An under-powered vehicle needs a lot of gears to help it adapt to different terrain and driving conditions. Modern bicycles with derailleur gears typically have a minimum of 16 gears while hub-gear bicycles will have seven (7) or more. Transport trucks have 12 or more gears and vehicles designed for off-road use will usually have a special gear reducer that effectively doubles the number of gears. Contrast this with personal automobiles, which in the past, could make do with as few as three and even now rarely have more than six (6).
A lot of motor conversion kits for bicycles have a very crude transmission set-up. One older system involved simply dropping a rubber wheel onto the front tire, but newer chain drives often aren't much better: there is only one gear and the pedals are only useful to kick-start the engine. On the one hand, transmission requirements for human versus gasoline power are very different because the former is high-torque, low RPM (revolutions per minute) and can produce generous torque at rest, while the latter is low-torque, high RPM and cannot produce any torque at rest. On the other hand, to save weight, the transmission ought to be shared between the two.
This is the solution I'm currently working. First the engine. I found this 2 hp gasoline engine, complete with magneto ignition:
Through a ratchet mechanism, the chainwheel is allowed to spin in a clockwise direction even when your feet aren't moving. What's missing is how to connect the engine to the chainwheel but seems obvious from the photos: just chain it directly from the small sprocket mounted on the end of the engine crankshaft to the larger of the two chainrings.
There's at least three problems with this solution. The first is that the engine achieves its horsepower peak at around 10000 rpm. In top gear a human will have to pedal at roughly 100 rpm to travel at a speed of 50 km/h. This implies a gear reduction of roughly 100:1! It's not quite that bad since you don't have to be in top gear when the engine is pushing the bike at top speed. There are multiple chainrings: potentially you could use just one very small one when the engine is engaged as long as there is still a reasonable spread.
With this in mind, notice that the chainwheels has been drilled out twice: first with a large spacing to accept this monster, 60 tooth chainring shown left and again with a smaller spacing to accept a standard 24-30 tooth "granny" ring shown at right.
The second problem is that the engine actually spins counter-clockwise, which hints at a solution to the first problem: just have the speed reducer in one with the reverse gear. Two gears with a tooth ratio of about 20:1 (a compound gear might be better for such a large ratio), 17:1 in combination with the giant 60 tooth ring or 14:1 with the little granny should do the trick. If both are employed, the ratio could be as low as 10:1.
Such large ratios suggest the use of worm gears but this makes it impossible to kick or jump-start the engine with foot power or momentum and a starter motor adds unnecessary weight. And third, we still haven't addressed the issue of engaging and disengaging the engine. In the setup described above, the engine is always engaged making it impossible to use the pedals except for starting the engine or possibly assisting it. This would only be acceptable for the earliest prototypes.
As a more mature, practical solution, I envision the motor being mounted beside the seat-tube with the crankshaft running perpendicular to the bottom-bracket (pedal-crank) axle rather than parallel. Two bevel gears connect the two: a small one at the end of the crankshaft and a very large one on the outside of the chainwheel. The engine is engaged and disengaged with a lever either by making the engine crankshaft extensible or through a pair of movable idler gears.
If this project interests you, you can make a donation to the Peteysoft Foundation here.