Kat,
Oh dear, this is one of those "how long is a piece of string" questions.
Let's have a go.
I'll make a lot of assumptions in the interests of simplicity and avoidance of unnecessary work. For my purposes, air offers no resistance, for example.
You are right about the bat breaking. As a matter of fact, if the ball is not of the right kind of construction, it might break even a brand-new (and very expensive) bat if a muscular slogger hits it fairly. I have heard of several cases locally, where cheap imported balls with inappropriately hard fillings broke bats.
Now, balls of reputable brands will also break a bat in the hands of a real slogger once the bat is old enough, and it seems to me that these observations give some indication that, given a standard bat and standard balls, the most impressive sixes that we see cannot be too far from the limit of what bat and ball will stand.
Now, in the interests of nice, round numbers, I shall assume that the ball is hit at an elevation of 45°. Let's also assume that some of those giant sixes that the likes of Boom Boom Afridi and Courtney Walsh humiliate bowlers with, travel for some 200 m before touching ground the first time. If my calculations are correct, that would require a ball speed of roughly 160 km/h, which, incidentally, is just about the world record bowling speed. Also incidentally, I believe that the world record for a long six is about 150 m, but since we are discussing possibilities rather than actualities, I'll put the discrepancy down to air resistance.
Since bats sometimes break, it seems that we are not too far from the right region.
On the other hand, since the bags don't break nearly every time, I shall assume that we have the bat fastened into a machine that provides us with inhumanly powerful batting that would break the bat more frequently.
Again, assuming that the back of my envelope doesn't need batteries, a 400 m six would need a launching speed of about 230 km/h.
I am open to correction on all the foregoing.
Of course, we could hit the ball a great deal harder, but if we hit it so hard that a spray of particles of leather and cork, and splinters of willow left the bat, it would travel neither very far nor very fast.
Cheers,
Jon
