Right, but the wheel edge is how you measure the bike riders speed - no?
Right – the speedo on the bike will show increasing speed in the corners. If you measure the rider’s speed just before the curve, and right after the exit, you would get an accurate measure of increases or decreases in speed. The “g” term in the Crr equation will increase in the curves, but I don’t know for sure what happens to axial wind speed on the rider. Andy would know…
But the main thing is that riders don’t slow down as much in the turns as they think they do.
So the bike-rider system actually speeds up in the turns and in shorter radius turns the acceleration is greater?
The bike-rider system doesn’t speed up – only its outer edge speeds up. That is, the wheel edge.
Of all the fascinating little bits of physics involved in cycling, this is one of my favorites. It’s rather counter-intuitive and neat.
Look at the graph of the bike speed as it goes around the track. Most bike computers calculate bike speed based upon wheel rpm. If the speed drops the wheel rpm drops. Bike speed normally drops (if power is kept constant) when one turns. I suspect what you are thinking is having the center of mass inside of the circle being traveled lessens the speed loss that would normally be present (because momentum must be maintained) but does not prevent it. This is probably true for all cornering on a bike because the bike leans into the turn, whether the track is banked or not.
Is it better for the race to hold back a little on the straights so as to be able to increase effort on the turns to maintain a constant speed or to ride at “constant” power (I doubt the power is really constant and the rider probably increases some coming out of the turn to bring speed back up, but I don’t know what really happens) and accept such speed variations between the turns and the straights? Which is the better strategy and how much difference does it make?
From a physical (physics) perspective, it’s essentially a wash. The same is true from a physiological perspective, except that it becomes increasing difficult to ‘lift’ one’s effort during the transition from turn to straight as fatigue develops (e.g., during a pursuit). From that perspective, then, riders may be able to go slightly faster if they try to “power the turns and float the straights” instead of “powering the straights and floating the turns”. This will only be true, however, if the differing strategies result in significant differences in average power output.
I slept on this a little bit and I have to ask you this. Have you actually done the calculations that “proves” this is a wash? It seems to me that the same principle applies here that it does when climbing, that we have been discussing in another thread. The only difference is instead of being a series of rollers (ups and downs) this is more like a stair step, short inclines followed by short flats. Anyhow, it seems the same principle applies that it is best to put out the maximum effort when everyone is going slower and a lesser effort when everyone is going faster compared to either a constant effort or the vice versa. Since these races are often decided by fractions of seconds a small advantage in speed could be a big racing advantage. The reasons this coach might think this an advantage is starting to make some sense to me. Wonder if it can be pulled off and what the size of the “advantage” might be. Any comments?
Have you actually done the calculations that “proves” this is a wash? It seems to me that the same principle applies here that it does when climbing
Yes, I have done the calculations (ironically, initially also at the behest of the coach of a national team), and yes, the principles (i.e., those of physics) are the same as when considering what happens when you climb or descend a hill, pedal in a pulsatile manner, etc.
Have you actually done the calculations that "proves" this is a wash? It seems to me that the same principle applies here that it does when climbing
Yes, I have done the calculations (ironically, initially also at the behest of the coach of a national team), and yes, the principles (i.e., those of physics) are the same as when considering what happens when you climb or descend a hill, pedal in a pulsatile manner, etc.
Hmmm, wonder if it was the same national team? European perhaps? Big time cycling nation but not top tier as track racing goes? No matter, as we are discussing this from a theoretical basis. Since you have done the modeling, as evidenced by the graph you posted, if should be a simple matter of changing the power on the curves and straights various amounts to see what changes occur. Could you do this, tell us what changes you made, and post the graph so we can see for ourselves how the changes affect the outcome? Since you agree the principles are the same it seems there should be an advantage, albeit, perhaps, a small one, such that it isn’t really “a wash”.
By “center of resistance” do you mean center of mass? I’m thinking of it as the inertial resistance to the acceleration.
The reason that I said “center of resistance” is that some resistances are mass-dependent (e.g., inertia, rolling resistance), whereas others (e.g., wind resistance) are not. Moreover, the center of mass and the center of wind resistance don’t necessarily coincide, nor are they really known/measured (although it’s easy enough to make reasonable approximations).
So the bike-rider system actually speeds up in the turns and in shorter radius turns the acceleration is greater?
Whether the mass of the entire system accelerates (i.e, whether the stored kinetic energy increases) or not as you pedal through the turn will depend on whether or not the rider’s power output plus the small reduction in potential energy (due to leaning over) are greater than the resistive forces - if they are, you will accelerate, but if they aren’t, you won’t.
even in cycling wouldn’t you have (for lack of a better word) Slippage up the track so you would be losing some speed and power on the bike to that force trying to push the bike to the outside? I think thats where the loss occurs, with you introducing another force to it.
Bicycles (and motorcycles) corner by pivoting around the contact patch of the rear tire, so there will be some increased rolling resistance due to this tire “scrub”. This is far smaller, however, than the increase in rolling resistance due to the increased normal force in the turns. Despite this, your apparent (i.e., wheel) speed increases, due to the fact that your center of resistance “cuts inside” the radius of the turn.
since these races are timed to the .001 sec it seems that there might be a possibility that a small advantage one way or the other might be a significant racing advantage if everyone else is using the lesser technique.
As I said, my calculations indicate that it is essentially a wash, i.e., the difference is insignificant, at least given realistic variations in power input. Moreover, keep in mind that even if one strategy were theoretically better than the other, it would be difficult for a track cyclist to precisely execute the better strategy…things simply happen too quickly and there’s too much else going on to expect, e.g., a kilo rider to try to perfectly titrate their power in the turns vs. the straights to gain that 0.001 s (or whatever).
Putting on my coaching hat (which I rarely wear ) for a minute, I’d counsel people to try to “power the turns and float the straights”, because even if the physics are a wash this tends to counteract the physiological/psychological tendency to “rest up” too much in the turns, thus producing less power and going slower overall.
When you bank the bike, you decrease the effective wheel circumference by riding on the “sidewall” of the tire, affecting cadence, angular velocity of the wheel, and aero drag of the wheel.
Not to beat a dead horse, but your effective wheel circumference may decrease by a tiny amount, increase by a tiny amount, or not change at all, depending on how your speed compares to that which results in you remaining perfectly vertical with respect to the banked track. Nonetheless, the speed of your wheels always tends to increase.
since these races are timed to the .001 sec it seems that there might be a possibility that a small advantage one way or the other might be a significant racing advantage if everyone else is using the lesser technique.
As I said, my calculations indicate that it is essentially a wash, i.e., the difference is insignificant, at least given realistic variations in power input. Moreover, keep in mind that even if one strategy were theoretically better than the other, it would be difficult for a track cyclist to precisely execute the better strategy…things simply happen too quickly and there’s too much else going on to expect, e.g., a kilo rider to try to perfectly titrate their power in the turns vs. the straights to gain that 0.001 s (or whatever).
Putting on my coaching hat (which I rarely wear ) for a minute, I’d counsel people to try to “power the turns and float the straights”, because even if the physics are a wash this tends to counteract the physiological/psychological tendency to “rest up” too much in the turns, thus producing less power and going slower overall.
Thanks. Can you give us an estimate as to how much power variation (around the average) it would take to maintain a constant speed around the track at normal racing speeds?
Can you give us an estimate as to how much power variation (around the average) it would take to maintain a constant speed around the track at normal racing speeds?
The short answer is “a lot”.
The long answer is “it depends on precisely what you mean by ‘normal racing speeds’, the radius of the turn, and the height of the center of mass”.
EDIT: Okay, I ran the numbers: for a bike+rider with a total mass of 78 kg that is centered 1 m off the ground, who is producing 300 W at the crank and traveling 13.07 m/s when they enter a turn with a radius of 24 m, the wheels will tend to accelerate even if the rider’s power output immediately drops to zero. IOW, the only way that they could maintain a perfectly constant wheel speed is if they actively resisted the cranks upon entering the turn.
I don’t know for sure what happens to axial wind speed on the rider. Andy would know…
That would depend, of course, on the radius of the turn, the height of their center of mass, how fast they are traveling entering the turn, how much they modulate their power output, and possibly other factors that I can’t think of at the moment. 
Looking at some of my wife’s data, though, it appears that the speed of her center of mass remains essentially constant during the transition from straight-to-turn and turn-to-straight during a pursuit. Assuming that her center of wind resistance is similar to her center of mass, this would imply that the axial wind speed (but not the velocity) remains essentially constant.
“… this would imply that the axial wind speed (but not the velocity) remains essentially constant.”
Could you clarify this? If speed is constant and direction is fixed since it’s limited to axial, how does velocity change?
“… this would imply that the axial wind speed (but not the velocity) remains essentially constant.”
Could you clarify this? If speed is constant and direction is fixed since it’s limited to axial, how does velocity change?
Perhaps I shouldn’t have said “axial” (although I was just attempting to address Ashburn’s question).
Anyway, my point was simply that on a track you follow a curved path that sees you rotate 180 deg counterclockwise every few seconds, such that speed and velocity aren’t necessarily interchangable.
Can you give us an estimate as to how much power variation (around the average) it would take to maintain a constant speed around the track at normal racing speeds?
The short answer is “a lot”.
The long answer is “it depends on precisely what you mean by ‘normal racing speeds’, the radius of the turn, and the height of the center of mass”.
EDIT: Okay, I ran the numbers: for a bike+rider with a total mass of 78 kg that is centered 1 m off the ground, who is producing 300 W at the crank and traveling 13.07 m/s when they enter a turn with a radius of 24 m, the wheels will tend to accelerate even if the rider’s power output immediately drops to zero. IOW, the only way that they could maintain a perfectly constant wheel speed is if they actively resisted the cranks upon entering the turn.
What you describe is truly an “imperceptible” and fleeting change as it is not reflected in the modeling you did that I posted to start this thread, at least that I could see. If it is, could you point it out.
Anyhow, let me rephrase my question. What would be the required power variation to keep the speed of the center of mass essentially constant around the track under the conditions you specified. I figured the answer might be “a lot”. I was looking for an answer something more like 25% (400 watt average, 450 in the curve, 350 in the straight) or something like that, whatever that number might be.
What you describe is truly an “imperceptible” and fleeting change as it is not reflected in the modeling you did that I posted to start this thread, at least that I could see. If it is, could you point it out.
I’m not sure that I follow. However, if you’re wondering why you can’t avoid having your wheels speed up even by coasting (if that were possible on a track bike), yet continuing to power the bike doesn’t result in large increase wheel speed, the answer is “inertia”.
Anyhow, let me rephrase my question. What would be the required power variation to keep the speed of the center of mass essentially constant around the track under the conditions you specified.
Now you’ve changed the point of reference from the speed of the wheels to the speed of the center of mass, in which case the answer is “not a lot” (since neither the change in potential energy nor the changes in rolling and wind resistance as a result of the transition from straight-to-turn and turn-to-straight are great in comparison to the rider’s inertia).
Isn’t that chart showing variations of about .2 m/s - .4 m/s? If so, we’re talking about a .4-.8% change in speed. That sure sounds “imperceptible” to me.
Do you think you’d be able to notice a less than 1% change in speed while riding at 30 mph?
What you describe is truly an “imperceptible” and fleeting change as it is not reflected in the modeling you did that I posted to start this thread, at least that I could see. If it is, could you point it out.
I’m not sure that I follow. However, if you’re wondering why you can’t avoid having your wheels speed up even by coasting (if that were possible on a track bike), yet continuing to power the bike doesn’t result in large increase wheel speed, the answer is “inertia”.
Anyhow, let me rephrase my question. What would be the required power variation to keep the speed of the center of mass essentially constant around the track under the conditions you specified.
Now you’ve changed the point of reference from the speed of the wheels to the speed of the center of mass, in which case the answer is “not a lot” (since neither the change in potential energy nor the changes in rolling and wind resistance as a result of the transition from straight-to-turn and turn-to-straight are great in comparison to the rider’s inertia).
I understand the physics of what is occurring here. And, I haven’t tried to change anything. I am simply trying to get an answer to the basic question, i.e., I am simply trying to figure out what it takes to minimize the peaks and valleys associated with the straights and turns in the little graph from the modeling (which corresponds well to “actual” data) you did. The rider is “going slower” (or slowing down) in the curves as compared to the straightaways (where she is either going faster or speeding up) in that graph isn’t she?
Isn’t that chart showing variations of about .2 m/s - .4 m/s? If so, we’re talking about a .4-.8% change in speed. That sure sounds “imperceptible” to me.
Do you think you’d be able to notice a less than 1% change in speed while riding at 30 mph?
The only reasons the changes in speed are so small is the duration of the changes are very brief and the momentum of the rider is quite large. Although I am not a track rider I am quite certain the rider can feel the difference in effort required to try to maintain the same speed on the curves as opposed to the straights, even though the speed doesn’t change much. Even if they cannot “feel” this speed change, the changes do occur and if the rider is aware of this they can possibly minimize it. Since many race with powermeters, if they knew what variation in power was necessary at the different parts of the track to optimize the race performance they could try to do so other than by “feel”. I guess this could be done by trial and error, but if the modeling has been done, we should be able to get an answer here.
I understand the physics of what is occurring here.
Uh, your final comment suggest otherwise (see below).
And, I haven’t tried to change anything. I am simply trying to get an answer to the basic question, i.e., I am simply trying to figure out what it takes to minimize the peaks and valleys associated with the straights and turns in the little graph from the modeling (which corresponds well to “actual” data) you did. The rider is “going slower” (or slowing down) in the curves as compared to the straightaways (where she is either going faster or speeding up) in that graph isn’t she?
No: the peaks in wheel speed correspond to the turns, whereas the valleys correspond to the straights. These flucuations in wheel speed cannot be prevented without very large changes in power output - in this case, to the point that they’d have to actively resist the pedals upon entering the turn.