Physics of Descending
 

It's been awhile since I did physics on a regular basis.

But on today's ride, I noticed that my fellow riders were really out-descending me. By a few MPH.

It appears that, if you assume negligble rolling resistance and that coefficient of drag are the same for each rider (which is a leap, bigger riders are likely to have more frontal area and thus more drag), that terminal velocity while going downhill is directly proportional to the square root of the mass of rider + bike.

Therefore, assuming that my fellow riders + bike weight are 20% more than me (which I think is accurate since my weight + bike is around 170 and theirs is around 205, which is 20% more than mine), their velocity going down a hill is roughly 10% faster than mine (square root of 1.2 is 1.095).

Any physics people out there to comment? I would like to think my assumptions and calculations are roughly correct. The calculations do seem consistent with what I observed, they were going around 10% faster than me.

If I screwed up anything obvious, please let me know and correct me. Please don't split hairs over rolling resistance (tire pressure etc.) or different frontal areas, I am assuming these are all the same for each of us.

P.S. from what I can tell, this analysis is correct regardless of the downhill slope. Yes??

Worrying about different frontal areas is hardly splitting hairs, especially when you indicate they're larger than you.

If you are bent over in a descent, I highly suspect the frontal areas are comparable. If you really wanted to help, you could incorporate the difference in frontal areas into the calculation, but that's going to be very complex and depends on rider's position.

Thanks for your input.

The analysis is totally correct to first order. Even better for heavier riders is that if they have more muscle due to that weight, they'll be able to really mash at the pedals when going downhill. Frontal area will have an effect, but I believe that the effect will be small, especially if everybody is hunched over in hashtag aero positions.

Do you reach terminal velocity? For more than a few seconds at a time? How fast doe you accelerate? How fast could you reach terminal velocity? The acceleration is the acceleration corresponding to the rider's mass and the NET force that is the difference between the ******ing forces and the gravitational pull (corrected for the grade). So differences is rider mass are magnified by subtracting the drag forces from gravitational force. Supposing your gravitational force going down is 0.1 of your weight at a 6 degree down slope. Supposing you weigh 180 lb. Joe Blow weighs 160 lb. Not such a big difference between 18 lb of descending force and 16 lb. but now subtract the same drag force from each. The relative difference is much greater. He will a accelerate much more slowly than you.

Frontal area to weight is inversely proportional.
Cycling: Uphill and Downhill

When descending I will pedal until I spin out my legs, then tuck in tight.
At 195 lbs. I have excellent descending "muscles":lol:
In our club rides I find the smaller riders drafting me on descents.

Doubling weight reduces frontal area by half?

If only.

I'd kick Cancellera's ass

How is ignoring rolling resistance splitting hairs? There are two terms in the equation of motion that scale with mass: 1) the driving force due to gravity, and 2) the ******ing force due to rolling resistance. How can you justify including the first, but ignore the second? Perhaps you meant changes in the coefficient of rolling resistance which will depend on tire size, construction, and inflation pressure; but not on weight.

Thus, the terminal velocity is roughly proportional to the square root of the ratio of M/A. Scaling reveals that larger cyclists have a greater ratio of mass to frontal area. They therefore descend hills faster as a consequence of purely physical, not physiological, laws

Just noticed asgelle's location. Albuquerque, Heisenberg, Coincidence?

I think not.

I am pretty sure that rolling resistance is not much of a player in this situation. Feel free to prove me wrong. But I think it's a reasonable assumption to get a ballpark estimate.

We're not looking at the effect. but the change in the effect with changes in mass. A 20% change in mass increases the driving force from gravity by 20% and also increases the ******ing force from rolling resistance by 20%. Since the OP wants to neglect this change, I'd say it's incumbent on him to show it's negligible. From the above, it's not obvious that it must be.

Your statement is both completely incorrect and not supported in the article you referenced. Frontal area increases monotonically with weight in general, bit there is no proportionality either direct or inverse. Because are is a second order function and mass is a third order function, mass increases more rapidly than frontal area.

It is a reasonable assumption that frictional forces contribute a minor fraction of the ******ing forces as compared to air drag.

It is not about terminal velocity racing down a hill it is about acceleration. If terminal velocity were important at all, it wouldn't be the magnitude of the terminal velocity, but rather how fast it is reached. We are not, in general, talking about bikes going as fast they they can down a straight ramp, but complex maneuvers with acceleting, braking, cornering, etc. Beside the handling issues, the most important characteristic is acceleration TOWARD terminal velocity, not riding at terminal velocity. That acceleration starts up again after every slowdown. So the net acceleration is what matters or weight acceleration offset by drag deceleration.

jesus christ

Not relevant.
Famous for ascending.

Steve Martin got it right...

http://speechable.s3.amazonaws.com/images/87016r02.png

:lol:

why wouldn't you also factor in the wheel hubs. Various hubs will enable less rolling resistance.

Small potatoes compared to air drag.

How dare you make such an unreasonable request here in the 41. :mad:

Oh man...Cackling over here... :roflmao2: