So, what really happens when you change the tire size on your golf cart? To demonstrate the mechanics involved, let’s take an example of a golf cart with somewhat typical characteristics and play with the numbers. We’ll create the following hypothetical golf cart for the purpose.
Our hypothetical cart has a wheel size of 18 x 8.5 x 8.
What does that mean?
The 18 means that the tire is 18 inches in diameter (D). This would be the distance if you measured from the outside of the tread of the tire to the same place 180 degrees away (the other edge of the tire). The diameter is equal to twice the radius (R), which is the distance from the center of the wheel to the outside of the tread of the tire. Most math projects that deal with circles talk about radius, so we will just note that the radius (R) is equal to half of the diameter (D). In our case, R = 9 inches (half of D, which is 18 inches).
The 8.5 refers to the width or thickness of the tire. If you laid the tire flat on the ground and put a board on top of it, the distance from the bottom of the board to the ground would be the width of the tire. It reflects the width at the “fattest” part of the tire.
The 8 means that the tire was intended to be placed on an 8 inch rim or wheel. If you look at the tire before it is mounted on the rim, you will see that there is a “lip” to provide an air-tight seat against the surface of the rim that it mounts on. The 8 inches does not include the “lip” but starts just where the tire can be seen at the edge of the “lip” when it is mounted.
Our hypothetical cart has a gear ratio of 12.5 to 1.
The gear ratio is set by the design of the rear end or differential or transaxle (whichever you prefer). This gear ratio actually determines how many revolutions of the motor will result in one complete revolution of the tire. The gear ratio can be “played with” to accommodate different demands of performance of the cart. The “lower” the gear ratio, the more power the cart exhibits, but it will not go as fast. In our example, we will use 12.5 because it is fairly representative of average carts and is easy to use.
Our cart also has a motor that spins at 3600 RPM with maximum voltage applied to it (full throttle).
To see what kind of speed our cart will go, we’ll start with how far the cart will move with one complete revolution of the tires. As the tires rotate, the cart will be moved one circumference of the tires (the distance of the outer edge of the tire where it touches the ground). If you were to put a tape measure around the tread of the tire, the circumference is what you would be measuring.
The circumference (which we will represent as “C”) of the tire is equal to 2 x the radius (R ) x pi (3.14159265), which we will call 3.14, and represent with the symbol π).
So we will express all of this as:
C = 2 x R x π
In out case:
C = 2 x 9 x 3.14 = 56.52 inches that the tire will cover in one revolution.
Since there are 12 inches in a foot, 56.52 inches / 12 = 4.71 feet that the cart will travel with one revolution of the tires.
So now, let’s start with the motor and see how things add up.
We know that the motor in our hypothetical cart will spin 3600 revolutions per minute (RPM) with maximum voltage applied (providing it is not overloaded). Because the speed of the cart is measured in miles per hour (MPH), we will take the 3600 RPM and multiply it times 60 (minutes in an hour) to come up with 216000 revolutions per hour.
So next, we need to account for the gear ratio that takes place in the differential. We are using 12.5 as a number for that. If we take 216000 and divide it by 12.5, we get 17280. That is the number of revolutions that the tires will make in an hour.
Now we said that each time the tires go around once, that the cart travels 4.71 feet, so in 17280 revolutions of the tires, the cart will travel 81388.8 feet. There are 5280 feet in a mile, so if we divide the 81388 feet by 5280 feet, we come up with 15.41 miles per hour.
It’s just that simple! A cart whose motor spins at 3600 RPM and has 18 inch diameter tires on it should be capable of going 15.41 MPH.
Another way of expressing this is:
MPH = (RPM of the motor x 60 minutes per hour / gear ratio) x (2 π R / 12 inches per foot / 5280 feet in a mile)
Or
If you do some multiplying and dividing of the constants in the formula, it can be expressed as:
MPH = RPM x D x .00297 / Gear Ratio
MPH = 3600 x 18 x .00297 / 12.5 = 15.40 (rounded) MPH
So now, let’s assume that we decide to go with a 22 inch diameter tire, instead of the standard 18 diameter tire.
MPH = RPM x 22 x .00297 / 12.5 = 18.82 (rounded) MPH
So in the process of changing from the 18 inch diameter tires to the 22 inch diameter tires, you speed the cart up by 22.2 % (difference of 3.42 / 15.4 = 22.2%).
If you went the other way in order to get more power and went from your 22 inch diameter tires to 18 inch diameter tires, you slow it down by 18% (difference of 3.42 / 18.82 = 18.2%).
If you were only interested in the % of difference in speed between two different tires and didn’t want to calculate the speed in MPH, you could simply take the difference between the two diameters and divide it by either the smaller tires diameter to get the % of increase or divide it by the diameter of the larger tire to get the % of decrease in speed. As in our case:
Difference = 22 -18 = 4
4 / 18 = 22.2 %
4 / 22 = 18.2 %
Ron Staley has published the following books, and you can get more information about them by just clicking on each title below:
Electric Golf Cart Repair 101 (and a half)
Techniques, Tips, Tools and Tales
Gas Golf Cart Repair 101 (and a half)
Techniques, Tips, Tools and Tales
4-Stroke Golf Cart Engines Explored
What Makes Them Tick
By an old Slot Machine Mechanic