SUMMARY OF ROCKET DATA ON THE STRUCTURE OF THE UPPER LAYERS OF THE ATMOSPHERE AS OF JANUARY 1952

Six months ago our journal published certain data on the temperature, pressure, and density of the atmosphere up to an altitude of 160 km¹. At present a critical summary has been published of all data on temperature, pressure, and density in the upper layers of the atmosphere obtained by measurements made with instruments carried on rockets². The summary covers 138 ascents carried out from April 1946 to January 1952 by four groups of researchers.

Fig. 1. Mean air temperature at various altitudes.

The first group (R. Havens, R. Koll, and H. Lagow) measured the pressure near the surface of a rocket at certain specially selected points at which, according to hydrodynamic calculations, the pressure (in the absence of rocket yaw) coincides with the pressure \(p\) of the surrounding medium. The authors of the summary used the data from six ascents that yielded the most reliable results. The temperature was determined from the altitude gradient of \(\lg p\). In addition, data from four ascents were used during which the hydrodynamic pressure in the nose section of the rocket was measured, from which the density \(\rho\) of the surrounding atmosphere was calculated.

The second group (M. Ference et al.) determined the air density from data on the vertical velocity of sound propagation, obtained by explosions of grenades carried on rockets, and by measuring the time of pro—

propagation of the sound wave to the earth’s surface (a total of 5 rocket launches).

The third group (H. S. Sicinski, N. W. Spencer, and W. G. Dow) determined the pressure at the surface of the conical nose section of the rocket, at the vertex of the cone and at some (small) distance from it, whence (on the basis of the hydrodynamic theory of flow around a cone) the Mach number was determined and, from it, the temperature of the surrounding air. The authors of the review point out that the theory underlying these measurements apparently ceases to be valid when the rocket has significant yaw.

The fourth group (Bartman, Lik, and Schaefer) measured, during one of the ascents, the angle of the shock wave at the nose of the rocket and from this determined the Mach number. Thus, the measurements were carried out by five different methods. In order to make these data comparable, in all cases the temperature was calculated, and it was assumed that over the entire height interval the density of the air remains constant and equal to 28.966 g/mole. This temperature is denoted below by $T_{29}$.

Table I

Observed mean and adopted values of the temperature $T_{29}$ at various heights (in °K)

A summary of the data obtained is given in Table I and in Fig. 1, where, along with the data of individual groups of investigators, the statistical weight of these data is indicated (in parentheses), as well as the weighted mean value of $T_{29}$ and the adopted mean value $T_{29}$, obtained by smoothing the curve of the dependence of $T_{29}$ on the height $h$ above sea level. For heights greater than 122 km

data are based on air-density measurements by group 1. In the height interval 61–73 km the values of \(T_{29}\) obtained in this way are somewhat higher than the data from direct measurement of the external pressure, but at greater heights the values of \(T_{29}\) obtained by both methods converge.

Group 1 made measurements only by day; group 2—only at night. In forming the mean \(T_{29}\), neither the diurnal nor the seasonal, nor the latitudinal differences in the measurement conditions were taken into account. In the data of group 2 there may be a systematic error not exceeding, however, \(4^\circ\) K. Below 30 km the data are tied to measurements made with radiosondes at the test range in Belye Peski. Near the earth’s surface the data are tied to the mean annual pressure (but not temperature).

Figure 1 also shows temperature values calculated under the assumption that above 80 km the mean molecular weight \(\mu\) changes as a result of the dissociation of oxygen and nitrogen, it being arbitrarily assumed that the dissociation of oxygen changes linearly from 0 at a height of 80 km to 100% at a height of 120 km, and the dissociation of nitrogen likewise linearly from 0 at a height of 120 km to 100% at a height of 220 km.

Table II (see pp. 149, 150) gives the adopted averaged values of \(T_{29}\), \(\lg p\) (in dyn/cm\(^2\)) and \(\lg \rho\) (g/cm\(^3\)). These data correspond to a smoothed curve of dependence on height above sea level, and the accuracy of the values given is considerably higher than the accuracy of the experimental data used in their calculation. This was done in order to ensure the proper accuracy in numerical integration of these data over height.

Above 160 km the reliability of the data decreases increasingly with height. These data are based on observations of group 1, which gave a density value \(\rho = 1.0 \cdot 10^{-13}\) g/cm\(^3\) at a height of 219 km (7 Aug. 1951). This value cannot be reconciled with the value \(\rho = 1.5 \cdot 10^{-12}\) g/cm\(^3\) at a height of 156 km, if a constant temperature gradient is assumed. In this height interval the constancy of the gradient of the so-called thickness of a homogeneous atmosphere is assumed:

\[ H=\frac{RT}{g\mu}. \]

Fig. 2. Mean air pressure at various heights.

The pressure values were obtained on the basis of the values of \(T_{29}\) by numerical integration (at 2-km intervals) from the equation

\[ \frac{d(\lg p)}{dh}=-\frac{1}{H}. \]

The mean data on the dependence of pressure and density on height are given in Figs. 2 and 3.

Table III (see p. 151) has been compiled on the basis of the above-mentioned assumption concerning the dissociation of oxygen and nitrogen. Up to 70 km, according to the rocket measurements, the mean molecular weight of the air is unchanged. Near 70 km insignificant deviations were observed. Data obtained from analysis

samples of air taken into three steel cylinders in the altitude interval 64–72 km showed an increase (approximately twofold) of the ratio He/N₂ in this altitude interval; the weak growth of the ratio Ne/N₂ and the weak decrease of the ratio A/N₂. In view of the uncertainty of the question of the diffusive separation of the components of air, it was not taken into account in calculating the dependence of $\rho$ on altitude.

The temperature values were determined from the relation

\[ T=\frac{\mu}{28.966}\,T_{29}, \]

the values of $g$ from the law of inverse proportionality to the square of the distance from the center of the Earth. The gas constant was taken equal to

\[ R=8.31436\cdot 10^{7}\ \text{erg}/\text{deg}\cdot\text{mole}. \]

The density was found from the equality

\[ \rho=\frac{\mu p}{RT}, \]

and the mean free path of molecules $\lambda$ from the inverse proportionality of it to the number of molecules per unit volume; at the Earth’s surface it was assumed that $\lambda=7.37\cdot 10^{-6}$ cm.

The authors of the survey note that the data of group 1 on density in the altitude interval 60–80 km are systematically higher than the average. Assuming that this is an instrumental effect, they nevertheless point out that the discrepancies of the data obtained by group 1 by different methods are smaller.

Further, the authors indicate that there are serious experimental grounds for believing that the mean density values they give poorly reflect the state of the atmosphere at any particular moment of time. In reality, apparently, there are significant diurnal, seasonal, and latitudinal variations. Thus, for example, group 2 found noticeable differences in the data obtained during the course of one and the same night with an interval of several hours. However, the available information is wholly insufficient for any reliable judgments about the nature of these variations and their correlation with solar activity, magnetic variations, auroras, and the state of the ionosphere.

Fig. 3. Mean air density of air at various altitudes.

The authors suppose that in reality the temperature maximum at altitudes of about 50 km at a given moment of time is not a smooth curve (Fig. 1), but has a number of peaks, with its height varying within about 10 km. The same, in the authors’ opinion, also applies to the temperature minimum around 80 km.

On the other hand, the rocket data do not reveal seasonal variations, whereas the meteor data indicate greater densities in summer than in winter, and this effect differs at different latitudes. It is also noted that meteor effects correlate with temperature in the winter surface layer and are expressed much more sharply at altitudes of 60–70 km (of the order of 0.3 units in $\lg \rho$) than at altitudes of about 90 km.

Table II

Accepted values of the temperature, pressure, and density of the atmosphere at various altitudes under the assumption of constancy of the molecular weight

From Current Literature

End of Table II

Table III

Data on the atmosphere at various altitudes

The latitude effect was noted by group 1. An analogous effect is also observed from meteor data and from sound-ranging data,[^4] which likewise reveal distinct seasonal variations both in the temperatures and in the speeds and directions of winds at altitudes of 30–60 km.

Thus, the question of variations in conditions in the upper layers of the atmosphere remains entirely open. The authors consider it likely that geographical factors are of substantial importance and that these variations have a clearly expressed meteorological character.

G. R.

References Cited

1. Uspekhi fizicheskikh nauk 43, 609 (1952).
2. Phys. Rev. 88, No. 5, 1027 (1952).
3. F. L. Wipple, Bull. Am. Met. Soc. 33, 13 (1952).
4. A. P. Crary, J. Meteor. 7, 233 (1950).