Projectile trajectories

By Marcus Wilson 01/07/2011 7






7 Responses to “Projectile trajectories”

  • Here is the density of 99.9% RH air at 20 degrees: 1188.709 g/m^3

    Here is the density of 50% RH air at 20 degrees: 1194.318 g.m^3

    I DO get frustrated with cricket commentators (especially) telling me that humid air has a greater density.

    We must thunk up another theory.

  • Yes Ross – that thought crossed my mind when writing – without looking anything up I know that the molecular mass of nitrogen is pretty well 28 g/mol, that of oxygen about 32 g/mol, but that of water (vapour) is about 18 g/mol – i.e. at the same temperature and pressure humid air will have less mass than dry air.

    However, if you are in an enclosed space (like centre-court at Wimbledon with the roof down), what happens to the temperature and pressure? Just thinking logically, if the space were completely enclosed, then any evaporation of water will put more molecules into the air, and so the density will go up. However, we don’t have a completely enclosed space (or the crowd would eventually suffocate). How does this change things? Not sure.

  • One thought could be the evaporation from the ground surface is reduced with higher humidity – and less irradienace form the sun/sky. This would mean that the surface becomes a weee bit more moist as the moisture moves from the subsoil. With the roof off I suspect the ground may have a harder surface due to being dried. The higher bounce may be the increased friction between the ball and the grass. This would cause greater “slow down” of the ball when it bounces. Top spun balls would then jump higher thats for sure. Sticky wickets being good for spin bowling come to mind.

    • Interesting. So it might well be that the ball is ‘fluffing up’ as it picks up moisture and has increased air resistance. Explains the tennis issue. Now, what about the cricket ball. That doesn’t fluff-up, surely?

  • Well 2 out of 3 ain’t bad. The fluffy one is interesting. There is no doubt the Great Selection Debate that goes on between player and ball boy is all about finding the least fluffy ball. They go faster. I heard that for the second serve balls they pick the fuffiest for the greater spin.

    So the idea that high humidity effectively expands the ball is pretty convincing.

  • It might be convincing, but is it correct? Give me a humidity-controlled room, Hawkeye system, a collection of tennis balls, a moderately good tennis player and a summer student and I’ll find out…

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