Tuesday, October 21, 2014

Juicer Math, Pt. 2 (or Why We Can't Just "Add More Cable" To A Run).

We all know (or at least we should) that Wattage = Volts x Amps. (Also known as Ohm's Law if you wanna get technical about it.) If you don't know what that means or why it's important, I suggest you look it up.

But how many of us know about line loss and voltage drop? And I mean, really know it?

Basically, your voltage is tied to the length and size of your cable and the amperage you draw. So the longer your cable run and/or the more amps you need, the lower your voltage will dip.

There are various problems associated with low voltage, such as equipment not running properly (HMIs won't run if voltage is too low and tungsten will dip in color temperature) and some safety issues as well. In fact, for our movie making purposes, the National Electric Code only allows us to a maximum drop of 3%. Math time: 3% of 120v* is 3.6v. Which means the lowest we could go voltage wise is (120 - 3.6 = ) 116.4v.

Now how do we calculate whether or now we're within those limits? By using the Voltage Drop Formula!

(√3·K·I·L)/ACM

Where...   √3 = 1.73 (Duh)
K = Resistance of the conductor being used
I = Amperage
L = Length or Distance in feet
ACM = Area of Circular Mills (aka: a really scientific way of saying how thick the cable is. This number is based on the gauge of the cable being used)

Since the "K" we're usually dealing with is copper, and the resistance of copper is 10.8, we'll simplify the formula a bit. √3·10.8 = 17.82, so the new formula becomes...

(17.82·I·L)/ACM

There. Isn't that better??

Okay. So what does that mean? It means that if you're running 400ft of banded cable (aka: #2 gauge wire; aka: ACM of 66360) and pulling 100amps/leg, your voltage drop is...

(17.82·100·400) / 66360 = 10.74 volts

Guess what? That's way more than the 3.6 volts we've already determined you're allowed to drop and the fire marshall can totally shut you down.

But what if you switched to using 4/0 (which has an ACM of 211600)?

(17.8·100·400) / 211600 = 3.37 volts

Congratulations! You're still within code and you get to run 400 feet of 4/0!

But let's say your show sucks in the sense that it doesn't have the money for a rigging crew, the 4/0, or the money to pay you for a pre-call to lay out all that cable if you just happened to have the 4/0 anyway. Basically, you're stuck with whatever banded you have on the truck. And by doing some basic algebra...

(17.82·100·L) / 66360 = 3.6
L = (3.6·66360) / 1782
L = 134'

... you know you can go 134 feet before being out of code.*** You lay in 150' of cable anyway because 1) you only carry 50' lengths on the truck and 2) when all is said and done, you've been averaging 90 amps/leg anyway which puts you right on the edge (at 90 amps/leg with 3% voltage drop, it comes down to be 148.9' if you want to be exact about it). So you're good! Yay!

So why am I giving you this mind-numbing lecture in mathematics (especially when there's surely an app for all this)? Because I'm trying to show there's a reason why we run the cable the way that we do. That the choices we make in placing the generator isn't based on our own personal whims, but is dictated by what's in or not in the shot, what production can afford, the amount of manpower we have, and what can be done safely. It's not that we don't give a shit about the sound department, but more often than not, this is as far as I can get the generator away from set based on the above criteria. We do the best with what we have, which is why it irks me to no end when conversations like this happen...

Locations/Sound Guy/Etc.: "We need to move the generator."
Me: "That's a little easier said than done..."
Them: "Why not? It's just another 50 feet."
Me: "Well, it's not just 50 feet. I have to go around that wall/building/can't just cut across that yard where the owner's sitting on his porch holding a shot gun. It may even only be 75 feet, but all my cable is in 50 feet lengths, so really, it's be at least 100 feet of cable."
Them: "Well, don't you have two more pieces of banded? I saw some on your truck when I passed by a minute ago."
Me: "Yeah, but-"
Them: "So what's the problem?"
Me: "The problem is that with banded and the amperage we're using on set, I can only go 134 feet before I'm breaking code and I'm already at 150 feet, so-"
Them: "Oh no no no no. Don't pull that number mumbo-jumbo shit on me. Just run the cable. Is that so hard?"

WHAT THE FUCK DO YOU SAY TO THAT WITHOUT SLAPPING THE ASSHOLE IN THE FACE WITH A CLIP BOARD???

Don't people think there's a reason why we sometimes need 2/0 or 4/0? For Pete's sake, if it was always as simple as just slapping on another piece of cable regardless of the gauge, I'd just be running stingers with a cube tap on the end straight out of the generator to run the entire set!

Stupid mutherfuckers. (Can you tell I've been through this a few times?)

Another stupid request? "Can't you just bump up the voltage on the generator?" I can, but not as much as you think. 1) Going too high with the voltage on the generator can mess up the generator, which is never good; 2) Voltage goes up when amperage goes down, so when we start turning lights on and off, someone with some very expensive and sensitive equipment plugged into our system may get a nasty surprise along with a repair bill; and 3) Upping the voltage at the generator is not an appropriate way to make up for the fact that you're running the wrong sized cable to begin with. You should do it right the first time. And again, if cranking up the voltage regulator was an option, don't you think we'd say fuck it to 2/0 and 4/0 every time and just run a damn stinger to run the whole set and just "bump up the voltage"??

So no, it's not that hard to physically lay out another two pieces of banded. But electricity is a bit more complicated than just laying out pieces of cable, asshole.

Juicer Math, Pt. 1

* 120v being the standard here in the good ol' U.S. of A.
** This is a formula for a 3-Phase system only. Hence, the √3. The Single-Phase formula is 2KIL/ACM. If you don't know the difference between a 3-Phase system vs a Single-Phase system, you probably shouldn't be the one planning all this out...
*** And that's just on a good day. Heat causes resistance, so if it's particularly hot out and/or the cable is laying on some sun-baked asphalt, the voltage drop can be higher.