The entire subject of a fixed "speed limit" on a 'vehicle' which
- can be operated with the motor off or disengaged
- can be operated faster with the motor off or disengaged that it can go with the motor on
- which has so little power that going up hills slows it down to a crawl or a stop
- Requires peddling when starting and going up hills
- which goes substantially faster with the wind at your back, and
- substantially slower when driving into the wind
seems VERY contrived to me.
I would suggest that a viable alternative be the ability for the motorized bike to go uphill without peddling. Define a standard slope and rider weight. Assume for argument, that the slope should approximate the maximum slope you would see on mountain roads. An 8% slope, while greater than the maximum allowable freeway slope, is often seen in hilly or mountainous roads. And, could assume a 180 pound weight for the mythical 'standard' rider.
Any 'motor vehicle' should be able to proceed under its own power on the nation's roads, even when climbing mountain roads.
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It's also fairly easy to calculate the maximum slope that a given motor, drive-train, and bike
should be able to climb unassisted.
For instance. Assuming a Staton chain drive, 'tuned' for a maximum speed on level ground of 30 mph. (18.75 to 1 gearbox reduction, 16t drive sprocket, 16t driven sprocket) Robin - Subaru EHO35 33.5cc motor, bike with 26 inch diameter wheels, 180 pound rider, and 85% efficient drive train, and that Bike + motor + fuel weighs 50 pounds.
Max torque is 1.3 foot-pounds (at the engine) at 5000 RPM
Speed at max torque (5000 RPM) on level terrain is 20.6 mph (assuming no air resistance)
Max torque at the rear wheel: 20.72 foot-pounds @266.7 RPM (assuming 85% efficiency.) The max force is therefore 20.72 foot-pounds/13 inch radius/12 inch per foot , or 19.1 pounds. At 21 MPH, the air resistance should be on the order of 5 pounds, spread out over the riders body. (A bike & rider just isn't very aerodynamic!) Thus, the NET driving force available is about 14 pounds at the engine's maximum torque RPM.
The total weight to be pushed up the hill is 180 + 50, or 230 pounds.
The maximum
possible slope that this bike could climb, without peddling, is *approximately the ratio of 14/230, which is a
6.1 percent grade (3.9 degrees.) At this slope, the bike would be right 'at the edge.' Any wind gust, any temporary greater slope would cause it to slow down a bit, which would pull the engine 'off' its max torque peak, which would cause the bike to slow more, pulling the torque down even more... and the bike slows to the point where the motor dies (or the centrifugal clutch will release.) Essentially, once the motor slows down, even a little, it can no longer produce its max torque, starting a downward spiral.
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* It is actually the tangent(inverse sine(14/230)) However, at angles less than 10 degrees, the sine and tangent calculations yield approximately the same result)