What Determines the Maximum Number of Gears on a Motorized Bike?

[tackyattack]

So I have this motorized bike I made and I'm thinking about adding gears on to it over the summer. Anyways, it got me thinking and I'm confusing myself. So say you have an engine with a two speed transmission on it. For take off, you're in the smallest (or, biggest in size actually) gear so you can get some torque to get moving. Then, once you're up to a nice moving speed and the engine is purring at its prime RPM, you kick it up a notch to the second gear. Slowly, you get faster and faster until you hit that prime RPM again. Now, my question is, what determines the max number of gears you can go? Is it infinite? Like if you were on a flat plane, could you keep going faster and faster as long as you had gears to support it? If so, would that only work on a flat plane? What if you introduced a hill? Would it still work, but take longer to advance through the gears as you wait for the momentum to pick up? Thank you!

 

[Dr. Courtney]

At some point, the frictional forces (rolling and air resistance) balance the forward force that the motor can apply in a higher gear.

 

[DTM]

Although taller gears increase your speed, they decrease torque. For the sake of a simple physics problem, if you had no friction or drag, you could continue to accelerate on a flat surface indefinitely, but with each taller gear, your rate of acceleration would be smaller. Also remember as gears exchange speed for torque (or vice versa), the power output of "perfect" gears remains unchanged. If you're going uphill, again with no friction or drag, your engine power would allow you to climb the hill at a rate equal to your rate of change of potential energy. For example, if your perfect frictionless car has 100hp = 55000 ft-lbs/s, and weights 1000lbs. Your vertical climb rate could be at most 55ft/s

 

[dean barry]

Top speed will be where maximum drive wheel power = resistance power ( air drag + rolling resistance ), so its not unlimited because resistance power increases with speed and is theoretically unlimited, so at some point the lines will cross (theoretical top speed)

Most road motorcycles have the top gear arranged to allow the engine to get hit peak power RPM at this top speed, thereby maximizing the bikes top speed.
Once you have established this top speed ( a lot of various size final drive sprockets and plenty chain required), you need to fill in the gaps between with enough gears to make the bike rideable.
Have you got any data ?
Engine power, is the bike faired / unfaired , weight with rider , is it chain final drive ?
How are you going to add a gearbox to it ?

 

[CWatters]

There is probably a way of working out the top speed by plotting two lines on a graph and noting where they cross. I think the two lines would be something like..

Required Power (eg drag force * velocity) vs Motor rpm (calculated from the velocity of bike and gear ratio)
and
Motor power vs Motor rpm from manufacturers data

The drag force could be measured by towing the bike at various speed and measuring the tension in the rope.

 

[Rx7man]

Some frictional forces are proportional to speed.. rolling resistance is close to it... others, like wind resistance are proportional to the square of the speed

If you plotted your total frictional forces as well as the resulting power required versus speed, you could get a pretty close approximation to your max speed if you know your engine output power, from there you could find the gearing to allow you to get to that speed