What's Your Vector Victor?

Remember the cockpit scene from Airport! when they are taking off?

Roger Murdock: We have clearance, Clarence.

Captain Oveur: Roger, Roger. What's our vector, Victor?

Tower voice: Tower's radio clearance, over!

Captain Oveur: That's Clarence Oveur. Over.

Tower voice: Over.

Captain Oveur: Roger.

Roger Murdock: Huh?

Tower voice: Roger, over!

Roger Murdock: What?

Captain Oveur: Huh?

Victor Basta: Who?

It makes more sense if you know that a vector is an arrow that represents the size and direction of a value. For example, if I say I flew 240 miles, I’ve only given you a distance. But if I say I flew 240 miles in the direction of north by northwest, then that can be graphically represented as a vector by drawing an arrow 240 miles long in the direction of travel, which is north by northwest. (Okay, it doesn’t really have to be 240 miles long because we can scale it down.)

Why would anyone use vectors? Because they make it easier to figure out complex problems. For example, suppose we take off from Austin and fly due east for 120 miles. Then we change course and fly north by northwest for 240 miles. Where would we end up? We can use vectors, as shown below, to find out.

The black arrow represents the first leg of the flight, and it’s 120 miles long in the easterly direction. The red arrow represents the second leg of the flight, and it’s 240 miles long in the north by northwest direction. The orange arrow represents where we end up, and it goes from the tail of the black arrow to the head of the red arrow. We can use the Pythagorean theorem to calculate the length of the orange vector. The Pythagorean theorem says that a² + b² = c², where a is 120 and c is 240.

120² + b² = 240²

b² = 240² - 120²

b² = 57,600 – 14,400

b = √(43,200)

b = 208

According to our vectors, we ended up 208 miles due north of where we started, so we would be somewhere around Dallas.

How does all of this apply to power distribution? I thought you’d never ask. The answer is right under your nose. Look at the illustration again (below), this time with the values for all three vectors included.

Do those numbers look familiar? They should if you know how a delta-delta connected feeder transformer works. In North America, the phase-to-neutral voltage (represented by the black vector) is 120V, the phase-to-phase voltage (represented by the red vector) is 240V, and the wild leg or high leg (represented by the orange vector) is 208V.

This is but one example of how vectors can be used to help make complex relationships easier to understand. There are many more. For example, why is it that, in North America, the voltage from phase A to neutral is 120V, the voltage from phase B to neutral is 120V, but the voltage from phase A to phase B is 208V and not 240V? You can use vectors to see why. The key is the phase relationship between phase A and B, which are 120° out of phase with each other. Try it, and if you get stuck, send me an email and I’ll send you an illustration.