For sailors, wind speed is given in knots, and the direction of the wind is the direction it comes from. A north wind is blowing from the north toward the south. A sea breeze is blowing from the sea toward the land. A land breeze is from the land toward the sea.
On the boat, we typically read the wind speed from an anemometer located at the mast head. Its spinning cups measure the speed, and an associated wind vane aligns with the direction of the wind, with the fin downwind, with the arrow pointing in the direction the wind comes from. The data are then transmitted digitally to instruments at the nav station and on deck.
The wind vane is calibrated to be oriented along the centerline of the boat, so the "wind direction" measured is not an actual direction on the horizon, but rather it is a wind angle relative to the heading (HDG) of the boat, called the apparent wind angle (AWA), which can vary from 0º for wind dead ahead, or 90º for wind on the beam, on around to 180º for wind on the stern. Wind dials or meters will then label the direction to be port or starboard, with the starboard side considered positive, if signs are given. Likewise, the wind speed we measure is called the apparent wind speed (AWS).
This measured wind from the masthead of a sailboat is called "apparent wind," because that boat can be moving, and when it starts to move, it creates its own wind. For example, if there were no wind from nature at all at the moment (dead calm), and the boat took off at 6 kts headed due west, the AWS would read 6 kts and the AWA would read 000º, wind dead ahead. We are making this wind with our own motion.
Figure 1. A boat creating its own wind, as it might appear in nav app meters.
Now if an actual meteorological wind from the north started to blow across the water at 8 kts, the anemometer would then feel two winds: 6 kts from the west created by the boat's motion and 8 kts from the north created by a local weather pattern. The anemometer would then reflect the combination of these two winds, which leads us immediately to the concept of vectors, which we cannot avoid when discussing wind on the water.The speed (of anything) is just a number, called a scalar, but the velocity (of anything) is a vector, it has both a speed and a direction. When we combine two winds, we are adding two velocity vectors to obtain a resultant third vector. Vector addition can be solved mathematically or depicted and solved purely graphically, as shown in Figure 2. When depicted graphically by arrows, the length of the arrow is proportional to the speed, and the direction of the arrow is direction of motion.
With wind velocity vectors, we must distinguish between the direction the wind is flowing, or being created, as in the case of the boat motion wind (BW), and the name of that wind, which is the opposite of the direction it flows. A true wind (TW) from the north flows toward the south (its vector points toward south), but the name of the wind displayed on a meter (true wind direction, TWD) is the opposite. This is illustrated below and can be important for understanding such diagrams.
Figure 2. Basic wind vectors on the left with arrows indicating wind flow, compared to the same triangle with arrows indicating named wind directions, plus sample meter displays.
In the top left we see how vector addition is presented graphically. The TW vector plus the BW vector is equal to (gets you to the same point as) the AW vector. You can draw these on paper and get the right answer: 8 units down, 6 units to the right, then measure what the AW is using a ruler on the same scale and a protractor.Here we have added three more meters (true wind angle, speed, and direction) to reflect what we have determined ourselves about this from the moving boat, even though all we had to measure was the apparent wind we actually felt. This is done by mathematically solving the vector triangle on the right, which is based on the measured AWS and AWA, along with the measured boat speed (knotmeter) and measured heading from a digital heading sensor. This is carried out either by the wind instrumentation itself, or, maybe more often, from within the nav app we are using to compile and analyze the instrument data.
We can learn a couple general wind rules from looking at these vector drawings. First, the true wind is always aft of the apparent wind. If we have wind coming over the beam in a moving vessel, we know the true wind on the water is coming from more toward the quarter. Apparent wind on the bow, means the true wind is more toward the beam.
Second, the faster we go in the same true wind the more the apparent wind moves forward. In the extreme case where the true wind is very small compared to our speed, then the apparent wind will be essentially dead ahead, as in Figure 1.
Figure 3. Apparent wind moves forward as our speed increases in the same true wind, and vice versa if we slow down.
We also learn very quickly that for these computations to be useful, all of the instruments involved must be carefully calibrated and checked on all points of sail: AWS, AWA, HDG, and BSP. The vector solutions can be very sensitive to small errors in any one of them. This is a big task for the navigator.
So big, in fact, that it is fair to ask, why should we go to all of this trouble, and indeed expense, in getting and calibrating quality instruments? You could say that we sail by the apparent wind and that is all we need to know; why do we care so much about the true wind?
The answer is, from the navigator's and tactician's point of view, the true wind is everything!
The sail trimmers and helmsmen live by and respond immediately to every change in the apparent wind, but the desired heading, determined by the navigator, and when it should change, is all based on the true wind. Plus, the evaluation of the present performance of the boat is based on the true wind, i.e., for the present TWS and TWA are we going as fast as we should be?
When we tack, our heading will change by twice the TWA, centered on the TWD. When we jibe, our stern crosses the TWD and our heading changes by twice (180 - TWA).
Figure 4. How TWD and TWA relate to our sailing tracks and laylines.
We will come back later to how the TWA enters into the important task of evaluating sailing performance using polar diagrams, which is also the basis of computing optimum routes across a varying wind forecast.
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In the above basic description, we determined the TWS, TWA, and TWD from AWS and AWA corrected for boat speed BSP and HDG through the water. Thus we were talking there about true wind relative to the water, and we have assumed that the water itself is not moving, meaning no current.
Once we are sailing in water with current, we have to be more aware of our terminology. It does not matter for sailing analysis what the cause of the wind might be, but in the presence of current, we have to be aware that the wind we are calling the "true wind" is not the same as what meteorologists, forecasts, and buoy reports call "true wind." These official wind forecasts are relative to the fixed ground.
If the local buoy reads 10 kts from the north (the meteorologist's true wind), and I hop in my boat headed due north in a current that flows 2 kts toward the north, and I am not yet moving through the water (BSP = 0; underway, but not making way), then I will read AWS = 12 kts with AWA = 00 (10 kts from the wind + 2 kts from the current). Then as a sailor I will interpret this a true wind of 12 kts, and indeed my sails would respond accordingly.
Once I start moving through the water, the AWS and AWA will change, but once I correct for HDG and BSP I will come back to a sailor's TWS = 12 and TWD = 360.
The way sailors distinguish these two true wind values is to call the meteorological true wind the ground wind. Thus we call wind relative to the water true wind and wind relative to the fixed earth ground wind. (It has been proposed that the sailor's true wind should be called the water wind, but this never did catch on, in part because sailors have used the term true wind for a long time, plus the polar diagrams use the term true wind as well.)
Figure 5. Finding sailor's true wind in the presence of current. The sailor has no knowledge of the presence of current with just this information. It will take GPS measurements to reveal the presence of current.
The distinction between how we compute true wind vs ground wind is very direct once we have GPS data. True wind is the measured apparent wind corrected for a boat wind determined by (BSP, HDG), whereas the ground wind is found by correcting the same apparent wind for a boat wind determined by (SOG, COG), which will be different if there is current and or leeway, as shown in the figure below.
Figure 6. Computing true wind vs ground wind. The true wind using HDG and BSP assume there is no leeway taking place. Later when we introduce leeway, these will change to CTW and STW for course and speed through the water.
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The above is the background to wind on the water for sailors, but we are not done if we want to do our very best with navigation and routing. We have dealt with idealized measurements and have not accounted for the important factors of heel and leeway, which have separate and related influences.
Heel has a basic geometric effect on the wind vane, in that when it is tilted the wind vane does not feel the full force of the wind, because the component perpendicular to the centerline is diminished. The net effect is the AWA and AWS we measure when heeled over are slightly too small, so we have to correct them. This in turn will affect the all important TWA and TWS.
The heel in turn is usually associated with a leeway that will further affect the most accurate values of TWA, TWS, and TWD, as well as GWS and GWD
The AW corrections, derived below, are sometimes corrected within the wind instruments (such as B&G 5000 or newer) or more commonly, within the nav app reading the apparent wind and computing the true wind. Here AWAm and AWSm are the measured values from the anemometer, and AWAc and AWSc are the corrected values that are used to compute the true wind. It is up to the nav app to decide which of these it chooses to display.
AWAc = atan [ tan(AWAm)/cos(heel) ]
AWSc = AWSm x cos(AWAm)/cos(AWAc)
Suppose wind instruments measure AWAm (34.3º) and AWSm (14.5 kt), and our digital inclinometer measures a heel angle (23º).
AWAc = atan [ tan(AWAm)/cos(heel) ]
= atan [ tan(34.3)/cos(23) ] = 36.5
AWSc = AWSm x cos(AWAm)/cos(AWAc)
= 14.5 x cos(34.3)/cos(36.5) = 14.5 x 1.03 = 14.9
These are both small changes, but they all add up, and these are the values that should be used in the final true wind computations. (For quick estimates, heel narrows the correct apparent wind angle by just under a factor of cos(heel), which at 20º heel is 0.94 or 6%.)
Figure 7. Overview of heel angle errors on AWA. For AWA = 30º with a heel of 25º, the uncorrected AWA will be too small by 2.5º. Diagram adapted from Ref 8
The derivation of the AWA and AWS corrections are shown below.
Figure 8. AWA and AWS corrections due to heel. When heeled over, the AWA and AWS we measure are slightly too small by the amounts indicated. We start with an apparent wind vector (AWSx, AWSy, 0), which means we assume the air flow over the meter is parallel to the water, without notable upwash from the sails. We are also neglecting the effect of mast twist. This is a common assumption, but it overlooks what could be an important correction. We look into how to incorporate that later on. When the boat heels, the y component (athwartship) of the apparent wind narrows, but the x component along the centerline does not change.
Now that we have corrected AWA and AWS for heel (putting off for now the upwash correction), we can look into finding an improved true wind. The presence of heel is often a reminder that the boat could be slipping to leeward to some degree, called the leeway angle (LWY), but it is important to note that heel does not cause leeway. A boat can stand essentially straight up and slip to leeward, especially in light air.
With leeway, the track of the boat through the water (CTW) is not the same as the heading of the boat. Instead, we have:
CTW = HDG + LWY.
When the boat is slipping to leeward, the proper reference for the true wind over the sails is not the centerline (HDG), but rather the track line (CTW). Leeway can, with some effort, be measured from the angle the wake of the boat leans to windward, or with sophisticated instruments (rare) that measure both translational (sideways) speed as well as the standard longitudinal (fore and aft) speed. Some wind instruments suggest dropping a series of markers off the stern and then taking a bearing to the line they make to compare with your heading.
It has been found, however, that a workable approximation to the leeway can be made from the theoretical balancing of the force on the sails and the lifting force of the water flow over the keel. This leads to the commonly used expression for LWY in degrees:
LWY = k x Heel / STW^2,
where k is called the leeway coefficient, which is typically 9 to 16 for sailboats, Heel is in degrees and STW^2 is the square of the boat speed through the water in kts. With a measured heel, we can compute the LWY and from that get CTW and then relate the heel-corrected apparent wind to the CTW for an improve value of the true wind and ground wind. We also get a better value for the current speed (CS) and current direction (C) correcting for leeway in this manner.
The geometry to be solved is shown in Figure 9.
Figure 9. Correcting apparent wind for heel and leeway. The bottom image is adapted from Ref. 1. In this image, the apparent wind and boat speed are assumed to be the values corrected for heel, thus: AWA=AWAc, AWS=AWSc, and STW=STWc.
We can solve for TWS as: TWS^2 = TWSy^2 + TWSx^2, where TWSy =AWSxSin(AWA+LWY) and TWSx=AWSxCos(AWA+LWY)-STW] and AWA = ATan(TWSy/TWSx).
Alternatively, define the AW vector as (AWS, AWD) with AWD=CTW+LWY+AWA, and the BW vector as (STW, CTW) and solve for the vector difference between them. For ground wind, use the same AW vector corrected for BW vector relative to ground,(COG, SOG).
To help understand the wind corrections that your favorite nav app is making, we created an app (WindCor) that computes the winds with No corrections, Corrections for heel only, and Corrections for heel and leeway. Below is the use of the app comparing to the outputs from the popular navigation and tactics app Expedition, to which we sent these simulated NMEA sentences for HDG, STW, AWS, AWA, COG, SOG, and Heel by UDP:
$GPGGA,040000.000,3813.55991,N,6848.559458,W,1,10,1.8,1,M,,,,,*28
$GPMWV,48.9,R,19.09,N,A*1E
$GPRMC,040000.000,A,3813.55991,N,6848.559458,W,10.788,145.1,230624,14.1,W*64
$GPVHW,161.2,T,,M,8.833,N,,K*46
$GPXDR,A,-25.61,D,HEEL,P,101789,P,PRESSURE*58
Figure 10. Meters (Number Boxes) in Expedition from expeditionmarine.com. Top has no Heel nor LWY input; middle data adds Heel input, but has k=0 to rule out LWY corrections; and bottom shows all inputs and all corrections. Data on the right are computed with WindCor using the formalism describe above. This GWS sample has the wind cups at 10m. The same example below shows results at 15m.
The agreement is not exact, but close enough to conclude that Expedition is making these standard corrections, with the convention of displaying the measured AWS and AWA, even though the corrected values are used for the true wind data.
The WindCor app can be used to check these results. The app is stored in our starpath.com/calc index to various computers. Below is a sample output.
Figure 11. Sample screen from WindCor
The importance of true wind for navigation is outlined above, but we also need the best value of TWS an TWA to evaluate sailing performance relative to the polar diagram for the boat. The original forms of these diagrams made by a VPP (velocity prediction program) or yacht designer assume the TWS and TWA are the actual values the sails are seeing, which means they are relative to the water not the boat.
The ORC VPP is a physics simulation that solves equilibrium equations for the boat as a body moving through the water. In that model, the boat experiences hydrodynamic forces along (and perpendicular to) its actual direction of motion through the water — i.e., its track through the water, not its centerline.
So in principle the best TW values to use when evaluating performance or building a better polar would be the TW value corrected for both heel and leeway.
Our accurate measurement of ground wind is used to evaluate model forecasts that predict the wind at 10 meters above the water, whereas anemometers at the mast head are typically higher than that. The wind speed increases with height above the water as it becomes less slowed by friction, so we must typically reduce the measured GWS to get the 10m values. This can be computed several ways, but a common one we use in WindCor is GWS10 = GWSc x (10/h)^0.11. This power can vary from 0.10 to 0.15.
References
1. Yacht Performance with Computers by David R Pedrick and Richard S. McCurdy, Chesapeake Sailing Yacht Symposium, January, 1981. (McCurdy was a co-founder of Ockam Instruments.)
"When polar curves are created by VPP programs, all TWA are measured from the wind to the boat’s course, NOT to its centerline..."
7. These nuances of true wind determination are discussed in Appendix 9 of
Modern Marine Weather. This book includes extensive discussion of the practice and value of using measured ground wind and pressure to evaluate model forecasts.
