There's physics in everything and it makes things a) more interesting and b) easier to understand when you spot it xD But then, I'm the kind of person who pictures force balances on her legs when she's walking, so ...
Understanding how the length and shape of shanks affects their strength is all to do with moments - forces acting about a pivot :) Here's a rough explanation, and you can skip over it if you think it's boring.
Moment = force x perpendicular distance from the pivot. This is all to do with balancing people on see-saws - you can get a 50kg person to balance a 100kg person if the lighter person sits twice as far away from the centre, because then you have the same moment going clockwise and anticlockwise. The pivot point is the centre of the see-saw (the point that it moves around), and the forces acting on it are the weights of the two people.
Basically the greater the difference in length between purchase and shank, the more force has to be exerted by the purchase on the poll to give the same moment about the bit as the rein is exerting. You're a light person pulling on the shank so you need a heavy person on the purchase to balance it.
Now, I'm less sure about the next bit (pun unintended), but fiddling around with mechanics problems has long been a favourite pasttime of mine, so let's consider this a fun learning exercise for me. Have I got the following bit right?
I've been thinking about the effect of curves on the shanks, and I'm pretty sure two factors lead to the varying strengths - one, the angle at which the rein applies the force, and two, the perpendicular distance from the pivot. The more the angle between rein and purchase deviates from 90 degrees, the less force will be exerted. Different curves change this angle.
If the shank curves back, it's milder, because the 'perpendicular distance' from the end of the shank to the bit is less. That is, if you measured the distance in line with the purchase, a 4" shank that curves back will have an end that's closer to the pivot point than a 4" shank that sticks straight out. This diagram might help explain that as the idea of 'perpendicular distance' can be hard to grasp. Pretend the reins are parallel ;)
The exact difference in strength between two bits depends a lot on the individual set-up and how the rider holds the reins, but it'd be pretty easy to set up a force balance and compare them once you knew the lengths and angles involved!
Have I got the basic idea right? I know there are other factors involved as well. It is half past midnight, and I've been on holiday for three months, so I might not be quite up to par when it comes to figuring this stuff out xD