# Picking Your Wire Sizes (New Word: Resistivity)

Back when I first started my project I picked my battery, controller and motor wire sizes the easy way.  I did what everybody else was doing.  (At that point ‘most everyone agreed that all you need is AWG4, but then a friend of mine used some of that awesome AWG2 audio cable and I got hooked on the look.)  After a while I decided it might actually be a good idea to understand this a little better.  Here we go.

First, check out the post I did on wire sizing terminology, just to get on the same page.  Here it is: Wire Size, AWG and Funny Numbers.

There’s one basic principle here.  Every conductor has some degree of resistance.  Resistance does two things – it generates heat, and reduces voltage, something that we understand by virtue of a Mr. Ohm and his Law.  So it follows that if you make a wire longer, you’re going to get more resistance, which will give you heat and drop your voltage.

But how much?

Here’s kind of a geeky description which introduces a new (made up) word: Resistivity.  This is the opposite of Conductivity, if you’re keeping score.  More information can be found on their main “Resistance” page, here, but here’s the talk about length:

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made (resistivity).

Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as resistance = resistivity x length/area

There’s also a good explanation of voltage drop, though more for electricians, here.

What is voltage drop? A voltage drop in an electrical circuit normally occurs when current is passed through the wire. The greater the resistance of the circuit, the higher the voltage drop.

How much voltage drop is acceptable? A footnote (NEC 210-19 FPN No. 4) in the National Electrical Code states that a voltage drop of 5% at the furthest receptacle in a branch wiring circuit is acceptable for normal efficiency. In a 120 volt 15 ampere circuit, this means that there should be no more than a 6 volt drop (114 volts) at the furthest outlet when the circuit is fully loaded. It also means that the circuit has a resistance that does not exceed 0.4 ohms.

What causes “excess voltage drop” in a branch circuit? The cause is usually:

1. High resistance connections at wiring junctions or outlet terminals, usually caused by poor splices anywhere in the circuit, loose or intermittent connections anywhere in the circuit, corroded connections anywhere in the circuit, orinadequate seating of wire in the slot connection on backwired “push-in type“ receptacles and switches.

2. The wire does not meet code standards (not heavy enough gauge for the length of the run).

Finally, here’s a good online calculator for figuring out your voltage drop.

Keep in mind, all this is based on a given starting ambient temperature.  The more a conductor heats up, the more resistance it develops, but for our purposes that’s probably more academic than a practical concern – the range of riding temperatures isn’t really going to have an effect on your battery and motor conductors.

So let’s get back to reality here.  For the voltages and loads we’re talking about, how are you going to determine what’s best for your system?  What’s a workable range?

I’ll start with something I know is bad…  that is, something I’ve melted – 12AWG wire.  That shows, using the calculator at 600amps and 90V for a meter of run, a voltage drop of almost 7%.  If I move to 6AWG, that goes to 1.73%.  OK, let’s move to what I started with for my actual, non-frankenstein wiring, 4AWG.  That gives me 1.09%.  Now, personal experience will tell me that these wires, running under normal conditions, will, in fact warm up a bit to the touch, so though 1% or so seems fine, you’re still on the edge.  Bump your cables to 2AWG, and now you’re looking at a .69% drop, and I can say, I never have had wires heat up when I’ve run the 2AWG stuff.  Keep in mind, I’m just using the wire heating up thing as more of an indicator of something that’s not quite right.  Just for the record, a buddy of mine with a factory bike brought the bike back to the factory this past summer, and they made a few upgrades.  One of which was re-doing some wiring and connections based on a thermal imaging analysis of the pack.  That allowed them to review every connection and cable, and re-do several crimps and connections that were making heat – so I’m not far off.

This makes me think we could do a curve that might be useful in showing where our decreasing returns start kicking in.  Hold on, I’m working on it.  OK, done.  Here you go:

Yeah, so around AWG2 or so, you start seeing the curve getting a lot shallower and some significantly decreasing payback.

The decision on wire size, then, becomes more an issue of practicality at a point.  When you get bigger, thicker wires they become a little harder to work with.  They also become more expensive, like, lots more expensive, especially if you get wires that are more flexible for a given huge size.  Everything else gets bigger and more expensive too – connectors, lugs, all that stuff.  Even the crimpers you can use will get to the point that they can’t handle a large size.

That said, look at this:

This, Johnny, is what AWG4/0 cable looks like.  And it’s yummy.  That’s AWG 0000, or “four-ot”.  I used this stuff for my solar trailer battery feed to the inverter because the AWG 2 was melting, and the voltage drop was dramatic, even for the meter-or-so that I was running.  It’s also surprisingly flexible and easy to work with.

Would I build a high-amp, high voltage bike with AWG4/0 cable?  You bet your ass I would.  Just for the yummy-badass factor alone.

Now, surely you want to know where to get this stuff.  See my Super Secret Magic Awesome Cable post here for that info.