Sigh... we aren't thinking very clearly about the one-speed vs.
multi-speed situation. It doesn't matter if it is an AC vs. DC drive.
What matters is that the motor+controller+transmission system produce
*enough* torque over a wide enough speed range.

The torque-speed curve for *BOTH* an AC drive and a DC drive looks like
this:

torque
  |__________
  |          \
  |           \
  |            \
  |             \
  |______________\____speed

The flat portion is when the controller is in current limit; fixed
current = fixed torque. The falling portion is when the controller comes
out of current limit, and battery voltage is limiting torque.

If the peak torque is high enough to spin the wheels, and the top speed
is high enough to reach your maximum desired road speed, then the
motor+controller is "big" enough to work without a transmission. A
single gear ratio can satisfy both your max torque and max speed needs.

If you pick a smaller motor+controller, its max torque and/or max speed
capability is less. But, you can boost the torque at low speeds with a
transmission.

torque
  |____low gear
  |    \
  |_____\______high gear
  |      \     \
  |       \     \
  |________\_____\____speed

Obviously, the peak horsepower isn't as high; but you have the same
torque (hill-climbing and accelleration capability) at low speeds, and
the same top speed as the more expensive motor+controller without a
transmission.

Or, you can look at it from a horsepower point of view. Horsepower is
torque times speed, so the horsepower curve for the large single-speed
motor+controller looks like this:

horsepower
  |         _
  |        / \
  |      /    \
  |    /       \
  |  /          \
  |/_____________\____speed

And a 2-speed transmission and smaller motor+controller horsepower curve
looks like this:

horsepower
  |
  | low gear
  |   _     _high gear
  |  / \   / \
  | /   \/     \
  |/___/_\_______\____speed

The smaller motor+controller+transmission delivers less peak horsepower,
but delivers its smaller horsepower over a wider range. In fact, an
ideal infinitely variable transmission would deliver constant horsepower
over a wide range, so a smaller motor+controller+transmission would
outperform a larger single-speed motor+controller.

The devil is in the details. Exactly how lossy is your transmission? How
fast can you shift? How wide a speed range can you get per gear ratio?
--
Lee A. Hart                Ring the bells that still can ring
814 8th Ave. N.            Forget your perfect offering
Sartell, MN 56377 USA      There is a crack in everything
leeahart_at_earthlink.net  That's how the light gets in - Leonard Cohen

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