Figure 1: Transmission wheel combinations

The faster the axle rotates in the bearing the more friction and drag it will have. A large wheel will allow the axle to rotate more slowly (if the car is to go at the same speed), and will waste less power in the bearings.
In nature, an analogy for wheel size would be leg length. Just as a horse and hamster will travel different distances if each takes one step per second, cars with large and small wheels will travel different distances with each wheel rotation.

1. Known Values
   

   Motor Speed	wm	8300 rpm	(revolutions per minute) under load 0.278 in-oz torque at that speed
   Vehicle Speed	V	300 cm/sec	winners cover the track in 6.5 seconds. Track distance = 20m (65.6 ft), V=20m/6.5sec -or- 3m/sec

2. Gear Ratio Known
   If we have a set of pulleys or a couple of mating gears then we already have the gear ratio. Now we just need to find out what size drive wheel(s) we need to be competitive. Figure 2 shows how a pulley or gear system might look.

   
   Figure 2: Pulley and Gear Systems

   The variable D is the diameter of the pulley, and variable N is the number of teeth on the gear. The subsript d refers to the gear or pulley attached to the drive axle and the subscript m refers to gear or pulley attached to the motor. For sample purposes we have supplied values for these - use your own values to do the calculations on your own transmission.

   	The variables for a Pulley System
   	Dm = 1.25 cm	Dd = 0.25 cm
   	The variables for a Gear System
   	Nm = 40 teeth	Nd = 8 teeth
   	The variables for a YOUR System
   	[__]m = [____]	[__]d = [____]

   Step 1: Determine the gear ratio.
   

   	For a Pulley System the gear ratio is
   	R = Dm / Dd	or	R =1.25 cm / 0.25 cm	or	R =5
   	For a Gear System the gear ratio is
   	R = Nm / Nd	or	R =40 / 8	or	R =5
   	For YOUR System the gear ratio is
   	R = [__]m / [__]d	or	R =[__] / [__]	or	R =[__]

   Step 2: Find out the speed of the wheel in rpm.
   

   	For a Pulley or Gear System wheel speed is
   	wd = wm / R	or	wd = 8300 rpm / 5	or	wd = 1660 rpm
   	For YOUR System wheel speed is
   	wd = wm / R	or	wd = [____] rpm / [__]	or	wd = [____] rpm

   Step 3: Find out wheel speed in revolutions per second.
   

   	For a Pulley or Gear System wheel speed in rps is
   	wd = wd / 60 spm	or	wd = 1660 rpm / 60 spm	or	wd = 27.6 rps
   	For YOUR System wheel speed in rps is
   	wd = wd / 60 spm	or	wd = [____] rpm / 60 spm	or	wd = [____] rpm

   Step 4: Calculate the wheel circumference.
   

   	To determine the wheel diameter we first need to know the circumference of the wheel (the distance the car will travel each time the wheel turns one full revolution).
   	For a Pulley or Gear System the circumference is
   	C = V / wd	or	C = 300 cmps / 27.6 rps	or	C = 11 cm
   	For YOUR System the circumference is
   	C = V / wd	or	C = [__] cmps / [__] rps	or	C = [__] cm

   Step 5: Determine the wheel diameter.
   

   	Now we can find out what diameter wheel, Dw we need. The wheel diameter is determined from the cicumference.
   	For a Pulley or Gear System the diameter is
   	Dw = C / pi	or	Dw = 11 cm / 3.14	or	Dw = 3.5 cm (1.4 in)
   	For YOUR System the diameter is
   	Dw = C / pi	or	Dw = [__] cm / 3.14	or	Dw = [____] cm

   Step 6: Check calculations.
   

   Now check to make sure the diamter of your wheel is bigger than the diameter of the drive gear. If it is, you're up and running. If it is not, you need to chose smaller pulleys or gears.

3. Wheel Size Known
   If we already have a wheel size we want to use we must find a suitable gear ratio to drive it. For sample purposes we have supplied values for these - use your own values to do the calculations on your own transmission.
   

   	The variables for a Wheel
   	Dw = 8 cm (3.1 in)
   	The variables for a YOUR Wheel
   	Dw = [____]

   Step 1: Calculate the wheel circumference.
   

   	For a Pulley or Gear System wheel circumference is
   	C = Dw * pi	or	C = 8 cm * 3.14	or	C = 25 cm
   	For YOUR System wheel circumference is
   	C = Dw * pi	or	C = [__] cm * 3.14	or	C = [____] cm

   Step 2: Find the wheel speed in revolutions per second.
   

   	For a Pulley or Gear System wheel speed in rps is
   	wd = V / C	or	wd = 300 cmps / 25 cm	or	wd = 12 rps
   	For YOUR System wheel speed in rps is
   	wd = V / C	or	wd = [__] cmps / [__] cm	or	wd = [___] rps

   Step 3: Find the wheel speed in revolutions per minute.
   

   	For a Pulley or Gear System wheel speed in rpm is
   	wd = 60 spm * wd	or	wd = 60 spm * 12 rps	or	wd = 720 rpm
   	For YOUR System wheel speed in rpm is
   	wd = 60 spm * wd	or	wd = 60 spm * [__] rps	or	wd = [___] rpm

   Step 4: Determine the gear ratio.
   

   	For a Pulley or Gear System the ratio is
   	R = wm / wd	or	R = 8300 rpm / 720 rpm	or	R = 11.5
   	For YOUR System the ratio is
   	R = wm / wd	or	R = [___] rpm / [___] rpm	or	R = [___]

   Step 5: Design the transmission.
   

   	Since the drive pulley or gear can be no larger than the drive wheel, we need to select a pulley or gear accordingly.
   	For a Pulley System we might select a drive pulley of 6 cm in diameter.
   	Dm = Dd / R	or	Dm = 6 cm / 11.5	or	Dm = .52 cm
   	For a Gear System we might select a drive gear of 69 teeth.
   	Dm = Dd / R	or	Dm = 69 teeth / 11.5	or	Dm = 6 teeth
   	For YOUR System select a drive pulley or gear that is appropriate
   	Dm = Dd / R	or	Dm = [__] / [__]	or	Dm = [___]

4. Notes
   In these calculations friction and wind drag were not considered. In a JSS car friction and drag will effect performance. To compensate we need to make the wheel diameter smaller, or the gear ratio bigger if we are going to get the best performance. This fine tuning of the car performance will need to come from experience gained by testing the car, but these calculations will give you an idea of where to start.
   Notice that we came up with two different combinations of gearing and wheel size. There is an infinte number of combinations that will work well. What you come up with for your car depends on what you have available to you for constructing your car.