Louis Winslow Austin - Austin-Cohen Formula

Austin-Cohen Formula

A mathematical model for propagation of radio frequency electromagnetic waves along the surface of the earth was for some decades one of the greatest mathematical challenges, engaging the minds of some of our foremost mathematicians. Throughout that period, as each new model was developed and promoted, it had to withstand the immediate question "how well does it match the Austin-Cohen formula?" This was the lasting testament of a few years circa 1911 of exacting measurements undertaken by Austin and his friend and colleague Louis Cohen. As in so many scientific accomplishments, there were elements of serendipity to the experiments. As is now well known the independent variables are frequency/wavelength, distance, surface conductivity. The latter variable is particularly troublesome varying greatly with the type of the ground (rock, soil, clay or sand), its depth profile, cover and moisture content; almost impossible to measure directly. A further complication is that the type of ground will itself vary over large distances of the order of 100s of kilometres. Today effective ground conductivity is mostly calculated from measurement of the actual attenuation of radio waves propagating over that surface. But Austin's then employer was the US Department of Navy and they were principally interested in communications shore to ship and ship to ship. Austin's measurements were almost entirely over sea which has the admirable quantity of both homogenity and constancy of surface conductivity. By eliminating conductivity from the variable set, Austin meticulous measurements with carefully calibrated but rudimentary instruments of the day, produced a clean set of data of field strength against frequency and distance. The resulting empirical model was simple, elegant and precise. It would provide for decades both his employers with a scientific basis to plan their naval radiocommunications services as well as the brightest mathematicians a yardstick against which to test their surfacewave propagation deterministic models. Had Austin extended his data to include the land of highly variable surface conductivity to the north, west and south of the transmitters available to him, the resultant data would have been almost chaotic for the day and likely necessitated a stochastic model for solution, similar to the problem of night-time skywave propagation to which he devoted much of his time in his remaining two decades.