# What goes up… must come down

By Marcus Wilson 26/03/2010

Yesterday morning while driving into work I was reminded that this week is ‘Balloons over Waikato‘ – the annual hot air balloon festival.  It was hard to miss; I counted 20 balloons making their way gracefully over south-east Hamilton and drifting slowly towards Morrinsville. (NB: I counted the balloons AFTER I had parked the car, not while driving, in case you are worried.)

Then this morning I was treated to the sight of a balloon landing on the University sports fields. I say ‘landing’, but don’t get the impression this was a smooth touchdown. There was a fair wind blowing – in fact I was surprised the balloons were flying at all –  and the balloon came down at about 45 degrees at a fair pace – hit the ground, did a short bounce, hit again, whereupon the basket was tipped onto its side and dragged for several metres before the balloonists manged to deflate the balloon a bit and reduce some of that lateral pull from the wind.  I’m sure it’s the kind of landing that could break bones if you’re not prepared for it.  (Not that I know – I’ve never been in a balloon – and this sight doesn’t encourage me to).

Being the physicist that I am, I think a few estimates are in order.

Wind speed – probably aroud force 3, so about 15 km/h or about 4 metres a second. Cross-sectional area of balloon – maybe about 10 metres by 10 metres, or 100 metres squared. Then, I’ll assume the balloon intercepts in one second a lump of air of size 100 metres squared times 4 metres, that’s  400 metres cubed, which weighs about 400 kg  (density of air is about 1 kg per metre cubed).  At 4 metres per second, the momentum transfered in one second is then 400 kg times 4 m/s or 1600 kg m/s.   The sideways force on the balloon, being rate of change of momentum, is then 1600 kg m/s /s, or 1600 newtons.

In context, that’s the same as the force of gravity on a mass of 160 kg.   I’m not sure how mass the basket has, but I’d imagine with a couple of people and some propane tanks it could be around 200 or 300 kg or so. So the lateral force of the wind on the balloon is fairly close to the force of gravity on the basket.  (And, while there’s still buoyancy in the balloon – the net downward force on the basket would be rather less than its weight, bringing them closer still.)

I don’t know what the coefficient of friction is for short grass, but probably not desparately high – so I’d expect that sideways force to be able to move the basket across the ground. Which is exactly what happened.

I have no idea what injuries, if any, were sustained by the crew (I was watching at a distance), but I saw one guy hop out without difficulty before I left to go to my office.