postal_bag said:
I understand that the required force is greater at a lower cadence compared to a higher one, when riding at a given power output.
Does anyone know of a graph or spreadsheet that would plot power and cadence, so that I could see what force was required at any combination of the two?
For some reason AC's link didn't work for me.
Excuse clumsy notation and possible clumsy physics and algebra. I don't know how to get better symbols out of my keyboard, and it's possible I can't remember how to do maths and physics (it's been a while!).
Defn: Power = Torque X Angular Speed
Therefore (I can't get the funky three dots on my keyboard so will go with "tf")
tf: Torque = Power(Angular Speed)^-1
Defn: Torque = Force (orthogonal to lever) X Lever Length (that is crank length)
tf: Force = (Power(Angular Speed)^-1)(Crank Length)^-1
Angular speed is radians per second (although what with radians being dimensionless, I guess it's nothings per second). A cadence of 60rpm is 2pi radians/second, so the conversion factor between cadence and radians per second should be 2pi/60
So we end up with:
Force = (Power) X [(2pi/60)XCadence]^-1 X (Crank Length)^-1
So a given power and crank length will yield a nice little constant and Force will vary as 1/Cadence. Yay!
Now will someone please explain to me how I got something wrong? High school physics was a good discipline for me and I need it back... never study law... never... it makes you forget everything else...