In practical terms, the actual variables involved here are mass, air resistance and rolling resistance. Of those variables, mass is the most important when comparing riders on similar bikes.

Tandems are a good example of this. Roughly double the mass of a single rider, but with almost equal air resistance. With twice the momentum and potential energy, tandems reach a much higher terminal speed.

I can confirm, as just about everyone I ride with is considerably heavier. In order to keep up with them downhill, I need to be more aero, more skilled, and more on my pedals out of each turn.

Steady state downhill coasting speed is a simple static force balance. On one side is:

weight * grade

On the other side is:

(rolling resistance * speed) + (drag coefficient * frontal area * 1/2 air density * speed^2)

A heavier rider descends faster because body mass scales more quickly than frontal area.

Assume a spherical cow in a vacuum.....

Why do changes in mass have a cubic function? Force due to gravity is linear with mass, so I must be missing something obvious?

Perhaps I should have stated same power with the same cadence.

But that's my question. Riding the SAME POWER, for example 180 watts in a headwind vs. 180 watts in a tailwind. It may be all in my head, but forget speed, it feels more taxing to my legs with the headwind than tailwind with the same wattage output.

Went out on a gusty day with the intent to keep at a fixed power and approximate heart rate. Result, it was a dismal failure. I pushed into the wind at about 190 W and with the tailwind, pushed even harder trying to get a PR on a 3 mile stretch at 280 W. I didn’t get the PR so it was a failure.

The more I think about it, the more I think you are right and hit the nail on the head... perhaps mine.

Of course I own a power meter. That's why I asked the question. The ride that caused me to write this had me riding the same power both into a headwind and a tailwind. I do like your idea of observing my HR in both situations. I didn't think of that.

My HS physics teacher clearly had issues with cats. Cats in a vacuum, a 15 lb cat hanging from a clothesline, a cat launched at a 30 degree angle, the coefficient of friction between the cat and the floor. Of course the infamous cat that drops just as the blowgun dart is fired. Can't remember his name, but he rode a BMW motorcycle in the 70's, which nobody did.

Steady state, I agree this is a good representation of the physics. What I am struggling with a bit is that lighter riders also tend to accelerate more slowly at the start of descents. Perhaps they just don’t put as much power into getting up to speed and if everyone coasted they would be more on a par.

Think of it as an advantage that's always there, but which gets larger as speeds increase. I've found that even coasting of softpedaling, I coast away from lighter riders on descents.

If the riders start the descent from a standstill, then they will accelerate at the same rate initially.

Very good question! Having thought more about it, I’m not sure it’s correct either. Here is the source of that specific info for reference.

https://www.cyclist.co.uk/in-depth/f...ownhill-faster

If we think in terms of max rolling speed, then terminal velocity is actually proportional to the square root of the mass. So not linear (as it is with the force) but certainly not cubic. Similarly, terminal velocity is also inversely proportional to the square root of CdA.

I think what they might have meant was that frontal area only scales in proportion to mass to the power of 1/3. So a large increase in mass only results in a small increase in air resistance.

I checked a few other articles but there were so many fundamental misunderstandings of the physics (some even coming from alleged post-,grad theoretical physicists!) that I gave up in the end. In particular, the classic feather vs cannonball freefall scenario becomes a large red herring once air and rolling resistance is added. That scenario also says nothing about the differences in potential energy (mgh) and momentum (mv) between the feather and cannonball.

For sure they would both start off rolling from a standstill with the same initial acceleration, but air resistance is building in proportion to the square of speed, so will soon start to take effect and slow the lighter rider more.

I think the frontal area should (roughly) scale with mass to the 2/3 power.

mmmmm…. I thought it was approx 1/3, but maybe I’m thinking of the combined CdA scaling.

Some info here:-

https://pubmed.ncbi.nlm.nih.gov/11560092/

Crank inertial load is still lower when riding into a headwind at the same power and cadence ie in a lower gear ratio. CIL is really the only mechanical difference in that scenario.

It looks like they came up with an empirical value of .76. The rough estimate* comes from:

area ~ r^2
mass ~ r^3
therefore, area ~ mass^(2/3)

* assuming a spherical cow

assuming none peddles won't they both just have the same acceleration? the only acceleration i can think of is gravity, also assuming they both experience the same effect due to wind.

Yes, and then CdA drops back to 0.31 when A is combined with Cd, which hardly changes with mass.

No

well that was concise.

after gravity what are the other forces being applied that would contribute to acceleration?

Rolling resistance of your tires, and how freely your wheels spin. That's leaving aside the aerodynamics.

That's because we have literally just been discussing this in some detail. Try reading the last few thread pages.