Capacitors on motors: why big C for starting, small for running?

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In single-phase capacitor motors, larger capacitance values are essential for starting to generate high torque, while smaller values are sufficient for running. The required electrical phase shift is influenced by the physical arrangement of the main and auxiliary windings, which can vary based on motor design. The amount of capacitance needed for a specific phase shift does not change with rotor RPM, but the start winding must handle significantly more current during startup. The impedance of capacitors also varies, with typical values showing a stark difference between start and run capacitors. The discussion highlights the complexity of motor design, particularly in how start and run coils interact within the motor's operation.
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Long story short, on single-phase capacitor motors, large values of capacitance are used for starting and much smaller values are used for running. Yet it would seem that the amount of electrical phase shift needed is dictated and fixed by the physical relationship between the main and auxiliary windings around the stator core. (E.g. on a small four-pole fan motor, the auxiliary winding is 45 degrees off from the main one.) Does the rotation of the rotor change the value of capacitance needed for a given degree of electrical phase shift, or is something else going on here?
 
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Usually the start windings are MUCH heavier.. it's not uncommon for capacitor start motors to have 400% or more starting torque, hence the bigger capacitors.
 
Thanks. However, that's not quite the direction I was going. To rephrase the question: Does it require more phase shift to start a motor than to keep it running (on a capacitor-run motor), or does the amount of capacitance required for a given amount of phase shift vary with the RPM of the rotor? If this isn't clear, please let me know. There are motors that use a large capacitor for starting, then once they're up to speed, a centrifugal switch cuts out the big capacitor but leaves the same auxiliary winding connected through a smaller capacitor. Back in the 1960s, when my parents owned a laundromat, we had a Frigidaire washer (remember the up-and-down agitator?) that used such a motor.
 
What you've described is a cap start/cap run split phase motor, and a 'Cadillac' among single phase motors. Are you sure about the 45° phase shift? Wouldn't the start versus run coils be displaced by 90°?

Several things factor into capacitor rating differences. A major reason is the start winding performs two different duties. It must conduct considerable current to generate high torque during start-up, but not nearly so much during normal run, or the winding would burn up.

XL=1/(2*pi*f*C).

At 60 Hz. line frequency, a 20 uF cap (typical size for a run cap) has an impedance of about 133Ω, while it is close to 33Ω for an 80 uF 'start' capacitor.
 
On a two-pole motor the start coils would be at 90°, but on a four-pole, opposite poles of the run coils appear every 90°. If I understand correctly, the start coils have to be in between the run coils, or at least that's how it appears on small fan motors.
 
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