Ough, I remember David Mariner of DM unicycles was studieng the same.
He made a (wired) pedal to measure pressure directly to a computer.
But you seem to search for some mechanical formula.
If I consider the two, then I wonder, even if you can translate it into a number or factor, then how much could you apply it to a person?
I’m sure there’s a lot of unicyclist out that that counteract (?*) themself, and others who keep calm and efficient at all times.
But we all know what you’re talking about, and there must be some law in there.
I know the plain length thing, but not the rim thing. Plus, I’d expect rider weight may be a factor to.
Curious for follow-up, cause this boring matter is pretty interresting.

The torque applied by the foot on the pedal + the crank length leverage can make things easy to calculate the torque forward at the hub.

However, the calculation of the “resistive” counter-torque is more complicated. It should factor in:
-> the tire friction (shape of the tire + pressure determines the contact patch)
-> the wheel diameter (including the tire)
-> the whole wheel weight
-> the road incline

…and plenty of other things.

The good news is: the first part will be constant between unicycles. The second part will be more specific.

Anyway, it can make for an interesting way of comparing unicycles (more than just the cranks length/diameter ratio I am using to have an idea of how different cranks will feel on different unis).

As intriguing as it is to ponder the absolute values, for the purpose of comparing uni-to-uni it would be interesting enough to assume those variables as constant (incline, tire pressure, etc) and just reduce it down to pedal pressure delta based solely on crank arm & wheel diameter factors.

Example: this 36" guy with 137 cranks kicks my butt! However, the same cranks on the 29" is manageable. But is that because it is only 1/2 as hard to pedal (all other things being equal)? Likewise, this same 36" is OK with 165mm cranks - did I ease the burden by 60%? More?

I figured this must be an easy calculation - but I got confused and came running to the unicyclist community for help.

If you are looking at quick & dirty calculation based only on the crank length, that is exactly what I was doing.

It is really easy to do: create a new spreadsheet and put the wheel sizes (20,24,26,29,36) in one column and the different crank lengths (in inches) in one line.

Then the formula to use at each intersection will be: crank-length / (diameter * 0.5)

This way, you get a rim/crank index (maybe a bit subjective but was useful to me to explain why certain combinations were working better for me than others).
The 0 would be the hub and 1 would be a crank as long as the radius of the rim.

I hesitate to disagree with Eric but one of my new unicycles gets a value of 7.7 and it’s one of my favorite rides. I think a value of around 6 would be a nice cruising cadence for a road unicycle.

That concept Total Gear Ratio could be more formula and less cheat-sheet;

when you take the distance per revolution and the gearing ratio (of geared hubs) and then the concept formula, you would have more precise numbers that includes the tyre (and has the real gearing ration applied to that).

how much does the weight of the load/rider factor into it?

Most of this is pure theory, which won’t help you ride. Practical considerations are (an we know this instinctively) sitting too much on the seat leads to UPDs when we encounter bumps in the road….