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 )

AtmosphereTable (last edited 2020-12-22 05:12:52 by KeithLofstrom)