Navigation – How to Compensate for a Crosswind.

You’re planning a round trip to an airport 100 nm due north. The wind is predicted to blow directly out of the west at 60 knots.You cruise at 100 KTAS (knots true airspeed).

You need to know how to stay on course and how long the trip will take.

Since there is no headwind component, the trip north will take the same time as the trip south. But to stay on course, the pilot must crab the plane into the wind so that it is flying through the wind to the west at the same speed as the air is moving from the west – 60 knots.

Looking at this diagram, you can see that the path over the ground (a.k.a. ‘ground track’) is the due north course.

Since the plane cruises at 100 kt, the plane follows the path through the air at 100 kt. The plane must turn left until its westward component through the air is exactly the same speed, but opposite to, the wind’s eastward movement. That way the airplane’s progress west, into the wind is exactly offset by the amount the wind pushes the airplane east. The airplane stays over the course line and makes progress, albeit slower, toward its destination.

Being lazy, I drew this so that the ground speed would be easy to calculate. Here it is 80 kt.

Don’t let this scare you: I know it is 80 kt because the triangle is a 3,4,5 triangle. Since the wind is perpendicular to the course line, the triangle formed by the ground speed (80 kts), the wind speed (60 kts) and the true airspeed (100 kts) must be a right triangle. We know from high school geometry that if one short side is 60, the other short side is 80, then the hypotenuse must be 100.

You should never have to do this calculation. I just want you to understand the concept.

The crab angle is about 54 degrees. But you don’t care about the theoretical crab angle at all.

Let’s get practical. The wind changes in both direction and intensity all the time. So what you do is turn into the wind until your airplane passes over the course line you drew on your map. That’s the right crab angle.

Let me point out that in the more complex case, when the wind is not perpendicular but from some other direction, the crab angle you’ll need is only determined by how fast the wind is perpendicular to your course line.

We call the wind perpendicular to our direction of travel the ‘crosswind component.’ Likewise the wind parallel to our course line is either the ‘tailwind or the headwind component.’

Of course in the real world the wind is never a pure crosswind, headwind or tailwind. That problem is even more complicated than those we have looked at so far.

I’m going to tell you how your flight computer solves the real world problem because you’ll have to do a first order approximation when you’re landing or taking off in a crosswind.

The computer separates the wind into its crosswind and headwind (or tailwind) components. Then it figures how much the crosswind component subtracts from your true airspeed (TAS) and it adds the tailwind component or subtracts the headwind component. The result is your ground speed (GS).

You do care about your ground speed. Screw up on that and run out of fuel before you get there. Not good.

This is not a high school math course, it’s practical navigation. Use a flight computer. I use an old analog computer bases on the World War II vintage E6B because I can use it with one hand.

If you’re thinking that with modern navaids, this sort of dead reckoning navigation is old hat. I’ve flown airplanes with no radios, and no GPS and occasionally in areas without ground-based navaids. I was glad I knew how to do this stuff.

Besides that, you’ll need to know these concepts to pass your written exams.

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