Theory of the rocket-grenade method of measuring temperature, pressure, density and wind velocity in the upper atmosphere

Abstract

A theory is presented for deriving the speed of sound and wind velocity as a function of height in the upper atmosphere from observations on the travel times of sound waves from accurately located grenades, released during rocket flight, to microphones at surveyed positions on the ground. The theory is taken to a second order of approximation, which can be utilized in practice if lower atmosphere (balloon) measurements are available. By means of the gas law and the vertical equation of motion of the atmosphere, formulae are obtained for deriving temperature, pressure and density from the speed-of-sound profile, and these also may be evaluated to a higher accuracy if lower atmosphere measurements are available. An outline is given of the computational procedure followed in the processing of data on the basis of this theory by means of the Pegasus computer. Methods of calculating the correction to travel times due to the finite wave amplitude are discussed and compared, and the effect of neglecting this correction in a particular set of experimental data is examined. Other errors which may affect the determination of pressure are also discussed. Consistency between the theory and experimental data obtained in 13 Skylark rocket flights at Woomera is checked in two ways: by examining least squares residuals associated with the sound arrivals at various microphones; and by treating the vertical component of air motion as unknown and examining its distribution about zero. The reduction in the least squares residuals which occurs when account is taken of second order terms is evaluated on the basis of these sets of experimental data.