Remember Superballs, aka Super Balls aka Bouncy Balls? Described here (wiki link).
Considering a golf ball sized version, in multicolor because that’s the coolest, what is the highest theoretical bounce possible? Does the answer change for different sizes?
I assume there is some point where the impact would destroy the ball, or otherwise render it unable to bounce to maximum height…
I don’t know, but finding the answer sounds like a fun way to spend an afternoon.
Are we talking simple drop (i.e., simply letting gravity take the ball until it reaches terminal velocity) or assisting gravity via some sort of Superball cannon?
I’m sure we’re talking about a cannon - obviously the OP has tried throwing the ball down forcefully and wants to know what happens if you take it to the next level.
I had one that bounced all the way up to the moon, off it’s surface, and back down to earth where I caught it in my teeth. Had the moon not been there it probably would have gone all the way up to the sun and melted, so I was lucky to get it back. I first told about my experience with the superball to a group of awe struck children on the playground circa 1968 at the age of 8 years old.
That’s my story, and I’m sticking to it!
I was thinking more along the lines of a simple drop. The problem with a cannon is that it would need to be aimed straight down, and would likely block the rebound. If that or similar complications can be avoided, I’d have no objection to a cannon.
Should we consider the effects of the atmosphere?
My guess with dropping it is that the rubber would be able to withstand terminal velocity, so you just need to figure out what that is for a sphere of that size and weight, and that will give you the limit.
Yes, particularly if we get into cannons or other means of assisting gravity. Probably also ought to give some consideration to the composition of the reflective surface. Dents, impact craters, and the like will probably affect bounce height.
Wouldn’t the answer be based strictly on the sphere’s diameter? It can only flatten so much so the rebound potential reaches its maximum (I presume) when the rubber ball is flattened as much as it can go.
I think that would give me the drop point, but not necessarily the height of the resulting bounce. Also kinda wondering if there is a point where increased velocity will not translate into a higher bounce…
ETA: Whack-a-Mole beat me to it.
I was just saying that would be the limit - it can’t possibly bounce higher. It may not get anywhere close if it’s limited by other factors such as the rebound potential of the rubber as Whack-A-Mole pointed out.
Once again, I think the best way to get to the bottom of this is with some experimentation (dropping a bucket of superballs from a plane maybe?).
edit: Actually I still think a cannon would be more practical for real testing. Just fire the cannon down at an angle of 10 degrees from vertical onto a surface at an angle of 95 degrees, and the balls should go pretty much straight up. Being 5 degrees away from a perpendicular collision will likely influence the maximum result a little but not enough to worry about for now.
Maybe Cecil has the stroke to score permit to drop a few dozen Superballs off the Sears Tower? We’d get useful data for later experiments…
Superballs have a coefficient of restitution of .92.
COR= sqrt(bounce height/drop height) against a perfectly hard surface.
So, it should bounce to about 85% of its drop height. A 1 meter drop, then, would result in a bounce of 85cm.
Of course, we need to account for air.
The terminal velocity of a superball is pretty easy to calculate:
Vt= sqrt(2mass g\DensityOfAirAreaCoefficientOfDrag)
The drag coefficient for a smooth sphere is about .5, the density of air is 1.29kg/m^3. I don’t know the density of a superball, but it’s probably a little more dense than water, so let’s guesstimate a 3.0 cm ball with waterish density.
The terminal velocity would then be about 34 m/s, or 75 mph.
That’s about equal to a fall of 250m. (I’m not showing my math on this one, because I used my calculator’s formula.) So the highest bounce from a dropped ball would be about 215m, give or take, depending the assumptions.
BUT - first we need to know how much force it takes to start permanently deforming the ball (cracking, bursting, etc). I’d wager it is more than the force you’d get at 75 mph.
If the ball breaks below 75 mph, then your max bounce would be lower. If it breaks at more than 75, the max bounce is obviously going to be higher, but you need some sort of way to get the ball moving faster than terminal velocity. The easiest and pretty much just as accurate way is just to ignore the effect of the atmosphere, figure out the maximum impact the ball can withstand, then figure out the height of your bounce from there.
Interestingly, glass spheres have a COR of .95 – way more than that of a superball. Of course, glass spheres tend to break more easily than a rubber ball, so the effect is harder to see at normal scales.
I’d like to know how far one would go if a pitcher threw a 100 mph fast ball using a Superball and Bonds hit it as hard as he could with the sweet part of his bat.
Hopefully the ball would start rising immediately so it wouldn’t decapitate the pitcher.
A few miles?
It probably would need some golfball like dimples, as a perfectly smooth sphere isn’t aerodynamically efficient at all.
My guess would be around a third mile maximum, probably more like a quarter mile or less. I can’t imagine a superball going farther than a golf ball, and the record for a golf ball is in the 525-ish yard range.
The golf ball is just sitting on a tee before it is hit. This dimpled superball is coming in at 100 mph before Bonds drives it over the wall.
Wouldn’t this make a difference as far as the distance it would go?
Way back when the Super Ball first came out we tried every possible “experiment” with them. That was about 4 decades ago, and I don’t know whether they’ve changed the composition of the ball since then, but I do remember two things clearly:
No matter what we did, the best we could get was about 90% return on a bounce. That corresponds with ivn1188’s .92 coefficient.
It is entirely possible to shatter a Super Ball by hitting it hard enough with a baseball bat. It’s kinda cool actually, since the individual shards bounce when they hit the ground, but it does pose a limit to the Barry Bonds vs. 100 mph fastball experiment.