Series Wound Motor
In an effort to better explain the Series Wound motor characteristics, I created some graphs to help show
the dynamics during acceleration. If you imagine starting from a stop, and pushing the pedal to the metal,
the motor amps would go up to the rating of the controller (say 500A). The controller would be limiting
current by preventing the PWM duty cycle from going higher. It would basically stay at 500A until you
lifted your foot, or the back EMF of the motor increased to allow an increase in duty cycle to maintain
current. Eventually you either run out of Battery Pack Voltage (HP limited, full PWM duty cycle) or RPM
limited (high battery voltage, PWM mode). For a direct drive system where a 1:1 ratio is used, you may
never see full PWM duty cycle, and you wouldn't see full power from the battery pack (motor amps =
battery amps). For larger (8" or greater) motors, the point where full battery current is reached can occur
at a lower RPM. So in effect, you could be at full battery pack current (peak HP) at a lower RPM.  
Here's a data table of the motor HP for a given
torque and increasing motor RPM. The motor
current isn't on the table, since we're looking at
the relationship between HP and RPM
(assuming the motor torque and amps are
related). So for this case, accelerating at 500
RPM, the motor is making a whopping 6.7HP!
Doesn't seem like much to get a car moving.
Accelerating should have the feeling like its
never going to taper off (provided battery
voltage is high enough to maintain full motor
current). As RPM ramps up, HP goes up and
you get that constant torque pull.
Let's say you have more amps or a larger
motor, the HP curve will ramp up more quickly.
With a clutch equipped vehicle, you could slip
the clutch to gain more low end HP, but this
would be a very bad idea, series motors
accelerate very quickly (unloaded) and can
overspeed resulting in a blown motor!
This graph shows the same thing, but in a linear representation (from 144V data above).
A lower voltage system will require more battery amps to make the same HP.
For a 500A controller, the red current data points would
reduced to 500A and the torque and HP would be less
than shown. HP is limited sooner at lower battery pack
With a transmission, the motor is able to spool up quicker, putting more HP to the ground sooner than with
a direct drive system. The variable then is time, how long or short it takes to get up to full speed.