# Thread: Tour De France Physics Question

1. Inspired by the Tour De France I have been running a poll on my local cycling group website asking whether a 'heavy' bicycle rider would roll down a hill faster than a 'lighter' rider.
Assuming the two riders (one 50kg, one 100kg) are on identical bikes and are stopped on top of hill then roll down the hill with no pedaling and no brakes and no corners to negotiate who would arrive at the bottom of the hill first and what physics principle would be involved ?

My cycle mates swear 'black and blue' the heavy rider would get to the bottom first.
kevinc

2.

3. If you assume the frictional force on each bicycle is proportional to the normal reaction of the slope on the bicycle, then the acceleration of each bicycle+rider is independent of mass. Hence both riders will both reach the bottom of the hill at the same time.

4. The heavier riders will have a higher sectional density, hence less wind resistance in proportion to the accelerating force.

5. Originally Posted by JaneBennet
If you assume the frictional force on each bicycle is proportional to the normal reaction of the slope on the bicycle, then the acceleration of each bicycle+rider is independent of mass. Hence both riders will both reach the bottom of the hill at the same time.
Thank you Jane, my basic theory was gravity would apply equally to both riders so they should arrive at the bottom at the same time, but my cycle friends on the Sunshine Coast Queensland disagree completely.

6. Originally Posted by Harold14370
The heavier riders will have a higher sectional density, hence less wind resistance in proportion to the accelerating force.
Thank you Harold, so does this mean a heavy rider will arrive at the bottom of the hill first?

7. Originally Posted by kevinc
Originally Posted by Harold14370
The heavier riders will have a higher sectional density, hence less wind resistance in proportion to the accelerating force.
Thank you Harold, so does this mean a heavy rider will arrive at the bottom of the hill first?
Yes.

8. Originally Posted by kevinc
Originally Posted by JaneBennet
If you assume the frictional force on each bicycle is proportional to the normal reaction of the slope on the bicycle, then the acceleration of each bicycle+rider is independent of mass. Hence both riders will both reach the bottom of the hill at the same time.
Thank you Jane, my basic theory was gravity would apply equally to both riders so they should arrive at the bottom at the same time, but my cycle friends on the Sunshine Coast Queensland disagree completely.
It depends significantly on what assumptions are being made. For example, I didnâ€™t take air resistance into account whereas Harold did, so our answers could be different. :P Besides, I assumed that the magnitude of the resisting force was proportional to the normal reaction â€“ but you might assume, instead, that itâ€™s proportional to the riderâ€™s velocity, and get a different answer again.

Even if time is mass-dependent, the question is whether the difference is significant enough in practical terms. If the hill is low and steep, the difference would most probably be practically insignificant.

9. It's the same idea as if you dropped a baseball and a foam rubber Nerf ball. The baseball is heaver and will hit the ground first.

I think wind resistance is a big factor in bicycle racing, especially on the downhill runs where they go the fastest. They wear those funny looking aerodynamic helmets, they ride in a hunched over position, and draft off the other riders.

10. They should arrive at the bottom at the same time. Weight makes no difference.

We tested this principle in the Cub Scout's Soap Box Derby, in which the boys built small wooden race cars that rolled down a slope to the finish line. There was a weight limit for the cars.

The boys tested heavier cars, lighter cars, nose-heavy cars (the weight in front is supposed to pull the cars faster), and so on. Within statistical error, weight or weight placement made no difference. The fastest cars were simply the best-built cars -- the ones that had best wheel alignment and reduced friction. (They all used the same wheels so we could not test the effects of moment of inertia.)

This answers your question to a first approximation. Next we have to put up with the pesky showoffs who will try to invoke secondary and tertiary effects, such as aerodynamics, friction in the bearings, flattening of tires, road conditions, and so on. Most of their remarks are pure guesswork. Intuition is often misleading.

Why don't you and your buddies just find a hill and test your respective theories?

Â*

11. I guess I plead guilty to being a pesky showoff, but in a race like this the secondary and tertiary effects become important. All the racers are top athletes with the best equipment. Everybody is looking for a tiny edge.

I seem to recall someone being disqualfied from a soap box derby because they had hidden a magnet in the front of the car. When the metal gate went down to start the race, it gave the car just enough extra impetus to win the race. Talk about a secondary or tertiaty effect.

12. Quite correct, Harold. It happened in the Soapbox Derby, an annual USA competition in which boys rode their home built cars down a slope. Here's a link to the news article:

http://www.time.com/time/magazine/ar...910720,00.html

This incident, and other cheating allegations, led to the quick demise of the competition.

Â*

13. Thanks Everyone, SteveF I have floated your suggestion onto the bike forum about a real world test and am waiting for a response http://groups.msn.com/hotgossipgreat...81699094903619

I have been informed that there is a 'chainless downhill Mountain Bike race' as well which should be interesting to have a close look at, altho this seems to require some skill from the competitors.

14. I found a bicycle simulator here.
http://www.analyticcycling.com/ForcesPower_Page.html

If you take the default values of .5 for the frontal area and 75 for the mass, then change the slope to -0.1 it displays a graph that shows for 0 power (coasting) the rider will be going at a speed of about 21.5.

if you increase the weight by 25 % to 93.75 and increase the frontal area by 16 % (1.25^(2/3))since the frontal area increases by the square of the dimension and the weight by the cube, the speed is a little over 22.

15. Originally Posted by SteveF
They should arrive at the bottom at the same time. Weight makes no difference.

We tested this principle in the Cub Scout's Soap Box Derby, in which the boys built small wooden race cars that rolled down a slope to the finish line. There was a weight limit for the cars.

The boys tested heavier cars, lighter cars, nose-heavy cars (the weight in front is supposed to pull the cars faster), and so on. Within statistical error, weight or weight placement made no difference. The fastest cars were simply the best-built cars -- the ones that had best wheel alignment and reduced friction. (They all used the same wheels so we could not test the effects of moment of inertia.)

This answers your question to a first approximation. Next we have to put up with the pesky showoffs who will try to invoke secondary and tertiary effects, such as aerodynamics, friction in the bearings, flattening of tires, road conditions, and so on. Most of their remarks are pure guesswork. Intuition is often misleading.

Why don't you and your buddies just find a hill and test your respective theories?

Â*
How much heavier did you make your cars? Also the surface area of the car and the very low speed makes the soap box car a poor experiment to prove that weight does not matter.

A bicycle rider on a special bike that had the spokes covered made it to 98 miles an hour. So wind is important to bikes.

I used to ride a Schwinn Continental I was just talking to a bike racer about it last night. He was saying that, the old Schwinn Continental was over 40 pounds and the newer racing bikes are well under twenty pounds. I weigh in at a heaping 215 and the fellow I was talking with is probably a lean 160 pounds.

A long time ago I was going down a block that runs just slightly downhill and the cars, although it is a 30 mile an hour zone. Often hit 50 miles an hour. I used to leave those cars in the dust on that block, the last block before I got home. And I could tell they were doing about 50 miles an hour.

But that slight incline and the sweet gearing of the Schwin was amazing.

Sincerely,

William McCormick

16. If both riders have very good bikes with bearings that do not exponentially loose lubricant power with weight, then the heavier rider would go a little faster, as long as they are not larger along with the weight, which would then cancel out the advantages of weighing more due to wind resistance.

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