Ballistic Research
Laboratory Report No. 395
Chandrasekhar/mel
Aberdeen Proving Ground, Md.
31 August 1943
ON THE DETERMINATION OF THE VELOCITY OF A PROECJECTILE FROM THE BEAT WAVES PRODUCED BY INTERFERENCE WITH THE WAVES OF MODIFIED FREQUENCY REFLECTED FROM THE PROJECTILE
Abstract
In this report we examine as to what the basic information is which is provided by following a projectile in motion by radio waves of high frequency and using the beats produced by interference with the reflected waves of modified frequency. It is known that by counting the number of beat waves in a specified interval of time we are in principle able only to infer the position of the projectile at the end of the interval considered from a knowledge of its position at the beginning of the interval. On the basis of this fact, a practical method is outlined for determining the approximate velocities of the projectile along its trajectory.
1. A method has recently been developed by the Westinghouse Co. in collaboration with this laboratory in which the radio Doppler effect is used to determine the velocities and the drag coefficients for the various projectiles. The principle of this method is quite simple: We allow the micro waves of a given frequency emitted by a transmitter to be reflected from a projectile in motion. On account of the Doppler effect these reflected waves have frequencies slightly different from that of the incident waves (see equation [1] below). Consequently, if we now superpose the reflected wave trains on a wave train having the same frequency as the incident waves we shall obtain a beat phenomenon. It is evident that quantitative measures based on the existence of this beat phenomenon should enable us to determine the dynamical characteristics of the trajectory. It is the object of this report to analyse as to what can be inferred directly from a record of the "beat-wave" and indicate how the velocity of the projectile along its trajectory can be derived.
