1HP is 746 watts, so if his motor delivers 1/2HP at the shaft and it's
80% efficient it'll be taking about 467 watts from the mains under
full load.
200 feet of #14 solid copper looks like about half an ohm, so we have,
for the startup case:
15A--->
240AC>---[0.25R]---+ <------+
| |
[16R] 233V
| |
240AC>---[0.25R]---+ <------+
Because of the wire resistance, instead of 15A in the circuit we'll
have 14.55A, and that will drop 233V across the motor.
233V is 97% of 240V, so there's only a 3% loss in the wire.
In the full load case we have this:
1.94A--->
240AC>---[0.25R]---+ <------+
| |
[123R] 239V
| |
240AC>---[0.25R]---+ <------+
so the loss is less than half a percent.
That is right on the mark.
It was always fun to un a 100 foot extension cord to a construction
work area and run a device like a circular saw or such. Then try it with
two 100 foot cords together for 200 feet. It (the difference) is very
noticeable.
Most of those cords are #14 at those lengths (or they'd better be), but
at the price difference for raw wire and a buried run, I'd say that
dropping to #12 or eve the #10 run was not an improper suggestion,
considering it was going to be a permanent install, and the device being
powered may not be, and wiring a service outlet is what we are doing.
So, yes, as you illustrate, #14 is sufficient, even good, considering
what I have seen houses and such wired with.
At 200 feet away, and not knowing if the device will be the only item
being powered, I would at least examine the cost tables for the job using
#10, #12 and #14 Thhn, no conduit.
As far as the conduit goes though, if one gets small diameter PVC, and
all the fittings, no 200 foot pull needs to be done. The segments and
fittings can all be fed down the wire bundle and build the conduit in
place right on the wires, then bury the finished run.