# Winning a skateboard marathon with physics?

1. Oct 17, 2012

### Atticus

I am to compete in an upcoming skateboard marathon. Recently we were discussing the use of skateboard wheels and whether the circumference of the wheel had any advantage given that a larger wheel would also generally mean a heavier wheel and would require more force to push it. The skateboard community consistently utters the mantra "small wheels accelerate faster, but large wheel hold momentum better". While this may be true, given the size of a typical skate wheel, does it really matter? Or is it better to use the larger wheel which would carry more momentum and thus have a higher overall speed and would be easier to push once underway.

Please excuse my lack of correct Physics terms, I have no idea how to figure this stuff out. I am here to learn.

So my question is this, would it be to my advantage to use a larger wheel in a flat skateboard race of 26 miles even if the wheel was heavier.

Assumptions:

The course is a flat loop on asphalt.
Wheel size: W1 is 90mm diameter, W2 is 97mm diameter
Wheel weight: W1 is .283kg, W2 is .334kg
Wheel contact patch is identical, 43mm across in both cases
Wheel cores are identical material, and are 45mm diameter
Wheels are made from identical durometer urethane
Winner is obviously the one who crosses the finish line the fastest
Assume I am a skating robot and each push stroke is the same length and force

2. Oct 17, 2012

Can you use one of these? http://www.tuvie.com/pedalboard-by-nicholas-g-sawyers/
I would expect wheels larger than 90mm would be better, as less friction if it is on a road.
Think of an olympic sprinting bike, larger wheels, thin cross section.
Just my opinion though.

3. Oct 17, 2012

### Surgikill117

You could also drill out some of the core material in the wheel to make it lighter, and the smaller a wheel is the more rpm's it will make to go the same distance as a larger wheel, which means more friction against the bearing inside. You could reach higher potential speeds with larger wheels but would need more energy to get them moving. You need to be able to find out how much force you can push with your leg and then derive an equation to find the best size wheel to maximize efficiency.

Disclaimer: I am a high school student and I just thought of this on the fly, I am sure somebody with more experience will have something better/different.

4. Oct 18, 2012

### Atticus

I can't use that, rules state 4 wheels.

5. Oct 18, 2012

### Atticus

Both wheels already have a large hollow core for this reason.

6. Oct 18, 2012

### Drakkith

Staff Emeritus
I don't have much experience in skateboarding, but I would guess that the way the wheel interacts with the ground is more important than the sheer mass of the wheel. For example, a larger wheel is more easily able to go over rocks and bumps and such.

7. Oct 18, 2012

### haruspex

According to http://en.wikipedia.org/wiki/Bicycle_wheel#Sizes, "Rolling resistance increases in near proportion as wheel diameter is decreased for a given constant inflation pressure." But no explanation is offered there, and I didn't follow up the reference. Maybe it's because the tyre undergoes a greater deformation during contact. Of course, that's for pneumatic tyres, but I imagine it would apply to solids.
It's not clear from your post what the turns will look like on the course. If there's a lot of deceleration and acceleration then there's benefit in small wheels. If not, you might as well go with larger ones and save on rolling resistance.

8. Oct 18, 2012

### Staff: Mentor

The mass of the wheel will be small compared to your mass, so it does not matter much. Rolling resistance is more important, and that is reduced with larger wheels as you are not so sensitive to small bumps on the road.

9. Oct 18, 2012

### A.T.

Yes. But the difference in rolling resistance will be small compared to air resistance. You should work on optimizing your aerodynamics. Not sure what the rules allow here though.

10. Oct 18, 2012

### Atticus

Thank you all for your responses. I am considering using an almost similar wheel, which is made out of the same exact urethane.

Yes, rolling resistance is one of the big factors here, but I'm trying to find mathematically if there is a trade off between weight of the wheel vs. circumference.

The course I will be on is here:

It is flat and has no sharp turns. The winners of these types of races are literally pushing all the time and are coasting very little. That being said, the momentum of the larger spinning wheel supposedly would decelerate less even if you were pushing every 1-2 seconds. In my mind you are accelerating with each push and then decelerating until you push again.

I came here because I could find nobody on the skating forums with enough physics background to assist in figuring it out. I have skated both wheels and the larger wheels definitely take more "effort" to push, with 4 wheels they are 12oz. heavier then the next size smaller.

Maybe as a thought experiment we could think of it this way. If I could create a pneumatic pushing mechanism that I could attach to the tail of two identical skateboards, and then back the boards up against a wall and trigger the push. How would the two boards react? Would the one with 90mm wheels get off the line faster but not travel as far? Remember that the 90mm wheeled board is lighter. Wheels are the same contact patch, same durometer of urethane and same core size of wheel, the only difference is diameter and weight.

Thanks!

EDIT: Grammar

Last edited by a moderator: May 6, 2017
11. Oct 19, 2012

### Staff: Mentor

Right.

Another issue which might be relevant: The height difference between board and track. It could influence the effort you need to kick. However, I don't think this can be answered with physics alone. I would expect that a smaller difference is better.
If you add your body weight, I would expect very similar results.

12. Oct 19, 2012

### haruspex

True, but when I mentioned acceleration and deceleration in post 7 I was really thinking of any such forced on you by the turns. Losses due to air resistance will be minimised if you can keep a more-or-less constant speed, and extra mass helps with that - you won't slow down as much between pushes. Conversely, extra mass will increase rolling resistance.
Unfortunately, a quantitative answer to your question would require plugging in a number of constants, some of which could only be determined by experiment.
Is it permitted to wear a fairing?

13. Oct 20, 2012

### Jupiter6

The skater in me thinks:

Get the largest wheel you can
Get the smoothest (fragile) bearings you can since there is no impact involved in the marathon
Get the highest durometer wheel you can (less resistance)

The engineer in me thinks:

There will be a point of diminishing returns you will reach with wheel mass vs. your leg strength. Extra wheel mass will certainly decrease the variations in acceleration and deceleration (like a capacitor or flywheel) but at the expense of high expended energy at startup.

Maybe you could set your board next to a bathroom scale and kick off that. Have someone else notate the scale reading and the angle of your leg and foot in relation to ground (I dunno...approximate). From there you could figure the forward force component you normally are exerting to move yourself and the board.

I realize it's rough but that's the best idea I could come up with in 5 minutes. I can tell you that with two otherwise identical boards, the one with the larger wheels always rolls easiest on asphalt.

14. Oct 20, 2012

### haruspex

... and increase rolling resistance, no? OTOH, I suspect larger radius reduces rolling resistance, but with diminishing returns.