# Thanksgiving Dinner Debate About GoPed Gearing

1. Dec 13, 2008

### LionTigerFire

Ok my friend and I are having a disagreement about gearing on a GoPed. I am stating that if you change the tire size of a California GoPed the speed of the GoPed will not change. This is all theory so am not taking into account friction, mass or the like.

For those of you who do not how a GoPed works the tire is NOT driven by the axel as it is on a car or by sprocket like a motorcycle, but is driven by a spindle rotating directly against the rubber of the tire.

I understand that if you double the the size of tire of a car(in theory) the car will go twice as fast. My grounds for this outcome not applying to a GoPed is that if you double the size of the tire will rotate half as fast.

If somepeople could prove to me right or wrong that would be awesome

2. Dec 14, 2008

### Danger

Welcome to PF, LionTigerFire.
It's 12:30am my time, so I'm not going to get into calculating anything. On the surface, though, I think that you are correct. It would be equivalent to eliminating the overdrive on a transmission and then shallowing out the differential gearing to make up for it.

3. Dec 14, 2008

### Ranger Mike

Car speed = (engine RPM) x (static Radius) / (168) x (axle ratio)

Note - Static radius is center of wheel hub to pavement or ground line
do not use D/2 as tire diameter in free state will differ from actual radius to pavement

Axle ratio = RPM/MPH x D/355

D is true tire diameter in free state ( measured when off the car)

Last edited: Dec 14, 2008
4. Dec 14, 2008

### LionTigerFire

Thanks Danger and sorry for the double post my friend is Physics Major(which is why i want to move my question here) with a minor in mathematics. I am gonging against him and every one else engaged in the discussion plus a university physics professor that was suppose to settle it. My friend has a argument involving angular velocity or someone thing like that is suppose to say I am wrong that I do not understand. I really need sound mathematical proof that I am right or wrong.

5. Dec 14, 2008

### Danger

I'm not a math guy. Mike seems to have a pretty good handle on it. Another fellow here, Stingray, is also brilliant at automotive math. I'm pretty much just a gear-head; I can build them and drive them, but the numbers are just a blur.

6. Dec 14, 2008

### Phrak

Your friend is right. What do we call the little wheel that drives the wheel on the ground? The 'little wheel', I guess.

If you give it a little thought, the velocity of the little wheel--the velocity of the surface of the little wheel, is the same as the ground velocity. The tire itself just acts to transmit the little wheel's velocity to the ground.

Edit: I misread who was arguing what, as Turbo points out. You're correct.

Last edited: Dec 14, 2008
7. Dec 14, 2008

### LionTigerFire

Yea I am visualizer understanding Ranger Mike's equation does not come natural to me. heres how I did the math on thanksgiving. The numbers and circumference are simple just for the sake of simplicity

Spindle has a circumference of 1in and is spinning at 100 RPM. I feel its safe to say that the surface of the spindle of the spindle is traveling 100in/min

the spindle on a 2in tire is 1:2 ratio the tire will spin at 50 RPM

2in tire @ 50 RPM = 100in/min

the spindle on a 4in tire is 1:4 ratio the tire will spin at 25 RPM

4in tire @ 25 RPM = 100in/min

Thus no change

8. Dec 14, 2008

### LionTigerFire

The tire is effectively no more than a idler gear between the the spindle and the ground and its size is irrelevant, correct?

9. Dec 14, 2008

### Ranger Mike

ifin the RPM and gearing are NOT changed, and the tire size is increased, speed will change. anyone who increased the tire size on a passenger car will have the speedometer reading incorrectly. the formula is correct.

btw Speed x Time = Distance

one mile per minute is 60 miles per hour..right??

so .... Distance / Time = Speed ( Miles per hour in this case)

when you change tire size , you are changing the amount of distance you travel in the same period of time..so u r changing the speed..
dig??

Last edited: Dec 14, 2008
10. Dec 14, 2008

### LionTigerFire

Changing the tire size on a GoPed DOES Change change the gear ratio. If you to use a pinion and sprocket to model a example the tire is effectively also the sprocket you cant cant change one without the other like you can on a passenger car.

11. Dec 14, 2008

### Ranger Mike

Ok..using your data , speed = (engine RPM) x (static Radius) / (168) x (axle ratio)

100 RPM x 1 / 168 x 1:2 = .49 MPH for 2 inch tire
100 RPM x 2 / 168 x 1:4 = .85 MPH for 4 inch tire

savvy?

12. Dec 14, 2008

### LionTigerFire

then my datas wrong

13. Dec 14, 2008

### LionTigerFire

i am not good with the math and i have my ratios wrong

14. Dec 14, 2008

### Ranger Mike

you are correct that the rotating SPEED of the tire in your calculations are correct. not the GROUND SPEED of the goped or scooter

the wrinkle is ,, the taller tire has more circumference and will travel farther in each revolution
circumference = 2 pi r or diameter times pi

so 2 inch tire has cir of 6.28 inches or rolls 6 inch in one turn of the tire
4 inch tire has cir of 12.56 inch

it goes twice as far as the smaller tire AT THE SAME RPM

15. Dec 14, 2008

### LionTigerFire

ok when i said 2in and 4in tire i meant circumference i was thinking about distances traveled

16. Dec 14, 2008

### turbo

You are correct. The spindle moves at a constant speed, and that speed (assuming perfect coupling with the driven wheel) is the ground speed of the vehicle. If you put on a larger-diameter wheel, the RPM of that wheel will be lower, but the ground-speed of the vehicle will stay the same.

17. Dec 14, 2008

### FredGarvin

Turbo is right.

I am assuming that the spindle drives the outermost surface of the big wheel.

Think of it in terms of two spur gears. The pinion (spindle) drives the bull gear (wheel). If the pinion gear has a set surface speed, then the larger gear MUST have the same surface speed. That surface speed is the vehicle speed. The only thing doubling the tire size will do is cause it to rotate at half the angular speed as before.

You are correct in making the analogy of an idler gear as well.

18. Dec 14, 2008

### schroder

Yes. As long as the RPM of the capstan (spindle) remains constant, changing the tire size, within reasonable limits, will have no net effect on the linear velocity on the outer circumference of the tire and hence no effect on the vehicle velocity. But that is an idealized situation. In the real world, changing the tire size will have some effect on the torque and also the RPM and hence the velocity. But within reasonable limits, you are correct LionTigerFire. If you want to increase or decrease the velocity for a fixed RPM, it would make sense to change the diameter of the capstan (spindle) and not the tire.

19. Dec 14, 2008

### Danger

I like that idler analogy. It's very simple and effective, with no need to involve math.

20. Dec 14, 2008

### Ranger Mike

i had to dig up the old power transmission stuff from years ago
the goped spindle thing was a real wrinkle for a while..

spur gears in mesh wit heach other or drive wheels in contact with each other share this.

the driven wheel has the same surface speed as the drive wheel.

but,, ifin you compare a 2 inch driven wheel with the same surface speed. to that of a 4 inch wheel with the same surface speed..guess who will get to the finish line first?