Normal shock tables

Normal shock tables: 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, $γ$ , 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 $γ$ to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5.

Contents

1 Normal shock table equations

2 The normal shock tables (for γ=1.4)

3 References

4 See also

5 External links

Normal shock table equations

Given an upstream Mach number, $M 1$ , and the heat capacity ratio, $γ$ , 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, $p 1$ .

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

Is the above equation correct? It doesn't give the values in the table. And doesn't quite match calculations from p117 of Ascher Shapiro's Compressible Fluid Flow. Will get review by professional aerodynamicist shortly.

The relationship between the post normal shock density, $ρ 2$ , and the upstream ambient density, $ρ 1$ 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

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

^ Anderson, John D. (2007). Fundamentals of Aerodynamics (4th ed.). McGraw-Hill. ISBN 0071254080.

See also

Normal shock

Mach number

Compressible flow

External links

University of Cincinnati shock relations calculator

Categories:
Aerospace engineering
Aerodynamics

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Academic Dictionaries and Encyclopedias

Normal shock tables

Contents

Normal shock table equations

The normal shock tables (for γ=1.4)

References

See also

External links

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M₁	M₂	p₂/p₁	ρ₂/ρ₁	T₂/T₁	p₀₂/p₀₁
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

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The normal shock tables (for γ=1.4)

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