A direct drive on a DC motor won't get you fast (just about 23MPH). It probably would work best with a Variator. Usually DC motors are limited to ~4.4k RPM (they just don't have a lot of torque at those RPMs). A 50cc doing 4.5k RPM, usually goes ~25-30MPH.
An AC motor is more difficult to feed. There are currently no AC batteries, and using a power converter to convert DC to AC, would take more energy than using a direct DC motor.
A motor spinning at 1500 rpm with an output wheel that's 13 inches is going to push you at 58mph if the differential is 1. That's without the variator, with it would kinda be a waste I think( unnecessarily high rpms to get to speed, possibly better if you maintain a higher speed tho)
Have you seen inside a CVT on a scooter (say a 50cc)? The final gear ratio is greater than 1, when the variator is maxed out. It could be because of the gears before the variator though. However, generally a 50cc scoot doing 7k RPM (double of an electric), goes ~50MPH, a 150 doing 7k rpm goes ~60.
But perhaps if there are no gears before the variator, and a 50cc scoot would direct drive the variator, it would go a lot faster (though have almost no torque to overcome the resistance).
The motors on the bike on the photo, are also not normal DC motors. They kinda look like a starter motor from a car.
Those are industrial motors, either that or a high torque work motor of some sort. I have been looking at some 2hp farm and industrial motors... they state they maintain the torque thru most of the rpm range (up to 3400rpm) and have fins just like the motors on those bikes. Only thing is they are ~$700. Time to search out a free pool pump motor to play with
An engine's starter might be a motor to look at, although it could overheat from prolonged use... I really don't know enough of electric motors to think of one that would make a great electric bike; however, there should exist 96V electric motors, used by most electric scooters, that seem to provide both enough torque, and power, and efficiency to drive a bike without problems...
Issue is if you're going for brushless, or brushed motors.
Well if you want some more well informed opinions and don't want to try to reinvent the wheel here, I suggest going to a forum called "E is for electricity" I am a member there, I have not logged in for a couple years but those guys are the experts on electric rides.
Have you tried changing the front sprocket to a larger one? It seems to me that you found a good top speed on that bike, with that motor, but perhaps you could extend the range by not making the motor run so fast? Acceleration and top speed might go down with a larger front sprocket (or smaller rear sprocket, or both), but you might extend range, as 12 miles is really small.
On my Xtreme Xb700Li, I had a ~35 miles range, but the battery was a 48V, 20A (40A peak). So that's a 960/1920Wh battery; probably larger than the one you have over there!
Yeah I was about to point out the sprocket sizes and ratios but I decided to leave it alone lol. ( I think the top one has a ratio of 0.33 or so.... that could be helped a lot in range and speed by smaller rear sprocket but no need to get into that on a randomly found picture :] )
I'm thinking of a 3 or 4 wheeled vehicle for my shopping runs that uses a gas genny to power my electric motor and take me to the winco, but that would require making and registering a vehicle from scratch.... too much time at the DMV for me
Then again... an electric vehicle that you always carry a generator in case you have to really charge (would always be on when driving so you can disconnect most of the batteries :] ) and you wouldn't have to do emissions
I personally had 2 batteries installed. The primary main battery of 48V, 20A (good for 25-35 miles) A secondary smaller battery of 48V 10A. (good for 10-15 miles) And once I burned through both, I could put them in parallel, to get the last 5 miles out of them; just in case. Generally I would not select tours that where further than 20 miles in radius, so I could always go and return. But worst case scenario, I could still pair both batteries, and hopefully get home. Never had the situation occur, for the entire time I had the scooter.