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PRESSURE, DENSITY, AND TEMPERATURE OF THE EARTH’S ATMOSPHERE AT ALTITUDES UP TO 160 km
The study of the stratosphere by means of rockets and meteors has made it possible to obtain some information on the pressure, density, and temperature of the stratosphere.
The papers reviewed present the methods and results of rocket1,3 and meteor2 investigations in the upper layers of the atmosphere, up to 160 km above sea level.
Pressure. To measure pressure, flights of a large number of rockets were used, chiefly in the area of White Sands Proving Ground (New Mexico, U.S.A., 32° N lat., 106° W long.)1; for the period from 1946 to 1950 the measurements cover all months of the year except April, June, and July. The flights were made, as a rule, in the daytime. The measuring apparatus was placed in the nose and tail sections of the rocket, at the locations indicated in Fig. 1.
Fig. 1. Placement of manometers on the rocket.
In accordance with experiments by German investigators in aerodynamic tubes, atmospheric pressure was measured with manometers located at points \(A\) of the rocket for altitudes below 80 km, while density was determined from pressure measurements at point \(C\). Above 80 km the pressure was measured with manometers located at points \(B\), and the density from pressure measurements at points \(A\) and \(B\). The manometers located at points \(A\) record pressure free from aerodynamic distortions up to altitudes below 80 km, and at points \(B\) above 80 km.
Pressure measurements were made with four types of manometers. Pressures from 760 mm Hg to 20 mm Hg were measured with aneroid-type manometers; from 2 mm to \(3 \cdot 10^{-3}\) mm Hg—with Pirani thermal manometers.
For lower pressures in the range \(10^{-3}\)—\(10^{-5}\) mm Hg, a Phillips magnetoelectric manometer was used. Later a manometer was employed that made it possible to measure pressures in the range from 1 atmosphere to \(1 \cdot 10^{-3}\) mm Hg.
To reduce temperature effects during flight, the manometers were mounted in heavy metal housings.
The measurement data were transmitted from the rocket to the ground by means of a telemetering system operating at a frequency of 1025 MHz.
As the authors indicate, the accuracy of the manometers was not worse than 10%; the inertia, as a rule, did not exceed 0.2 sec.
The altitude of the rocket flight was determined by optical and radar measurements with an accuracy of up to 0.2 km, except for two flights, when the error reached 1 km.
Paper1 gives a large number of tables and curves showing the course of the change of pressure with altitude. According to these data, at an altitude of 160 km the pressure has a value of \(2 \cdot 10^{-6}\) mm Hg.
Figure 2 shows the dependence of the mean pressure on altitude for winter and summer. The measurement error at altitudes up to 75 km reaches 10–15%, and above 75 km, 100%.
As can be seen from the figure, the results of mean summer and winter measurements of pressure at different altitudes coincide, with the exception of the altitude interval near 65 km, in which the summer pressure is somewhat lower than the winter pressure. A comparison of the results of measurements obtained by Havens and others on the night flight of December 12, 1950, with the results of daytime measurements carried out on March 7, 1947, January 22, 1948, and January 28, 1949, shows that the difference between the mean daytime and nighttime pressures does not exceed the experimental errors.
Fig. 2. Variation of mean pressure with altitude for winter and summer.
On the basis of other measurements, a number of investigators have proposed the existence of variations of atmospheric pressure as a function of geographic location, time of day and year, and solar activity. However, there is still not a sufficient amount of experimental data necessary to establish the reliability of these variations.
Density. Information on the density of the atmosphere has been obtained mainly by two methods: by measuring the dynamic and static pressure on a rocket, and by the rate of deceleration of meteors. In the first case, for small altitudes and small free paths, density calculations were made with the aid of Rayleigh’s formula, which, for the case \(\gamma = 7/5\), leads to the following expression for the density of air:
\[ \rho = 0.144 \frac{P}{V^{2}} - \frac{0.066}{V^{2}} p + \cdots, \tag{1} \]
where \(P\) is the dynamic pressure, \(V\) is the speed of the rocket, and \(p\) is the static pressure of the air.
At high altitudes, where the mean free path of molecules is greater than the diameter of the rocket, this equation is invalid. For these altitudes the calculations were carried out by the formula
\[ \rho=\frac{\Delta P}{\sqrt{\pi v V_1}}, \tag{2} \]
where \(V_1\) is the component of the rocket velocity perpendicular to the inlet opening of the manometer, \(\Delta P\) is the difference between the readings of the manometers located respectively on the front and rear sides of the rocket relative to the direction of motion of the rocket, and \(v\) is the speed of the gas molecules.
Fig. 3. Dependence of density on altitude.
Formula (1) was used for altitudes below \(100\)—\(110\) km, and formula (2) for altitudes above \(110\) km. Figure 3 gives density values calculated by various methods from measurements carried out in the state of New Mexico. The circles represent density values obtained with rockets; the crosses, from meteor data.
As can be seen from the figure, the rocket and meteor measurements give coinciding values of the density of the stratosphere. The solid curve in Fig. 3 gives, on a logarithmic scale, the density values obtained from rocket and meteor observations at White Sands, with an accuracy of 0.15 up to altitudes of 60 km, 0.2 up to 77 km, and 0.3 up to 100 km. Above 100 km the density values are unreliable.
Whipple maintains that the difference in the density values obtained in Massachusetts (\(42.5^\circ\) N latitude) (dotted curve) and at White Sands (\(32^\circ\) N latitude) (solid curve) is explained by the difference in geographical location.
FROM CURRENT LITERATURE
Preliminary meteor data show the presence of variations in density depending on the time of year, geographical position, or solar activity.
The maximum density corresponds to the summer solstice, the minimum—to winter.
Temperature. The temperature of the upper layers of the atmosphere was not measured directly, but was calculated either from pressure or density, or from the speed of sound. In doing so, constancy of the composition of the atmosphere at all altitudes was assumed, except for the region of 80–100 km, where molecular oxygen is completely dissociated. Fig. 4 shows the course of the temperature variation with altitude, calculated by three different methods: from pressure values (solid line), from the mean
Figure legend:
— temperature obtained from pressure
—·— temperature obtained from the mean density calculated from rocket and meteor data
○ ○ ○ — temperature obtained from the speed of sound
Axes:
Vertical: altitude, km
Horizontal: temperature, °K
Fig. 4. Dependence of temperature on altitude.
density from rocket and meteor data (dash-dotted line), and from measurements of the speed of sound (circles). The measurements were carried out at White Sands (32° N latitude).
Temperature values determined from the speed of sound in the region of 60–70 km agree well with the values obtained by other methods, but give lower temperatures for altitudes of 50 and 80 km. From the figure it is clear that the mean temperature in the stratosphere (from rocket and meteor data) rises rapidly from 225°K at an altitude of 30 km to a maximum temperature of 290°K near 50 km. Then the temperature falls sharply, reaching a minimum of approximately 200°K in the region of 70–80 km. Thereafter the temperature increases continuously at least up to 160 km. (Above 120 km the determination of temperature from rocket and meteor measurements is unreliable.)
Whipple, Plexus, and others propose the existence of seasonal and geographical variations in atmospheric temperature.
In particular, it is assumed that the discrepancy between the atmospheric temperatures measured in Massachusetts (the dotted curve in Fig. 4) and the temperatures obtained in the state of New Mexico (the solid curve) is caused by the difference in geographical location.
The table gives mean values of the pressure, density, and temperature of the atmosphere at altitudes up to 160 km above sea level.
| Altitude in km above sea level | Pressure in mm Hg | Density, g/m³ | Temperature °K (N₂, O₂) M = 29 | Temperature °K (N₂, O) M = 24 | Speed of sound, m/sec | Mean free path in cm (N₂) |
|---|---|---|---|---|---|---|
| 0 | 760 | 1220 | 290 | — | 345 | 6.5·10⁻⁶ |
| 10 | 210 | 425 | 230 | — | 310 | 1.9·10⁻⁵ |
| 20 | 42 | 92 | 210 | — | 295 | 8.6·10⁻⁵ |
| 30 | 9.5 | 19 | 235 | — | 315 | 4.2·10⁻⁴ |
| 40 | 2.4 | 4.3 | 260 | — | 325 | 1.8·10⁻³ |
| 50 | 7.5·10⁻¹ | 1.3 | 270 | — | 330 | 6.1·10⁻² |
| 60 | 2.1·10⁻¹ | 3.8·10⁻¹ | 260 | — | 325 | 2.1·10⁻² |
| 70 | 5.4·10⁻² | 1.2·10⁻¹ | 210 | — | 295 | 6.6·10⁻¹ |
| 80 | 1.0·10⁻² | 2.5·10⁻² | 190 | — | 280 | 3.2·10⁻¹ |
| 90 | 1.9·10⁻³ | 4.0·10⁻³ | 210 | — | 295 | 2.0 |
| 100 | 4.2·10⁻⁴ | 8·10⁻⁴ | 240 | — | 315 | 10.0 |
| 110 | 1.2·10⁻⁴ | 2.0·10⁻⁴ | 270 | 220 | 330 | 40 |
| 120 | 3.5·10⁻⁵ | 5.0·10⁻⁵ | 330 | 270 | 370 | 1.5·10² |
| 130 | 1.5·10⁻⁵ | 2.0·10⁻⁵ | 390 | 320 | 400 | 4·10² |
| 140 | 7·10⁻⁶ | 7·10⁻⁶ | 450 | 370 | 430 | 1·10² |
| 150 | 3·10⁻⁵ | 3.0·10⁻⁶ | 510 | 420 | 460 | 2.5·10³ |
| 160 | 2·10⁻⁵ | 1.5·10⁻⁶ | 570 | 470 | 480 | 5·10³ |
Mean atmosphere up to 160 km.
Measurements of pressure and density were made on rockets at White Sands (state of New Mexico).
V. M.
Cited Literature
- R. Havens, R. Koll, H. Lagow, J. Geophys. Res. 57, No. 1 (1952).
- F. L. Whipple, Bull. Amer. Meteorol. Soc. 33, No. 1 (1952).
- B. Havens, H. Logow, Mémoires de la Société Royale des Sciences de Liège, quatrième série, t. XII, fasc. I—II, 185 (1952).