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I know that on a flat road drag is the main force, I have to provide as much force as the drag (and the friction in the drive train) produces. I can also see that the faster I ride, the harder it gets and at speeds over 35 km/h that if I bend down to the handlebars, I can ride faster. But what about steep climbs? On a 15% climb I can barely ride at 5-6 km/h and the drag doesn't seem to be noticeable (I don't seem to go any faster when there's a moderate tailwind). I need to produce more force to combat gravity, but that does not depend on my speed - why can't I ride on the same climb at e.g. 9 km/h speed?

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On a steep climb we can ignore drag and friction. If you wish to sustain higher velocity, you need to invest the same amount of energy in a shorter time, i.e. you need more power. This energy goes into your gravitational potential energy, given by $E_p = mgh,$ where $m$ is your mass (together with your bicycle), $g$ is gravitational acceleration and $h$ is height.

If your velocity is $v$ and angle of inclination you climb is $\alpha$, then your vertical component of velocity is $$v_z=\frac{d h}{d t}=v \sin\alpha.$$ In order to sustain this, the required power is $$P = \frac{d E_p}{d t} = mgv_z = mgv\sin\alpha.$$

You can see that the required power is linearly proportional to velocity. If the maximum power you can sustain is $P$, the top speed you can sustain is given by: $$v_{max}=\frac P{mg\sin\alpha}$$

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  • $\begingroup$ So it's the power (and not the force) that my body can produce is the limiting factor. $\endgroup$ – user2414208 Nov 16 '18 at 14:50
  • $\begingroup$ You need too exert a certain amount of force within a certain time. No use using a really low gear and pushing really hard if it barely moves. $\endgroup$ – PhysicsDave Nov 16 '18 at 23:24

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