On Coasting Downhill

Q: Do you coast downhill faster/farther if you are heavier?

After an engaging discussion of the whole family..

The short answer is, a heavier person will coast down hill faster than a lighter person, if all other factors are the same.

A person coasting downhill has 3 forces working on him and the bike.

• F1: A downward force parallel to the surface. F1 is proportional to the weight. (F1 = cos(angle) * M * g). Given the same hill cos(angle) is the same, and "g" is a constant, the heavier (M -- mass), the bigger F1.
• F2: The rolling resistance. I can't speak of it thoroughly, so I quote wikipedia. Basically, F2 is also proportional to weight.
• F3: Is the air resistance, which includes air displacement (like bumping into somebody) and friction. Both of these factors are related to shape and speed, but has nothing to do with weight.

So the acceleration force F = F1 - F2 - F3 = M * a.

• If F3 = 0, the acceleration will be the same for everybody, since F1 and F2 are proportionate to M.
• When F3 > 0, its net negative effect to a lighter person is greater to a heavier person.

Solely and only due to the effect of F3, a heavier person is impacted less by air resistance (comparatively speaking), and therefore coasts faster.

A side note on F3, specifically the disproportionate impact to a lighter object. The air displacement is the amount of air an object pushes to the side. This is the impact if I decide to rush through a crowd of people by knocking everybody down, of course with a few bruises on myself as well. However, my bruises are smaller if I am running through children (now all moms hate me), compared to running against a crowd of football players. By the same token, a bigger car, SUV, 18 wheeler, etc, has more advantage in an accident. All in all, slowing down more when coasting down the hill is very mild compared to other unpleasant consequences.

The above statement is corroborated by the advice given at Pinewood Derby races of cub scouts -- you shall make your car as heavy as possible (within the limits), and put weight as farther back as possible without losing balance.

• Since the car coasts downhill, the heavier the car is, the faster it goes.
• Arranging the weight to the back achieves the effect of raising the center of mass higher, since the race starts at the higher end of the track. This arrangement makes absolutely no difference all the way till the front of the car reaches the bottom of the track.While the car slides from a downward incline position to a level position, the weight at the rear provides additional potential energy to continue accelerating the car, compared to the ones that front-load the mass. This is the reason you see some cars "jumping ahead" of others the moment they reach the bottom of the ramp. Just so now you know.