Tennis ball bounce reference footage & research

Started doing a little planning for the first of the three ball bounce exercises - the tennis ball. I did try in vain to get hold of my own ball to film, but was completely unsuccessful. The only ones I could find that weren't professional grade were 74p from Pets at Home and didn't bounce properly - so, until such a time I'm able to get hold of one, I'll have to make do with raiding Youtube.

I did find an interesting website called Animation Physics that offers a large number of handouts covering details of real-world physics and their application to animation. It's incredibly heavy reading and very, very mathematical. Their handout on the physics of timing and spacing refers specifically to dropping and bouncing balls of varying types. It's very heavy stuff, with lots of precise formulae and calculations regarding drop speed and air resistance etc. I wasn't able to make complete sense of it but I did manage to pick out a few key pointers that I thought would be useful:

The spacing between poses of a falling object can be calculated using a principle called "the odd rule." Basically, it means that the spacing of the object will increase following a ratio of 1:3:5:7:9:11. So, following the first pose (or drawing, whatever) the second will be spaced three times as far, then 5 times, then 7, etc. etc.

To be totally honest, it sounds really convulted and confusing and mathematical - I think, to really dumb it down, what it's saying is "make sure a falling object gets faster." Which makes those last two paragraphs completely redundant. Oh well.

The tutorial does come bundled with some lovely reference clips however, including some rather excellent footage of a ball being dropped in slow motion:

It's fair to assume that it's probably not a tennis ball - it looks like one, but doesn't bounce as high as you'd expect one to. It only reaches a third of its initial height, when tennis balls tend to reach around half their original height (as shown in the videos below.) It is useful for analysing overall drop speed and spacing, however!

There's an astonishing lack of bouncing tennis balls online, but after a bit of digging I was able to unearth a couple of other decent clips:

This one is particularly interesting as it breaks down the speed of the ball's drop in a fair amount of detail. The video highlights the fact that the ball loses half of its height with each successive bounce - it's dropped from a height of 2 metres, which means that with each bounce it would hit 1 metre, 1/2 metre, 1/4 metre, 1/8 metre and so on until its energy is exhausted.

The height isn't specified in this video, but if we assume that it's also dropped from about 2 metres we can again see that the ball's height is roughly halved with each bounce. The ball bounces around 6 times until its energy is completely depleted and it comes to a rest. The ball takes around 16 frames to drop from its apex (peak) and hit the floor - using this as a basis we could assume that a ball dropped from 1 metre would take around 12 frames (half a second) to hit the floor. Giving the ball 4 -5 bounces until its energy is depleted would make the total time around 2 - 2 1/2 seconds (about 50 frames).

I'm starting to sound very mathematical, but I'm just using this as a rough guide to get me started, a basis to work from - I'd imagine that the final animation will end up deviating from these times somewhat! What's physically correct in reality doesn't necessarily look good on screen. A lot of the timings will be tweaked by eye in order to avoid getting something stiff and a bit lifeless.