How would you study the vertical radiation pattern of your omnidirectional antenna? You'd need a signal source flying over the antenna at any given angle, far away.
For VHF and UHF antennas you may find that HAM satellites are handy for this task too.
Depending on your location, some LEO bird will pass over your antenna at a good selection of elevation angles. The best pass is one that puts the satellite as much above your head as possible. An FM satellite is even better, since it provides a carrier of constant power, like AO-51 downlink on 70 cm.
So, make a prediction of an usable pass. Don't forget to check the satellite operating schedule, if any. Draw or print or write down a selection of time, elevation angle and frequency +/- doppler. Azimuth is not relevant if your omnidirectional antenna has a clear view of the horizon. Sit back and wait. Then look closely at the S-meter (better if analogue).
So far I have received AO-51 UHF downlink on two antennas, one shorter than lambda/4 and one 3/4 wave (a VHF whip). Both magmounted on the car. At a certain point I noticed AO-51 signal at S2 on my S-meter with the VHF whip, as much as I could get with the Moxon beam!
Back to the computer, I used MMANA to simulate this antenna at UHF. It was not a surprise to see that at 45° elevation this antenna has a 5.5dBi gain. Moxon rectangles are said to have about 6dBi gain, so we're in the ballpark.
As a conclusion, I can say the 3/4 lambda at UHF is good to receive almost any AO-51 pass above 10°. Unfortunately it is not enough to hit the satellite repeater with 5W. With a proper S-meter, the vertical radiation pattern of an antenna can be drawn per-points.