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I read a related post on bicycle gears and I still have a doubt. In low gear, the output force exerted on the ground is larger than the output force that would be produced in high gear. A large output force implies a large acceleration which leads to achieving a higher speed in a shorter amount of time. Of course, the energy source is the cyclist who input energy in the system (the bike) at a certain rate, hence the input power.

From personal experience, I know that, in low gear, we end up pedaling too fast and don't actually achieve a high speed. Low gear seems to only produce a high starting acceleration and is helpful on sloped terrain.

Conceptually, why wouldn't the large force produced in low gear lead to a higher bike speed? Is the cyclist unable to generate the same input power in low gear as in high gear?

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    $\begingroup$ The low gear would produce higher speed if your legs could move faster. $\endgroup$
    – garyp
    Commented Dec 22, 2021 at 12:19
  • $\begingroup$ Some useful concepts are Mechanical Advantage and Velocity Ratio. $\endgroup$
    – ItWasLikeThatWhenIGotHere
    Commented Dec 22, 2021 at 13:19
  • $\begingroup$ Two minor comments. (1) Your "related post": a link might be helpful. (2) In its current version (v2) the title of this question does not help identify what the question is. Consider an edit. $\endgroup$
    – rob ♦
    Commented Dec 22, 2021 at 14:51
  • $\begingroup$ @garyp, if the leg were indeed able to spin faster, would the pedal force be constant or increase as well leading to an increase in the bike's speed? Why wouldn't the pedal force also increase as the pedal force increases? Is there a physiological limit? What if we were talking about an engine instead? $\endgroup$
    – Brett Cooper
    Commented Jan 1, 2022 at 16:53
  • $\begingroup$ There are two good answers here (at the time of my writing) that explain what's going on. The practical limit is physiological. Add an engine and you have a motorcycle. An engine produces more force and can spin faster. The limiting factors are mechanical and electrical, of course. Parts heat up and expand, the electrical system has a limit to how fast it can operate switches and fire spark plugs, etc. $\endgroup$
    – garyp
    Commented Jan 1, 2022 at 19:59

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The bicycle's transmission system (pedals, chain, gears, wheels) fairly efficiently transmits work (power) from the rider to the vehicle. If you had an engine that could output constant power at all speeds, there would be no need for different gears.

But the human leg only has maximum power in a particular range of pedal speeds. When the speed is too low (forces high), your leg is doing exertion that doesn't lead to work. If you push on a wall, your muscles are consuming energy, but you're doing no work. When the speed is too high (forces low), your legs are doing exertion to move the mass of your leg around rather than to push on the pedal.

So there are inefficiencies in the different speeds that are occurring before the power reaches the pedal.

why wouldn't the large force produced in low gear lead to a higher bike speed? Is the cyclist unable to generate the same input power in low gear as in high gear?

Exactly. Above some pedal cadence, your power drops. Your muscles can't fire quickly enough to get any power in during the down stroke. They're busy pushing the mass of your leg around and there's not much left to push on the pedal.

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When a cyclist reaches his 'maximum velocity' it is when his 'input power' i.e the muscle power he can generate is EQUAL to the power expended on wind resistance and frictional resistance. (Power is equal to resistance force x velocity) edit: OR in going uphill.

Thus a more powerful cyclist can achieve a faster speed (given same conditions)

This 'terminal speed' corresponds with a specific wheel rotation speed (depending on the diameter of the wheel).

HOWEVER - that wheel speed can be achieved in high gear with low input revs OR in low gear with high input revs.

Now the human body evolved to run, not to cycle, and hence our legs and muscles are optimised to work best at a rate approximately corresponding with the way they would work when running.

So we choose a gear that produces an input speed that the cyclist can maintain for long periods. We cannot pedal fast enough to reach high speeds in low gear.

This similar to how we use gears for a petrol engine - it cannot produce power at low revs, and power declines at high revs, so we choose gearing to deliver the maximum power of the engine at a suitable road speed..

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  • $\begingroup$ Running is considerd 'good' at approx 170 strides per minute, and cycling at approx 75 revs per minute. There are 2 'strides per rev' so the comparison is clear... $\endgroup$
    – Wreckless
    Commented Dec 22, 2021 at 18:09
  • $\begingroup$ Hello Wreckelss, I get that as the cadence increases, we somehow, physiologically, cannot apply the same force on the pedals. Would you also know why, when shifting from a high to low gear the RPM go down even if we keep the foot on the accelerator? What causes that decrease in RPM that happen with a bicycle and a car? $\endgroup$
    – Brett Cooper
    Commented Jan 2, 2022 at 16:26
  • $\begingroup$ It is easier to see this in an automatic gearbox car, but the principal is the same. The gearbox is essentially a fixed link between the wheel speed and the engine speed. When you change gear you do not immediately change speed, so you will notice both with your rev counter and your legs that the speed changes. This is because the wheels are still going at the same speed but the link between the wheels and the motor (legs) is changed. . $\endgroup$
    – Wreckless
    Commented Jan 3, 2022 at 10:50
  • $\begingroup$ In a manual car you normally lift off accelerator when changing - and when you re-engage the clutch the revs will adapt to suit the new gear ratio. Incidentally - when you change to a 'lower' gear the revs go UP $\endgroup$
    – Wreckless
    Commented Jan 3, 2022 at 10:54

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