6M Es Single Hop Range Estimates (WA5IYX and K1SIX with k Factor).

6M Es Single Hop Range Estimates.

Note 1: MOST angles only from previous table by WA5IYX. The MILES column uses the supplied angular values to recalculate corrected values based upon E-Layer height using Spherical Geometry with the M Excel formulas used shown below.

Note2: FoEs values are recalculated for MUF value entered in cell H2.

Note 3: BEST CASE Earth (Radio) radius adjustment for "standard" 4/3 "k factor" to account for accepted values of atmospheric refraction for path segments below 3 km which could extend the range by a factor of the SQUARE ROOT of 4/3 or 15.4%. k factors < 1 will reduce range.

The full benefit for extremely low takeoff angles is unlikely as local terrain, clutter and obstruction losses become an increasing factor! KM values are simply converted from the mileage values used in the computation. Earth Radius Used: 3,959 miles (the r input to the formula). Use 6,371 if km units is desired.

MS Excel Converted Formulas used:

d= distance or range result (miles used here, can be km if desired)

h= height of E-Layer refraction (miles used here, change to km units if desired)

r= Earth's Radius (miles used here. MUST be in same units as the values used for d and h)

a= The takeoff ANGLE in degrees from an observer on the surface of the earth

"MILES"=d= r*2*(90-a-DEGREES(ASIN(r*SIN(RADIANS(a+90))/(r+h))))/57.3

"k-Factor (MI)" =Kf ONLY FOR Takeoff angles =< 10° and full path k-Factor at 0° to avoid an error.

Thus Kf=MIN(d*SQRT(4/3),(d-(2*1.86411/SIN(RADIANS(a)))+(2*1.86411/SIN(RADIANS(a)))*SQRT(4/3))),d*SQRT(4/3))

"Angle b°"= DEGREES(ASIN((r/(r+h))*SIN(RADIANS(a+90))))

"M-Factor"= 1/SIN(RADIANS(90-Angle b))

Tim M0BEW.

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