Friday, October 19, 2007

The Wheel Deal Part 2: Wheel Size (again)

Bigger wheels are faster on rough surfaces, as I pointed out in my last post, because more of the forces that they experience as they roll over bumps pushes the wheel up rather than pushing backwards and slowing the wheel and rider down.

So, why not just ride the largest wheels you can find? Unfortunately, when it comes to skateboarding and inline skating, larger wheels simply don't roll as well on smooth surfaces. The problem is that the urethane they're made of changes shape when you ride.

A simplified model of a skate wheel might look like this, where the jagged lines are meant to be springs that represent the compressible urethane. That's not to say that there are actual springs inside the wheels. It's just that the urethane acts much like springs, and it's simpler to understand the way wheels work if you pretend that they're are made of springs.

As you can see in this sketch (I've exaggerated things a lot to make it easier to visualize), a wheel deforms as you ride along, resulting in a flat spot where the wheel touches the ground.

Most skate wheels are solid cylinders of material, except for the hole running through the middle where the bearings sit and the axle passes through. The springy urethane compresses when your weight pushes down on it. If you look at two wheels that are identical in shape except that one is large and the other is small, and both are made of exactly the same urethane, the larger wheel will deform more under the same weight.

This is where we can use physics to understand what's going on a little more precisely. Physicists think about springs in terms of something called the spring constant (usually symbolized with the letter k). The higher the spring constant, the more force you need to stretch or compress the spring.

If you connect two springs end to end, the total spring constant goes down (from k to k/2). In other words, it will be easier to stretch two springs connected in a row than it is to stretch just one. (You can test this yourself by tying rubber bands end to end.)As you can see in this sketch, attaching two springs side by side increases the total spring constant (from k to 2k), making them harder to stretch.

If you cut a spring in half, it will double the spring constant. It's like taking the two springs connected end-to-end and getting rid of one, which doubles the spring constant from k/2 to k.

This is relevant to skate wheels because you could always make a small wheel by shaving down a big wheel. If you were to do that with the model of a wheel that I drew above, you're essentially shortening the springs. This makes the wheel stiffer (which is to say, less springy). Your weight pressing down on a small wheel will not deform the wheel as much because it's effective spring constant is much higher than it would be for a wheel that's identical in very way except for its larger size.

This makes larger wheels slower because compressing and stretching springs, or springy urethane, takes energy. With a perfect spring, you get all the energy back as it springs back to its natural shape. But no springs are perfect, and urethane is usually far from perfect.

Urethane is fairly resilient, which means that once it's deformed it bounces back into shape and gives back some of the energy that deformed it, just like stretching and releasing a spring. Depending on the exact formula of the urethane, a portion of the energy is always lost. Most of the lost energy turns into heat that warms the wheel and escapes into the air. If you squish a skate wheel you can expect to get back no more than 75% of the energy you put into it, and usually you get back a lot less. As a rough estimate, the deformation that comes with rolling on a urethane wheel will cause a large wheel to lose twice as much energy as one half its size. That's what makes larger wheels slower.

There are several ways to reduce the amount of energy lost due to the squishing of skate wheels. One common solution is to replace some of the urethane with a rigid core, like this Spitfire wheel.

Another possibility is to make the wheels wider, like these old school wheels.

Take a look at the cutaway sketch below that shows why wider wheels are less squishy. By widening the wheels, you're adding more springs (well, springy urethane anyway) in parallel. If you recall the diagram above, adding more springs side-by-side increases the total spring constant and makes it harder to stretch or compress the springs.

The wheel on the right is three times wider, and should be three times more rigid than the wheel on the left.

So, if you want bigger wheels that will roll as fast as smaller wheels, you have to make them wider. That leads to other problems. For one thing, wheels that are wide and have big diameters are heavy. That's not so good for all the ollie-based street moves, but fine for ramp, bowl and downhill skaters.

Another problem, which can be bad for all sorts of situations, is that the wider you make a wheel the harder it is to corner. If you try to ride in a circle, the outer edge of the wheel travels farther than the inner edge. Because both parts have to roll at the same speed, either the outer part of the wheel ends up turning too slowly or the inner part turns to quickly. That can lead to lots of wear and tear on the wheels, as well as extra friction that will slow you down whenever you change direction.

I've already explained why you need large wheels for riding on rough surfaces. Now you can see why smaller wheels are better for skating park concrete and obstacles. So, why not get REALLY tiny wheels for skating on smooth surfaces? Unfortunately, when wheels get too small other problems start to crop up. This post is already long enough, so I'll tell you about those issues some other time.