None of the mic suggestions in this thread will do what you want by themselves, in eliminating music in favor of aircraft sound. But its good the suggestions were made, because its an opportunity to understand something about sound and microphones.
A microphone is not like a lens that "sees" only what it's pointed at. Rather, it picks up sound from all directions to a greater or lesser degree. And that's true for all mics. The reason is that sound is made up of a very wide spectrum of frequencies from very high to the very low. Another way to look at frequency is wavelength. For example, a mid-band tone at 1KHz has a wavelength of just over 1 foot, where a mid bass note of 100Hz has a wavelength of 11 feet.
Now, knowing that, take a look at how directional microphones work. Any directional microphone achieves its pickup pattern, not by focussing sensitivity forward, but by cancelling sensitivity in other directions. A typical cardiod mic (you can always tell its directional because there is a pickup area in the front, but also slotted ports on the side), has a null in sensitivity directly to the rear, peak sensitivity forward, but also does have sensitivity to the sides too, just a bit less. "Shotgun" mics are exactly the same, only more so, less to the sides, but oddly, somewhat worse to the rear.
Circling back to wavelength...if you look at the pickup pattern of a directional mic at higher frequencies, where wavelengths are small, it could look pretty directional, almost flashlight beam in it's pattern. That's because the shorter wavelengths are easly handled in the acoustic cancellation design of the mic. But, if you look at the same mic at 100Hz, well...that flashlight beam pattern is now gone, and it's picking up energy to the sides, even to the rear. This is because the 11' wavelengt of 100Hz is soooo long that it hits the front of the mic with the same pressure as the side ports, virtually short-circuiting the acoustic cancellation that makes the mic directional. Some cardiods become nearly omnidirectional and lower frequencies, and shotgun mics are better, but only a little.
Here's a link to the 416's data sheet with polar plots. Note how they differ with frequency.
So a cardiod for this job is no good. A shotgun, even a relatively long one (longer means it works better at lower frequencies) is only a little better. What about a parabolic?
Well...a parabolic works by reflecting energy and concentrating it at the mic diaphragm. But again, there's a problem with wavelength. This time it relates to the diameter of the reflector. Even the big parabolics are only 3' or so in diameter, and that means wavelengths longer than 3' cannot be concentrated the same as shorter waves. It also means those long waves will hit the mic directly, and all that means is, that highly directional parabolic is nothing of the kind at low frequencies. Parabolics generally have their low end severely rolled of in post, or in a live mix.
So, in short, no mic is fully directional across the audio spectrum. Nearly all but some exotics are only very directional above 1KHz (mid-band), and that in turn means they're not going to cut down on load PA music at your airshow nearly enough to avoid the YouTube scanners.
What's a filmmaker to do? One solution is to grab some "wild sound" from a flying field when there's no show, and no music, and drop it into your video in place of the actual location sound. Yes, it's a fake-out. But that's actually how it's done. Very, very little location sound can be used, even in documentaries and event coverage.
If you still must have authetic aircraft sound, several things:
1. Use a shotgun mic on camera, the longest you can afford. Physically long mics hold their directional patterns to lower frequencies. Most have a built-in low-cut. Use it.
2. Get as close as possible to the aircraft, and as far away from the music as possible. With sound, when you cut the distance to the aircraft in half, you double the sound pressure level at the mic (that's +6dB), and inversely, when you double the distance to the music, you cut the sound pressure level in half (-6dB). A 12dB ratio improvement is huge.
3. Cut the low end off in post. Model aircraft, the ones I've heard, don't have much in the way of low frequencies in their sound, so it won't hurt the believability of their sound to steeply cut of below 500Hz, perhaps even higher. Bass in music outdoors propegates like crazy, but the highs don't. So if you cut the low end, you're also cutting the most audible part of the music. But do it in post so you can experiment.
4. If you have a camera with two mic inputs that get can be recorded on separate tracks (typically left and right), use the left for your shotgun mic, and plug a second mic, a cardiod, omni, or whatever, into the right channel. The idea is to record the shotgun as your primary sound, and record the ambience with the second mic (you can even point it at the music if you like) then in post, roll off the high end of the right channel, invert it (flip phase), and mix a bit of it back into the same track as the shotgun. What will happen is you will begin to phase-cancel more and more of the music while not cancelling so much of the aircraft. Level adjustment will be critical, and you may have to slip sync to adjust timing too. This is excactly what a noise-cancelling mic does, only taken to a grander scale. You'll want both the shotgun and the second mic to be fairly close together with their diaphragms lined up. The diaphgram(s) of a shotgun mic is usually somewhere near the middle of the slotted section of the body.
Don't expect miracles, but that, and the other 3 ideas above, might just add up to a win for you.
Don't forget a windscreen for any mic outdoors.
