# Would the different weight affects the speed of bicycle when coming down slope.?

## Main Question or Discussion Point

Hi there,

If there are 2 bicycle riders who use exactly the same type of bicycle, start at the same spot but one rider is 100kg and another rider is 50kg.. would the heavier rider coming down the slope faster than the lighter rider? basically, I just want to know if the weight would affects the speed on slope..

Thank you :)
Manie

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So far as acceleration due to gravity, no there wouldn't be a difference.

Drag on the other hand could be a different issue.

Andrew Mason
Homework Helper
Hi there,

If there are 2 bicycle riders who use exactly the same type of bicycle, start at the same spot but one rider is 100kg and another rider is 50kg.. would the heavier rider coming down the slope faster than the lighter rider? basically, I just want to know if the weight would affects the speed on slope..
If the road friction and aerodynamic drag was negligible, there would be no difference. That is because the force (gravity) on each is proportional to mass so their accelerations would be identical (time of descent = $$\sqrt{2d/a}$$) is independent of mass).

If you factor in road friction, there still should be no difference. This is because the force of friction is, generally, proportional to the normal force, which is proportional to mass. So accelerations will be identical.

However, if you factor in air resistance, there can be a difference. This is because air resistance depends on shape and surface area. And for a human, surface area is not necessarily proportional to mass. The aerodynamic drag force on each cyclist could be about the same, in which case the net force on each would not be proportional to mass, so the accelerations of each would not be the same.

AM

Thank you very much for prompt replies :)
Regards,
Manie

Hi there,

If there are 2 bicycle riders who use exactly the same type of bicycle, start at the same spot but one rider is 100kg and another rider is 50kg.. would the heavier rider coming down the slope faster than the lighter rider? basically, I just want to know if the weight would affects the speed on slope..

Thank you :)
Manie
And for a human, surface area is not necessarily proportional to mass.
AM
Actually, surface area correlates very well with mass in humans.

In practice, there will be a significant difference (well known among experienced bike racers) due to the drag (the force of which is proportional to frontal area and v^2) - especially with that kind of weight difference between the riders. There will also be significant differences depending on tire pressure due to elastic hysteresis, i.e., rolling resistance.

IOW, the fat guy's going to "bomb the descent" while the "climber" pedals his/her legs off to catch him.

You can play with the parameters here:
http://analyticcycling.com

The conversation has been about acceleration so far but would the riders not have different terminal velocities? Assuming same drag force (close enough) but higher gravitational force for heavier rider, the top speed would be higher for heavier rider

Unless I am missing something?

berkeman
Mentor
I believe the terminal velocity is different, even when the aerodynamic drag is the same. Otherwise, there would not be a weight limit on bobsled teams and their bobsleds.... http://en.wikipedia.org/wiki/Bobsleigh
wikipedia said:
Modern day sleighs combine light metals, steel runners, and an aerodynamic composite body. Competition sleighs must be a maximum of 3.80 m (12.5 ft) long (4-crew) or 2.70 m (8.9 ft) long (2-crew). The runners on both are set at 0.67 m (2.2 ft) gauge. Until the weight-limit rule was added in 1952, bobsleigh crews tended to be very heavy. Now, the maximum weight, including crew, is 630 kg (1,388.9 lbs) (4-man), 390 kg (859.8 lbs) (2-man), or 340 kg (749.6 lbs) (2-woman). Metal weights may be added to reach these limits, as greater weight makes for a faster run.

cjl
It seems to me that the heavier rider would go faster, even if rolling resistance and air resistance were neglected. This is because the heavier the rider, the less proportion of the total mass is rolling (as opposed to purely translating), so proportionally less energy goes into spinning the wheels (and more goes into pure forward motion).

I was under the impression terminal velocity was down to the friction forces acting on the object. Air resistance will be the largest factor on a bike going down a hill, but if we are assuming a relatively equal body surface area, the only difference will be rolling resistance which will be higher for the heavier rider.

The difference in gravity due to differing masses, at these small scales, will be negligible.

I don't think the gravitational force difference is negligible - because the riders have different masses the acceleration balances out to be the same but when you look at terminal velocity, the higher grav force wih the heavy rider is a bigger proportion of the losses (air drag primarily) for a given speed

I could be wrong

Last edited:
Andrew Mason
Homework Helper
Actually, surface area correlates very well with mass in humans.
Assuming the density of the body is the same, if surface area is proportional to mass, all people must be the same thickness front-to-back. How can that be?

In practice, there will be a significant difference (well known among experienced bike racers) due to the drag (the force of which is proportional to frontal area and v^2) - especially with that kind of weight difference between the riders. There will also be significant differences depending on tire pressure due to elastic hysteresis, i.e., rolling resistance.

IOW, the fat guy's going to "bomb the descent" while the "climber" pedals his/her legs off to catch him.
It seems to me that this must be because surface area, hence drag, will not be proportional to mass. In this case, the drag on the 100kg rider will be less than double the drag on the 50 kg rider, so the 100kg rider will have higher acceleration.

AM

Andrew Mason
Homework Helper
The conversation has been about acceleration so far but would the riders not have different terminal velocities? Assuming same drag force (close enough) but higher gravitational force for heavier rider, the top speed would be higher for heavier rider
Exactly. When the drag force is equal in magnitude to the gravitational force (for simplicity, let's ignore rolling friction) the rider stops accelerating. So if the force of air resistance of the 50 kg rider is more than half of that of 100 kg rider (because his surface area is more than half that of the 100 kg rider) the drag force will equal gravitational force at a lower speed for the lighter rider.

AM

Assuming the density of the body is the same, if surface area is proportional to mass, all people must be the same thickness front-to-back. How can that be?
The mass comment was a separate idea from the problem. Why assume (falsely) that the density of the body is the same for everyone? Anyway, I didn't say that surface area was proportional to mass. I said that in practice (on a bike was the context) it correlates pretty well. Surface area correlates better with height, but neither is absolute.
http://www.halls.md/body-surface-area/refs.htm

Your frontal area on a bike is really a function of your size and flexibility. So if you gain mass (likely in your belly) it forces you to sit up more which further increases your frontal area. That's all I meant. Again, this is common knowledge in bike racing.

For this problem we can assume the 2 riders have the same frontal area, and the heavier rider will go faster. That's the main point.

Assuming the density of the body is the same, if surface area is proportional to mass, all people must be the same thickness front-to-back. How can that be?
But surface area is not linearly related to volume.

Cylinder
Volume = pr^2 x height
Surface = 2p radius x height

A 150lb person may have half the mass of a 300lb person, but he certainly doesn't have half the surface area.

uart
But surface area is not linearly related to volume.
Exactly right. The ratio of aerodynamic drag force to gravitational force is generally less for the heavier rider. For a racing style bike at the type of speeds you descend a hill the overwhelming majority of resistance on the bike and rider is due to air resistance. So yes, as any cyclist can attest to, this effect is quite noticeable in practice. Heavy riders can typically descend faster and with less effort than lighter riders. The light weight riders of course can often whoop the heavier riders backsides going uphill.

Ranger Mike
Gold Member
see Tiny Tims post in Mech Eng Forum

About 2 vehicles going down hill

Jan27-11, 05:41 PM

he did a great job summing up how mass effects acceleration

sophiecentaur
Gold Member
My experience was always that I always had to keep braking to let my kids catch up with me when freewheeling down long, gentle slopes. The tyres weren't identical and could have accounted for some of the effect, I guess but the difference in terminal velocity was very noticeable.
It's not surprising if you consider the extremes of Elephants and Bumblebees. You just don't get flying elephants but bumblebees can keep up by flapping very small wings (not much bigger than Dumbo's Ears aamof) in an atmosphere which, for them, is almost like treacle - viscous forces being much more significant than gravitational forces at that small scale of things.
Aerodynamics must play a big part in cycling or else why would racing cyclists use pointy hats? (It can't just be a fashion statement . . . . . . could it?)

So really load up with energy bars in your pockets at the top and throw them in the ditch at the bottom of the hill. Allez!

sophiecentaur