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142 Build Your Own Electric Vehiclemust flow through this field winding as through the motor armature itself, it is woundwith a few turns of heavy gauge wire.TorqueAs equation (5) showed, Torque 5 K 3 f 3 I a, and the current in the series field is I a. I acan be substituted for f and the series motor torque equation can be written asTorque 5 K' 3 I a2This shows that in a series motor, torque varies with the square of the current—afact substantiated by Figure 6-3’s actual torque versus armature current graph. Thegraph is actually a little misleading because at startup there is no counter electromotiveforce (EMF) to impede the flow of current in the armature of a series motor, and startuptorque can be enormous; with no current limiting, you can start up at torque values farto the right of the full load line for a series motor. In actual use, the armature reactionand magnetic saturation of the series motor at high currents sets upper limits on bothtorque and current, although you might prefer to limit your circuit and components tofar lower values. High starting torque makes series motors highly desirable for tractionapplications.SpeedAs the following equation shows,Speed 5 (V t– I aR a)/K4)Once again, I acan be substituted for f, and the series motor speed equation can berewritten asSpeed 5 (V t– l a(R a+ R f))/Kl awhere R aand R fare the resistances of the armature and field, respectively. This showsthat speed becomes very large as the current becomes small in a series motor—a factsubstantiated by Figure 6-3’s actual speed versus armature current graph. High rpms atno load is the series motor’s Achilles heel. You need to make sure you are always ingear, have the clutch in, have a load attached, etc., because the series motor’s tendencyis to run away at no load. Just be aware of this and back off immediately if you hear aseries motor rev up too fast.Field WeakeningThis technique is an interesting way to control series motor speed. You place an externalresistor in parallel with the series motor field winding, in effect diverting part of itscurrent through the resistor. Keep it to 50 percent or less of the total current (resistorvalues equal to or greater than 1.5 times the motor’s field resistance). The byproduct isa speed increase of 20 to 25 percent at moderate torques without any instability inoperation (hunting in rpm, etc.). Used in moderation, it’s like getting something fornothing.Frank G. Willey, a member of the EAA, created the first pulse width modulatedmotor speed controller using silicon power transistors. He was recognized by the IEEEin the early 1980s for doing so.Offered in kit form or completely assembled and tested, the Model 9 had ratings of450 amps for traction pack voltages from 24 to 120 volts. Today, most motor controllers