5,000 fps coyote rifle?

I've got a 257 wby. with 30" barrel, pushing the 80gr. ttsx at 4240fps. Not exactly what you're looking to do but sighted 1" high at 100 it is only 8" low at 400. Was set up for a similar purpose so that I don't have to worry about holdover on called wolves.
 
Years ago when I lived in Phillips County Montana I had a similar urge but my goal was 600 yard coyote rifle.
I built a 6-06 12 twist 28" barrel. Zeroed at 300 it only dropped a few inches at 500. I barely herald high at 600.
75 Sierra bullets going well over 4000
Dang thing only lasted 500 rounds but what fun to shoot.
My gunsmith does 22-284 in 9 twist and absolutely hammers the steel at 700-1200 yards. He shoots 80 grain Sierra bullets. Of course he dials his scope, but gets incredible small groups on the 1200 yard steel. Being a gunsmith he doesn't care how long the barrel lasts.
After this long winded story time, I want to say your 22-284 idea should work well. 12 or even 14 twist for those light bullets would make for some incredible velocities and hopefully decent accuracy could be obtained.
Don't worry about the 5000 number. You will have done the best you can do.
I have launched some 39 Sierra 20 cal bullets at well over 4000 from 20BR and 20-250. Very flat and accurate until you get so fast they blow up(below 5000fps). They do not deliver much energy beyond 500. Sure terrorized a prairie dog town though. Will have somewhat better barrel life from my experience.
Good luck on your endeavor.
 
As far as 400 yards coyote point blank, I figure no higher than 3" at highest point, and no lower than 3" at max range, and 400 yards is kind of the minimum. I would prefer to have as far as a +3-3 zero as possible. The majority of adult western coyotes only measure 6"-7", they are of course bigger with fur, but the part that the bullet cares about is only around 6ish inches, so that is where I came up with the +3-3 zero.
It should be a fun project.
When I was hunting coyotes more and fiddled around trying to get the best mpbr in a few rifles.
I found once 40gr bullets dropped below 2000fps they're performance on coyotes was disappointing.
Running the numbers a 40gr at 5000 is at 2000fps at 550yards.
Often its the female that sits down on guy at the 550-650 range and if you shoot her first, male(s) will run out to 450-500 and give you a shot.
My best combo, granted I never dabbled in wildcats but just worked with rifles I had, wasn't a 55gr in my 240wby at 4000fps but a 90gr blitzking in my 257wby. It basically was a point and shoot out to 350yds but could hammer those coyotes that sit on the outer range and served as a do all coyote gun. I would've gone down To the 70-75gr .257 bullets but the 90s were a struggle for accuracy in the wby freebore and I never bothered going lighter.
If it was me, I'd build a 25sherman max and run a 70gr hammer bullet as fast as you could. Just my food for thought.
Good luck with it
 
Another way to reach the 5k mark is with sabot loads. Remember that old Remington Accelerator load? While not as accurate as a standard caliber varmint load, I have played with a couple of manufacturer sabots in 30/22 with vels above 5k with 55gr bullets in a 30-06 with 4,800 giving better accuracy. However as stated and at or above 5k, I could never get the accuracy below about 2 MOA.

On a whim, we loaded some turned and hardened 45gr steel bullets for those sabots, and their ability to penetrate steel plates at shorter ranges was extreme.

Forgot, we also loaded the old Speer 70gr SP one season, around 4,400fps I believe, and used them on deer with interesting DRT results under 200. Again, insufficient accuracy was not conducive to use much beyond 300.
 
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A 6MM Mach IV will push a 70 grain at 4400 in a 26 inch barrel. Not sure about a 30 inch barrel and lighter bullets. I'm not sure if most bullets will stay together at 5000 fps.
 
If you experiment with the shape of the venturi area of the neck of the case so the powder is not sandblasting your barrel you can lengthen the barrel life. Turn your own bullets out of brass and size them for your barrel with the coating applied. Sizing will be trial and error on too tight to too loose. Length of barrel? Long enough to burn powder and build pressure any more will rob speed. Play with the crown at the end of the barrel the shock wave on 5000 fps is critical to accuracy and needs to filmed with a high speed camera. If you can stabilize the shock wave, then higher speeds with accuracy are possible. Barrel diameter? because of heat build up, 2nd or follow up shots might not be accurate. So cooling vents on the barrel needed. Maybe even fins like a 2 stoke engine. Bullet length? short bullets will not stabilize, will they be accurate at 400yds ? maybe, will they be stabile not likely. The envelope that surrounds the bullet has to be looked at very closely, wind tunnel type experimenting so you can see the shape of the envelope. When you can stabilize the envelope then speeds will go up, look at the tip of the bullet experiment to change the shape of the envelope. How to make a wind tunnel? Use a make shift tent that you can shoot through, set your camera up to view the inside of the tent, fill the tent with Hollywood smoke or something similar. Have the camera start filming at trigger movement. So to make an accurate rifle at 5000fps and beyond? Rethink or create the parameters. Bullets have been handicapped and stopped at the 4000-5000 range for a long time because experimentation becomes expensive. To exceed where others have failed you have to think outside the box.

A quick note about a thought that came to mind when I read the first line of this response : A guy named Mic McPherson worked with a strange-looking shoulder profile on rifle cartridges, and I think it had to do with shock waves on ignition, as well as directing the expanding gases out of the case in a manner that reduces throat damage. He may already have done a lot of the work you need to do to make this project doable. If he has, checking in with him maybe helpful. This may save you from re-inventing the wheel.
 
It should be a fun project.
When I was hunting coyotes more and fiddled around trying to get the best mpbr in a few rifles.
I found once 40gr bullets dropped below 2000fps they're performance on coyotes was disappointing.
Running the numbers a 40gr at 5000 is at 2000fps at 550yards.
Often its the female that sits down on guy at the 550-650 range and if you shoot her first, male(s) will run out to 450-500 and give you a shot.
My best combo, granted I never dabbled in wildcats but just worked with rifles I had, wasn't a 55gr in my 240wby at 4000fps but a 90gr blitzking in my 257wby. It basically was a point and shoot out to 350yds but could hammer those coyotes that sit on the outer range and served as a do all coyote gun. I would've gone down To the 70-75gr .257 bullets but the 90s were a struggle for accuracy in the wby freebore and I never bothered going lighter.
If it was me, I'd build a 25sherman max and run a 70gr hammer bullet as fast as you could. Just my food for thought.
Good luck with it
I burned up a couple 240 wby barrels in my early years with 55grain ballistic tips. Made a spectacular splash on coyotes
 
Another way to reach the 5k mark is with sabot loads. Remember that old Remington Accelerator load? While not as accurate as a standard caliber varmint load, I have played with a couple of manufacturer sabots in 30/22 with vels above 5k with 55gr bullets in a 30-06 with 4,800 giving better accuracy. However as stated and at or above 5k, I could never get the accuracy below about 2 MOA.

On a whim, we loaded some turned and hardened 45gr steel bullets for those sabots, and their ability to penetrate steel plates at shorter ranges was extreme.

Forgot, we also loaded the old Speer 70gr SP one season, around 4,400fps I believe, and used them on deer with interesting DRT results under 200. Again, insufficient accuracy was not conducive to use much beyond 300.

I've used the 70-grain Speer bullet on deer as well, out of a 22-250 at around 3200 fps. It killed them quite handily, and didn't blow up all the grinding meat. The 64-grain Winchester Power Point was also an excellent performer. Both bullets have fairly thick jackets, so they might stand up to the rotational stresses. He'd be giving up close to 1000 fps from his desired velocity target, though, so neither is going to fit the bill for this guy's project.
 
I shot a antelope at 525 yards with a etip solid copper bullet at 4000 fps in a 6mm mach IV and it was a complete mess. Got the hind quarters and back straps there rest was toast.
 
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