en>Helpful Pixie Bot: ISBNs (Build KG)

2012-05-11T06:32:13Z

ISBNs (Build KG)

New page

The '''Normal shock tables''' are a series of tabulated data listing the various properties before and after the occurrence of a [[Normal shock|normal shock wave]].<ref>{{cite book | author=Anderson, John D.| title=Fundamentals of Aerodynamics | publisher=McGraw-Hill | edition=4th |year=2007 | isbn=0-07-125408-0}}</ref> 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]], <math>\gamma</math>, equal to 1.4. The upstream Mach number, <math>M_1</math>, 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 <math>\gamma</math> 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, <math>M_1</math>, and the ratio of specific heats, <math>\gamma</math>, the post normal shock Mach number, <math>M_2</math>, can be calculated using the equation below.

<math> M_2 = \sqrt{\frac{M_1^2\left(\gamma - 1\right)+2}{2\gamma M_1^2 - \left(\gamma - 1\right)}}</math>

The next equation shows the relationship between the post normal shock pressure, <math>p_2</math>, and the upstream ambient pressure, <math>p_1</math>.

<math> \frac{p_2}{p_1} = \frac{2\gamma M_1^2}{\gamma + 1} - \frac{\gamma - 1}{\gamma + 1}</math>

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

<math> \frac{\rho_2}{\rho_1} = \frac{\left(\gamma + 1\right)M_1^2}{\left(\gamma - 1\right)M_1^2 + 2}</math>

Next, the equation below shows the relationship between the post normal shock temperature, <math>T_2</math>, and the upstream ambient temperature, <math>T_1</math>.

<math> \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)}</math>

Finally, the ratio of stagnation pressures is shown below where <math>p_{01}</math> is the upstream stagnation pressure and <math>p_{02}</math> occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is [[Adiabatic Process|adiabatic]].

<math> \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}</math>

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

{| border="0" cellpadding="2"
|-
|width="100"|'''M1'''
|width="100"|'''M2'''
|width="100"|'''p2/p1'''
|width="100"|'''ρ2/ρ1'''
|width="100"|'''T2/T1'''
|width="100"|'''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==
{{reflist}}

==See also==
*[[Normal shock]]
*[[Mach number]]
*[[Compressible flow]]

==External links==
[http://cfdrl.uc.edu/WebPage/Courses/comp_flow/cf_flow_calc.html University of Cincinnati shock relations calculator]

[[Category:Aerospace engineering]]
[[Category:Aerodynamics]]

Toeplitz operator - Revision history

en>Stephen Balaban: Added link to basis (lin alg.)

en>Helpful Pixie Bot: ISBNs (Build KG)