Friday, February 4, 2011

Corrections to the apparent wind angle

In a previous post, we have been able to calibrate the apparent wind angle (AWA) relative to the axis of the sensor itself. However, if the sensor axis is not aligned with the centerline of the boat (remember that we are seeking a resolution of 0.1 degree), we have to measure this offset. Here how it is done with this system.

We go on the water on a (nearly) windless day, and we keep motoring straight ahead against the wind (if there is some). During a period of say 30 seconds, we record the apparent wind angle. After that, we take the average (this is about 300 data points), and this is the offset that we will have to substract from now on:

awa_corrected_for_offset (awa_coff)  = awa_measured - offset

We also have the make a correction when the boat is heeling. Because the sensor is not on a 3-axis swivel, there is a purely geometric error induced when the AWA is not exactly a multiple of 90 degrees (0, 90, +-180, -90). For an explanation of the phenomenon and the required correction, see page 8 of the following document:
So we have to apply this second correction:
awa_corrected_for_heel  = atan { tan(awa_coff) / cos(heel) }
The following figure presents the error in degrees at sailing points between 0 and 90 degrees, for different heel angles. If you are beating at 30 degrees AWA while heeling at 20 degrees, your displayed apparent AWA is 1.5 degree in error without this correction, which is not done in many (most?) commercial systems, with some nasty consequences on further calculations of true wind, wind direction and vmg.


  1. Hi Merlin,

    In your example, you suppose the effect of heel perturbs only the AWA.

    But the apparent wind can be seen as a vector :

    x = AWS * cos(AWA)
    y = AWS * sin(AWA)

    And to correct the apparent wind

    x = AWS * cos(AWA)
    y = AWS * sin(AWA) / cos(Heel)


    AWA_corrected_for_heel = atan2(y,x);
    AWS_corrected_for_heel = sqrt(x² + y ²);

    When do you think ?

  2. Hi Doug,

    When the boat is heeling, the anemometer will see a vertical component of its own apparent wind, even if the apparent wind vs water is completely horizontal. So I agree that a correction to the AWS would be required for an anemometer that has a near ideal ‘cosine response’, like wind-turbine anemometers.


    “Cup anemometers also suffer from poor 'cosine response'. This means that as the wind direction changes to hit the sensor from below or above the horizontal the response of the sensor deviates from the ideal response, which is spinning at a rate proportional to the cosine of the angle of the wind above or below horizontal. For most designs the cups will actually spin faster for a wind a few degrees above or below horizontal.” (

    This means that the poor ‘cosine response’ eliminates in part or totality the theoretical correction. It may even go the other way and require a correction in the opposite direction. So without wind tunnel results of the cosine response of a particular anemometer, the conservative approach is to do nothing.

    This being said, I would love to get wind tunnel results from my anemometer and program an exact correction if required.

  3. Thanks! I would also love to get wind tunnel results from my anemometer !!!

    But the corrections to apparent wind angle can be improved by a clinometer (or IMU) to measure the trim angle ?

  4. Merlin,

    In Arvel Gentry's paper referenced above, the formula he uses - attributed to David Pedrick Richard McCurdy - to adjust apparent wind speed for heel is

    AWS_corrected = AWS_measured * cos(AWA_measured) / cos(AWA_corrected)

    Mr. Gentry's paper indicates that this equation is used because of the issues a cup-anemometer has with heel: which you call cosine response. I wonder how this applies to ultrasonic wind instruments like the Airmar WeatherStation or the Maretron WSO100. Both of which are 2D ultrasonic amemometers. It would seem to me that they'd be pretty much immune.

    Perhaps even better would be a 3D ultrasonic anemometer like this one[1] from Wimers Me├čtechnik. In addition to being able to accurately measure the apparent wind vector in 3D space and therefore definitely correct for heel in both angle and speed, it should also be able to give you a handle on upwash from the sails.

    Upwash is an issue unless you can get your anemometer up and away from the sails. B&G even make a 1.8m (6ft) wand to get the instrument out of the upwash. I know Ockam can adjust for upwash with some calibration and I assume B&G, Nexus, and NKE can as well. What I don't know is how useful these adjustments are. I would assume that upwash changes depending on the set of the sails. Certainly two reefs in the main is going to look different to the anemometer than none at all and a big 155% genoa will look different than a 100% jib.


    Mr. McCurdy is the cofounder of Ockam Instruments, so it's pretty safe to assume that Ockam uses a formula similar to that for their correction calculations. His master's thesis on the subject of sailing instruments is also worth reading.