To work out the energy in a projectile is in principle very easy. It's a bit cumbersome in Imperial units (grains, pounds, feet and so on) but in Metric units it's a doddle.
Energy is equal to half the mass multiplied by the square of the velocity. To do the calculations I'll convert everything to Metric units first (see footnote).
In the Metric (SI) system, energy is measured in Joules, mass is measured in kilograms, and velocity in metres per second.
Most .177 pellets weigh in the region of 8 to 10 grains, and .22 pellets about twice that.
Let's say that the pellet weighs eight grains and it travels at 800 feet per second. I will do the sums on a calculator to avoid rounding errors that might result in a jail sentence.
A grain is 64.79891 milligrams exactly. So eight of them is .00051839128 kilograms exactly.
One foot is 0.3048 metres exactly. So 800 feet per second is 243.84 metres per second exactly.
So the energy in the pellet is (half mass x velocity squared) which is
1/2 x 0.00051839128 x 243.84 x 243.84 = 15.411240262877184 Joules. To get a less unwieldy number, to be on the safe side for comparison with the legal limit I'll round that UP to 15.42 joules.
If the velocity is 1000 feet per second instead of 800, the velocity is 1.25 times greater. But the energy is 1.25 x 1.25 times greater so that's over 24 joules. (It's the velocity
squared which gives the energy.)
One ft.lb. of energy is (rounded DOWN) 1.3562 joules approximately, so the UK legal limit of 12 ft.lbs. of energy is about 16.27 joules. As you can see an air rifle which shoots an 8 grain pellet at 800 feet per second can be used without a license in the UK, because the energy is only about 15.42 joules. But there is no way that one which will impart a velocity of 1000 feet per second to an eight grain pellet could be legal in the UK without a Firearms Certificate, the energy would be 50% more than the unlicensed limit.
There's a handy online calculator here:
http://www.airgun1.com/articles/kineticenergy.html
Incidentally, other things being equal an air rifle pellet will be a lot more accurate at 800 feet per second than it will at 1000 feet per second.
Footnote:
In the Imperial weights and measures system the unit of mass is NOT the pound. The pound is actually a unit of force, not of mass. The unit of mass is called the 'slug', and it confuses the hell out of everybody because you have to start dividing by the acceleration due to gravity if you use pounds instead of slugs. In the metric system, the unit of mass IS the kilogram so things are simpler. The SI unit of force is the Newton, but we don't care about that as we aren't using it here.
