# Acceleration VS Speed w/ Wheel Sizes

One of my teammates proposed using small wheels on his robot, when I asked him why he would do that, he said small wheels would accelerate faster than larger wheels. After consulting many teachers much smarter and wiser than me, they also confirmed that small wheels indeed would accelerate faster than the large wheels, but the large wheels would have a higher maximum velocity than the small wheels. So my question is at what distance and time would large wheel catch up to the small wheel? Thank you.

Refer to the VEX Speed charts here: https://vexforum.com/wiki/index.php/Motion.

At the same axle RPM, a larger wheel is faster. You can see why this is pretty easily, since the wheel will travel its circumference in one revolution of the motor. The 4" wheel will travel 4pi inches in one revolution, while the small wheel will travel only 2.75pi inches. So, you have to gear the small wheel up with bigger gearing than the small one if you want the robot to have the same top speed. A robot with small wheels geared up 36:12, or 3 to 1, has a theoretical maximum speed of 3.6 inches per second, while a robot with 4" wheels would need about 2:1 gearing for the same speed. The robot with smaller wheels should accelerate faster because of the lower rotational inertia.

In practice, it may or may not make much difference, but I prefer the small package size of the 2.75" wheels, and the small omnis are the lightest of all the VEX wheels.

Both blue robots in this video weighed about eight pounds and used 2.75" wheels geared at 36:12:[http://www.youtube.com/watch?v=aIsQckNv9zM. Notice how quickly they accelerate and stop.](http://www.youtube.com/watch?v=aIsQckNv9zM. Notice how quickly they accelerate and stop.)

Hey Rick,

FYI: The 2nd link was the same as the first …

Fixed. (10char)

Yep I figured this out the hard way lol

But to find out the wheels top speed its pretty simple, to calculate circumference do (2*pi * r) then multiply that by the rpm of the wheel which will give top speed per minute (in whatever unit the radius was in feet, inches, cm ect…). Calculating the acceleration could be done but I think you would have to collect data to create a formula as to how fast a wheel will accelerate.

One little thing to add to Rick’s message is that each gear stage introduces losses - I hate to introduce those losses.

Blake

if your using a 4 wheeled holonomic drive, would the smaller omni wheels be the better deal?
because the 4 inch ones seemes more stable
thanks

I had wrote a whole bunch more to my above post but for some reason it didn’t post so I will write it again.

Acceleration depends on many more factors, its not just gear ratios or wheel size. Things such as friction and weight can impact acceleration a lot.

The best way to determine your robots acceleration would be to record data about your robot. Build the robot and put it on the surface you intend to use it on. Then add a simple encoder to the wheels and program in a timer. When the program starts it will run the timer and start the motor at full voltage. After this have the micro controller continually calculate the rpm of the shaft until it reaches the maximum rpm that you designated in the code. Then have it report the time & max rpm back to the computer via the print function (in easy c for example). Do this multiple times at different max rpm’s (0 to 25, 50, 75, and 100) then a put it in a list on a graphing calculator and have it make an equation that best fits the data (or do it manually on paper).

The reason I would do the above is because its not just the circumference that changes with the bigger wheels. They are heavier, the actual rubber outside is wider, and there are treads on the wheels which add a good deal of friction.

I would go this route just to be more precise but to sum it up bigger wheels have a higher top speed and smaller wheels accelerate faster.

Weight of the robot makes a HUGE difference.

We tried a direct drive Holo with small wheels whose job was to carry ALL of the balls on the field (mega dumper - lots of weight). We assumed we would need the small omni-wheels to minimize the strain on the motors to carry all the weight. Unfortunately, The small narrow wheels sank into the foam surface and the robot wouldn’t budge.

Switched to the large omni’s, and the thing ran all over the field with no issues at all.

The larger surface area of the large omnis made all the difference in the world (and it made faster too!).

• Rick F

Rick,

Exactly how heavy was that bot? This is rather important to me if you don’t mind finding out.

Thanks,
-Cody

Hi Cody,

The Robot or the whole thing?

The Robot was extremely light - just a bare min frame, 4 wheels, 4 motors and a processor. It was just a proof of concept - not a real functioning robot. The balls were placed in a cardboard box and set on top of the robot.

Hang on …

Ok, just went and measured it …

Robot chassis was 4lbs

Box of all green balls = 8lbs.

Don’t have numbers handy on orange balls.

Hmm… old brain cells are fading - Now I’m thinking that test was only using GREEN balls. or maybe it was all of hte balls on one side of the field …

We’ll re-run it next time we get together …

• Rick

12lb + maybe 6lb of medium balls

Hummmmmmmmmmmmmmmm… Thinking…

I think my idea is still fine, a 4lb base is by no means light, not in terms of what Team Polynomic is doing. Problem is that we will be lugging around two batteries.

Must go figure out the weight of the medium ball and several other Vex items…

Please see if you can rerun that, in fact, if possible a video would be great. I would like to know how much weight those small omni’s can support in terms of speed loss due to them digging into the foam.

Hahaha. Mr. Folea addressed the exact issue that had me concerned, and that was if the smaller wheels would sink into the mat or not.

Thanks Mr. F!!!

Sunny: Are you guys coming to the IDEA FACTORY/Workshop this weekend?

We were debating changing our 3.25" speed X drive to a 2.75" turbo X drive. How would this reduction in wheel size affect friction on rollers, since the rollers are almost always used when drivng an X?

Wow, might be better to start a new thread next time…

2.75" wheels are generally worse. They are the heaviest wheels Vex sells, and the rollers have more friction in them than the other omni wheels Vex sells. But theoretically, here are the calcs:

160 rpm * 3.25 = 520
240 rmp * 2.75 = 660

So theoretically the 2.75" wheels on turbos are about 27% faster than the 3.25" wheels. Note that the calculation above isn’t done for tangential velocity though, I was too lazy to do that.

In sports there are fast people and there are quick people. You might not be able to catch the fast ones, but you won’t be able to stop the quick ones.

Being quick isn’t about how fast you can go… it’s how long it takes you to get from being stopped at point A to being stopped at point B.

If you never reach your peak velocity, then it is pretty much irrelevant to your speed.

Jason