[math-fun] Bowling Ball physics
I have no idea what the underlying dynamics are for a spinning bowling ball -- I'd have thought it was relatively simple: that you could model a variable-density sphere as a uniform density sphere with an offset [point] weight. But apparently not. The bowling ball manufacturers have continued to come out with fanciful and interesting "core layouts" for bowling balls. I mentioned this once before [year or two back] but I happened to recently run across a "directory" of recently released balls with core layouts. For your amusement: <http://www.fantasyfarm.com/bowl> /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
Gene would know more about this than I do. But off-the-cuff, the dynamics is going to be determined by the inertia tensor (3 components, modulo isometry) in addition to the mass and centre of gravity (1+1, assuming sphericity). So you do have a few variables to play with. There's also the finite density range, though probably not also the elasticity, of available materials to take into account. Incidentally, can we assume that the (interior) of the ball is entirely rigid? If so, it does seem difficult to imagine how some of the configurations on offer can be justified by dynamical considerations alone! WFL On 3/9/08, Bernie Cosell <bernie@fantasyfarm.com> wrote:
I have no idea what the underlying dynamics are for a spinning bowling ball -- I'd have thought it was relatively simple: that you could model a variable-density sphere as a uniform density sphere with an offset [point] weight. But apparently not. The bowling ball manufacturers have continued to come out with fanciful and interesting "core layouts" for bowling balls. I mentioned this once before [year or two back] but I happened to recently run across a "directory" of recently released balls with core layouts. For your amusement:
<http://www.fantasyfarm.com/bowl>
/Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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On 10 Mar 2008 at 0:05, Fred lunnon wrote:
Incidentally, can we assume that the (interior) of the ball is entirely rigid?
Yes -- things aren't allowed to slide around inside or anything interesting like that.
If so, it does seem difficult to imagine how some of the configurations on offer can be justified by dynamical considerations alone! WFL
Yup, that's what I've been thinking. But month after month they come out with more "core designs". The two big things they talk about are "radius of gyration" and the "RG differential". I'd think that even if those are the key "dynamic criteria" that determine how a ball reacts, it'd be easier to get a particular set of values with some sensible-seeming mass-distribution, rather than these mushrooms, stacks, wedding cakes, etc... Another interesting thing behind the core shape is the idea of "track flare". What happens is that the ball is drilled so that when the bowler throws it the rotation-axis is NOT aligned with the weight-axis. This means, of course, that the ball "wobbles" as it rolls until it settles down to a true roll [with the weight-axis aligned with the rotational axis]. What's happening is that the surface of the bowling ball is, basically, sandpaper but sandpaper that "clogs" very easily [in this case, it clogs with the oil/dressing on the lane]. If the ball rolls consistently, after a rotation or two the ball-surface contacting the lane will be all oiled-up and the friction will go WAY down [and the ball will basically just-skid and not hook]. BUT: with the "Wobble", with each revolution, as the ball precesses, *new*surface* keeps coming into contact with the lane and so there's lots of friction [and so lots of 'grab'] for a long way]. That wobble is called "track flare". /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
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Fred lunnon