Wind correction angle and ground speed, with an example

Updated

Two numbers in a nav log do most of the work: the wind correction angle and the ground speed. The first tells you where to point the nose, and the second tells you how long each leg will take. This guide explains both with real numbers, shows a quick way to estimate them in your head, and then shows where to find them in a plan.

What the wind does to a flight

The air you fly in is moving over the ground. Your aircraft moves through that air at its true airspeed (TAS), and the air carries you along with it. The track you make over the ground is the sum of the two movements.

If you point the nose along your course and ignore the wind, a crosswind pushes you sideways and you end up on a track beside the one you drew on the chart. A headwind or a tailwind does not push you off the line, but it changes how fast you cover the ground.

Wind correction angle

To stay on the line you point the nose a little into the wind, so that the sideways push is cancelled by the sideways part of your own speed. That angle between your course and your heading is the wind correction angle (WCA). Your true heading is the true course plus or minus the WCA, turned toward the side the wind comes from.

The wind direction is the direction it blows from, in degrees true, as in a forecast. The formulas are:

  • WCA = asin( wind speed / TAS × sin(wind direction − course) )
  • Ground speed = TAS × cos(WCA) − wind speed × cos(wind direction − course)

You will rarely work them out by hand, but they show you what matters: the part of the wind across your course sets the correction, and the part along your course sets the ground speed.

Example 1: a crosswind

You fly a course of 090° (due east) at a TAS of 100 kt. The wind is 360° at 20 kt, so it blows from the north, from your left.

  • WCA = asin( 20 / 100 × sin(360° − 090°) ) = asin( −0.2 ) = −11.5°, a correction of 11.5° to the left.
  • True heading = 090° − 11.5° = 078.5°.
  • Ground speed = 100 × cos(11.5°) − 20 × cos(270°) = 98 kt.

The crosswind costs you a little ground speed even though the wind has no component along your course, because you are flying slightly sideways through the air. A 60 NM leg takes about 36.7 minutes, against 36 minutes in still air.

Example 2: a headwind and a tailwind

Now fly a course of 270° (due west) at 100 kt TAS with a wind of 270° at 20 kt. It blows straight from where you are going. There is no crosswind, so the correction is zero and the heading is the course. The ground speed is 100 − 20 = 80 kt, and 60 NM takes 45 minutes instead of 36.

On the way back, with a course of 090° and the same wind, the ground speed is 100 + 20 = 120 kt and the same 60 NM takes 30 minutes. The wind that you lose on one leg you do not win back on the other: the round trip takes 75 minutes, against 72 in still air. This is why a headwind leg needs more fuel than the tailwind leg saves.

Example 3: a wind from ahead and to the side

A course of 045° at 100 kt TAS, with a wind of 090° at 25 kt. The wind blows from the right and ahead of you. It has a part across your course and a part against it.

  • WCA = asin( 25 / 100 × sin(090° − 045°) ) = asin( 0.177 ) = 10.2°, to the right.
  • True heading = 045° + 10.2° = 055.2°.
  • Ground speed = 100 × cos(10.2°) − 25 × cos(45°) = 80.8 kt.

A 60 NM leg takes about 44.6 minutes, against 36 in still air. Most real legs look like this one.

A quick estimate in the air

When the wind changes, you can estimate the correction in your head with the one-in-sixty rule. Take the part of the wind that is across your course, divide it by your TAS and multiply by 60. For a 20 kt crosswind at 100 kt TAS, that is 20 / 100 × 60 = 12°, close to the 11.5° that the formula gives. For the ground speed, add the tailwind part or subtract the headwind part. The estimate is good enough to check a plan or to correct in flight, and the plan gives you the exact figures before you take off.

From true heading to the compass

The WCA gives you a true heading, measured from true north. Your compass points to magnetic north, so you correct for the magnetic variation of the place. With east variation positive, the magnetic heading is the true heading minus the variation. With a variation of 2° west, a true heading of 078.5° becomes a magnetic heading of 080.5°. AirPlotter calculates the variation of each leg with the World Magnetic Model, at the middle of the leg and for the day of the flight.

Finding it in a nav log

In AirPlotter, you draw the route and the nav log shows, for every leg, the wind (the direction in degrees true that it blows from, and the speed), the true course with its WCA, the true heading with the variation, the magnetic heading, the TAS and the ground speed. The magnetic heading is the one you fly on the compass, and the ground speed is what sets the ETE.

The wind is a forecast for the level and the time at which you fly each leg, so it changes along the route and through the flight. You can also enter a wind of your own. If the wind is so strong across your course that the aircraft cannot hold the line, the leg is flagged: the plan is not flyable in that wind, and a different altitude, time or route is the answer.

For more on the other columns, read how to read a VFR nav log.