© 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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