Nikola Tesla's Work In Wireless Power Transmission Page 24

-3- to a "Loran" type phase radio navigation system. A storm progressing across such a system would produce maxima and nulls at the receiver as the storm crossed the maxima and null type hyperbolic lines-of-position. Only, along the distance, d, would the nulls and maxima correspond to the wavelength of the crest of the spectrum, 6.4 kc, but at any other azimuth the spacing would be greater and hence, the apparent standing wavelength would correspond to a lower frequency.

The system, Fig. 3, can be deduced by considering the direct wave from the storm propagated over the distance, x, and the re-radiated wave propagated over the distance, y, subject to a re-radiation constant, cy and the constant distance, d, between the receiver and the point re-radiator. The waves will tend to cancel or produce nulls when the phase difference, Δφ,

Δφ = (ω/c) [x - y - d] + φx - φy - φd + cy = π, (1)

Assuming, for simplicity, an infinitely conducting earth,

φx = φy = φd = 0, (2)

and a perfect re-radiator,

cy = 0, (3)

then,

(ω/c) [x - y - d] = π (4)

or,

x - y = C, a hyperbola,

where,

C = c / (2f) + d = 2.34 (10^4) + d, (f = 6.4 kc)