Wednesday, April 18, 2018

Effect of Leeway on Knotmeter Speed

This note is about a very small effect that we can normally ignore and usually do. But when it comes to optimum sailboat routing computations, small effects can matter, so we have to address all we can. There are so many unavoidable uncertainties in the process, we are obligated to do our best to correct the ones we know about.

One key thing we need in routing is accurate true wind so we can monitor our progress properly and also build proper polar diagrams from measured wind and performance data. With no current and no leeway, we can figure true wind (TW) from apparent wind (AW) in standard ways using either knotmeter boat speed (BSP) and true heading (HDG) or SOG and COG. As soon as we have current or leeway, things get more complex.

We address these issues in the new third edition of Modern Marine Weather, but one of these small effects is just stated without further illustration, and this note is intended to clarify that point. Namely, when a knotmeter paddlewheel is slipping through the water when we have leeway, it is not measuring the speed we want.  It displays BSP, but we want the actual speed through the water (STW), which is slightly different.

Figures 1 and 2 show a typical knotmeter assembly and the paddlewheel. Each blade of the paddle wheel has a small magnet inside, and each time it passes a closed wire loop it generates a small electric current pulse in that circuit.  The rate these pulses are received is converted to a boat speed, and the integrated sum of the pulses is converted into a log record  (odometer) of distance traveled through the water.

Figure 1. A knotmeter through-hull fitting.

Figure 2.  The paddlewheel (these may be from different models).

Figure 3 shows the geometry of the paddlewheel slipping through the water in the presence of leeway. The idea here is, since the axis of the paddlewheel is rigid, the only component of the motion that turns the wheel is that which is perpendicular to the paddlewheel, which is not a true measure of how fast we are actually moving through the water.  Recall that leeway, unlike current, is actual motion through the water. You are sailing, just not quite in the direction the boat is pointed.

Figure 3. Geometry of the paddle wheel moving through the water

A common way to estimate leeway digitally for routing is to compute it based on the measured heel angle. This means that you have to measure leeway directly a few times for your boat do determine the value of k, which typically varies from 9 to 13 or so and may vary with wind speed. Generally leeway is only a factor going to weather. For modern sailboats, it diminishes quickly as you fall off the wind. Note leeway is large for low boat speeds.

BSP is what is displayed on the knometer read out, but you are in fact going slightly faster than that at normal heel angles. Numerical values are shown in Table 1.

Some wind instruments and associated displays account for this if they include a heel sensor. Navigation programs that compute accurate true wind account for this as well, if they ask for leeway or heel inputs. The distinction between BSP and STW is noticeable in some displays; in other cases, the correction is used in true wind computations, but it does not show up in the displayed BSP.

Below is an example from the Tactics plugin to OpenCPN, which does show when it makes this correction.

Figure 4. OpenCPN with Tactics plugin, not correcting BSP for leeway

In this picture the right hand panel is the normal OpenCPN dashboard; the left two panels are from the Tactics plugin. With "Correct STW for leeway" shut off,  the two STW displays are the same—OpenCPN does not use the term BSP. Below, when we turn on the correction, the value shown in the Tactics display reflects the change.

Figure 5. OpenCPN with Tactics plugin, correcting BSP for leeway turned on. Compare results with Table 1.

To make these tests,  we simulated the NMEA input (GPS, wind, heel, current, HDG, BSP) using the NMEA Converter plugin to OpenCPN.

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