Does crank length affect the number of gears a bicycle needs? When I was a child I noticed that as I out-grew my bike (or when I rode a smaller child's bike) I felt like I could accelerate better. The smaller bike seemed 'nippier', and in hindsight it was similar to driving a diesel with quite a flat torque curve. I now imagine this is what it would be like to ride with short cranks.
So the question is: if I rode with 135mm cranks could I get away with fewer gears than when riding with 175+mm cranks?
Edit:
I have read a similar question now. It doesnt address the biomechanics of how cranklength effects the varying proportion of glute and quads during the rotation. The closest this was addressed was in a comment to that question that noted the difference between doing a half squat and a full squat. I feel long cranks tends to a full squat, which feels weak.
The gain ratio is valid but fairly intuitive.
It would be great to find papers that reference anatomical models that have muscle length force functions coupled with the thigh and shin bone levers that can be converted into graphs of force/torque  contributions of muscles at the pedal over a whole cycle for varying power levels and cranklengths.
Or experimental data on max cadence range at which varying power levels (say 50%,60%,70%,80%,90%) can be maintained for different cranklengths.
Not really. You might want different gears, but probably not fewer.
Shorter crankarms give you less mechanical advantage—they're functionally equivalent to being in a higher gear. So you might want a lower gear range to compensate.
It is common to express mechanical advantage as &quot;gear inches&quot;—this is
(front sprocket/rear sprocket) × wheel diameter
This obviously doesn't account for crankarm length. Sheldon Brown proposed a measure he called the gain ratio that would do exactly that:
(front sprocket/rear sprocket) × (wheel radius/crankarm length)
From this, you can see that wheel radius/crankarm length will typically be about 2. If the denominator is smaller, the quotient is bigger, so for a given set of gears, the net gain ratio would be higher. For that reason, you'd probably want a  proportionately lower gear range.