Normal shock tables
Encyclopedia
The Normal shock tables are a series of tabulated data listing the various properties before and after the occurrence of a normal shock wave. 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
, , equal to 1.4. The upstream Mach number, , 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 to be 1.4 over the entire Mach number range leads to errors over 10% beyond Mach 5.
The next equation shows the relationship between the post normal shock pressure, , and the upstream ambient pressure, .
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, , and the upstream ambient density, is shown next in the tables.
Next, the equation below shows the relationship between the post normal shock temperature, , and the upstream ambient temperature, .
Finally, the ratio of stagnation pressures is shown below where is the upstream stagnation pressure and occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic
.
Mach number
Mach number is the speed of an object moving through air, or any other fluid substance, divided by the speed of sound as it is in that substance for its particular physical conditions, including those of temperature and pressure...
, the post-shock Mach number can be calculated along with the pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
, density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, and stagnation pressure
Stagnation pressure
In fluid dynamics, stagnation pressure is the static pressure at a stagnation point in a fluid flow.At a stagnation point the fluid velocity is zero and all kinetic energy has been converted into pressure energy . Stagnation pressure is equal to the sum of the free-stream dynamic pressure and...
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
Heat capacity ratio
The heat capacity ratio or adiabatic index or ratio of specific heats, is the ratio of the heat capacity at constant pressure to heat capacity at constant volume . It is sometimes also known as the isentropic expansion factor and is denoted by \gamma or \kappa . The latter symbol kappa is...
, , equal to 1.4. The upstream Mach number, , 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 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, , and the heat capacity ratio, , the post normal shock Mach number, , can be calculated using the equation below.The next equation shows the relationship between the post normal shock pressure, , and the upstream ambient pressure, .
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, , and the upstream ambient density, is shown next in the tables.
Next, the equation below shows the relationship between the post normal shock temperature, , and the upstream ambient temperature, .
Finally, the ratio of stagnation pressures is shown below where is the upstream stagnation pressure and occurs after the normal shock. The ratio of stagnation temperatures remains constant across a normal shock since the process is adiabatic
Adiabatic process
In thermodynamics, an adiabatic process or an isocaloric process is a thermodynamic process in which the net heat transfer to or from the working fluid is zero. Such a process can occur if the container of the system has thermally-insulated walls or the process happens in an extremely short time,...
.
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 |