True Wind from Apparent Wind –– Revisited.

There are several ways to define the wind. For weather work at sea we care only about the true wind. This true wind is the speed and the direction of the wind relative to the fixed earth under the ocean. Tied up at the dock, we feel the true wind. Once we get underway, our own motion changes the wind we feel, and then it is called the apparent wind.  (In sailboat performance work there is a further distinction true wind and ground wind.)

Many sailors argue that the apparent wind is all they care about, and that can be well argued when it comes to setting sails and judging performance.  But to know about the weather patterns causing the wind,  we need to know the true wind. Furthermore, we often need to know this as accurately as possible. Shifts in the true wind direction are usually the first sign of changing patterns.  If we do not figure this properly, we can miss an important shift. This is not a simple observation––which is more or less the point of this article. Slight changes in true wind speed, for example, affect boat speed, and in turn the apparent wind speed and direction, which can easily mask a small but important shift in the true wind direction.

Let's bring in some shorthand:

AWS = Apparent Wind Speed (relative to the boat)
AWA = Apparent Wind Angle (relative to the bow, 0 to 180, starboard plus, port minus)
AWD = Apparent Wind Direction (relative to true north)

S = Knotmeter speed (relative to the water)
H = Heading (relative to true north)

DFT = Current Drift (speed, relative to fixed earth)
SET = Current Set (direction it flows toward, relative to fixed earth)

SOG = Speed Over Ground (relative to the fixed earth)
COG = Course Over Ground (relative to the fixed earth)

TWS = True Wind Speed (relative to the fixed earth)
TWA = True Wind Angle (relative to the bow)
TWD = True Wind Direction (relative to true north)

Since wind directions are almost always discussed in terms of true directions, not magnetic, we forget the compass for now, and consider all directions discussed as being true directions. Our actual use of compass directions in navigation do indeed complicate things a bit, but that can be sorted out later. It is not really related to the subject at hand.

To review the issues involved, we start with the basics.  It can be dead calm at the dock, and I take off under power headed due north with my knotmeter reading 5.0 kts, and sure enough,  I will have 5.0 kts of apparent wind, right on the bow. S=5.0, H=000, AWS = 5.0; AWA = 0, implying AWD = 000.

If I then turn to H=090, I will still have AWS = 5.0 and AWA =0, but now AWD = 090. In short, there is no wind here at all; I am making it all myself.

A bit closer to the point at hand, I could do this same thing, still with S=5 and then I notice that I now have AWS =7.0 kts of wind, still with AWA=0.  Something changed. I check the GPS and see that my SOG=7.0 kts, and that accounts for the extra wind.  I am in a current that is moving the boat 2.0 kts. Now I need to look at the COG. If the COG is exactly equal to my Heading, then this current is right on my stern, pushing me forward, toward. DFT=2.0, SET=090.

Now if I shut off the engine and slow to S=0, still with H=090,  I should see AWS=2.0, still with AWA=0, providing the COG=090, and SOG=2.0 (still H= 090), and I can conclude that I have measured two things: The true wind is calm, and the current is setting toward 090 at 2.0 kts. If this were not the case, one of these numbers had to be different. 

When TWS is not zero, this analysis gets more complex and a vector triangle must be solved, but the key point is always the difference between COG and H.  If COG = H, meaning you are moving the direction you are headed, then all of the standard vector triangle solutions for finding true wind will work fine. You just substitute SOG for the S that is in the equations or plotting routines.

Generally these formulas and plotting routines solve for true wind angle (TWA) based on AWA, AWS, and S. Then you apply the TWA to H to get the TWD. That all works fine in those cases, and we have several free true wind computers available at starpath.com (downloads section) or there is a nice one in what we call the NIMA Nav Calculators a free download at www.starpath.com/navpubs.

Once you are being set off course and COG ≠ H, then the standard formulas for computing true wind from apparent will not work properly, because we measure the wind direction relative to H, but our actual motion is in direction of COG. Thus you can no longer simply work with apparent wind angle (AWA); you have to switch to using apparent wind direction (AWD) and solve the vectors relative to COG, as shown in the sketch below.

Also it seems to me that the typical equations we see in books (including our own) that use some form of Law of Cosines might not be able to handle all the various combinations of directions. This has to be checked. I am not 100% sure of that. Just my impression.  It seems safer to get the answer from x-y coordinates, and so we present here these formulas, written in a way that can go direct into a spread sheet or calculator.

      AWA = + for Starboard,  - for Port
      AWD = H + AWA ( 0 < AWD < 360 )

      u = SOG * Sin (COG) - AWS * Sin (AWD)
      v = SOG * Cos (COG) - AWS * Cos (AWD)

      TWS = SQRT ( u*u  + v*v )

      TWD = ATAN ( u / v )

Remember in a spread sheet all the angles have to go in as radians, ie COG = COG(º)*(Pi/180). In a spread sheet you can write AWD = MOD(H+AWA;360).

Below is a sample computation of an extreme case of strong current showing how different the true wind results are if the COG-H difference is not accounted for. In that table, TWS-x = u, TWS-y = v.

Note the above picture is more complicated than we need in practice.  Once you have figured AWD, you can use your standard plotting method to get the true wind.  In other words, usually you do not have to compute SOG and COG, you measure them from the GPS.

However, it is likely simpler now to plot it with actual bearings, rather than as a relative plot using COG as 000.  Below is a sample. It is the green triangle that you plot, ie plot SOG/COG and plot AWS/AWD, and connect the end points to get TWS/TWD.

The spreadsheet format that does compute everything, makes it easier to experiment with various interactions of sailings and currents to see how this affects the final answer. You can download a copy of this spreadsheet with the equations in it at the tech support page for Modern Marine Weather (www.starpath.com/weatherbook)... with the CAUTION that you need to check it.  No guarantees that it is right!

Also please keep in  mind, that these measurements assume the instruments are calibrated and the wind sensors are located away from disturbing wind from the sails or other rigging on a power driven vessel.  We have seen cases where the masthead instruments are affected by updrafts from the sails, which is why on some race boats there is often a rather large arm holding the instruments a ways off of the masthead.

One easy test is to measure true wind on one tack compared to the other tack, as you tack back and forth in smooth water. This exercise might expose other important issues, namely that your speed varies noticeably on each tack, implying the speed sensing is not purely symmetric, assuming the sail trim is.  In big waves, you often expect the speed to be different opposite tacks, but if the speed sensors are working properly, the true wind will be the same on each tack.  Ditto for opposite gybes.