## Introduction

This article discusses leeway and its influence on measurements of the True Wind Direction using standard sailboat instruments. In particular I will addresses the notion that is presented in other sites online that leeway can be added to apparent wind angle. I will show that this is not the case and discuss the implications of leeway on measurement accuracy. Along the way I will explain leeway.

## Definitions

The wind is blowing at a strength and from a direction. Someone on land would feel this as what I will call the land wind. On a boat we don't generally care about land wind. We care about what is generally called the true wind or more precisely the water wind but nobody calls it that so we will just call it the true wind. The difference between the land wind and the water wind is current. The best way to think of the effect of current on wind is just add the current to the wind. To realize that is appropriate think of a sailboat in a river with a 10 knot current and no land wind. That boat will experience a wind of 10 knots and be able to easily sail across the river. Following are the definitions used in this article.

True Wind Direction (TWD): The direction the wind is coming from as observed by a stationary boat.
True Wind Speed (TWS): The speed of the wind as observed by a stationary boat.
Apparent Wind Speed (AWS): The speed of the wind observed by someone on a boat that is moving (or not). This is a measurement and it is influenced by the motion of the boat thought the water. That motion consists of measurable motion plus leeway.
Apparent Wind Angle (AWA): This is also a measurement and is the apparent direction of the wind relative to the boat's heading. It is not influenced by leeway but only by where the boat is heading and its speed as well as the true wind.
True Wind Angle (TWA): This is calculated from the AWA and AWS and Boat Speed. That calculation is the subject of this article.

## Sailing Upwind

Sailboats can sail upwind because the net balance of all forces point more forward than sideways. The diagram below shows those forces. The blue arrow is the net force of the wind on the boat. This force can be resolved into a lift and drag vector. It can also be resolved into a heading and leeway vector. The heading vector is the forward force on the boat that moves us forward. The leeway vector tries to move us sideways and the boat needs to develop a force equal to that force and hopefully can do that and yet still have the boat go mostly forward. That is the job of the keel. The keel's job is to develop very little force countering the forward motion of the boat yet at the same time to develop a large force to counter the leeway force. Consider that the keel is a flat surface moving forward through the water. The way that surface can develop a force to counter the leeway force is to go through the water at a slight angle. Water is a lot denser than air so a small angle to the forward direction and create a large force. Because the keel is aligned with the boat, this leeway angle causes the boat to have to point upwind from its direction of travel. Translating that to the frame of reference of the boat that means that leeway makes the boat travel at an angle away from the wind by the leeway angel. Thus while the boat may be 45 degrees to the true wind, it might be traveling only 50 degrees to the true wind direction. That would mean the boat had 5 degrees of leeway.

## Measuring Leeway

The question of how much leeway a given boat has is not an easy thing to determine. With perfectly calibrated instruments you can measure leeway plus current but from the standpoint of the boat, you cannot measure leeway unless you know the current. The method explained HERE uses that fact to measure leeway. Two runs are made, one upwind where leeway plus current is measured,and one downwind where there is no leeway so current is measured. The difference is leeway. Let me caution you that small errors in the heading compass can create very significant errors so if you have not spent hours calibrating your log and compass you will be wasting your time trying to measure leeway.

## Calculating Leeway

The measurement above will determine leeway for one wind force. Calculating it for other wind forces typically uses a model. These models typically have a constant that is boat specific, and some things that can be measured such as boat speed, heel, or wind speed and angle. The most common model uses a constant K, boat speed, and heel angle. The theory is that the heel angle is a good measure of the leeway force. That model is leeway = (K * heel) / (speed * speed). Another model uses the same basic model but boat speed cubed instead of squared. I use a model that relies on wind speed and direction rather than heel angle. There if very little actual data on leeway but what data I have suggests the model using wind is more accurate but the one with speed squared is so widely accepted that I built a heel gauge into my Race Box and use it. To me, the accuracy of this model remains an open question.

## Measuring Wind Direction with Leeway

Because the boat is heading one way and going another the question comes up as to how to measure the wind direction when all you have are measurements taken on the boat and it is not heading where it is pointing. Some references you may find online suggest subtracting leeway from the apparent wind and using that to calculate the true wind direction. This is only half the story and if you do that, you will make a huge error. The way to calculate the wind direction given leeway is to think in the frame of reference of both the boat heading and the direction of travel. What we want for calculating the true wind direction is apparent wind measurements from the standpoint of the boats direction of travel. We then use vector math to find the true wind direction. You may notice in the sketch that the boat vector includes leeway. But your instruments are sitting on the boat which is pointing higher than it is traveling in order to generate the opposing force (keel lift) to the leeway force. The way to deal with this mathematically is to just compensate the readings so they are what they would be if they were moving on a platform pointing in the direction the boat is actually moving. This turns out to be a fairly simple translation. If you look carefully at the picture above you can see that if the instruments had been on a platform pointing where the boat is moving the angle to the wind would have been more by the leeway and the heading would have been less by the leeway. These two items tend to change the TWD in opposite directions so the net change is less than either alone. Specifically, if the TWD (true wind direction) were 0 degrees as it is in the vector above, and the boat was sailing (pointing) at 7 knots in 20 knots of wind at 45 degrees to the TWD, the apparent wind would be 34 degrees and 25.4 knots. But with leeway, the wind instruments are going to read slightly different 33 degrees and 25.1 knots. If you do the math, the TWA will be 43.8 degrees and with the heading of 45 degrees off the TWD, the math would give an error of 1.2 degrees. That isn't very much. To do the math correctly, take the wind speed of 25.1 knots but add 5 to the TWA and you get 50 degrees to the TWD. The boat is pointing 45 degrees but subtracting the 5 degrees of leeway gives a TWD of 0, which is correct.

The first thing you should notice is that this is a small number. The error from ignoring leeway in wind direction calculations is small. But it gets smaller when you consider updraft. Updraft and leeway oppose each other according to Ockam so if you have not calibrated updraft, don't compensate for leeway. The main point here is that leeway is a poorly known quantity whose effect on measurements is small and unless you have a very well calibrated set of instruments, having spent days doing the calibration, just ignore it. The one thing you don't want to do is what is suggested by other posts on the web and that is to subtract leeway from the apparent wind reading. That done alone is just wrong. In fact, the apparent wind reading is a reading and as such is correct by definition. The math on it should only be done as part of a calculation of TWD and then only on a well calibrated set of instruments.

## Leeway and Current

On the other hand, leeway must be subtracted from set to get current. Leaving this out is just a total error in the direction of the current. That means if you use heading, speed, sog, and cog to calculate set and drift, you then need to add or subtract leeway from the set number. That said, you may not care if the direction of the current is known to 5 or 10 degrees. The magnitude is going to be of more interest most likely. If you leave it out, realize your headings of the current will change with point of sail.