I want to run a small motor from a series of alternators. I suspect it doesn't really take 110 volts to turn the motor. Low load on the motor.

It may very well need 120 VAC. Motors are wired for specific voltages and with low voltage the motor may/will burn out.

I suspect it doesn't really take 110 volts to turn the motor.
No, it takes whatever voltage the motor is rated for. You can't just pick whatever voltage you think it needs.

Voltage doesn't turn a motor, Amperage does. Voltage is simply the amount of Electrical Pressure the motor is designed to use to push said amperage through the coils. If a motor calls for 110V, and you feed it 60V, it will likely pull twice the amperage and cook itself to output the same mechanical power.

According to NEC - Article 430, Table 430.248, the "Full Load Current" for a single phase, 1/6 hp motor will require:

4.4 amps @ 115 volts
2.5 amps @ 200 volts
2.4 amps @ 208 volts
2.2 amps @ 230 volts

Neither 2 phase or 3 phase tables list a 1/6 hp motor.

I suppose using Ohms law and if you knew the resistance of the motor, you might get the voltage but I have to ask if it is worth it to go through the trial and effort when it would be far simpler and much more safer (protecting the motor life) to follow the NEC guidelines.