was the de facto method from its development until it was superseded by solid state thyristor systems. It found service in almost any environment where good speed control was required, from passenger lifts through to large mine pit head winding gear and even industrial process machinery and electric cranes. Its principal disadvantage was that three machines were required to implement a scheme (five in very large installations, as the DC machines were often duplicated and controlled by a tandem variable resistor). In many applications, the motor-generator set was often left permanently running, to avoid the delays that would otherwise be caused by starting it up as required. Although electronic (thyristor) controllers have replaced most small to medium Ward-Leonard systems, some very large ones (thousands of horsepower) remain in service. The field currents are much lower than the armature currents, allowing a moderate sized thyristor unit to control a much larger motor than it could control directly. For example, in one installation, a 300 amp thyristor unit controls the field of the generator. The generator output current is in excess of 15,000 amperes, which would be prohibitively expensive (and inefficient) to control directly with thyristors. Torque and speed of a DC motor A DC motor's speed and torque characteristics vary according to three different magnetization sources, separately excited field, self-excited field or permanent-field, which are used selectively to control the motor over the mechanical load's range. Self-excited field motors can be series, shunt, or a compound wound connected to the armature. Basic properties Define , counter-electromotive force (V) , armature current (A) , counter EMF equation constant , speed equation constant , torque equation constant , armature frequency (rpm) , motor resistance (Ω) , motor torque (Nm) , motor input voltage (V) , machine's total flux (Wb) Carter's coefficient (kC) is a parameter that is often used as a way to estimate the effective slot pitch in the armature of a motor with open (or semi-enclosed) slots. Counter EMF equation The DC motor's counter emf is proportional to the product of the machine's total flux strength and armature speed: Voltage balance equation The DC motor's input voltage must overcome the counter emf as well as the voltage drop created by the armature current across the motor resistance, that is, the combined resistance across the brushes, armature winding and series field winding, if any: Torque equation The DC motor's torque is proportional