Why would putting the batteries in parallel offer more torque?
My guess is that this is putting the coils in parallel, not the batteries.
According to that link, the applied voltage determines the speed and the applied current determines the torque. I don't know the exact configuration of the windings in these motors, but having the coils in series should be putting a higher voltage on the motor (higher resistance), and having the coils in parallel should have more current (lower resistance).
Pretty neat way to get a "2 speed" transmission. Of course, it's not going to be as good as the current generation of BLDC motors (variable speed is tricky with bang-bang control...), but for the time it's a pretty clever solution.
Could someone clarify?
If the two coils are in series, you'll have a total coil resistance of 12 ohms (13 ohms incl internal resistance), and will get 0.923A (12V/13ohm) through the motor, with a terminal voltage of 11.07V (12V x 12ohm/13ohm).
If the two coils are in parallel, you'll have a resistance of 3 ohms, and a current of 3A through the motor (12V/4ohm), and a terminal voltage of 9V (12V x 3ohm/4ohm). Lots more current, but lower terminal voltage.
Edit: formatting
It's almost identical to how the two speed "transmission" works on 12 volt Power Wheels toy ride-on vehicles.
In those, there are two motors connected to the rear wheels; one for each wheel. Using a couple of switches on the "shifter", the motors can be connected to the battery in series (high speed) or parallel (low speed).
Also interesting is that by using two separate motors in that manner, you gain a form of "electromechanical" differential (not that it matters much, as the plastic wheels have insane amount of slippage on most surfaces).
See the patent: https://patents.google.com/patent/US4639646A/en?assignee=%22...