Cycling UK Forum

I’m wondering whether there is any data, ideally in graphical form, on how (crankset) torque and power vary with cadence. What data there is is probably for elite athletes, stuff for fat old blokes would be more helpful but you’ve got to take what you’re offered. Mostly I’m just looking for indicative stuff.

Carlton green wrote: ↑11 Oct 2023, 8:33pm I’m wondering whether there is any data, ideally in graphical form, on how (crankset) torque and power vary with cadence. What data there is is probably for elite athletes, stuff for fat old blokes would be more helpful but you’ve got to take what you’re offered. Mostly I’m just looking for indicative stuff.

It isn't cadence vs torque and power - the three are absolutely linked.

Power = Force x Velocity.
However we're talking circular momentum (pedalling) so the equation changes a bit.
Force in a circle is torque.
Velocity in a circle is cadence.

So: Power = torque x cadence.

It's a lot easier to show this on a fixed geared bike by the way - gearing and freewheel (and, related to that, the gradient of the road) wildly affects the equations.

rareposter wrote: ↑11 Oct 2023, 8:49pm

Carlton green wrote: ↑11 Oct 2023, 8:33pm I’m wondering whether there is any data, ideally in graphical form, on how (crankset) torque and power vary with cadence. What data there is is probably for elite athletes, stuff for fat old blokes would be more helpful but you’ve got to take what you’re offered. Mostly I’m just looking for indicative stuff.

It isn't cadence vs torque and power - the three are absolutely linked.

Power = Force x Velocity.
However we're talking circular momentum (pedalling) so the equation changes a bit.
Force in a circle is torque.
Velocity in a circle is cadence.

So: Power = torque x cadence.

It's a lot easier to show this on a fixed geared bike by the way - gearing and freewheel (and, related to that, the gradient of the road) wildly affects the equations.

Oh dear, I don’t seem to have made myself clear, sorry.

What I’m looking for are maximums at any particular cadence, something like the charts that one used to see for IC Engines.

Rather than write it all out, I cheated and snapped this, from where someone else has already made the effort!

Nearholmer wrote: ↑11 Oct 2023, 9:56pm Rather than write it all out, I cheated and snapped this, from where someone else has already made the effort!

Yes, that’s the relationship between cadence, torque and power … but as above what I’m looking for are performance curves for maximum available power and torque through the cadence range.

This gives the general form of the curve, and I suspect is what the widely held belief that c80rpm is optimal, comes from, but it doesn’t tell us anything about the particular individual pedalling, or, for instance how long the efforts were sustained (the power figures look low to me for instantaneous efforts, even by an untrained cyclist, for instance).

I was about to suggest precisely the same diagram!

: - )

Jonathan

Nearholmer wrote: ↑11 Oct 2023, 10:13pm This gives the general form of the curve, and I suspect is what the widely held belief that c80rpm is optimal, comes from, but it doesn’t tell us anything about the particular individual pedalling, or, for instance how long the efforts were sustained (the power figures look low to me for instantaneous efforts, even by an untrained cyclist, for instance).

Thanks, a good start point and just the type of power versus cadence curve I was looking for.

My guess is that a similarly plotted curve for torque versus cadence would show a steady decrease of torque across the cadence range (from a peak at very low speed).

Carlton green wrote: ↑12 Oct 2023, 8:59am

Nearholmer wrote: ↑11 Oct 2023, 10:13pm This gives the general form of the curve, and I suspect is what the widely held belief that c80rpm is optimal, comes from, but it doesn’t tell us anything about the particular individual pedalling, or, for instance how long the efforts were sustained (the power figures look low to me for instantaneous efforts, even by an untrained cyclist, for instance).

Thanks, a good start point and just the type of power versus cadence curve I was looking for.

My guess is that a similarly plotted curve for torque versus cadence would show a steady decrease of torque across the cadence range (from a peak at very low speed).

You can derive the relation between torque and cadence from that graph:
• For as many points as you wish:
• Read the power and cadence at that point
• Divide the power by the cadence, giving the torque
• Plot the torque against the cadence.

Jonathan

You can back-calculate torques from the power vs cadence data points.

But, this plot poses so many questions, and has so few data points that I’m not at all sure that it can even be taken as “the general shape of the curve”, so in idle moments (I think there will be many today; I’ve copped a horrible cold!) I will see whether I can find something better on-line, and will consult my bro who probably has the right standard textbooks and papers (there is a lot of blather from sports trainers/coaches on-line, but little solid basic information, and I’m not convinced that all the blather is actually based on sound interpretation of science …… a lot of it reads like “puff” to me).

I also can’t understand why the curve doesn’t show high power and torque at very low cadence, because I know from bitter experience that trying to crunch the pedals round on a steep climb when you’ve got no lower gears left involves high power (for very short durations in my case!) and high torque, and that something similar applies when accelerating from rest in a high gear. I need to think about this more.

If what you are interested in doing is relating this to the characteristics of some form of engine/motor, I think you need to bear in mind a couple of points:

- time, as in duration of effort, is probably even more important when thinking about the human engine than it is when thinking about other engines, because we are quite difficult engines to which to supply energy while working, and we have several different fuel (energy) stores and modes of fuel (energy) consumption; and,

- although it’s most common to see performance curves for internal combustion engines, there are multiple other forms of engines and motors with very different characteristics (I’m into electric motors for traction applications, for instance, and they have characteristics hugely different from, say, petrol engines) and it may be that the human engine is not really directly like any of them (I suspect that it has several different, overlapping, characteristics that relate to which fuel stores are being accessed, rather than a simple curve, for instance).

Jdsk wrote: ↑12 Oct 2023, 9:08am

Carlton green wrote: ↑12 Oct 2023, 8:59am

Nearholmer wrote: ↑11 Oct 2023, 10:13pm This gives the general form of the curve, and I suspect is what the widely held belief that c80rpm is optimal, comes from, but it doesn’t tell us anything about the particular individual pedalling, or, for instance how long the efforts were sustained (the power figures look low to me for instantaneous efforts, even by an untrained cyclist, for instance).

Thanks, a good start point and just the type of power versus cadence curve I was looking for.

My guess is that a similarly plotted curve for torque versus cadence would show a steady decrease of torque across the cadence range (from a peak at very low speed).

You can derive the relation between torque and cadence from that graph:
• For as many points as you wish:
• Read the power and cadence at that point
• Divide the power by the cadence, giving the torque
• Plot the torque against the cadence.

Jonathan

Yes, indeed, such unpicking is possible but it’s no ideal and maybe the data already exists in the form sought. Also the cadence versus power graph starts from 50 rpm and I’m (also) looking towards lower speeds than that. Observation of the graph shows that torque must be dropping away as speed increases. Whatever, I’m hopeful that more data is available somewhere.

I’ve found several which all seem to be based on “all out” effort for short durations by super-athletes, and which all seem to show very similar general shapes of curves.

I like this one best, because it includes indications of what the limiting factors are:
Looking at the various ones, some of which have more than one individual cyclist plotted, it’s possible to see that the fitter/more trained a person is, the higher the power peak, and the higher up the scale the torque curve runs, but they all seem to indicate maximal power output in the 80-130 rpm range.

Is that real data... all of the points are on the lines!

Jonathan

That one I think must be “idealised”.

Here’s a nice messy one for you:
Several of the others are simply curves, with no data points.

: - )

Jonathan