1.6794 0.7255 2.0000 0.5774 4.5000 2.6667 1.6875 0.7209 2.0100 0.5757 4.5468 2.6815 1.6956 0.7162 2.0200 0.5740 4.5938 2.6962 1.7038 0.7115 2.0300 0.5723 4.6411 2.7109 1.7120 0.7069 2.0400 0.5707 4.6885 2.7255 1.7203 0.7022 2.0500 0.5691 4.7363 2.7400 1.7285 0.6975 2.0600 0.5675 4.7842 2.7545 1.7369 0.6928 2.0700 0.5659 4.8324 2.7689 1.7452 0.6882 2.0800 0.5643 4.8808 2.7833 1.7536 0.6835 2.0900 0.5628 4.9294 2.7976 1.7620 0.6789 2.1000 0.5613 4.9783 2.8119 1.7705 0.6742 2.1100 0.5598 5.0274 2.8261 1.7789 0.6696 2.1200 0.5583 5.0768 2.8402 1.7875 0.6649 2.1300 0.5568 5.1264 2.8543 1.7960 0.6603 2.1400 0.5554 5.1762 2.8683 1.8046 0.6557 2.1500 0.5540 5.2262 2.8823 1.8132 0.6511 2.1600 0.5525 5.2765 2.8962 1.8219 0.6464 2.1700 0.5511 5.3270 2.9101 1.8306 0.6419 2.1800 0.5498 5.3778 2.9238 1.8393 0.6373 2.1900 0.5484 5.4288 2.9376 1.8481 0.6327 2.2000 0.5471 5.4800 2.9512 1.8569 0.6281 2.2100 0.5457 5.5314 2.9648 1.8657 0.6236 2.2200 0.5444 5.5831 2.9784 1.8746 0.6191 2.2300 0.5431 5.6350 2.9918 1.8835 0.6145 2.2400 0.5418 5.6872 3.0053 1.8924 0.6100 2.2500 0.5406 5.7396 3.0186 1.9014 0.6055 2.2600 0.5393 5.7922 3.0319 1.9104 0.6011 2.2700 0.5381 5.8450 3.0452 1.9194 0.5966 2.2800 0.5368 5.8981 3.0584 1.9285 0.5921 2.2900 0.5356 5.9514 3.0715 1.9376 0.5877 2.3000 0.5344 6.0050 3.0845 1.9468 0.5833 2.3100 0.5332 6.0588 3.0976 1.9560 0.5789 2.3200 0.5321 6.1128 3.1105 1.9652 0.5745 2.3300 0.5309 6.1670 3.1234 1.9745 0.5702 2.3400 0.5297 6.2215 3.1362 1.9838 0.5658 2.3500 0.5286 6.2762 3.1490 1.9931 0.5615 2.3600 0.5275 6.3312 3.1617 2.0025 0.5572 2.3700 0.5264 6.3864 3.1743 2.0119 0.5529 2.3800 0.5253 6.4418 3.1869 2.0213 0.5486 2.3900 0.5242 6.4974 3.1994 2.0308 0.5444 2.4000 0.5231 6.5533 3.2119 2.0403 0.5401 2.4100 0.5221 6.6094 3.2243 2.0499 0.5359 2.4200 0.5210 6.6658 3.2367 2.0595 0.5317 2.4300 0.5200 6.7224 3.2489 2.0691 0.5276 2.4400 0.5189 6.7792 3.2612 2.0788 0.5234 2.4500 0.5179 6.8362 3.2733 2.0885 0.5193 2.4600 0.5169 6.8935 3.2855 2.0982 0.5152 2.4700 0.5159 6.9510 3.2975 2.1080 0.5111 2.4800 0.5149 7.0088 3.3095 2.1178 0.5071 2.4900 0.5140 7.0668 3.3215 2.1276 0.5030 2.5000 0.5130 7.1250 3.3333 2.1375 0.4990 2.5100 0.5120 7.1834 3.3452 2.1474 0.4950 2.5200 0.5111 7.2421 3.3569 2.1574 0.4911 2.5300 0.5102 7.3010 3.3686 2.1674 0.4871 2.5400 0.5092 7.3602 3.3803 2.1774 0.4832 2.5500 0.5083 7.4196 3.3919 2.1875 0.4793 2.5600 0.5074 7.4792 3.4034 2.1976 0.4754 2.5700 0.5065 7.5390 3.4149 2.2077 0.4715 2.5800 0.5056 7.5991 3.4263 2.2179 0.4677 2.5900 0.5047 7.6594 3.4377 2.2281 0.4639 2.6000 0.5039 7.7200 3.4490 2.2383 0.4601 2.6100 0.5030 7.7808 3.4602 2.2486 0.4564 2.6200 0.5022 7.8418 3.4714 2.2590 0.4526 2.6300 0.5013 7.9030 3.4826 2.2693 0.4489 2.6400 0.5005 7.9645 3.4937 2.2797 0.4452 2.6500 0.4996 8.0262 3.5047 2.2902 0.4416 2.6600 0.4988 8.0882 3.5157 2.3006 0.4379 2.6700 0.4980 8.1504 3.5266 2.3111 0.4343 2.6800 0.4972 8.2128 3.5374 2.3217 0.4307 2.6900 0.4964 8.2754 3.5482 2.3323 0.4271 2.7000 0.4956 8.3383 3.5590 2.3429 0.4236 2.7100 0.4949 8.4014 3.5697 2.3536 0.4201 2.7200 0.4941 8.4648 3.5803 2.3642 0.4166 2.7300 0.4933 8.5284 3.5909 2.3750 0.4131 2.7400 0.4926 8.5922 3.6015 2.3858 0.4097 2.7500 0.4918 8.6562 3.6119 2.3966 0.4062 2.7600 0.4911 8.7205 3.6224 2.4074 0.4028 2.7700 0.4903 8.7850 3.6327 2.4183 0.3994 2.7800 0.4896 8.8498 3.6431 2.4292 0.3961 2.7900 0.4889 8.9148 3.6533 2.4402 0.3928 2.8000 0.4882 8.9800 3.6636 2.4512 0.3895 2.8100 0.4875 9.0454 3.6737 2.4622 0.3862 2.8200 0.4868 9.1111 3.6838 2.4733 0.3829 2.8300 0.4861 9.1770 3.6939 2.4844 0.3797 2.8400 0.4854 9.2432 3.7039 2.4955 0.3765 2.8500 0.4847 9.3096 3.7139 2.5067 0.3733 2.8600 0.4840 9.3762 3.7238 2.5179 0.3701 2.8700 0.4833 9.4430 3.7336 2.5292 0.3670 2.8800 0.4827 9.5101 3.7434 2.5405 0.3639 2.8900 0.4820 9.5774 3.7532 2.5518 0.3608 2.9000 0.4814 9.6450 3.7629 2.5632 0.3577 2.9100 0.4807 9.7128 3.7725 2.5746 0.3547 2.9200 0.4801 9.7808 3.7821 2.5861 0.3517 2.9300 0.4795 9.8490 3.7917 2.5976 0.3487 2.9400 0.4788 9.9175 3.8012 2.6091 0.3457 2.9500 0.4782 9.9862 3.8106 2.6206 0.3428 2.9600 0.4776 10.0552 3.8200 2.6322 0.3398 2.9700 0.4770 10.1244 3.8294 2.6439 0.3369 2.9800 0.4764 10.1938 3.8387 2.6555 0.3340 2.9900 0.4758 10.2634 3.8479 2.6673 0.3312 3.0000 0.4752 10.3333 3.8571 2.6790 0.3283 3.0100 0.4746 10.4034 3.8663 2.6908 0.3255 3.0200 0.4740 10.4738 3.8754 2.7026 0.3227 3.0300 0.4734 10.5444 3.8845 2.7145 0.3200 3.0400 0.4729 10.6152 3.8935 2.7264 0.3172 3.0500 0.4723 10.6862 3.9025 2.7383 0.3145 3.0600 0.4717 10.7575 3.9114 2.7503 0.3118 3.0700 0.4712 10.8290 3.9203 2.7623 0.3091 3.0800 0.4706 10.9008 3.9291 2.7744 0.3065 3.0900 0.4701 10.9728 3.9379 2.7865 0.3038 3.1000 0.4695 11.0450 3.9466 2.7986 0.3012 3.1100 0.4690 11.1174 3.9553 2.8108 0.2986 3.1200 0.4685 11.1901 3.9639 2.8230 0.2960 3.1300 0.4679 11.2630 3.9725 2.8352 0.2935 3.1400 0.4674 11.3362 3.9811 2.8475 0.2910 3.1500 0.4669 11.4096 3.9896 2.8598 0.2885 3.1600 0.4664 11.4832 3.9981 2.8722 0.2860 3.1700 0.4659 11.5570 4.0065 2.8846 0.2835 3.1800 0.4654 11.6311 4.0149 2.8970 0.2811 3.1900 0.4648 11.7054 4.0232 2.9095 0.2786 3.2000 0.4643 11.7800 4.0315 2.9220 0.2762 3.2100 0.4639 11.8548 4.0397 2.9345 0.2738 3.2200 0.4634 11.9298 4.0479 2.9471 0.2715 3.2300 0.4629 12.0050 4.0561 2.9598 0.2691 3.2400 0.4624 12.0805 4.0642 2.9724 0.2668 3.2500 0.4619 12.1562 4.0723 2.9851 0.2645 3.2600 0.4614 12.2322 4.0803 2.9979 0.2622 3.2700 0.4610 12.3084 4.0883 3.0106 0.2600 3.2800 0.4605 12.3848 4.0963 3.0234 0.2577 3.2900 0.4600 12.4614 4.1042 3.0363 0.2555 3.3000 0.4596 12.5383 4.1120 3.0492 0.2533 3.3100 0.4591 12.6154 4.1198 3.0621 0.2511 3.3200 0.4587 12.6928 4.1276 3.0751 0.2489 3.3300 0.4582 12.7704 4.1354 3.0881 0.2468 3.3400 0.4578 12.8482 4.1431 3.1011 0.2446 3.3500 0.4573 12.9262 4.1507 3.1142 0.2425 3.3600 0.4569 13.0045 4.1583 3.1273 0.2404 3.3700 0.4565 13.0830 4.1659 3.1405 0.2383 3.3800 0.4560 13.1618 4.1734 3.1537 0.2363 3.3900 0.4556 13.2408 4.1809 3.1669 0.2342 3.4000 0.4552 13.3200 4.1884 3.1802 0.2322 3.4100 0.4548 13.3994 4.1958 3.1935 0.2302 3.4200 0.4544 13.4791 4.2032 3.2069 0.2282 3.4300 0.4540 13.5590 4.2105 3.2203 0.2263 3.4400 0.4535 13.6392 4.2179 3.2337 0.2243 3.4500 0.4531 13.7196 4.2251 3.2472 0.2224 3.4600 0.4527 13.8002 4.2323 3.2607 0.2205 3.4700 0.4523 13.8810 4.2395 3.2742 0.2186 3.4800 0.4519 13.9621 4.2467 3.2878 0.2167 3.4900 0.4515 14.0434 4.2538 3.3014 0.2148 3.5000 0.4512 14.1250 4.2609 3.3151 0.2129 3.5100 0.4508 14.2068 4.2679 3.3287 0.2111 3.5200 0.4504 14.2888 4.2749 3.3425 0.2093 3.5300 0.4500 14.3710 4.2819 3.3563 0.2075 3.5400 0.4496 14.4535 4.2888 3.3701 0.2057 3.5500 0.4492 14.5362 4.2957 3.3839 0.2039 3.5600 0.4489 14.6192 4.3026 3.3978 0.2022 3.5700 0.4485 14.7024 4.3094 3.4117 0.2004 3.5800 0.4481 14.7858 4.3162 3.4257 0.1987 3.5900 0.4478 14.8694 4.3229 3.4397 0.1970 3.6000 0.4474 14.9533 4.3296 3.4537 0.1953 3.6100 0.4471 15.0374 4.3363 3.4678 0.1936 3.6200 0.4467 15.1218 4.3429 3.4819 0.1920 3.6300 0.4463 15.2064 4.3496 3.4961 0.1903 3.6400 0.4460 15.2912 4.3561 3.5103 0.1887 3.6500 0.4456 15.3762 4.3627 3.5245 0.1871 3.6600 0.4453 15.4615 4.3692 3.5388 0.1855 3.6700 0.4450 15.5470 4.3756 3.5531 0.1839 3.6800 0.4446 15.6328 4.3821 3.5674 0.1823 3.6900 0.4443 15.7188 4.3885 3.5818 0.1807 3.7000 0.4439 15.8050 4.3949 3.5962 0.1792 3.7100 0.4436 15.8914 4.4012 3.6107 0.1777 3.7200 0.4433 15.9781 4.4075 3.6252 0.1761 3.7300 0.4430 16.0650 4.4138 3.6397 0.1746 3.7400 0.4426 16.1522 4.4200 3.6543 0.1731 3.7500 0.4423 16.2396 4.4262 3.6689 0.1717 3.7600 0.4420 16.3272 4.4324 3.6836 0.1702 3.7700 0.4417 16.4150 4.4385 3.6983 0.1687 3.7800 0.4414 16.5031 4.4447 3.7130 0.1673 3.7900 0.4410 16.5914 4.4507 3.7278 0.1659 3.8000 0.4407 16.6800 4.4568 3.7426 0.1645 3.8100 0.4404 16.7688 4.4628 3.7575 0.1631 3.8200 0.4401 16.8578 4.4688 3.7723 0.1617 3.8300 0.4398 16.9470 4.4747 3.7873 0.1603 3.8400 0.4395 17.0365 4.4807 3.8022 0.1589 3.8500 0.4392 17.1262 4.4866 3.8172 0.1576 3.8600 0.4389 17.2162 4.4924 3.8323 0.1563 3.8700 0.4386 17.3064 4.4983 3.8473 0.1549 3.8800 0.4383 17.3968 4.5041 3.8625 0.1536 3.8900 0.4380 17.4874 4.5098 3.8776 0.1523 3.9000 0.4377 17.5783 4.5156 3.8928 0.1510 3.9100 0.4375 17.6694 4.5213 3.9080 0.1497 3.9200 0.4372 17.7608 4.5270 3.9233 0.1485 3.9300 0.4369 17.8524 4.5326 3.9386 0.1472 3.9400 0.4366 17.9442 4.5383 3.9540 0.1460 3.9500 0.4363 18.0362 4.5439 3.9694 0.1448 3.9600 0.4360 18.1285 4.5494 3.9848 0.1435 3.9700 0.4358 18.2210 4.5550 4.0003 0.1423 3.9800 0.4355 18.3138 4.5605 4.0158 0.1411 3.9900 0.4352 18.4068 4.5660 4.0313 0.1399 4.0000 0.4350 18.5000 4.5714 4.0469 0.1388 4.0100 0.4347 18.5934 4.5769 4.0625 0.1376 4.0200 0.4344 18.6871 4.5823 4.0782 0.1364 4.0300 0.4342 18.7810 4.5876 4.0938 0.1353 4.0400 0.4339 18.8752 4.5930 4.1096 0.1342 4.0500 0.4336 18.9696 4.5983 4.1254 0.1330 4.0600 0.4334 19.0642 4.6036 4.1412 0.1319 4.0700 0.4331 19.1590 4.6089 4.1570 0.1308 4.0800 0.4329 19.2541 4.6141 4.1729 0.1297 4.0900 0.4326 19.3494 4.6193 4.1888 0.1286 4.1000 0.4324 19.4450 4.6245 4.2048 0.1276 4.1100 0.4321 19.5408 4.6296 4.2208 0.1265 4.1200 0.4319 19.6368 4.6348 4.2368 0.1254 4.1300 0.4316 19.7330 4.6399 4.2529 0.1244 4.1400 0.4314 19.8295 4.6450 4.2690 0.1234 4.1500 0.4311 19.9262 4.6500 4.2852 0.1223 4.1600 0.4309 20.0232 4.6550 4.3014 0.1213 4.1700 0.4306 20.1204 4.6601 4.3176 0.1203 4.1800 0.4304 20.2178 4.6650 4.3339 0.1193 4.1900 0.4302 20.3154 4.6700 4.3502 0.1183 4.2000 0.4299 20.4133 4.6749 4.3666 0.1173 4.2100 0.4297 20.5114 4.6798 4.3830 0.1164 4.2200 0.4295 20.6098 4.6847 4.3994 0.1154 4.2300 0.4292 20.7084 4.6896 4.4159 0.1144 4.2400 0.4290 20.8072 4.6944 4.4324 0.1135 4.2500 0.4288 20.9062 4.6992 4.4489 0.1126 4.2600 0.4286 21.0055 4.7040 4.4655 0.1116 4.2700 0.4283 21.1050 4.7087 4.4821 0.1107 4.2800 0.4281 21.2048 4.7135 4.4988 0.1098 4.2900 0.4279 21.3048 4.7182 4.5155 0.1089 4.3000 0.4277 21.4050 4.7229 4.5322 0.1080 4.3100 0.4275 21.5054 4.7275 4.5490 0.1071 4.3200 0.4272 21.6061 4.7322 4.5658 0.1062 4.3300 0.4270 21.7070 4.7368 4.5827 0.1054 4.3400 0.4268 21.8082 4.7414 4.5995 0.1045 4.3500 0.4266 21.9096 4.7460 4.6165 0.1036 4.3600 0.4264 22.0112 4.7505 4.6334 0.1028 4.3700 0.4262 22.1130 4.7550 4.6505 0.1020 4.3800 0.4260 22.2151 4.7595 4.6675 0.1011 4.3900 0.4258 22.3174 4.7640 4.6846 0.1003 4.4000 0.4255 22.4200 4.7685 4.7017 0.0995 4.4100 0.4253 22.5228 4.7729 4.7189 0.0987 4.4200 0.4251 22.6258 4.7773 4.7361 0.0979 4.4300 0.4249 22.7290 4.7817 4.7533 0.0971 4.4400 0.4247 22.8325 4.7861 4.7706 0.0963 4.4500 0.4245 22.9362 4.7904 4.7879 0.0955 4.4600 0.4243 23.0402 4.7948 4.8053 0.0947 4.4700 0.4241 23.1444 4.7991 4.8227 0.0940 4.4800 0.4239 23.2488 4.8034 4.8401 0.0932 4.4900 0.4237 23.3534 4.8076 4.8576 0.0924 4.5000 0.4236 23.4583 4.8119 4.8751 0.0917 4.5100 0.4234 23.5634 4.8161 4.8926 0.0910 4.5200 0.4232 23.6688 4.8203 4.9102 0.0902 4.5300 0.4230 23.7744 4.8245 4.9279 0.0895 4.5400 0.4228 23.8802 4.8287 4.9455 0.0888 4.5500 0.4226 23.9862 4.8328 4.9632 0.0881 4.5600 0.4224 24.0925 4.8369 4.9810 0.0874 4.5700 0.4222 24.1990 4.8410 4.9987 0.0867 4.5800 0.4220 24.3058 4.8451 5.0166 0.0860 4.5900 0.4219 24.4128 4.8492 5.0344 0.0853 4.6000 0.4217 24.5200 4.8532 5.0523 0.0846 4.6100 0.4215 24.6274 4.8572 5.0703 0.0839 4.6200 0.4213 24.7351 4.8612 5.0882 0.0832 4.6300 0.4211 24.8430 4.8652 5.1063 0.0826 4.6400 0.4210 24.9512 4.8692 5.1243 0.0819 4.6500 0.4208 25.0596 4.8731 5.1424 0.0813 4.6600 0.4206 25.1682 4.8771 5.1605 0.0806 4.6700 0.4204 25.2770 4.8810 5.1787 0.0800 4.6800 0.4203 25.3861 4.8849 5.1969 0.0793 4.6900 0.4201 25.4954 4.8887 5.2151 0.0787 4.7000 0.4199 25.6050 4.8926 5.2334 0.0781 4.7100 0.4197 25.7148 4.8964 5.2518 0.0775 4.7200 0.4196 25.8248 4.9002 5.2701 0.0769 4.7300 0.4194 25.9350 4.9040 5.2885 0.0762 4.7400 0.4192 26.0455 4.9078 5.3070 0.0756 4.7500 0.4191 26.1562 4.9116 5.3254 0.0750 4.7600 0.4189 26.2672 4.9153 5.3440 0.0745 4.7700 0.4187 26.3784 4.9190 5.3625 0.0739 4.7800 0.4186 26.4898 4.9227 5.3811 0.0733 4.7900 0.4184 26.6014 4.9264 5.3997 0.0727 4.8000 0.4183 26.7133 4.9301 5.4184 0.0721 4.8100 0.4181 26.8254 4.9338 5.4371 0.0716 4.8200 0.4179 26.9378 4.9374 5.4559 0.0710 4.8300 0.4178 27.0504 4.9410 5.4747 0.0705 4.8400 0.4176 27.1632 4.9446 5.4935 0.0699 4.8500 0.4175 27.2762 4.9482 5.5124 0.0694 4.8600 0.4173 27.3895 4.9518 5.5313 0.0688 4.8700 0.4172 27.5030 4.9553 5.5502 0.0683 4.8800 0.4170 27.6168 4.9589 5.5692 0.0677 4.8900 0.4169 27.7308 4.9624 5.5882 0.0672 4.9000 0.4167 27.8450 4.9659 5.6073 0.0667 4.9100 0.4165 27.9594 4.9694 5.6264 0.0662 4.9200 0.4164 28.0741 4.9728 5.6455 0.0657 4.9300 0.4163 28.1890 4.9763 5.6647 0.0652 4.9400 0.4161 28.3042 4.9797 5.6839 0.0647 4.9500 0.4160 28.4196 4.9831 5.7032 0.0642 4.9600 0.4158 28.5352 4.9865 5.7224 0.0637 4.9700 0.4157 28.6510 4.9899 5.7418 0.0632 4.9800 0.4155 28.7671 4.9933 5.7611 0.0627 4.9900 0.4154 28.8834 4.9967 5.7806 0.0622 5.0000 0.4152 29.0000 5.0000 5.8000 0.0617

## References

1. ^ Anderson, John D. (2007). Fundamentals of Aerodynamics (4th ed.). McGraw-Hill. ISBN 0-07-125408-0.