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Chapter 4:
Motor Selection and Performance
Direct current (DC) motors have two unique characteristics: the motor speed is 63
proportional to the voltage applied to the motor, and the output torque (that is,
the force producing rotation) from the motor is proportional to the amount of
current the motor is drawing from the batteries. In other words, the more voltage
you supply to the motor, the faster it will go; and the more torque you apply to the
motor, the more current it will draw.
Equations 1 and 2 show these simple relationships:

4.1
4.2

The units of K are RPM per volt and K are oz.-in. per amp (or in.-lb. per amp).
v t
Torque is in oz.-in. and RPM is revolutions per minute. K is known as the motor-
v
speed constant, and K is known as the motor-torque constant.
t
These equations apply to the “ideal” motor. In reality, certain inefficiencies exist
in all motors that alter these relationships. Equation 1 shows that the motor speed
is not affected by the applied torque on the motor. But we all know through expe-
rience that the motor speed is affected by the applied motor torque—that is, they
slow down. All motors have a unique amount of internal resistance that results in
a voltage loss inside the motor. Thus, the net voltage the motor sees from the bat-
teries is proportionally reduced by the current flowing through the motor.
Equation 3 shows the effective voltage that the motor actually uses. Equation 4
shows the effective motor speed.

4.3
rpm = K V motor = K (V in − in 4.4
I R)
v
v
Where V is the battery voltage in volts, I is the current draw from the motor in
in in
amps, R is the internal resistance of the motor in ohms, and V is the effective mo-
motor
tor voltage in volts. It can easily be seen in Equation 4 that as the current increases
(by increasing the applied torque), the net voltage decreases, thus decreasing the
motor speed. But speed is still proportional to the applied voltage to the motor.
With all motors, a minimum amount of energy is needed just to get the motor to
start turning. This energy has to overcome several internal “frictional” losses. A
minimum amount of current is required to start the motor turning. Once this
threshold is reached, the motor starts spinning and it will rapidly jump up to
the maximum speed based on the applied voltage. When nothing is attached to the
output shaft, this condition is known as the no-load speed and this current is
known as the no-load current. Equation 5 shows the actual torque as a function of
the current draw, where I is the no-load current in amps. Note that the motor de-
0
livers no torque at the no-load condition. Another interesting thing to note here is