Unless you have the money and facilities to work with Taconic or Rogers Duroid PCB material then forget about it. In any case, phenolic or QT is quite absorptive at these frequencies and you don't really want your antenna in close proximity to that. It's pretty easy to make a fin antenna to work against a groundplane on the body of the rocket.
I've had some very good result by just poking a dipole antenna out the side of the rocket. Yes, it's a bit draggy but the improved video performance more than makes up for that and it's no barrier to going very fast. I've done this above Mach 1 at least half a dozen times with no ill effects.
You can see it sticking out the side of the avionics rig in
Hey! Haigh-Farr makes good antennas. There are two (2.3 GHZ telemetry) on the nose of this beast:
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I have been wanting to build a GPS antenna but the one thing that is stopping me at this point is test equipment. I need to be able to test the antenna to verify/tweak the tuning.
Materials are fairly easy to get from:
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You will find it very difficult to add a duroid radome because the bonding film requires very high pressures and elevated temperatures to work correctly. But for most applications something less robust than duroid should work fine.
While their test setup wasn't too bad they didn't do enough testing. Radiation patterns are usually tested with a wrap around antenna installed on the vehicle or at least a representative structure because the conductive body effects the pattern. In addition you want to take more than a single roll pattern at 90 degrees. Otherwise you will never know what the full pattern is like.
In any case it looks like their pattern was hurt by the use of a single element that didn't go all the way around. Depending on the diameter, different approaches are possible. From extending the width till it goes all the way around on smaller diameters to a corporate feed network to multiple patches on larger diameters.
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