As mentioned earlier, I’ve been doing a little “light” reading. Light reading being in the form of a 1500-page physics textbook which was purchased in my first year of engineering.

I’ve just been reading through it revising the material. Not doing the actual problems but just refreshing my memory, I figure I’ll go back and do selected problems once I’ve gone over everything.

I figured I’d see something that would perhaps jog my memory, or inspire me in one form or another.

One area was Hooke’s law, which relates the force exerted on a spring to its amount of displacement. I figure as a model of the brain, this might be one way to model it, not as a single mass, but as a series of “marbles”, if you will, connected by springs, as an analogy to the concept of neurons and their interconnections. The thought that, perhaps brains are not solid, but are a very dense mesh.

I’ll have to ponder this a bit more I guess. It’s basically a finite-element analysis approach to modelling the brain and what goes on inside. It’d be interesting to try a physical modelling of that mathematical model. Lead sinkers and strain gauges perhaps? I don’t know there.

The other was in relation to my test apparatus that I described earlier. In flicking through the problems, I found this:

Now, there are obvious differences, but really the headform moves the centre of mass closer to the end. If we can find the details of the centre of mass, we can derive what the headform is doing. Moreover, it might be useful to model the mass of the cyclist’s body in the form of mass in that rod, perhaps a bulk mass towards one end.

In short though, the equations needed to answer the above question are undoubtedly in that book, and moreover, I do have a worked copy of that example, but we won’t look at that just yet, that would be cheating.

I was doing some thinking last night, then it occurred to me. We are trying to do simulations of crashes using linear motion. Dropping a helmet vertically. That’s linear.

For sure, it’s a good-enough approximation when you hit something head-onâ€¦ or is it? If you come off and fly through the air, then maybe, you’ll strike something dead-level.

More probable though, is you’ll follow an arc, under projectile motion. The most likely scenario is that as the bicycle/motorcycle tilts over, you follow it. It’s not going to be a direct-to-the-ground vertical drop of your head, but rather, a circular arc.

So how do we test for it? I suppose like this: