asgelle

And that right there is why the definition fails. Beside there is already a term for what you mean, "minimizing resistance force."

HTupolev

Depends on where you're looking at "resistance force."

At equal speed, the biggest reason that high cadences burn more calories is that spinning the legs in circles at a higher rate intrinsically adds effort regardless of how hard you're pushing on the pedals, not added aerodynamic drag from the legs spinning fast or whatever.

Doge

Pedaling 100RPM pushing 10lbs vs 50RPM pushing 20lbs on the pedals many would say is half the force. The mechanical work excluding human and frame heat loss is the same, the pedal force is 100% different.
Would you say both those have the same "resistance force"?

So I assume we all get kinematics. There is a human on the bike moving their legs, breathing, moving side to side.
The same bike speed up that hill will have different human calorie requirements depending on how they ride.

asgelle

Since your definition invoked speed, I assumed you meant the speed of the bike/rider system so by resistance forces I mean the sum of forces opposing motion of that system.

Doge

But how does the rider get up the hill in the same time for the least calories? I think sum of forces is not descriptive enough.
How is the sum of the forces different than work. And how is the work/time different than power? We still have (and maybe you met that) what the human can do. Muscles loading up, switching cadence, standing, sitting, shifting, etc.
Serpentine a lot, or a little. Out of the saddle at the end, or not at all, or sometimes in the middle. What cadence - do you vary it?

If you wanted to get up up the hill the fastest. You would likely stand a bit, vary cadence. Load up at a lower cadence, shift and work on another cadence. You may cut an apex, or take a higher area on the turn to sweep down.
I would not expect it to be the most efficient, just the fastest.

asgelle

O.K. I disagree. To get up the hill as fast as possible for a given rider power, minimize - weight (gravitational resistance force), CdA (drag resistance force), tire/tube losses (rolling resistance force), and drivetrain friction (drive train resistance force). There might be others but that fall way down on the list. After all that, as a second or third order effect, will be the efficiency (using the actual definition work produced per unit of energy consumed) of the rider so produce the power with 60-65 rpm cadence.

If power can vary, you look at the same resistance forces, and you can see the work performed is minimized by going as slow as possible at as low a cadence as possible. Gravity and rolling resistance are unaffected, but drag and drivetrain go as speed.

Doge

I'm trying to take it to cadence up a hill - this thread. Say all the mechanics and aero factors are exactly the same.
I don't think you are saying arriving in the same time, on the same road any RPM 40-110 will use the same calories. Are you including the human 40RPM vs 110RPM in your sum of forces. If so, I agree that is accurate, but I don't think it is common speak.

What average RPM and range do you think will use the least total energy by the human?

If this were for max speed, I'd expect a mix of cadence to be faster than a steady one, and a mix of power output to be faster than smooth power.

asgelle

If you're saying all resistance forces are kept the same, and the power produced by the rider is held constant*, then as I wrote earlier, the most efficient cadence (i.e., lowest energy consumed) will depend on the individual, but most people's most efficient cadence falls between 60-65 rpm.

That would answer your question, but I don't think it's especially relevant if you're worried about how long it takes to do a climb. Speed will be limited by fatigue (the inability to maintain a level of effort for a desired time period) not energy supply (since the body has more than enough fat stored to power any climb,) and fatigue is multifactorial and complex. After all, I can produce more power than any ProTour rider uses for any climb. The problem is the time I can maintain that power is measured in seconds while theirs is measured in minutes. The reason I'm not a professional isn't how much power I can produce, but the how long I can maintain it.

*That is, fatigue is being ignored and it is assumed the power and cadence can be maintained for the entire climb.

Amt0571

Today I did an experiment, and tried to do my commute climb (a 7.3km climb with a gradient that varies from 6% to 10%) at a cadence between 80 and 90, while trying to get to the top averaging at least 14.6km/h (which is fast for me). HR was higher than when I climb hard at a lower cadence, mostly around 165/170bpm, almost the max HR I can sustain for any meaningful length of time.

When doing the same climb with a lower cadence, I found less limited by breathing and high HR, but felt my legs more tired when I reached the top, so maybe there's something good on higher cadence. Or maybe I just had a feel good day. I'll have to keep experimenting.

Carbonfiberboy 

As I hope the gentle reader can discern from the above, climbing cadence will vary with the individual and length of climb. Those well endowed with aerobic ability usually climb at a higher cadence, but not always, because those well-endowed with muscular endurance usually climb at a lower cadence, see Lance vs. Ulrich. I used to ride with a guy who rode a 90" fixie in the mountains, just because he could. He climbed at ~60 cadence on geared bikes and climbed really, really fast. I've also ridden with rando guys who climb at 90+ cadence, also fast. So there are general guidelines to get started with, but basically one simply has to experiment.

guadzilla

Your power numbers just increased my self-loathing by a very large margin....

Carbonfiberboy 

I hadn't looked that this closely earlier and didn't see that you were only varying cadence for at most maybe 30 seconds, though I'm surprised not to see bigger power spikes when you shifted. Most of us shift to maintain a relatively steady cadence. My road bike has about 5 rpm between cogs. No, I can't maintain the same power on a long climb at both 70 and 105 cadence. My idea is to get up the climb as fast as possible, not blow up halfway through. If I vary cadence by more than about 5, my power will eventually drop off, sooner if the cadence is higher, later if it's lower, just what lab tests would predict. Of course I could do this for short bursts as training, but I prefer to do that training differently. Lance would occasionally do one hill repeat at 50 and the next at 100. I think that's more effective. I could do them at the same power, but not either one at FTP, so less effective than doing each one at max sustainable power for that cadence. Or not? Shorter, harder efforts elicit a different training response. IDK. You're right, Cat 1 has nothing to do with this, it's just training, though I'd be at maybe 1/4 of your watts. Working on that, though.

Leinster

I think you just demonstrated the exact theory behind the Armstrong method. At the higher cadence, your heart and lungs worked harder and your legs worked less.

Sy Reene

Not sure you'd really say the legs worked less. They're pushing less per revolution, but doing more revolutions.
Maybe it's like weightlifting or such, difference between a few lifts of a lot of weight, or lots of lifts of a lower weight?