Atmosphere Table
In order to compute launch drag and heating, I will eventually need a table of atmospheric model data near the equator, over the year, and hour by hour. The only tables I have now are from the US Standard Atmosphere 1976, which are computed for a reference latitude ( 45° 32' 33" = 45.5425 North ) using geopotential altitudes rather than geometric altitudes. I will also need variance and turbulence estimates, to determine how much post-launch velocity adjustment will be necessary.
For now, I would rather be vaguely right than exactly wrong. Below is a table of relevant parameters at 1 km vertical altitude steps. Vehicles will accelerate on the launch loop between 40 and 80 km altitude, and exit the remaining atmosphere following Kepler orbit elliptical trajectories.
Vehicles following those ellipses will seem to accelerate vertically, and climb out of the dense, trajectory-modifying portion of the atmosphere in minutes. Hence, the upper altitude numbers are not as important, but will be added to the table to make calculation easier. Calculations will truncate the kilometer value to an integer index value, and use the fractional part to interpolate to the next index value.
There are more sophisticated ways to do this, involving interpolations within complicated functions between "standard" geopotential altitudes, and those will be used by professionals, when launchloops are designed and built.
Parameters like undisturbed mean free path, viscosity, and composition will also matter, but will change radically during hypersonic vehicle passage. Those will be ignored for now.
Tables
Molecular weight MW=28.964 unless noted
index |
temp. |
pressure |
density |
sound |
||
km |
K |
Pascals |
kg/m³ |
m/s |
||
0 |
288.150 |
1.0133e+5 |
1.2250e+0 |
340.29 |
|
mean free path MFP=67nm, 7e9Hz collisions/sec |
1 |
281.651 |
8.9876e+4 |
1.1117e+0 |
336.43 |
||
2 |
275.154 |
7.9501e+4 |
1.0066e+0 |
332.53 |
||
3 |
268.659 |
7.0121e+4 |
9.0925e-1 |
328.58 |
||
4 |
262.150 |
6.1660e+4 |
8.1935e-1 |
324.59 |
||
5 |
255.676 |
5.4048e+4 |
7.3643e-1 |
320.55 |
||
6 |
249.187 |
4.7217e+4 |
6.6011e-1 |
316.45 |
||
7 |
242.700 |
4.1105e+4 |
5.9002e-1 |
312.31 |
||
8 |
236.215 |
3.5651e+4 |
5.2579e-1 |
308.11 |
||
9 |
229.733 |
3.0800e+4 |
4.6706e-1 |
303.85 |
||
10 |
223.252 |
2.6499e+4 |
4.1351e-1 |
299.53 |
||
11 |
216.774 |
2.2699e+4 |
3.6480e-1 |
295.15 |
||
12 |
216.650 |
1.9399e+4 |
3.1194e-1 |
295.07 |
||
13 |
216.650 |
1.6579e+4 |
2.6660e-1 |
295.07 |
||
14 |
216.650 |
1.4170e+4 |
2.2786e-1 |
295.07 |
||
15 |
216.650 |
1.2111e+4 |
1.9476e-1 |
295.07 |
||
16 |
216.650 |
1.0352e+4 |
1.6647e-1 |
295.07 |
||
17 |
216.650 |
8.8497e+3 |
1.4230e-1 |
295.07 |
||
18 |
216.650 |
7.5652e+3 |
1.2165e-1 |
295.07 |
||
19 |
216.650 |
6.4674e+3 |
1.0400e-1 |
295.07 |
||
20 |
216.650 |
5.5293e+3 |
8.8910e-2 |
295.07 |
||
21 |
217.581 |
4.7289e+3 |
7.5715e-2 |
295.70 |
||
22 |
218.574 |
4.0475e+3 |
6.4510e-2 |
296.38 |
||
23 |
219.567 |
3.4668e+3 |
5.5006e-2 |
297.05 |
||
24 |
220.560 |
2.9717e+3 |
4.6938e-2 |
297.72 |
||
25 |
221.522 |
2.5492e+3 |
4.0084e-2 |
298.39 |
||
26 |
222.554 |
2.1883e+3 |
3.4257e-2 |
299.06 |
||
27 |
223.536 |
1.8799e+3 |
2.9298e-2 |
299.72 |
||
28 |
224.527 |
1.6161e+3 |
2.5076e-2 |
300.39 |
||
29 |
225.518 |
1.3904e+3 |
2.1478e-2 |
301.05 |
||
30 |
226.509 |
1.1970e+3 |
1.8410e-2 |
301.71 |
||
31 |
227.500 |
1.0312e+3 |
1.5792e-2 |
302.37 |
||
32 |
228.490 |
8.8906e+2 |
1.3555e-2 |
303.02 |
||
33 |
230.973 |
7.6730e+2 |
1.1573e-2 |
304.67 |
||
34 |
233.743 |
6.6341e+2 |
9.8874e-3 |
306.49 |
||
35 |
236.513 |
5.7459e+2 |
8.4634e-3 |
308.30 |
||
36 |
239.282 |
4.9852e+2 |
7.2579e-3 |
310.10 |
||
37 |
242.050 |
4.3324e+2 |
6.2355e-3 |
311.89 |
||
38 |
244.818 |
3.7713e+2 |
5.3666e-3 |
313.67 |
||
39 |
247.584 |
3.2282e+2 |
4.6268e-3 |
315.43 |
||
40 |
250.350 |
2.8714e+2 |
3.9957e-3 |
317.19 |
||
41 |
253.114 |
2.5113e+2 |
3.4564e-3 |
318.94 |
||
42 |
255.878 |
2.1996e+2 |
2.9948e-3 |
320.67 |
||
43 |
258.641 |
1.9295e+2 |
2.5989e-3 |
322.40 |
||
44 |
261.403 |
1.6949e+2 |
2.2589e-3 |
324.12 |
||
45 |
264.164 |
1.4910e+2 |
1.9663e-3 |
325.82 |
||
46 |
266.925 |
1.3134e+2 |
1.7142e-3 |
327.52 |
||
47 |
269.684 |
1.1585e+2 |
1.4965e-3 |
329.21 |
||
48 |
270.650 |
1.0229e+2 |
1.3167e-3 |
329.80 |
||
49 |
270.650 |
9.0336e+1 |
1.1628e-3 |
329.80 |
||
50 |
270.650 |
7.9779e+1 |
1.0269e-3 |
329.80 |
||
51 |
270.650 |
7.0458e+1 |
9.0690e-4 |
329.80 |
||
52 |
269.031 |
6.2214e+1 |
8.0562e-4 |
328.81 |
||
53 |
266.277 |
5.4873e+1 |
7.1791e-4 |
327.12 |
||
54 |
263.524 |
4.8337e+1 |
6.3901e-4 |
325.43 |
||
55 |
260.771 |
4.2525e+1 |
5.6810e-4 |
323.72 |
||
56 |
258.019 |
3.7362e+1 |
5.0445e-4 |
322.01 |
||
57 |
255.268 |
3.2782e+1 |
4.4738e-4 |
320.29 |
||
58 |
252.518 |
2.8723e+1 |
3.9627e-4 |
318.56 |
||
59 |
249.769 |
2.5132e+1 |
3.5054e-4 |
316.82 |
||
60 |
247.021 |
2.1958e+1 |
3.0968e-4 |
315.07 |
||
61 |
244.274 |
1.9157e+1 |
2.7321e-4 |
313.32 |
||
62 |
241.527 |
1.6688e+1 |
2.4071e-4 |
311.55 |
||
63 |
238.781 |
1.4515e+1 |
2.1178e-4 |
309.77 |
||
64 |
236.036 |
1.2605e+1 |
1.8605e-4 |
307.99 |
||
65 |
233.292 |
1.0929e+1 |
1.6321e-4 |
306.19 |
||
66 |
230.549 |
9.4609e+0 |
1.4296e-4 |
304.39 |
||
67 |
226.436 |
8.1757e+0 |
1.2503e-4 |
302.57 |
||
68 |
223.695 |
7.0529e+0 |
1.0917e-4 |
300.75 |
||
69 |
222.325 |
6.0736e+0 |
9.5171e-5 |
298.91 |
||
70 |
219.585 |
5.2209e+0 |
8.2829e-5 |
297.06 |
||
71 |
216.846 |
4.4795e+0 |
7.1966e-5 |
295.20 |
||
72 |
214.263 |
3.8362e+0 |
6.2374e-5 |
293.44 |
||
73 |
212.308 |
3.2802e+0 |
5.3824e-5 |
292.10 |
||
74 |
210.353 |
2.8008e+0 |
4.6386e-5 |
290.75 |
||
75 |
208.399 |
2.3881e+0 |
3.9921e-5 |
289.40 |
||
76 |
206.446 |
2.0333e+0 |
3.4311e-5 |
288.04 |
||
77 |
204.493 |
1.7286e+0 |
2.9448e-5 |
286.67 |
||
78 |
202.541 |
1.4673e+0 |
2.5239e-5 |
285.30 |
||
79 |
200.590 |
1.2437e-0 |
2.1600e-5 |
283.92 |
||
80 |
198.639 |
1.0524e-0 |
1.8458e-5 |
282.54 |
||
81 |
196.688 |
8.8923e-1 |
1.5750e-5 |
281.15 |
||
82 |
194.739 |
7.5009e-1 |
1.3418e-5 |
279.75 |
||
83 |
192.790 |
6.3167e-1 |
1.1414e-5 |
278.35 |
||
84 |
190.481 |
5.3105e-1 |
9.6940e-6 |
276.94 |
||
85 |
188.893 |
4.4568e-1 |
8.2196e-6 |
275.52 |
|
MFP=1cm, 38KHz |
86 |
186.87 |
3.7338e-1 |
6.958e-6 |
274.04 |
est |
|
88 |
186.87 |
2.6173e-1 |
4.875e-6 |
274.04 |
est |
|
89 |
186.87 |
2.1919e-1 |
4.801e-6 |
274.04 |
est |
|
90 |
186.87 |
1.8359e-1 |
3.416e-6 |
274.04 |
est |
|
91 |
186.87 |
1.5381e-1 |
2.860e-6 |
274.04 |
est |
|
92 |
186.96 |
1.2887e-1 |
2.393e-6 |
274.11 |
est |
|
93 |
187.25 |
1.0801e-1 |
2.000e-6 |
274.32 |
est |
|
94 |
187.74 |
9.0560e-2 |
1.670e-6 |
274.68 |
est |
|
95 |
188.42 |
7.5966e-2 |
1.393e-6 |
275.18 |
est |
|
96 |
189.31 |
6.3765e-2 |
1.162e-7 |
275.82 |
est |
|
97 |
190.40 |
5.3571e-2 |
9.685e-7 |
276.62 |
est |
|
98 |
191.72 |
4.5057e-2 |
8.071e-7 |
277.57 |
est |
|
99 |
193.28 |
3.7948e-2 |
6.725e-7 |
278.70 |
est |
|
100 |
195.08 |
3.2011e-2 |
5.604e-7 |
280.00 |
est |
MFP=14cm, 2.68KHz, MW=28.40 |
101 |
197.16 |
2.7192e-2 |
4.695e-7 |
281.48 |
est |
|
102 |
199.53 |
2.3144e-2 |
3.935e-7 |
283.17 |
est |
|
103 |
202.23 |
1.9742e-2 |
3.300e-7 |
285.08 |
est |
|
104 |
205.31 |
1.6882e-2 |
2.769e-7 |
287.24 |
est |
|
105 |
208.84 |
1.4477e-2 |
2.325e-7 |
289.70 |
est |
|
106 |
212.89 |
1.2454e-2 |
1.954e-7 |
292.50 |
est |
|
107 |
217.63 |
1.0751e-2 |
1.643e-7 |
295.74 |
est |
|
108 |
223.29 |
9.3188e-3 |
1.381e-7 |
299.56 |
est |
|
109 |
230.33 |
8.1142e-3 |
1.161e-7 |
304.24 |
est |
|
110 |
240.00 |
7.1042e-3 |
9.708e-8 |
310.56 |
est |
|
111 |
252.00 |
6.2614e-3 |
8.111e-8 |
318.23 |
est |
|
112 |
264.00 |
5.5547e-3 |
6.838e-8 |
325.72 |
est |
|
113 |
276.00 |
4.9570e-3 |
5.811e-8 |
333.04 |
est |
|
114 |
288.00 |
4.4473e-3 |
4.975e-8 |
340.20 |
est |
|
115 |
300.00 |
4.0096e-3 |
4.289e-8 |
347.22 |
est |
|
116 |
312.00 |
3.6312e-3 |
3.720e-8 |
354.10 |
est |
|
117 |
324.00 |
3.3022e-3 |
3.246e-8 |
360.84 |
est |
|
118 |
336.00 |
3.0144e-3 |
2.847e-8 |
367.46 |
est |
|
119 |
348.00 |
2.7615e-3 |
2.509e-8 |
373.97 |
est |
|
120 |
360.00 |
2.5382e-3 |
2.222e-8 |
380.36 |
est |
|
121 |
371.89 |
2.3401e-3 |
1.977e-8 |
386.59 |
est |
|
122 |
383.55 |
2.1635e-3 |
1.767e-8 |
392.61 |
est |
|
123 |
394.99 |
2.0055e-3 |
1.585e-8 |
398.42 |
est |
|
124 |
406.22 |
1.8635e-3 |
1.428e-8 |
404.04 |
est |
|
125 |
417.23 |
1.7354e-3 |
1.291e-8 |
409.48 |
est |
|
126 |
428.04 |
1.6194e-3 |
1.171e-8 |
414.75 |
est |
|
127 |
438.64 |
1.5141e-3 |
1.065e-8 |
419.86 |
est |
|
128 |
449.04 |
1.4183e-3 |
9.717e-9 |
424.80 |
est |
|
129 |
459.25 |
1.3307e-3 |
8.889e-9 |
429.61 |
est |
|
130 |
469.27 |
1.2505e-3 |
8.152e-9 |
434.27 |
est |
|
131 |
479.09 |
1.1769e-3 |
7.494e-9 |
438.79 |
est |
|
132 |
488.74 |
1.1092e-3 |
6.904e-9 |
441.37 |
est |
|
133 |
498.20 |
1.0468e-3 |
6.374e-9 |
447.45 |
est |
|
134 |
507.48 |
9.8907e-4 |
5.897e-9 |
451.60 |
est |
|
135 |
516.59 |
9.3568e-4 |
5.465e-9 |
455.64 |
est |
|
136 |
525.53 |
8.8617e-4 |
5.074e-9 |
459.56 |
est |
|
137 |
534.29 |
8.4018e-4 |
4.719e-9 |
463.38 |
est |
|
138 |
542.80 |
7.9739e-4 |
4.396e-9 |
467.05 |
est |
|
139 |
551.34 |
7.5751e-4 |
4.101e-9 |
470.71 |
est |
|
140 |
559.63 |
7.2028e-4 |
3.831e-9 |
474.24 |
est |
|
141 |
567.76 |
6.8550e-4 |
3.584e-9 |
477.67 |
est |
|
142 |
575.73 |
6.5294e-4 |
3.358e-9 |
481.01 |
est |
|
143 |
583.56 |
6.2243e-4 |
3.150e-9 |
484.27 |
est |
|
144 |
591.24 |
5.9380e-4 |
2.958e-9 |
487.45 |
est |
|
145 |
598.78 |
5.6691e-4 |
2.781e-9 |
490.55 |
est |
|
146 |
606.17 |
5.4162e-4 |
2.618e-9 |
493.56 |
est |
|
147 |
613.43 |
5.1781e-4 |
2.466e-9 |
496.51 |
est |
|
148 |
620.55 |
4.9538e-4 |
2.326e-9 |
499.38 |
est |
|
149 |
627.54 |
4.7421e-4 |
2.196e-9 |
502.19 |
est |
|
150 |
634.39 |
4.5422e-4 |
2.076e-9 |
504.92 |
est |
MFP 33m, 33Hz, MW=24.1 |
151 |
641.12 |
4.3533e-4 |
1.963e-9 |
507.59 |
est |
|
152 |
647.72 |
4.1746e-4 |
1.859e-9 |
510.20 |
est |
|
153 |
654.20 |
4.0054e-4 |
1.761e-9 |
512.74 |
est |
|
154 |
660.56 |
3.8451e-4 |
1.670e-9 |
515.23 |
est |
|
155 |
666.80 |
3.6930e-4 |
1.585e-9 |
517.66 |
est |
|
156 |
672.92 |
3.5487e-4 |
1.505e-9 |
520.03 |
est |
|
157 |
678.93 |
3.4116e-4 |
1.431e-9 |
523.35 |
est |
|
158 |
684.83 |
3.2813e-4 |
1.361e-9 |
524.61 |
est |
|
159 |
690.61 |
3.1574e-4 |
1.295e-9 |
526.82 |
est |
|
160 |
696.29 |
3.0395e-4 |
1.233e-9 |
528.98 |
est |
|
161 |
701.86 |
2.9272e-4 |
1.175e-9 |
531.09 |
est |
|
162 |
707.33 |
2.8201e-4 |
1.121e-9 |
533.16 |
est |
|
163 |
712.70 |
2.7181e-4 |
1.069e-9 |
535.18 |
est |
|
164 |
717.96 |
2.6207e-4 |
1.021e-9 |
537.15 |
est |
|
165 |
723.13 |
2.5278e-4 |
9.750e-10 |
539.08 |
est |
|
166 |
728.20 |
2.4390e-4 |
9.319e-10 |
540.97 |
est |
|
167 |
733.18 |
2.3541e-4 |
8.911e-10 |
542.81 |
est |
|
168 |
738.07 |
2.2730e-4 |
8.525e-10 |
544.62 |
est |
|
169 |
742.86 |
2.1953e-4 |
8.161e-10 |
546.39 |
est |
|
170 |
747.57 |
2.1210e-4 |
7.815e-10 |
548.11 |
est |
|
171 |
752.18 |
2.0499e-4 |
7.488e-10 |
549.80 |
est |
|
172 |
756.71 |
1.9817e-4 |
7.178e-10 |
551.46 |
est |
|
173 |
761.16 |
1.9164e-4 |
6.883e-10 |
553.07 |
est |
|
174 |
765.53 |
1.8537e-4 |
6.604e-10 |
554.66 |
est |
|
175 |
769.81 |
1.7936e-4 |
6.339e-10 |
556.21 |
est |
|
176 |
774.01 |
1.7360e-4 |
6.086e-10 |
557.72 |
est |
|
177 |
778.14 |
1.6806e-4 |
5.846e-10 |
559.21 |
est |
|
178 |
782.19 |
1.6274e-4 |
5.618e-10 |
560.66 |
est |
|
179 |
786.17 |
1.5763e-4 |
5.401e-10 |
562.09 |
est |
|
180 |
790.07 |
1.5271e-4 |
5.194e-10 |
563.48 |
est |
|
181 |
793.89 |
1.4799e-4 |
4.997e-10 |
564.84 |
est |
|
182 |
797.65 |
1.5345e-4 |
4.809e-10 |
566.18 |
est |
|
183 |
801.34 |
1.3907e-4 |
4.630e-10 |
567.48 |
est |
|
184 |
804.96 |
1.3487e-4 |
4.459e-10 |
568.76 |
est |
|
185 |
808.51 |
1.3081e-4 |
4.295e-10 |
570.02 |
est |
|
186 |
812.00 |
1.2691e-4 |
4.139e-10 |
571.25 |
est |
|
187 |
815.42 |
1.2315e-4 |
3.990e-10 |
572.45 |
est |
|
188 |
818.78 |
1.1952e-4 |
3.847e-10 |
573.63 |
est |
|
189 |
822.08 |
1.1603e-4 |
3.711e-10 |
574.78 |
est |
|
190 |
825.31 |
1.1266e-4 |
3.581e-10 |
575.91 |
est |
|
191 |
828.49 |
1.0940e-4 |
3.456e-10 |
577.02 |
est |
|
192 |
831.61 |
1.0627e-4 |
3.336e-10 |
578.10 |
est |
|
193 |
834.67 |
1.0324e-4 |
3.222e-10 |
579.17 |
est |
|
194 |
837.67 |
1.0031e-4 |
3.112e-10 |
580.21 |
est |
|
195 |
840.62 |
9.7491e-5 |
3.006e-10 |
581.23 |
est |
|
196 |
843.51 |
9.4763e-5 |
2.905e-10 |
582.22 |
est |
|
197 |
846.35 |
9.2127e-5 |
2.809e-10 |
583.20 |
est |
|
198 |
849.14 |
8.9580e-5 |
2.626e-10 |
584.16 |
est |
|
199 |
851.87 |
8.7117e-5 |
2.626e-10 |
585.10 |
est |
|
200 |
854.56 |
8.4736e-5 |
2.541e-10 |
586.03 |
est |
MFP=240m, 3.9Hz, MW=21.3 |
300 |
976.01 |
8.7704e-6 |
1.916e-11 |
626.29 |
est |
MFP=2.6km, 0.42Hz, MW=17.7 |
400 |
995.83 |
1.4518e-6 |
2.803e-12 |
632.61 |
est |
MFP=16km, 72mHz, MW=16.0 |
500 |
999.24 |
3.0236e-7 |
5.215e-13 |
633.70 |
est |
MFP=77km, 16mHz, MW=14.3 |
600 |
999.85 |
8.2130e-8 |
1.137e-13 |
633.89 |
est |
MFP=280km, 4.8mHz, MW=11.5 |
700 |
999.97 |
3.1908e-8 |
3.070e-14 |
633.93 |
est |
MFP=730km, 2.2mHz, MW=8.0 |
800 |
999.99 |
1.7036e-8 |
1.136e-14 |
633.93 |
est |
MFP=1.4Mm, 1.4mHz, MW=5.5 |
900 |
1000.00 |
1.0873e-8 |
5.759e-15 |
633.94 |
est |
MFP=2.1Mm, 1.0mHz, MW=4.4 |
1000 |
1000.00 |
7.5138e-9 |
3.561e-15 |
633.94 |
est |
MFP=3.1Mm, 0.7mHz, MW=3.9 |
index |
temp. |
pressure |
density |
sound |
||
km |
K |
Pascals |
kg/m³ |
m/s |
est sound speed = sqrt( 401.875 * K )