Atmosphere

© 2009 Auld -- www.aerodynamics4students.com

Properties of the Atmosphere 1. International Standard Atmosphere (ISA). The International Standard Atmosphere (ISA) has been agreed to by many representative countries and entities in the aviation field. It is a representative model of the atmosphere and not an average. Many of the participants in aviation are in the northern hemisphere so their standard will need to be adjusted to suit local conditions elsewhere.

2. Sea Level Conditions Property

Metric unit

Imperial Unit

Pressure, P

101.3 kPa

2116.7 lbf/ft2

Density, ρ

1.225 Kg/m3

0.002378 slug/ft3

Temperature, T

15oC 288.2 K

59 oF 518 oR

Speed of Sound, a

340.3 m/s

1116.4 ft/s

Viscosity, μ

1.789 x 10-5 Kg/m/s

3.737 x 10-7 slug/ft/s

Kinematic Viscosity, ν

1.460x10-5 m2/s

1.5723x10-4 ft2/s

Thermal Conductivity, k

0.02596 W/m/K

0.015 BTU/hr/ft/oR

Gas Constant, R

287.1 J/Kg/K

1715.7 ft lbf/slug/oR

Specific Heat, Cp

1005 J/Kg/K

6005 ft lbf/slug/oR

Specific Heat, Cv

717.98 J/Kg/K

4289 ft lbf/slug/oR

Ratio of Specific Heats, γ

1.40

Gravitational Acceleration, g

9.80665 m/s2

32.174 ft/s2

3. ISA Variation with Altitude Pressure, temperature, density, viscosity and speed of sound variation for the international standard atmosphere (ISA) can be calculated for a range of altitudes from sea level upward. This is done using an exact solution to the hydrostatic equation for a column of air. The air is assumed to be a perfect gas. In the lower region, the troposphere, the atmosphere has a lapse rate (L) of 6.5K/Km . At an altitude of 36089 ft the stratosphere starts and the temperature remains constant at 217K. The hydrostatic equation, perfect gas law and the lapse rate equations are,

∂P =− g , ∂h where the variables used are, P -- Pressure (Pa) g -- Gravitational acceleration (9.8

m/s2);

P= R T and T =T o−L. h

T -- Temperature (K) TO -- Standard sea level temperature (288 K);

R -- Gas constant for air (287 m2/s2/K);

h -- Altitude above sea level (m),

L -- Lapse rate (0.0065 K/m) and

ρ -- Air density, ( Kg/m3);

Figure 1. Atmospheric Layers and Temperature Variation with Altitude. Solving the hydrostatic equation with a constant lapse rate gives the resulting pressure variation in the troposphere. g L.R

 

T P = o Po T

where sea level pressure, Po , is set at the standard 101.3 kPa. Solving the hydrostatic equation with a constant temperature gives the resulting pressure variation in the stratosphere.

P =e Ps



g hs −h RT S



where conditions with subscript (s) are values of altitude (hs), pressure (Ps) or temperature (Ts) at the tropopause, the start of the stratosphere; the line dividing the two distinct atmospheric regions.

Once pressure has been calculated at a particular altitude, density is then calculated using the perfect gas law. Viscosity and kinematic viscosity are found by applying the Sutherland law

=0.1456×10−5

T



1−

110 T



And finally speed of sound is found based on the temperature,

a= R T

Based on the above equations, several applications are available that show atmospheric properties for a specific altitude. The applications can also be used to predict Mach Number, Dynamic Pressure and other altitude dependent properties if an input speed and reference length are given. •

Atmosphere Properties Web Calculator

•

Atmosphere Properties Calculator (MS Windows Executable)

•

Table of Atmosphere Properties.

4. Variation of Local Ground Conditions. On many occasions the ground temperature and pressure will not exactly be equal to ISA standard conditions. In these cases it is possible to adjust the atmosphere model to suit local conditions. As the depth of the atmosphere is very small (125Km-150Km) local variations in temperature and pressure will substantially effect the full depth of the atmosphere. Where local sea level temperature is above 15oC an ISA+ model is used. In this model the complete atmosphere is incremented by the temperature difference between the current sea level temperature and the standard value of 15oC. For example, on a 20oC day, an ISA + 5 model is used. Temperature at all levels of the atmosphere model are incremented by 5oC. With this adjustment, the previous formulae for pressure, density, viscosity and speed of sound variation can still be used. No adjustments are made for ground surface altitude, all calculations are done based on model starting at sea level. If the local ground level locally is well above sea level then the atmospheric model will still be based on sea level and will start at the altitude of the ground compared to sea level.

5. Variation of Density due to Humidity. The density of the air for a given level of humidity can be found by applying a correction factor to the above calculated perfect gas density.

=PG . K h ,

 PG=

P RT

The correction factor, Kh, can be found by using wet and dry bulb temperature measurements to predict relative humidity as shown in the table below. The relative humidity can be used to obtain the density correction factor from the following graph. Note that the density correction factor produced assumes approximately sea level pressure in the application of these formula.

Table 1. Relative Humidity (%) based on measured Temperature Difference, Relative Humidity (%) Temperature Difference,oC TDRY - TWET

Dry Bulb oC

1

2

3

4

5

6

7

8

9

10

11

12

81

64

46

29

13

2

84

68

52

37

22

7

4

85

71

57

43

29

16

6

86

73

60

48

35

24

11

8

87

75

63

51

40

29

19

8

10

88

77

66

55

44

34

24

15

6

12

89

78

68

58

48

39

29

21

12

14

90

79

70

60

51

42

34

26

18

10

16

90

81

71

63

54

46

38

30

23

15

8

18

91

82

73

65

57

49

41

34

27

20

14

7

20

91

83

74

66

59

51

44

37

31

24

18

12

22

92

83

76

68

61

54

47

40

34

28

22

17

24

92

84

77

69

62

56

49

43

37

31

26

20

26

92

85

78

71

64

58

51

46

40

34

29

24

28

93

85

78

72

65

59

53

48

42

37

32

27

30

93

86

79

73

67

61

55

50

44

39

35

30

32

93

86

80

74

68

62

57

51

46

41

37

32

34

93

87

81

75

69

63

58

53

48

43

39

35

36

94

87

81

75

70

64

59

54

50

45

41

37

Reference: "Handbook of Chemistry and Physics" Ed R.C.Weast, The Chemical Rubber Co., Ohio, 1964

Figure 2. Humidity Correction Factor.

Table 2. Variation of Atmosphere with Altitude Altitude

Temperature

P/Po

ρ/ρo

μ/μo

ν/νo

Speed of Sound

m

ft

oC

0

0

15.2

1

1

1

1

340.3

152

500

14.2

0.9821

0.9855

0.9973

1.0121

339.7

304

1000

13.2

0.9644

0.9711

0.9947

1.0243

339.1

457

1500

12.2

0.947

0.9568

0.992

1.0367

338.5

609

2000

11.2

0.9298

0.9428

0.9893

1.0493

338

762

2500

10.2

0.9129

0.9289

0.9866

1.0622

337.4

914

3000

9.3

0.8962

0.9151

0.9839

1.0752

336.8

1066

3500

8.3

0.8798

0.9015

0.9812

1.0884

336.2

1219

4000

7.3

0.8637

0.8881

0.9785

1.1018

335.6

1371

4500

6.3

0.8477

0.8748

0.9758

1.1155

335

1524

5000

5.3

0.832

0.8617

0.9731

1.1293

334.4

m/s

Altitude

Temperature

P/Po

ρ/ρo

μ/μo

ν/νo

Speed of Sound

1676

5500

4.3

0.8166

0.8487

0.9704

1.1434

333.8

1828

6000

3.3

0.8014

0.8359

0.9677

1.1577

333.2

1981

6500

2.3

0.7864

0.8232

0.9649

1.1722

332.6

2133

7000

1.3

0.7716

0.8106

0.9622

1.187

332

2286

7500

0.3

0.7571

0.7983

0.9595

1.202

331.4

2438

8000

-0.6

0.7428

0.786

0.9567

1.2172

330.8

2590

8500

-1.6

0.7287

0.7739

0.954

1.2327

330.2

2743

9000

-2.6

0.7148

0.762

0.9512

1.2484

329.6

2895

9500

-3.6

0.7012

0.7501

0.9485

1.2644

329

3048

10000

-4.6

0.6877

0.7385

0.9457

1.2807

328.4

3200

10500

-5.6

0.6745

0.7269

0.943

1.2972

327.8

3352

11000

-6.6

0.6614

0.7155

0.9402

1.314

327.2

3505

11500

-7.6

0.6486

0.7043

0.9374

1.331

326.6

3657

12000

-8.6

0.636

0.6932

0.9347

1.3484

326

3810

12500

-9.6

0.6236

0.6822

0.9319

1.366

325.4

3962

13000

-10.6

0.6113

0.6713

0.9291

1.384

324.7

4114

13500

-11.5

0.5993

0.6606

0.9263

1.4022

324.1

4267

14000

-12.5

0.5875

0.65

0.9235

1.4207

323.5

4419

14500

-13.5

0.5758

0.6396

0.9207

1.4396

322.9

4572

15000

-14.5

0.5643

0.6292

0.9179

1.4588

322.3

4724

15500

-15.5

0.5531

0.619

0.9151

1.4783

321.7

4876

16000

-16.5

0.542

0.609

0.9123

1.4981

321

5029

16500

-17.5

0.5311

0.599

0.9094

1.5183

320.4

5181

17000

-18.5

0.5203

0.5892

0.9066

1.5388

319.8

5334

17500

-19.5

0.5098

0.5795

0.9038

1.5596

319.2

5486

18000

-20.5

0.4994

0.5699

0.9009

1.5809

318.5

5638

18500

-21.5

0.4892

0.5604

0.8981

1.6025

317.9

Altitude

Temperature

P/Po

ρ/ρo

μ/μo

ν/νo

Speed of Sound

5791

19000

-22.4

0.4791

0.5511

0.8953

1.6244

317.3

5943

19500

-23.4

0.4693

0.5419

0.8924

1.6468

316.7

6096

20000

-24.4

0.4595

0.5328

0.8895

1.6696

316

6248

20500

-25.4

0.45

0.5238

0.8867

1.6927

315.4

6400

21000

-26.4

0.4406

0.515

0.8838

1.7163

314.8

6553

21500

-27.4

0.4314

0.5062

0.8809

1.7403

314.1

6705

22000

-28.4

0.4223

0.4976

0.8781

1.7647

313.5

6858

22500

-29.4

0.4134

0.4891

0.8752

1.7895

312.9

7010

23000

-30.4

0.4046

0.4806

0.8723

1.8148

312.2

7162

23500

-31.4

0.396

0.4723

0.8694

1.8406

311.6

7315

24000

-32.3

0.3876

0.4642

0.8665

1.8668

311

7467

24500

-33.3

0.3793

0.4561

0.8636

1.8935

310.3

7620

25000

-34.3

0.3711

0.4481

0.8607

1.9207

309.7

7772

25500

-35.3

0.3631

0.4402

0.8578

1.9484

309

7924

26000

-36.3

0.3552

0.4325

0.8548

1.9766

308.4

8077

26500

-37.3

0.3474

0.4248

0.8519

2.0053

307.7

8229

27000

-38.3

0.3398

0.4173

0.849

2.0345

307.1

8382

27500

-39.3

0.3324

0.4098

0.846

2.0643

306.4

8534

28000

-40.3

0.325

0.4025

0.8431

2.0947

305.8

8686

28500

-41.3

0.3178

0.3953

0.8402

2.1256

305.1

8839

29000

-42.3

0.3107

0.3881

0.8372

2.1571

304.5

8991

29500

-43.2

0.3038

0.3811

0.8342

2.1892

303.8

9144

30000

-44.2

0.297

0.3741

0.8313

2.2219

303.2

9296

30500

-45.2

0.2903

0.3673

0.8283

2.2553

302.5

9448

31000

-46.2

0.2837

0.3605

0.8253

2.2892

301.9

9601

31500

-47.2

0.2772

0.3539

0.8223

2.3239

301.2

9753

32000

-48.2

0.2709

0.3473

0.8194

2.3592

300.5

Altitude

Temperature

P/Po

ρ/ρo

μ/μo

ν/νo

Speed of Sound

9906

32500

-49.2

0.2647

0.3408

0.8164

2.3952

299.9

10058

33000

-50.2

0.2586

0.3345

0.8134

2.4318

299.2

10210

33500

-51.2

0.2526

0.3282

0.8104

2.4692

298.6

10363

34000

-52.2

0.2467

0.322

0.8073

2.5074

297.9

10515

34500

-53.2

0.241

0.3159

0.8043

2.5463

297.2

10668

35000

-54.1

0.2353

0.3099

0.8013

2.5859

296.5

10820

35500

-55.1

0.2298

0.3039

0.7983

2.6264

295.9

10972

36000

-56.1

0.2243

0.2981

0.7952

2.6677

295.2

11000

36089

-56.5

0.2234

0.2971

0.7947

2.6751

295.1

11277

37000

-56.5

0.2138

0.2843

0.7947

2.7948

295.1

11582

38000

-56.5

0.2038

0.271

0.7947

2.9324

295.1

11887

39000

-56.5

0.1942

0.2583

0.7947

3.0768

295.1

12192

40000

-56.5

0.1851

0.2462

0.7947

3.2283

295.1

12496

41000

-56.5

0.1764

0.2346

0.7947

3.3872

295.1

12801

42000

-56.5

0.1681

0.2236

0.7947

3.554

295.1

13106

43000

-56.5

0.1602

0.2131

0.7947

3.729

295.1

13411

44000

-56.5

0.1527

0.2031

0.7947

3.9126

295.1

13716

45000

-56.5

0.1456

0.1936

0.7947

4.1052

295.1

14020

46000

-56.5

0.1387

0.1845

0.7947

4.3073

295.1

14325

47000

-56.5

0.1322

0.1758

0.7947

4.5194

295.1

14630

48000

-56.5

0.126

0.1676

0.7947

4.7419

295.1

14935

49000

-56.5

0.1201

0.1597

0.7947

4.9754

295.1

15240

50000

-56.5

0.1145

0.1522

0.7947

5.2203

295.1

15544

51000

-56.5

0.1091

0.1451

0.7947

5.4773

295.1

15849

52000

-56.5

0.104

0.1383

0.7947

5.747

295.1

16154

53000

-56.5

0.9909-1

0.1318

0.7947

6.03

295.1

16459

54000

-56.5

0.9444-1

0.1256

0.7947

6.3268

295.1

Altitude

Temperature

P/Po

ρ/ρo

μ/μo

ν/νo

Speed of Sound

16764

55000

-56.5

0.9001-1

0.1197

0.7947

6.6383

295.1

17068

56000

-56.5

0.8579-1

0.1141

0.7947

6.9652

295.1

17373

57000

-56.5

0.8176-1

0.1087

0.7947

7.3081

295.1

17678

58000

-56.5

0.7793-1

0.1036

0.7947

7.6679

295.1

17983

59000

-56.5

0.7427-1

0.9878-1

0.7947

8.0454

295.1

18288

60000

-56.5

0.7079-1

0.9414-1

0.7947

8.4416

295.1

18592

61000

-56.5

0.6746-1

0.8972-1

0.7947

8.8572

295.1

18897

62000

-56.5

0.6430-1

0.8551-1

0.7947

9.2932

295.1

19202

63000

-56.5

0.6128-1

0.8150-1

0.7947

9.7508

295.1

19507

64000

-56.5

0.5841-1

0.7768-1

0.7947

10.231

295.1

19812

65000

-56.5

0.5566-1

0.7403-1

0.7947

10.735

295.1

20116

66000

-56.5

0.5305-1

0.7056-1

0.7947

11.263

295.1

20421

67000

-56.5

0.5056-1

0.6725-1

0.7947

11.818

295.1

20726

68000

-56.5

0.4819-1

0.6409-1

0.7947

12.399

295.1

21031

69000

-56.5

0.4593-1

0.6108-1

0.7947

13.01

295.1

21336

70000

-56.5

0.4377-1

0.5822-1

0.7947

13.65

295.1

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