Racing Power Wheels Part 3: Selecting Sprocket Size and Calculating Speed

So in the previous post I decided to go with the WMS Tuck and Run #35 Sprokcet from BMIKarts.com. 

BMI Karts lets you have the choice of selecting the sprocket ranging from a 53 to a 75 tooth sprocket. The product description didn't provide the outside diameters for each different tooth sprocket. So I went online to look for a chart that displays the outside diameter for a #35 chain size sprocket for different numbers of teeth. I found this chart online from Azusa Engineering regarding sprocket diameters of #35 chain size sprockets at http://www.azusaeng.com/Sprockets/AzSDno35.pdf.

I also found another website that provided the same information at http://ablproducts.com/35-chain-sprocket.html. So a 53 tooth sprocket would be about 6.5" in diameter and the 75 tooth sprocket would give about a 9.17" diameter. So I can pick a sprocket in between these measurements. So If I decide to go with a 65 tooth sprocket, I'll have a sprocket with a diameter of about 8" (7.978"). I can use this number to help me in determining the speed of the Boca Dune Racer.

The 36V 1000W motor has rated speed of 3000rpm. The sprocket on the shaft of the motor is a 11 tooth 8mm 05T sprocket. I am not sure what the 05T means but I found the diameter of this sprocket at this website https://electricscooterparts.com/sprockets8mmchain.html. They list the OD of this sprocket as 1-1/4".

I won't actually use this sprocket once I have received all the parts since it won't be compatible with the #35 sprocket on the axle. I will swap out the motor's sprocket with a #35 sprocket. The same website where I found the OD of the motor's stock sprocket sells #35 sprockets to be mounted onto motor. I will just wait for now until the motor arrives here at Boca Bearings to be able to see how the stock sprocket is secured onto the motor. Then I can select a #35 sprocket that uses the same way of attachment. I will also need to measure the motor's shaft to make sure the #35 sprocket has a bore that will fit on the motor's shaft. For now I will just calculate the speed with a 1-1/4" sprocket for the motor.

The main equation I will use to calculate the speed of the Boca Dune Racer will be the following:

V = r * w

Where V is linear speed, r is the radius of the sprocket, and w is angular velocity. To start things off, we know the angular velocity of the motor w but we need to convert it to radians per second. So we simply convert it from rpm to rad/s as shown below.

(3000 revolutions/minute) x (2π radians/revolution)
= 6000π radians/minute

(6000π radians/minute) x (1 min/60 seconds)
= 100π radians/second = 314.16 radians/second

Or it can be seen below in a slightly different format to make it easier to understand.

In the above format it can be seen how units can be converted to other units. Units like 2pi radians/ 1 revolution is equivalent to 1. Whatever is in the numerator is equal to what's in the denominator. So you're multiplying the value to just simply convert it to different units. Once you cross out the units that cancel each other, you will be left with the units you have converted to. This is seen below.

So the angular speed of the motor is 100π radians/second.

The diameter of the motor sprocket is 1-1/4", so the radius is 5/8" which is 0.625". So now we have the radius, r, of the motor sprocket and the angular velocity, w, of the motor so now we can utilize the equation V = r * w  to calculate the linear speed of the chain. Below is a picture with where V, r, and w is on the sprocket.

I got the drawing of the chain and sprocket from http://etc.usf.edu/clipart/17800/17817/sprocket_17817.htm. Below is a more simplified version of the sprocket with the parameters shown on it.

So V is the speed of the chain and this speed will remain constant at all points on the chain as shown in the image with the sprocket and chain. Below, the linear speed of the chain is calculated.

So as stated before, the linear speed calculated is the same everywhere on the chain as shown below by the green arrows.

Knowing the linear speed of the chain can help us in calculating the angular speed of the axle. We stated that the diameter of the axle sprocket is about 8", so the radius of the axle sprocket is 4". So now we have V from the previous calculation and we know r of the axle sprocket; therefore, we can calculate w of the rear axle solving for w from V = r * w.

Now we have the angular velocity of the rear axle. This angular velocity, w, is the same for the rear sprocket and for the rear wheels since they both move together about the axle. One cannot move faster than the other since both will be fixed together as a rigid body, like a sprocket on a bicycle's wheel. 

For now, I will say that I'll select wheels with a 14" diameter. So the radius of the wheels is 7". With the radius of the wheel and the angular velocity of the axle, we can now calculate the speed of the Dune Racer as follows.

So according to these calculations if I am right, the Boca Dune Racer will achieve a theoretical speed of 19.5MPH with the use of 1-1/4" motor sprocket, 8" axle sprocket, and 14" wheels. In real life, this theoretical speed may not be reached because of weight, friction, motor efficiency, and wind drag. So we might be around up there in the 19's MPH. I was going to decide to go with a larger sprocket to obtain more torque but I will then lose top speed and to me 19MPH sounds ok to me. I don't really want to have a low top speed. But I will test the Dune Racer once I have all the necessary parts to do a test run.

The motor has recently arrived but our hand throttle came crushed. I tried to test the motor with the throttle since it seemed that only the plastic housing was damaged but it didn't work. I was trying to read the voltages across the hand throttle with a volt meter but there wasn't any. So I guess the hand throttle is permanently damaged. But I spoke with Monster Scooter Parts and they quickly reshipped another throttle for no cost. So I am just waiting for the throttle to arrive and then I can test the motor.

I will also need to find a way where I can mount a #35 motor sprocket on the motor. The stock sprocket has a double D (DD) bore instead of a regular circular bore.

So I'll have to do some research on how I can mount on a #35 sprocket on the motor. Another issue I came across from reading online is that standard #35 motor sprockets don't have bores that will be small enough to mount on the motor shaft securely. I've read online that people have welded a #35 sprocket onto the stock sprocket. So I'll consider that method if all else fails. I'll cover more about it in the next post and I will most likely then have some video of the motor being tested.