## Monday, February 7, 2011

### Leeway calibration

Leeway calculations are usually based on the following formula:

leeway  =  K * heel / speed2

where leeway and heel are in degrees and the boat speed is in knots. The only problem is to find the constant K for your boat. Different methods have been proposed that all present practical difficulties and do not lead to accurate results.

Here is a method that relies on the capacity of this system to record several concurrent values in real time, and most importantly, on a precise calibration of the gyro compass.

It is also based on a trial run where you sail on a tack with a sensible heel angle, while recording: measured boat speed, heel angle, heading, SOG and COG. When you have reached stable conditions for one or two minutes, you turn around, set the sails wing on wing, and go straight downwind until the conditions have stabilized for another minute or two. This last step is necessary to measure the effect of the current, as the leeway angle will then be zero.

In the second part of the trial test, we have measured the GPS speed over ground (SOG2), the GPS course over ground (COG2), and the measured boat speed that is also the real speed through water (STW2) as there is no leeway. From these values, we calculate the speed of the current (SOC) and its direction (DOC). We will need the SOC and DOC to calculate the leeway from the results of the first part.

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During the first part of the test (tack) , it is important to note that the measured boat speed is NOT the real speed through water. The speed sensor is aligned with the boat centerline, and what it measures is the component of the real STW along the heading axis (the dashed arrow in the figure). In order to calculate the leeway, we will need first to calculate the direction of the real STW arrow (the solid blue arrow). It can be calculated by adding the SOG1/COGm1 green arrow with the negative SOC/DOC arrow. Once we have the direction of the STW, the leeway angle is simply the difference between it and the compass heading.  These calculations involve some non-trivial trigonometry, and I will present in a future post the exact equations for that.

I use the Airmar speed sensor model without the fins on each side of the paddlewheel. I consider that the fins are prone to bring local disturbances that are detrimental to the measurement accuracy.

Once we have the leeway angle from the test, we can calculate the constant K, using the boat speed and the heel angle from the first part of the test.

K = leeway  * speed2 / heel

1. Hi,

Thank you for a great blog! Do you know where I can read more about the mathematical modeling of leeway. In particular, I would be interested in where this formula comes from:

leeway = K * heel / speed2

Thank you very much!

Jonas

1. Hi Jonas. The earliest reference that I could find for this formula is the paper "Yacht Performance Analysis with Computers" by Pedrick and McMurdy (1981), currently found at :
2. 3. 