# Explanation of physics of rolling resistance in drive trains

Hey all, I am from the vexU team GATR2 and I wanted to open this thread as discussing with people on discord it seems this topic is a very little known topic or completely misunderstood with many people in vex despite being a huge factor when dealing with drive trains. To begin, I want to say that this post will be long but if you have never heard of rolling resistance it is definitely worth reading as I will try to go into detail into this crucial topic of physics for vex drivetrains. Additionally, if I get anything wrong please comment correcting me.

Rolling resistance is defined by Wikipedia as â€śRolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body rolls on a surface.â€ť This can be understood as the grip between the ground and the wheels of your drivetrain. This may be a good or bad thing, if you are looking to push someone then rolling resistance is your friend, but if you want to build a fast drive train, then it is your enemy because rolling resistance is still a frictional loss even if it may help you push other bots.

While that is easy to understand and may seem obvious the factors that increase or decrease rolling resistance are less obvious. I have seen many people who increase the number of wheels thinking more wheels=more grip (aka rolling resistance) however the exact opposite is true. To understand why we have to look at the math behind rolling resistance. Similar to normal friction, rolling resistance is calculated as force normal * a constant, unitless coefficient. The equation is as follows: F = Crr*N where F is rolling resistance, Crr is the coefficient of rolling resistance and N is force normal. The rolling resistance of a full chassis would be the rolling resistance at each wheel added up. With this we can start to see what adding more wheels does for rolling resistance: It will decrease the rolling resistance at each wheel but the total rolling resistance will be unaffected. So automatically we can see the thought that more wheels = more grip is untrue. However, in the real-world the rolling resistance does not go unchanged due to adding more wheels because the coefficient of rolling resistance changes depending on a great number of factors. The most obvious change is the material type of the wheels in where traction wheels would have the highest rolling resistance. But less obvious changes in the coefficient of rolling resistance include the change of number of wheels and wheel choice. While under the assumption that Crr stays the same when adding more wheels means rolling resistance goes unchanged, adding more wheels decreases the Crr so that means that more wheels means less rolling resistance. This is why I said in the beginning that more wheels = more grip for defenses it the opposite of the truth. This chart sums up the relationship between wheel size and wheel number and the Crr:

If there is one thing you take away from this post just know that less and smaller wheels is for defensive bots and more wheels and bigger wheels is for fast bots. From my personal experience I can say that I have experienced much less burn out on my drive trains the more wheels and bigger wheels I use. I personally choose to never go less than 6 wheel drive on 3.25" wheels as 3.25" wheels and this year I my chassis looks like this with 8 wheels for less rolling resistance as I am running a 600rpm drive.

Hope this helps!

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In this statement:

This sounds like something best determined by testing.

Youâ€™ve got wheel deformation to deal with, surface deformation, and wheel/surface contact friction just off the top of my head. This is to say nothing about drivetrain losses, gearing, chains, shaft/bearing friction, etc.

Also, the difference between straight line resistance and turning friction needs to be accounted for as the wheel scrubs/slides/twists on the playing surface.

In short, these are some very complex issuesâ€¦ but on the good side, they can be measured experimentally fairly easily.

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this post has quite a bit of misinformationâ€¦ i would recommend doing actual research on tire contact patch dynamics before posting and not just looking at one wikipedia page before misguiding new users to building absurd drive trains. in reality this information makes little to no difference and in theory it is just incorrect.

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Most basic physics courses just gloss over rolling friction by stating that it is very complicated and then simplifying it to be directly proportional to the normal force (if they even discuss rolling friction.)

This treatment is fine for a basic application that is making many other assumptions, but masks the underlying factors. Iâ€™ve used the video below in class as it does a good job of exploring the underlying issues with lots of visuals in a brief 5 minutes. Iâ€™d recommend watching it if you are interested in Rolling Friction (aka rolling resistance) and checking out some of LESICS videos on other topics too.

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