From whence the Fresnel Zone constant of proportionality?

[joe80211]

Calculation of the Fresnel Zone given as r=M*sqrt( 1/F * (d1d2/(d1+d2))) uses 72.1 and 17.3 as the constant of proportionality (M) for r in feet and meters respectively. Does anyone know where this constant comes from? I've tried plugging-and-chugging with feet-to-miles, and f=c/lambda, but I can't see how M converts units and comes out from under the root.

 

[photistor]

In the 7th edition of Reference Data for Engineers (edited by Edward C. Jordan, published by Sams) chapter 33 page 16/17 there is a reference to the radius at the first Fresnel zone at point P:
R1^2(squared)=lambda(d1d2/d) where all quantities are in the same units.

Also, the following equation is given when in mixed units:
R1m=2280*sqr(d1d2/Fd)
where R is the radius in feet
d is in miles
F is in Megahertz

Also maybe these refernces may help:

http://www.softwright.com/faq/engineering/Fresnel Zone Clearance.html

http://www.wirelessapplications.com/wireless/services/lostFound/images/path_clear2_Final.pdf

http://www.cocom.com/pdffiles/App_Note_7_PTZ-3_Range_Calculations.pdf

(scroll down to Fresnel calc)

 

[joe80211]

Good info, thank you! I'm starting to suspect that where F appears in the denominator it actually started its life as c/F to make the units under the root all be distance. I'm trying to work through getting sqrt(c) and the distance units conversion factor out from under the root to see if that's where 72.1 comes from.

Joseph Bardwell