OK asknott, on to rolling resistance. You understand that, as zut says, rolling resistance is small potatoes compared to wind resistance, so this is an academic debate at best.
But I submit the larger rider has an advantage, going downhill. Reasoning is that some portion of the rolling resistance is proportional to weight (call this proportional rolling resistance, or p.r.r.). Since gravity’s force is also proportional to weight, then the p.r.r. affects the speed of both riders equally (The rider that’s twice as heavy has twice the p.r.r. force of drag, but has twice the gravitational force pulling him down, too. So the p.r.r. essentially reduces the gravitational force by the same percentage for each rider).
But there is probably some portion of the rolling resistance that is constant and/or depends on speed. For instance, if the rider is pedalling, there’s friction from the chain and gears, which won’t depend on weight). And this non-weight dependent part of the rolling resistance will slow the heavier rider less.
Now, it’s likely (I’ll even say probably) true that the biggest part of rolling resistance is in fact proportional to weight, so I’m not saying the effect is large or noticeable. But then again, as we said this is all academic anyway.
Ah I see. I agree with you that the friction force for the heavier biker would be greater. However that does not translate to any practical difference becuase the two bikers will have the same max acceleration correct?
** AskNott **
I did not include the rolling friction becuase its extremely hard if not impossible to calculate without experimenting.
Ain’t no way. A heavy guy on a bike rolling down a hill doesn’t come close to the bearing’s capacity.
If you have any doubts, consider what the bearing has to cope with under shock loads (hitting a bump, say). Those shock loads woud be orders of magnitude higher than the load the bearing is under on a smooth surface.
Bearings are only very rarely damaged. Even with rough handling.
They are nowhere near their capacity under normal rolling conditions.
You have a cite for that? I know plenty of guys who are up round the 260 mark who don’t have any tire problems, or get noticeably hot tires, or have problems with damaged rims (which they’d have to from bumps if they were riding perilously close to zero margin between rim and ground).
Everything else being equal, it shows that going from a 160 to a 260 pound rider will, for the same power output, at say 45-50km/hr result in about 1 km/h speed difference.
45-50 km/h would be a common downhill speed for a modest hill.
That doesn’t follow. I would expect a heavier bike to be faster, even without a rider, even starting from a dead stop. The rolling resistance will certainly be greater for a heavier bike, but the question is whether it’s a greater proportion of the forces on the bike.
What it gets down to is this. Everyone agrees that rolling resistance is greater if the weight of the bike/rider is greater - the rolling resistance is monotonically increasing with weight. But is it a linear increase? For example, with a 2x heavier bike+rider, will the rolling resistance be 3x? Or 2x? Or 1.5x? All this argument that it is monotonically increasing doesn’t address the key question of whether it’s linear. I suspect that it’s slightly less than 2x, giving yet another advantage to the heavier rider in downhill speed.
But in any case, the variation from linearity for rolling resistance is dwarfed by the variation from linearity in wind resistance. A 2x heavier bike+rider will not have anywhere near 2x increased wind resistance, and this is the key that makes the heavier rider go faster downhill.
The equations are set out in that cite I gave in my last post. Rolling resistance is linear.
To give perspective, I weigh about 210 pounds including bike. According to the calculator given in that cite, by the time I’m doing 11 mph air resistance equals rolling resistance. A quick experiment on the modestly sloping street outside my house showed that I reached that after about 5 seconds and about 15 yards.
No, your cite approximates rolling resistance as a linear function. It doesn’t show how accurate this approximation is. I think CurtC is right, it increases slightly slower than linearly. If it were truly linear, then adding extra wheels to a vehicle (while keeping the total vehicle weight constant) would not increase rolling resistance. This seems unlikely to me. (And in my experience, a trike is always slower than a bike with similar weight and similar rider position.)
I was puzzled by this same question. I frequently ride bikes with my sons, who are about 50 lb while I am 180 lb. I coast MUCH faster than they do.
They have less weight AND less cross section. More weight should increase friction (rolling and otherwise), so that doesn’t help at all.
However, according to Newton:
sum(F) = ma = m*(rate of change of speed, dv/dt)
m * dv/dt = mg (if no air resistance and dv/dt = g, so mass doesn’t matter).
HOWEVER, if we model air resistance using the standard constant time velocity squared:
m dv/dt = mg - Kv^2
If we assume the constant K is the same for both riders (both have the same bike, same cross section, etc etc) then:
dv/dt = g - (K/m) * v^2
We see that the term “K” gets divided by mass, so the effect on the heavy rider is that air resistance is significantly less. He is experiencing the same force, but not the same deceleration.
I am surprised and dismayed that in the 21st century people don’t understand such a simple question. Do people really not know that in the absence of a vacuum a Styrofoam ball will fall slower than a ball bearing of the same size? WTF do they teach in school?
I understand that the more subtle questions of rolling friction and the relative cross section of heavier people vs lighter is not obvious.
I couldn’t find it but in the ‘Jumping with a balloon tied to you’ thread, people where still arguing that they where right mathematically even after videos proving they where wrong where posted :rolleyes:
Do you all have the same kind of bikes? I used to ride with my girlfriend. I had a 10-speed road bike and she had a hybrid bike and I would overtake her on flat stretches while she was pedaling and I was just coasting. Weight didn’t have much to do with it, it was mostly the tires.