For a 10M/11M antenna, 36 feet is the minimum height for optimum ground wave (local) coverage. An extra 15 feet will improve ground wave (local talking) a bit. That extra 15 feet will do nothing for your DX coverage, as you're already at the minimum height for good DX. That extra 15 feet is a very small difference to the ionosphere which reflects your DX signal. At about +/- 1000 miles up, the ionoshphere won't notice the difference.
Here are some examples of changing the height of a three element ten meter NBS Yagi-Uda (Mr. Uda was Mr. Yagi's partner in designing the Yagi antenna. Both gentlemen were Japanese.) at 28.025 MHz modeled with EZNEC+ 5.0 Pro:
Let's talk about gain.
Gain can be measured in two ways dBi and dBd. Most antenna manufacturers publish their gain figures as dBi because it sounds better, but it really means gain compared to a isotropic dipole in free space. Unless you can put your Yagi-Uda in space dBi doesn't mean much, so I'm going to use the calculator at
Pure ERP And EIRP Calculator to calculate the true ERP, not the EIRP, using 100 watts of power.
I. At .5 wavelength (17.5481 feet) gain should be 13.15 dBi = 1259.378 watts ERP. with a radiation angle of 24 degrees.
II. At 1 wavelength (35.0962 feet) gain should be 14.62 dBi = 1766.673 watts ERP and a radiation angle of 15 degrees.
III. At 1.5 wavelength (52.6443 feet) gain should be 15.12 dBi = 1982.240 watts ERP and a radiation angle of 9 degrees.
IV. At 2 wavelengths (70.1924 feet) gain should be 15.09 dBi = 1968.594 watts ERP and a radiation angle of 6 degrees.
Hey! Wait a minute! We lost some gain! More later...
Notice that as we raise the height of the antenna the angle of radiation goes down, but in our last calculation we lost some gain.
Let's talk about angle of radiation:
The ionosphere is a reflective surface (not always ;o) ) and it is a sphere, so when we hit it from an angle of 24 degrees the signal bounces off at a different angle (probably the best angle for local communication) than at 6 degrees. Now you guys who shoot pool know that when you want to bounce the cue ball further down the table, you shoot at a shallow angle, not a high angle. Well the radio waves from your antenna are sort of like a cue ball. The higher the radiation angle of the signal the shorter the hop around the earth will be, so our dream antenna should have a radiation angle that is as low as practical (zero ain't practical), so by lowering the angle of radiation our signals bounce further around the earth.
In example IV we lost .03 dBi of gain, or 13.646 watts ERP. Do you think our loss of ERP can be detected on the other end? The answer is no.
My investigation seems to show that raising the height of a Yagi-Uda antenna improves it's performance up to 2 wavelengths in height.
73 from North Central Texas
Tom, N5GE