I just did....

I didn't see any equations...

Here's the math:
https://www.bikeforums.net/road-cycli...ml#post6854653

And here for the general case:
https://www.bikeforums.net/road-cycli...ml#post6854805

This is not a new problem.

Ok I guess you didn't see my equations

Force=mass x acceleration
acceleration= force/mass
Substitute for force you get acceleration=mass x acceleration/mass (a=mg/m)
Giving you a=g which is the gravitational constant

This is true for two objects with with same coefficient of drag.

And you are right, this isn't a new problem, it's been known for a long time that gravitational acceleration is independent of mass, given the same coefficient of drag.

I don't see anything related to drag force in your getup there. Show me how the accelerations are identical taking drag into account mathematically. Take a look at my links and show me where I'm wrong.

crickets...

Here's the almost identical thread from seven years ago:
https://www.bikeforums.net/road-cycli...downhills.html

What I hate about the science of this is that I used to pride myself for going so much faster than my fellow riders downhill. I wanted to believe that is was due to superior biking skills. But that illusion has been shattered (along with my ego). Vanity leads us to accepts "truths" that science dispels.

I already said that given the same coefficient of drag, acceleration will be the same. What's different is the terminal velocity, which will be slower for a lighter rider, causing the heavy rider to be faster on the descent, but this is referring to velocity, not acceleration.

*popcorn*

Look I'm not saying the heavier rider isn't faster, they definitely are faster, that is talking about velocity, not acceleration. What I'm saying is that the acceleration is the same for both riders, but the heavier rider will reach a greater velocity due to the increase in gravitational force.

Again, I'm talking about acceleration, not velocity.

Almost right.

Coefficient of drag and frontal area are two parts of the model. Need both. Narrow is no good if clothing flop around

Are you not understanding my math? Maybe you can't follow the links? Those two links clearly show acceleration for the heavier rider is greater than for the lighter rider with the same CdA. I mean, it directly shows this. Like, numbers in, numbers out, acceleration for heavier is a bigger number than acceleration for lighter.

Don't hand wave. Show me the mathematical calculations that demonstrate your point. Otherwise, you ain't standing on solid ground.

Right, the coefficient of drag is the effectiveness of the frontal area as an air blocker. The fraction (coefficient less than 1.0) reduces the frontal area's contribution to ******ing force.

My head hurts after reading this....but one thing I know is this--guys with small frontal areas are always the ones claiming the size is negligible and irrelevant. The rest of us know better.

I see that. I should have bumped that thread. Sigh.

My frame is long and I am heavy, which aside from my understanding of the physics involved are my only attributes helping in the hills. When others drop me on Brevets, I know I will catch as long as the gap is less than 15 seconds and burning matches to stay is a waste because I will be jambing the brakes. I can't ride with small riders who blast up hills and then crawl on the flats and trying to stay with them. I cover the distance quicker at my own pace....a bit faster on the flats, a bit slower on the climbs, and way, way faster on the descents. Ah, the joys of blubber in expensive kit.

Don't worry about that. The physics argument works both ways. I used to say to the climbers of our group: "well, put a 50lb bag of rice on your back and see how fast you climb".

As a bigger dude...who tucks rather well, I find that I definitely have an advantage in terms of accelerating on downhills, but I also brake more aggressively into corners, and accelerate harder out of them. If anyone is going to catch me it's at the corners, and it's what I obsess about when descending. I need more work there, but is it inherent with being heavier as well?

lmao... I resemble that remark!

@greenlight149, I just intend to be helpful on the math problem, without the conflicts I sense shaping up.

Look first at the total force on each cyclist. Let's say straight down for simplicity.

First, force of gravity on him, which is mass * g.
Second and opposing, force of drag, which is the same or more for the heavier rider.

Total force on the cyclist is the former minus the latter. F=Fgravity - Fdrag. His acceleration is total force /mass , or (Fgravity - Fdrag)/m. The m cancels out on the first term so it's just "g", but not so for the second term. So the heavier guy's drag is divided by a bigger mass than the lighter guy, so he accelerates faster.

This is much simplified btw so there's more to it, but loosely speaking the heavier but otherwise identical object falls (accelerating) faster in air.

i saw a good sale on ladders recently

whatever the math is, I'm a lightweight guy on a bike with a higher headtube and bars than a road bike, 28s, a rear fender and rack, a helmet with a visor and a mirror--and I always get left behind on downhills by heavier riders combined with cleaner aero road bikes. Its frustrating because I am comfortable going fast so if there are turns and braking and whatnot I can easily keep ahead of people, but on straight downhills, it is very frustrating to be behind folks in a tuck and be dropped back.

So I figure its a double whammy, weight and aero.

there is an supported event my wife and I do usually every summer and you tend to see the same riders year to year. There is always a tall lady who outweighs me by quite a bit and this has happened with her and I-- she just laughed and said..."gravity my dear, gravity" as she knows her extra weight wins out. Each year when I see her I say hello in French "bonjour Madame gravity who descends faster than me" and she remembers it with a chuckle.

This is a bit tougher problem because there are significant secondary effects. On first glance though, at the same speed/same corner, a heavier person needs proportionally more cornering force as the lighter person. However, the heavier person has proportionally higher traction as well. First order estimate: it's a wash.

That said, a heavier person is also less affected by surface irregularities while the lighter person doesn't have to "groove" as hard into the corner (they can change their cornering path more easily) because they have less momentum. The heavier person doesn't bounce around as much and can push closer to the edge of traction. Whereas the lighter person's wheels will start chattering as they approach the edge of traction, the heavier person's wheels will be stuck to the ground right up until they wash out.

All in all, I think it will be the case that the heavier person can corner somewhat faster, but the lighter person has somewhat more margin for error.

you have the physics backward and need to apply some model theory.

Simply put, mass is the cube of dimensions, while frontal area is the square. So larger/heavier riders gain advantage as their mass increases faster than their frontal area.

Simple rule ----- the terminal velocity increases with size, which is why squirrels don't get hurt falling out of trees and humans do.

The concept is captued nicely by Haldane in his essay On Being the Right Size

Brian i did the math again, you are right. my apologies.