Computer Modelling

A few years ago I found myself in Aberystwyth, Wales, teaching Newton’s laws of motion to undergraduate sports science students. The topic was projectile motion, which is the motion of objects with no forces acting on them other than gravity. Basically, if we can assume that air resistance is negligible, anything you throw in the air (a ball? an egg? your computer in frustration?*) is a projectile.

If you think about throwing a ball, you’d probably guess that things like the height from which you throw it, how you angle it, and how fast you throw it will affect how far the ball will go. The mathematical equations that describe the motion of projectiles (which you can read about here) contain those exact parameters. If you specify the height, angle and initial speed, the equations will predict how far the ball will go. Maths is cool!

If you input these equations into a computer, you have a computer model of projectile motion. So you get the computer to do your homework — bit lazy, I hear you say. Don’t judge me yet! There’s a couple of good reasons to use a computer for this.

First, what if I want to predict how far the ball will go for many different initial speeds? I have to solve these equations over and over again. A computer can do millions of these calculations in the time it takes me to reach for my pencil. Computer-pencil: 1–0.

For my sports science students, I created a computer model that they could use to predict the movement of a basketball. They could alter the height, angle and initial speed, and try to get the basketball in the hoop. I wrote it in Matlab, which unfortunately is not free, but if you want to have a look, the code is here: https://github.com/dblana/modelling

Another advantage of computer models is that they can find solutions to mathematical problems that are just too complex to solve. For example, for some practical problems (such as rocket motion), we can’t ignore air resistance, and we might need to take into account other things as well, such as crosswinds. The mathematical equations then become too complex to solve exactly. But we can use computers to approximate the solution. Computer-pencil: 2–0.

So what does all this have to do with our prosthesis project? We have mathematical equations that describe the movement of the human hand: how muscles generate force, how each muscle attaches to the skeleton, and how the forces of all the muscles add up to make our fingers move. As you can guess, these equations fall under the too-complex-to-solve-exactly category.

Computer models have allowed us to study how we move in more detail than ever before! In future posts I’ll go into a bit more detail about how we model human hands.

* Your computer would not make a very good projectile, because its shape means that we cannot really neglect air resistance. Please do not throw your computer in the air.