Crosswind Calculations – Made Easy

I presume you are reading this in a comfortable arm chair, or on a train, or maybe even in a flying school with the rain pounding on the windows. Possibly there’s a favourite tipple in one hand and some gentle music in the air. Under these conditions, if I asked you to do some mental sums (and you were aged over 25), it would probably take you less than five seconds to work out “2/3 of 25”.

But now imagine the situation when you are at the holding point for runway 24: you call “ready for departure” and the tower replies with “cleared take-off; wind 280, 25 knots”. What’s the crosswind component? What’s the headwind component if the performance is a bit tight? – is it the same as you used in your performance calculations?

Not as easy as when you were on the train, is it?

Or maybe you are at the end of a long flight, typically slightly longer than the comfortable endurance of your bladder. You are flying an approach which is a bit more turbulent than part of your anatomy would prefer when, at five hundred feet, you call “final” for runway 35 and the tower replies “cleared to land; wind 030, 25 knots”. What is the crosswind component?

Let’s be honest with each other. Do you actually calculate the crosswind component every time you are told the wind strength and direction after a call of “ready for departure” or “final”? Do you always think about the wind direction and make an appropriate aileron input? Honestly?

During my time as an instructor and examiner it has been VERY rare that a pilot has volunteered the crosswind or headwind components on an approach or before take-off. If I ask them, the answer is usually (with some honourable exceptions) “errr” followed by a semi-random number. Frequently they don’t even know whether the wind will be from the left or the right without looking at the windsock!

It’s an unfortunate aspect of aviation that we all lose a significant proportion of our intellectual capacity when we have an aircraft strapped to our back. I can not tell you why it happens but I can show you a way around the problem when it comes to crosswinds and headwinds. The purpose of this article is to present a simple method which will allow you to assess the crosswind and headwind components with as much accuracy as you like, without any sums, without any gadgets, in less than 5 seconds, and whilst flying an aeroplane.

Figure 1

To make a start we need to go back to basic geometry – but, if that idea doesn’t appeal, you could just skip to the description of the method. Figure 1 shows an aircraft lined-up on runway 36 and a wind arrow from approximately 310°. We can see from the drawing that the crosswind component is simply the wind speed multiplied by the sine of the angle between the nose of the aircraft and the wind direction (called the relative wind angle). We can also see how the headwind component could be calculated, either as the wind speed multiplied by the cosine of the relative wind angle, or as the wind speed multiplied by the sine of the angle between the beam of the aircraft and the wind direction.

People don’t usually like to memorise sine tables so students are traditionally taught the “rule of sixths”, or the “clock face” rule, for crosswind assessment, and nothing at all (except the wiz wheel) for the head or tail wind.

The “rule of sixths” makes use of the happy coincidence that the sine of 10 degrees is very close to 1/6^th, sine 20 degrees is very close to 2/6^ths and so on. Table 1 shows the full story. This method is a fairly accurate approximation for most relative wind angles but we can see that there is a significant error at 60 degrees. Because of this some pilots modify the rule for 60 degrees and use 0.9 rather than 6/6^ths, in order to get the error down from 13% to 3%.

To use this “rule” you first determine the relative wind angle, and then multiply the reported wind strength by the appropriate fraction. So, if the reported wind is 350/25 and you are using runway 03:

• the wind angle is 40 degrees
• 40 degrees gives 4/6^ths
• the crosswind component is therefore 4/6^ths of 25: 17kts’ish.

If a second table were produced, with the wind angle column turned upside down, this same method could be used to calculate the head/tail wind component.

So why don’t people use it in practise? Well … all we have to do, at 500 feet on a bumpy day, having drunk too much coffee three hours ago, with someone in the back asking why something-or-other is happening and with ATC talking on the radio, is work out the wind angle and then multiply the wind speed by the appropriate fraction! The honest truth is that the sums are too complicated for many people to perform whilst flying an aeroplane. It’s therefore no surprise that most pilots don’t bother to calculate the components and occasionally get an unpleasant surprise.

What we need is a simple technique for accurately estimating the crosswind component; a technique which requires virtually NO brain power for those days when the remaining brain cell has had enough. Something visual and easy that doesn’t require sums or a gadget. Here it is.

The Method

Figure 2

In virtually every aircraft there is a Direction Indicator that looks vaguely like the one shown in Figure 2 and we can use this as a form of analogue computer (those of you who have an older style ribbon DI need not despair, I’ll discuss how you can use the same techniques a little later).

At first reading this may sound complicated but believe me, with a little practise it is VERY easy.

You are going to mentally draw the vector triangle on the face of the DI. The distance from the centre of the DI to the edge represents the reported wind speed. Once you are lined up on final approach, simply find the reported wind direction on the outside of the DI scale and mentally drop a vertical line down on to the horizontal centre line. The proportion of the centre line that lies between the vertical line and the centre line is the proportion of the wind speed that is at right angles to your direction; in other words, the crosswind.

Let’s look at that more slowly.

Figure 3

Look at Figure 3. You are either lined-up for take off, or on final approach, for runway 35 and the wind is reported as 040/25. Imagine the DI being a picture of the horizontal situation, drawn with a radius that represents the wind strength in some scale or other. In other words, if the wind is 25 knots the radius of the DI represents 25 knots.

1. The first step is to find the reported wind direction on the outside of the DI (shown as a large black arrow). You now have the first piece of information; the wind is from the right.
2. Next, mentally drop a vertical line down from the wind direction on the outside of the DI to the horizontal centre line.
3. The horizontal centre line represents the crosswind axis so visually scale-off the crosswind component as a proportion of the length of the crosswind axis, i.e. the wind speed. In Figure 3 it looks like the crosswind component is just less than 20 knots (mathematically the answer is 19 knots).

With a little bit of practise this is fast, and as accurate as you choose to make it. It also inherently wakes you up to whether the wind is from your left or your right – it’s written on the face of the DI.

Once you are comfortable with the technique it can be used to estimate the head or tail wind component in addition to the crosswind.

Look at Figure 4. You are lined up for departure, or on final approach, or simply want to know the wind components on heading 135.

The wind is reported as 180/30; what are the headwind and crosswind components?

You already know how to assess the crosswind component and can estimate that it’s close to 20 knots. We can use the same technique to assess the headwind component. Just project a horizontal line from the wind direction on the outside of the DI to the vertical centre line (which represents the head or tailwind axis) and visually scale-off the headwind component as a proportion of the length of the headwind axis, i.e. the wind speed. In Figure 3 it looks like the headwind component is about 22 knots (mathematically the answer is 21 knots).

What could be easier?

But what, you might say, if you aren’t lined-up with the runway and want to know the crosswind and head/tailwind components? Maybe you are at the holding point, at dispersal or approaching the airfield. There are two solutions; one is simply to rotate the DI so that the runway heading is at the top, but a better answer is to use the ADF or VOR indicators in exactly the same way as described for the DI. This is also the answer for those with a ribbon DI: use one of the other compass roses in the cockpit.

Possibly you’re flying a very basic aircraft with a ribbon DI and nothing else … if you stick or draw a compass rose on your knee board you can still use the method. In fact, with a compass rose of any type, regardless of whether you are in the bath or the aeroplane, you are now able to accurately estimate wind components without doing sums. Isn’t that a relief?

Going back to that bumpy approach with an uncomfortable bladder …

Figure 5 shows the DI during the approach (wing down technique, of course); the wind is 030/25.

Estimate the crosswind component; is it inside the demonstrated crosswind capability of your aircraft?

Figure 5

Dave Sawdon