K4SAV generated some useful numbers  thank you.
    
Here are some EZNEC numbers for a three element Yagi
turned either vertically of horizontally.
Height ___ Horz Antenna ______ Vert Antenna ____ Gain Difference
20 ______ 9.6 dBi at 36 deg ___ 4.8 at 17 deg ______ 4.8 dB
30_______11 dBi at 28 deg _____ 5.7 dBi at 15 deg __ 5.3 dB
35 _____ 11.6 dBi at 25 deg ____5.9 dBi at 13 deg __ 5.7 dB
40 _____ 11.9 dBi at 23 deg ___ 6 dBi at 12 deg ____ 5.9 dB
80 _____ 12.7 dBi at 12 deg ___ 8 dBi at 9 deg _____ 4.7 dB
100 ____ 12.9 dBi at 10 deg ___ 8.8 dBi at 8 deg ___ 4.1 dB
120 ____ 12.9 dBi at 8 deg ____ 9.4 at 7 deg _______ 3.5 dB
150 ____ 13 dBi at 7 deg ______ 10.1 dBi at 6 deg __ 2.9 dB
200 ____ 13.2 dBi at 5 deg ____ 10.8 dBi at 5 deg __ 2.4 dB
300 ____ 13.1 dBi at 3 deg ____ 11.6 dBi at 3 deg __ 1.5 dB
    
This is only part of the story, however. Look at the angle for peak gain
for heights of 80 feet or less. Which is more useful for DXing? It is also
useful to compare the difference in gain between the two antennas as a
function of vertical angle. You will find a dramatic difference in favor of
the vertical antenna at low angles, which are precisely the takeoff angles
needed for opening and closing bands and for minimizing the number of hops
over really long distances, such as from the Pacific to Europe. Mounting
the yagi vertically is not a panacea, but in some circumstances makes a big
difference.
73, Ward N0AX
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