N/A Improved accuracy with higher FPS?

I've had heavy .177 shooting from a lower powered gun improving on accuracy as I increased the FPS but it's not like 970fps was better than 880-900. More like 880-900fps was better than 700fps. I'm sure they're exceptions but only slugs in my testing really gained noticeable accuracy above 900fps.
 
Accuracy is generally correlated with decreasing velocity. Higher velocities exaggerate the effects of imperfections in the barrel and projectile.

The one case where increasing velocity may improve accuracy is if the project is not quite stable coming out of the barrel. Increasing velocity will increase the spin rate of the projectile. That may be enough to make the projectile stable in some niche cases.

Most people target a velocity between 700-900 fps with Diablo pellets.
 
Your question only deals with one side of an equation. The important thing to think about is range. How far are you shooting? If you are shooting 25 yards or less then yes it will be possible to crank up the fps and shoot what appears to be a good group, but those pellets may be flying horribly. At close distances it will be less noticeable because you can overcome bad ballistics with short ranges. At longer ranges that’s where you’ll be able to see if it’s truly accurate or if you’re just using brute force to give the illusion of accuracy.

Does that make sense? It’s probably best to shoot at multiple distances to see if this accuracy is not just a fluke at whatever distance you are shooting from. It would likely be HIGHLY unstable.
 
It is very rifle and especially barrel depending.
My RedWolf .177 HP with ART Polygon barrel shoots 13.43 Knockouts like a lazer out to +100 meter
My Delta Wolf with the 600 mm ART polygon Barrel shoots the same perfect but best around 920-930 fps.
If I shoot them faster fliers start to appear.

So it Is very barrel and Speed depending.

My Delta Wolf also shoots Zan 20 gr slugs great at 910-920 fps - all the way out to 200 meter.
The redwolf shoots the Zan 20 best at 960 fps.
 
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Your question only deals with one side of an equation. The important thing to think about is range. How far are you shooting? If you are shooting 25 yards or less then yes it will be possible to crank up the fps and shoot what appears to be a good group, but those pellets may be flying horribly. At close distances it will be less noticeable because you can overcome bad ballistics with short ranges. At longer ranges that’s where you’ll be able to see if it’s truly accurate or if you’re just using brute force to give the illusion of accuracy.

Does that make sense? It’s probably best to shoot at multiple distances to see if this accuracy is not just a fluke at whatever distance you are shooting from. It would likely be HIGHLY unstable.

Absolute truth. You may get sufficient accuracy shooting a pellet super fast at 25-50 yards, but at your chosen max range, the groups may fall apart. If you want to shoot out to 100 yards, for example, shoot at that distance and see how the accuracy is.
 
My mental model for what is happening when you pull the trigger is a sine wave starts down your barrel because of the excitation of the release of air. The barrel wants to move a tiny, tiny amount in some direction due to the excitation. When you tune the gun you are trying to find a pellet (most important variable by far in my experience) and tune that minimize the difference in this movement shot to shot. Lots of things, including temperature, can influence what is "best". My one 177 gets tuned to shoot faster than most of my other guns partially because it can. I've tried a variety of speeds in it and not seen much difference in accuracy. So I set it up to shoot 880-900 in part because I want to be able to cleanly kill squirrels (which it does very nicely).

In short, speed is a secondary variable in my opinion which does not strongly affect accuracy. Logically a stronger pulse from air could lead to more excitation of the barrel and potentially less accuracy but I have not seen it. 177s do not use a lot of air per shot and the barrel tends to be thicker than other calibers so if this is a factor at all it would be significantly less for 177. As many others have said, you have to test and see what you think.