Differences between revisions 8 and 14 (spanning 6 versions)
⇤ ← Revision 8 as of 2020-12-22 01:21:34 →
Size: 11884
Editor: KeithLofstrom
Comment:
← Revision 14 as of 2020-12-22 02:29:22 → ⇥
Size: 13334
Editor: KeithLofstrom
Comment:
Deletions are marked like this. Additions are marked like this.
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|| 21 || 217.581 || 4.7289e+3 || 7.5715e-2 || 2 ||
|| 22 || 218.574 || 4.0475e+3 || 6.4510e-2 || 2 ||
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|| 32 || 228.490 || 8.8906e+2 || 1.3555e-2 || 2 ||
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|| 198 || 849.14 || e-7 || e-10 || x ||		 || 21 || 217.581 || 4.7289e+3 || 7.5715e-2 || 295.70 ||
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|| 168 || 738.07 || 2.2730e-4 || 8.525e-10 || x ||
|| 169 || 742.86 || 2.1953e-4 || 8.161e-10 || x ||
|| 170 || 747.57 || 2.1210e-4 || 7.815e-10 || x ||
|| 171 || 752.18 || 2.0499e-4 || 7.488e-10 || x ||
|| 172 || 756.71 || 1.9817e-4 || 7.178e-10 || x ||
|| 173 || 761.16 || 1.9164e-4 || 6.883e-10 || x ||
|| 174 || 765.53 || 1.8537e-4 || 6.604e-10 || x ||
|| 175 || 769.81 || 1.7936e-4 || 6.339e-10 || x ||
|| 176 || 774.01 || 1.7360e-4 || 6.086e-10 || x ||
|| 177 || 778.14 || 1.6806e-4 || 5.846e-10 || x ||
|| 178 || 782.19 || 1.6274e-4 || 5.618e-10 || x ||
|| 179 || 786.17 || 1.5763e-4 || 5.401e-10 || x ||
|| 180 || 790.07 || 1.5271e-4 || 5.194e-10 || x ||
|| 181 || 793.89 || 1.4799e-4 || 4.997e-10 || x ||
|| 182 || 797.65 || 1.5345e-4 || 4.809e-10 || x ||
|| 183 || 801.34 || 1.3907e-4 || 4.630e-10 || x ||
|| 184 || 804.96 || 1.3487e-4 || 4.459e-10 || x ||
|| 185 || 808.51 || 1.3081e-4 || 4.295e-10 || x ||
|| 186 || 812.00 || 1.2691e-4 || 4.139e-10 || x ||
|| 187 || 815.42 || 1.2315e-4 || 3.990e-10 || x ||
|| 188 || 818.78 || 1.1952e-4 || 3.847e-10 || x ||
|| 189 || 822.08 || 1.1603e-4 || 3.711e-10 || x ||
|| 190 || 825.31 || 1.1266e-4 || 3.581e-10 || x ||
|| 191 || 828.49 || 1.0940e-4 || 3.456e-10 || x ||
|| 192 || 831.61 || 1.0627e-4 || 3.336e-10 || x ||
|| 193 || 834.67 || 1.0324e-4 || 3.222e-10 || x ||
|| 194 || 837.67 || 1.0031e-4 || 3.112e-10 || x ||
|| 195 || 840.62 || 9.7491e-5 || 3.006e-10 || x ||
|| 196 || 843.51 || 9.4763e-5 || 2.905e-10 || x ||
|| 197 || 846.35 || 9.2127e-5 || 2.809e-10 || x ||
|| 198 || 849.14 || 8.9580e-5 || 2.626e-10 || x ||

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

index

temp.

pressure

density

sound

km

K

Pascals

kg/m³

m/s

0

288.150

1.0133e+5

1.2250e+0

340.29

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

86

186.87

3.7338e-1

6.958e-6

x

87

186.87

3.1259e-1

5.328e-6

x

88

186.87

2.6173e-1

4.875e-6

x

89

186.87

2.1919e-1

4.801e-6

x

90

186.87

1.8359e-1

3.416e-6

x

91

186.87

1.5381e-1

2.860e-6

x

92

186.96

1.2887e-1

2.393e-6

x

93

187.25

1.0801e-1

2.000e-6

x

94

187.74

9.0560e-2

1.670e-6

x

95

188.42

7.5966e-2

1.393e-6

x

96

189.31

6.3765e-2

1.162e-7

x

97

190.40

5.3571e-2

9.685e-7

x

98

191.72

4.5057e-2

8.071e-7

x

99

193.28

3.7948e-2

6.725e-7

x

100

195.08

3.2011e-2

5.604e-7

x

101

197.16

2.7192e-2

4.695e-7

x

102

199.53

2.3144e-2

3.935e-7

x

103

202.23

1.9742e-2

3.300e-7

x

104

205.31

1.6882e-2

2.769e-7

x

105

208.84

1.4477e-2

2.325e-7

x

106

212.89

1.2454e-2

1.954e-7

x

107

217.63

1.0751e-2

1.643e-7

x

108

223.29

9.3188e-3

1.381e-7

x

109

230.33

8.1142e-3

1.161e-7

x

110

240.00

7.1042e-3

9.708e-8

x

111

252.00

6.2614e-3

8.111e-8

x

112

264.00

5.5547e-3

6.838e-8

x

113

276.00

4.9570e-3

5.811e-8

x

114

288.00

4.4473e-3

4.975e-8

x

115

300.00

4.0096e-3

4.289e-8

x

116

312.00

3.6312e-3

3.720e-8

x

117

324.00

3.3022e-3

3.246e-8

x

118

336.00

3.0144e-3

2.847e-8

x

119

348.00

2.7615e-3

2.509e-8

x

120

360.00

2.5382e-3

2.222e-8

x

121

371.89

2.3401e-3

1.977e-8

x

122

383.55

2.1635e-3

1.767e-8

x

123

394.99

2.0055e-3

1.585e-8

x

124

406.22

1.8635e-3

1.428e-8

x

125

417.23

1.7354e-3

1.291e-8

x

126

428.04

1.6194e-3

1.171e-8

x

127

438.64

1.5141e-3

1.065e-8

x

128

449.04

1.4183e-3

9.717e-9

x

129

459.25

1.3307e-3

8.889e-9

x

130

469.27

1.2505e-3

8.152e-9

x

131

479.09

1.1769e-3

7.494e-9

x

132

488.74

1.1092e-3

6.904e-9

x

133

498.20

1.0468e-3

6.374e-9

x

134

507.48

9.8907e-4

5.897e-9

x

135

516.59

9.3568e-4

5.465e-9

x

136

525.53

8.8617e-4

5.074e-9

x

137

534.29

8.4018e-4

4.719e-9

x

138

542.80

7.9739e-4

4.396e-9

x

139

551.34

7.5751e-4

4.101e-9

x

140

559.63

7.2028e-4

3.831e-9

x

141

567.76

6.8550e-4

3.584e-9

x

142

575.73

6.5294e-4

3.358e-9

x

143

583.56

6.2243e-4

3.150e-9

x

144

591.24

5.9380e-4

2.958e-9

x

145

598.78

5.6691e-4

2.781e-9

x

146

606.17

5.4162e-4

2.618e-9

x

147

613.43

5.1781e-4

2.466e-9

x

148

620.55

4.9538e-4

2.326e-9

x

149

627.54

4.7421e-4

2.196e-9

x

150

634.39

4.5422e-4

2.076e-9

x

151

641.12

4.3533e-4

1.963e-9

x

152

647.72

4.1746e-4

1.859e-9

x

153

654.20

4.0054e-4

1.761e-9

x

154

660.56

3.8451e-4

1.670e-9

x

155

666.80

3.6930e-4

1.585e-9

x

156

672.92

3.5487e-4

1.505e-9

x

157

678.93

3.4116e-4

1.431e-9

x

158

684.83

3.2813e-4

1.361e-9

x

159

690.61

3.1574e-4

1.295e-9

x

160

696.29

3.0395e-4

1.233e-9

x

161

701.86

2.9272e-4

1.175e-9

x

162

707.33

2.8201e-4

1.121e-9

x

163

712.70

2.7181e-4

1.069e-9

x

164

717.96

2.6207e-4

1.021e-9

x

165

723.13

2.5278e-4

9.750e-10

x

166

728.20

2.4390e-4

9.319e-10

x

167

733.18

2.3541e-4

8.911e-10

x

168

738.07

2.2730e-4

8.525e-10

x

169

742.86

2.1953e-4

8.161e-10

x

170

747.57

2.1210e-4

7.815e-10

x

171

752.18

2.0499e-4

7.488e-10

x

172

756.71

1.9817e-4

7.178e-10

x

173

761.16

1.9164e-4

6.883e-10

x

174

765.53

1.8537e-4

6.604e-10

x

175

769.81

1.7936e-4

6.339e-10

x

176

774.01

1.7360e-4

6.086e-10

x

177

778.14

1.6806e-4

5.846e-10

x

178

782.19

1.6274e-4

5.618e-10

x

179

786.17

1.5763e-4

5.401e-10

x

180

790.07

1.5271e-4

5.194e-10

x

181

793.89

1.4799e-4

4.997e-10

x

182

797.65

1.5345e-4

4.809e-10

x

183

801.34

1.3907e-4

4.630e-10

x

184

804.96

1.3487e-4

4.459e-10

x

185

808.51

1.3081e-4

4.295e-10

x

186

812.00

1.2691e-4

4.139e-10

x

187

815.42

1.2315e-4

3.990e-10

x

188

818.78

1.1952e-4

3.847e-10

x

189

822.08

1.1603e-4

3.711e-10

x

190

825.31

1.1266e-4

3.581e-10

x

191

828.49

1.0940e-4

3.456e-10

x

192

831.61

1.0627e-4

3.336e-10

x

193

834.67

1.0324e-4

3.222e-10

x

194

837.67

1.0031e-4

3.112e-10

x

195

840.62

9.7491e-5

3.006e-10

x

196

843.51

9.4763e-5

2.905e-10

x

197

846.35

9.2127e-5

2.809e-10

x

198

849.14

8.9580e-5

2.626e-10

x

199

851.87

8.4736e-5

2.541e-10

x

index

temp.

pressure

density

sound

km

K

Pascals

kg/m³

m/s

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