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I am building a sumo-bot and our competitors have thin sticky tires, while we have wider and less sticky tires. The diameter is the same, and the gearbox/motor is the same. Who will win?

PS: Sticky tires: https://www.pololu.com/product/694 & wide tires: https://www.pololu.com/product/62

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  • $\begingroup$ What leads you to think that the tire friction is the sole factor that will determine who wins the competition. Offhand, I'd say that sounds like a relatively naive assumption. $\endgroup$
    – user16
    Sep 29, 2015 at 15:15
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    $\begingroup$ Voting to close - this question is far too broad and does not have anywhere near enough information to provide an answer. $\endgroup$
    – grfrazee
    Sep 29, 2015 at 15:55
  • $\begingroup$ I'm voting to close this question as off-topic because you asked the same question, at the same time, on (at least) 2 other sites, physics and robotics $\endgroup$
    – Chuck
    Sep 29, 2015 at 20:25
  • $\begingroup$ I'm voting to open because the question is clear to me (and obviously to Chuck also, who has been able to answer it), and also because I think it fits better here than on the other sites. $\endgroup$
    – AndyT
    Sep 30, 2015 at 14:20

1 Answer 1

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Assuming everything about the vehicles is the same - mass especially, but also shape, center of gravity, etc., such that the entire problem boils down to tire grip, you will lose.

See this answer for more information, but essentially, assuming your vehicle weight is low enough that you're not going to deform the competition surface, static friction is given by:

$$ F_{\mbox{friction}} = \mu_{\mbox{static}} P_{\mbox{tire}} A $$

where $\mu_{\mbox{static}}$ is the static coefficient of friction, $P_{\mbox{tire}}$ is the pressure the tires exert on the ground, and $A$ is the contact surface area. However, because:

$$ P_{\mbox{tire}} = \frac{F_{\mbox{normal}}}{A} $$

where $F_{\mbox{normal}}$ is the normal force of the vehicle, you wind up with:

$$ F_{\mbox{friction}} = \mu_{\mbox{static}} \frac{F_{\mbox{normal}}}{A} A $$

or

$$ F_{\mbox{friction}} = \mu_{\mbox{static}} F_{\mbox{normal}} $$

So, again, assuming everything else about the two robots is the same, and that you're not operating on a surface like mud or something else that will appreciatively deform under the tires, then the traction/friction force will be higher in the vehicle with a higher coefficient of friction.

That is, your tires should start slipping before theirs do, and since static friction is greater than dynamic friction, once your tires start to slip they get a significant "pushing" advantage over you.

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