Calculating the voltage drop in a split-phase system

Question

We are working with an electrician to install permanent wiring to a large trailer unit - it will be a 120/240 V split-phase system (the trailer itself uses a NEMA 14-50 dryer plug) delivering 50 amps at a distance of 300 ft.

I (think I) understand that this wiring set up effectively gives us three circuits - two 120 V/50 A circuits and a single 240 V/50 A circuit.

What I am struggling to understand is how I determine the proper wiring size for the system, given the parameters of the circuit and our voltage drop needs ( <3% ). Following Ohm's Law, I have been using the formula to calculate the expected voltage drop for particular wire gauges (4 AWG or 1 AWG):

Vd = 2 * L * R * A

Where:

Vd: voltage drop

L: one way distance (in thousands of ft)

R: resistance of wire (in Ohms per 1000 ft)

A: load current (in amperes)

Ex. 1 1 AWG wire, 300ft, 50A

Resistance of 1 AWG wire / 1000ft = .124 Ohms

Vd = 2 * 50 * (.3) * (.124)

Vd = 3.72 V

Ex. 2 4 AWG wire, 300ft, 50A

Resistance of 4 AWG wire / 1000 ft = .249 Ohms

Vd = 2 * 50 * (.3) * (.249)

Vd = 7.47 V

Based on this information, my numbers suggest that we would need to use 1 AWG wire, but the electrician has said that 4 AWG is more than sufficient. I have complete confidence in this electrician, so I am sure there is something that I am missing. How does the presence of the split-phase 240 V system affect voltage drop considerations (if at all?).

Any comments or help is greatly appreciated!

Answer 1

The 50A breaker pair feeding the NEMA 14-50 plug limits the current on any phase to ... 50A, period, no matter how you load your phases. The breakers are linked, so if you have a single-phase fault on L1, it will trip itself and L2.

Your electrician will use that breaker panel limit not only to calculate the IR drop, but also the allowable cable temperature rise given the ambient temperature, conduit type, wire material and insulation type, as these all affect the 'ampacity' of the wire.

As for the voltage drop, the NEC specifies a maximum drop of 5%, not 3%. See https://www.mikeholt.com/technnical-voltage-drop-calculations-part-one.php

At 300ft and 50A, #4 ga. copper will be less than that, about 3.5%. So, plenty.

Your electrician knows what they're doing.

BONUS: An IR drop calc, with a wire resistance chart: https://www.calculator.net/voltage-drop-calculator.html

tl; dr:

• resistance of #4 ga. is 0.2485 ohm/1000ft
• One-way IR drop for 300' at 50A = 50 * 300/1000 = 3.73V
• Two-way IR drop is 7.46V, or 3.1%