Knots and crosswinds

Last weekend, the weather was perfect—or so I thought. Although it was sunny, by the time I got to the airport, there was just enough wind to be a nuisance. My friend and wingman had gone out first, but he only managed to get as far as "lining up" at the end of the runway before the wind increased past the operational limit of the Tiger Moth and he had to come back in again. Flying can be a tease like that.
So how do you know if it is too windy to go out? Tiger Moths don't mind a lot of wind, so long as it's straight-on to the runway: what they don't like is crosswind (where the wind blows across the runway). This wouldn't have been a problem when they were built.
In the first half of the twentieth century, an airfield was just that: a roughly circular (part of a) field, at least 600 m in diameter. There was never any crosswind because you took off and landed in whichever direction the wind was coming from. But during and after the War, airplanes got heavier and larger: they needed a longer run to take off and land, so it became impractical to have a field long enough in every direction; and they needed special concrete runways instead of grass, to take the extra weight and decrease drag. Modern airfields have the main runway(s) in the direction the wind most commonly comes from at that location, and fewer or smaller runways in one or two other directions. Usually only one runway direction is used at a time, and they pick the one that's closest to the wind direction.
When you're sitting on the runway, you know what direction it points: it's the name of the runway times ten. For example, at Cambridge, the main runway is runway 23 (pronounced two three, not twenty-three), so it's at 230°. (Note that if you go the other way along the same runway, it's called runway 05, and is at 050°.) If there are several runways in the same direction, they get names based on their position (e.g. 23 right), or another distinguishing characteristic (e.g. 23 grass).
A diagram of the wind and runway given in the example

You know what direction the wind is blowing. Even a non-towered airport will have one or more windsocks (often at both ends of the runway, as above), letting you get a good estimate of wind speed and direction. If you're in a towered airport, they will have an anenometer near the runway somewhere, with a read-out in the tower, and the tower will tell you on the radio before you depart. "Two seven five one five knots," they say, meaning an angle of 275°, and a 15 knot speed (shown in blue). Any fool can tell you that's blowing at an angle of 45° to the runway, but how much of that is crosswind?
If you remember SOH-CAH-TOA from school trigonometry, the sine function is the obvious method to use, making a triangle of the wind, the crosswind component (green), and the runway centreline. But you've only got a few seconds to decide, and you can't have sine tables flapping around the cockpit, so there's a simple rule of thumb. Divide the angle by 60°, and multiply the result by the wind speed. If the angle's more than 60° to start with, then just treat the whole wind speed as crosswind. So in this case, our 45° angle is two-thirds of 60°, and two-thirds of 15 knots is 10 knots. That's right on the crosswind limit for a Tiger Moth. You wouldn't go out in such a wind, in case it gets worse while you're airborne, but you might accept it for landing.
If you really remember your school trigonometry, you might recognise this as the "small angle approximation", where you assume sin(x) ~ x in radians. 1 radian is a little under 60°. By the time you get to 60°, the approximation is already about 20% inaccurate, but it's good enough when you're working in your head, and it's almost certainly less than the amount the wind changes while you're taking off or landing anyway.

I was hoping to get lucky with the weather this winter, but I haven't managed it. I've had three sorties cancelled for weather reasons, and the one nice weekend we've had in January, I couldn't book a slot. March winds and April showers may well bring forth May flowers, as the old saying says, but if they also bring a lack of flying until late Spring, I won't be a happy bunny.

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