Design problem of DC motor Starter

In this design problem, an automatic starter circuit is to be designed for a 4-point shunt motor rated at 20-hp, 240-V, and 60-A. The armature resistance of the motor is (0.62) Ohm, and the shunt field resistance is (121) Ohm. The motor is to start with no more than (151) percent of its rated armature current, and as soon as the current falls to its rated value, the starting resistor stage must be cut out.

a) Draw a neat diagram of a 4-point dc shunt motor starter?

b) Determine the number of steps required in the starter and the value of the resistors in each step?

The started current of motor is supposed to be 151 % of the rated armature current. On no load conditions the terminal voltage and armature voltage is same.

Shunt field current                                                 

Shunt field current                  

The field current is corresponding to the current and becomes

 In case if there is no load, 

Starting condition         

For the nth stage                                   

Solving for n gives                                         

The number of steps yields 2.82.