Finger strength, hold spacing, and height

[psathyrella]

Feel free to remove if this is too tenuously related to training, but I thought some people here might find it mildly entertaining.

So despite being profoundly tired of irl discussions of the relative benefits of being tall vs short, since despite everyone's best efforts they inevitably devolve into I-didn't-send-what's-an-excuse (myself of course included), I have one persistent question. Setting aside the relative prevalence of reachy vs scrunchy moves, which depends on where you climb and what the last climb was that you didn't send, it's intuitively obvious to me why reachy moves are hard for my shorter partners. It's much less obvious to me, though, why my taller partners get shut down by scrunchy moves, so I thought I'd run through a quick calculation to try to work it out. I'm defining "scrunchy" as moves where feet and hands are forced to be close together vertically, either because hands are forced low (e.g. underclinging a roof or setting up for a deadpoint to a high hold) or feet are forced high (e.g. when you've just gone over a roof).

I'm attaching the actual work, but the result I get is that force at the fingers is roughly

F = mgl / 2z

for m (weight), g (gravitational constant), l (total length finger tips to toes), and z (vertical distance from foot holds to hand holds). This suggests that scrunchy difficulty is just a result of your mass acting on a longer lever arm (i.e. your butt is further out), requiring larger finger force to counteract the resulting torque. Note also the divergence as z goes to zero: keeping your feet low when laybacking is not a small effect.

To compare numbers, we have to decide on a mass to plug in. Now of course force required and "inherent" finger strength both tend to increase with weight, and we could plug in some proportionality between the two. For instance Fig 6 in this suggests that if you double a human's weight (e.g. make them taller), that their maximum trainable strength to weight ratio decreases by about a third. But whatever, let's just stick to the geometric effect of hold height, since the natural level of finger strength varies way tf more between people than any of this other stuff anyway. So to compare a couple different heights and z values I just use a common weight of 145lb. To convert length to height I used a proportionality of 1.25, which for sure varies from person to person (higher ape index means more finger strength required in this scenario), but this is fine for a rough estimate.

Anyway, the numbers I get are that for hand holds 4 feet above foot holds, going from 5'5" to 6'0" increases finger force by maybe 10lb. If the holds are 2 feet apart, this difference grows to about twenty pounds. This conforms to my expectation of at most perhaps a letter grade or two of difference from watching different sizes of people on various moves.

Here's a plot from google, if you plug in this search text it makes it easy to read off the numbers (units are inches and pounds for x and y), and the three lines are 5'0", 5'6", 6'0":

And the calculation:

And lastly, I wouldn't be remotely surprised if I messed up the algebra, do lmk if you see something funky.

[acmesalute76]

I love that you did a free body diagram for this, but I think the force your feet apply is not as linear as your hands due to angle. As a tall person, I hate scrunchy sit starts because I have to contort myself in horrible ways just to get my feet on the wall, and I often end up using worse holds, or holds in a bad location, or I’m just in a bad position to generate force through my feet. So in addition to being pushed out from the wall, my feet are far less effective at removing weight from my arms than if I could stretch out a little, and I think more so than a linear model accounting for angle represents.

Also I think because you are scrunched your mechanics are thrown off, and you can’t do a clean backstep or whatever because you’re in some terrible locked off position.

Anyway, nice analysis, but I think there’s a lot more variables involved.

[psathyrella]

Yeah, those are good points. I definitely agree that a large part of good technique consists of arranging our non-waist joints to make our center of mass as close to the wall as possible, and in a lot of circumstances being taller makes it impossible to adopt the optimal position. And the model above with just a waist joint doesn't capture any of this.

On the other hand, I'm not sure that we need a more complicated model in order to arrive at much larger force differences than I quote in the typed text above. That example is still in a quite flat part of the plot, but if we move closer to the divergence the numbers increase. For instance comparing 5'0" to 6'0" with a 1.5ft hand-foot distance you get 60lb, which is what, maybe a number grade or two? Or, alternatively, many years of hangboard phases.