Sunday, April 21, 2013

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.

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 (downloads section) or there is a nice one in what we call the NIMA Nav Calculators a free download at

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 ( 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.


  1. Hi David,

    I agree with your definitions 100% but do you realize that most racing sailors, and their instruments, define True Wind differently? They correct Apparent Wind with Speed Through the Water to get "True Wind" relative to the water surface. It was easier to do before easy GPS SOG & COG and the value is useful for establishing sail performance base lines, but unfortunately many sailors now think of it as the one and only True Wind value. What you call True Wind they call Ground Wind, and what they call True Wind I call Water Wind. It's gotten very confusing!

    I wrote about it some here:

  2. Thanks Ben. You have a good treatment of this subject at that link, with many cross references. I will have to look into this some more. I know for sure that many instruments do it that way (ie compute "water wind" when they want true wind), regardless of the type or purpose of the boat they are used on. What I have to learn more of is the logic behind a value to the "Water Wind" to sail performance analysis. It escapes me for the moment. More soon.

  3. David, a short note to let you know I too am curious about the answer to Ben's question, as perhaps other readers of Panbo. Look forward to your reply.

  4. The question i see from Ben is do i realize that most racing sailors think of this differently? Having been a racing sailor for very many years, i would have to say that *most racing sailors* have not thought about this detail at all, one way or the other. I can easily imagine that *some* racing navigators, sail makers, and yacht designers have addressed the point, but I really need to first check the several references Ben provided and then think on the basics myself some. I hope to get to that next week.

    Thanks for the reminder.

    Also i can easily imagine that wind instruments do this in a variety of ways. For example, there were wind instruments computing true wind before they even had the option of doing it with cog and sog. And in fact my own recent interest in the subject stems from discussions with a colleague when he was telling me how the AirMar system did it. I will check these things and get back shortly.

    An example that comes to mind is the wind instruments on a round drift buoy.

  5. I would agree with you that most racing sailors don't think about this detail at all in the context of true wind angle. But when it comes to true wind speed, I would disagree if your with sailors that sail in current like we have hear on Long Island Sound and it's connected bays and harbors. Here we have currents exceeding 1.25 knots four times a day.

    I have learned in recent conversations that most sailors understand true wind speed to be water wind speed, and lack clarity of what true wind angle is.

    Focusing on true wind speed, when I first learned to sail, I learned true wind speed as water wind speed. When I advanced into navigation classes far beyond what most people learn, the angle of the wind relative to earth became important to me, and it became frustrating that the value was not available to me thru my instruments while under sail (e.g. leeway, etc.). Those advanced classes had me viewing true wind angle as ground wind and almost forgot the importance of water wind.

    When I started racing my big cruising boat I became reoriented to water wind. I learned the equivalent of the links below. They are an example of a tutorial provided to novice race sailors how to use water wind. I choose this one of many on google, partially because it was the first I found but also I like it because the writer is making a point that the sailor can succeed without fancy instruments and describes true wind like the (non racing) sailing class I took here on Long Island 12+ years ago.

    Here are the links

    Clearly the writer believes true wind speed is water wind speed.

  6. Sorry for the long delay. I will be looking into your references very shortly. In passing, we also have strong currents in Pac NW racing waters. On some popular courses there are places (ie Admiralty Inlet) it can reach over 4 kts, not uncommonly. Also, needless to say, sailors do race in the Gulf Steam, where there is longer time to deal with these subtleties in such strong currents.

    My first impression is with calibrated instruments well placed, we should be able to compute all the factors and then use whatever is wanted.

    This question might be more a matter of terminology choices. The terms true wind, true wind speed, and true wind direction have very precise and unambiguous meanings. So that leaves us to define other terms as best meets the needs at hand.

    There are other subtleties for larger vessels that have the anemometers located what we would call a boat length off the center line. These do not qualify as "well placed" instruments. Also some commercial vessels do not use the center line as the apparent wind direction reference, so they have even more to unfold in the computations.

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  7. I am currently investigating the possibilities of adding true wind calculations to our range of NMEA multiplexers and I am running into the same confusion.

    The NMEA standard defines the MWV sentence for true and apparent wind (marked by an 'R') and also the MWD sentece for the wind across the earth's surface.

    It appears to me that it all boils down to using the right terminology:
    True wind: the wind speed and direction across the earth
    Relative wind: the wind speed and direction measured on your boat, not moving
    Apparent wind: the wind speed and direction measured when your boat is sailing/moving.

  8. I would check the definition of Relative. Often R is used on commercial and military vessels as an alternative to true or magnetic bearings, namely bearings relative to the bow. ie 090R is starboard beam, 180R is astern, 270R is to port. This would apply to any bearings, wind or nav targets. This would not depend on the motion of the boat at all. I do not know of any directions convention that depends on the speed of the vessel.

    1. Relative bearings are also used routinely in radar applications in the head-up mode on all vessels, large and small.

  9. Sir David Burch, may i know the formula for this problem : vessel is in course 135 degrees, speed 18 knots, true wind speed 24.5 knots, apparent wind direction 40 degrees. what is the speed of apparent wind?

  10. The formulas are given above, but if you want these formulas using law of sines and cosines, please see and then download the information package there. It includes the theory and several calculators. Or you can get your answer immediately at in the true wind computer part of the weather computers.

    1. Actually, i did not read your question carefully enough. I apologize. You want apparent from true. we have that calculator in our weather trainer live program, but let me check to see if it is in the package i referenced and i will get back.

    2. OK. the downloadable exe (windows only) works fine for finding apparent from true. Just drag around the dots to set your values. I am not sure how well the java app works anymore, but it might work online as well, but it is old code.

    3. Oddly enough, I read more carefully the NMEA 0183 spec yesterday, and saw a definition of true wind that I'd never seen before. Don't know about other types of sailor, but in navies around the world, true wind has always been defined as wind speed and direction with respect to true North, while stationary with respect to ground. And relative wind is defined as wind speed and direction relative to ship's heading, i.e. the bow defines 000 degrees relative.

      Version 4.0 of the NMEA 0183 spec defines something they call "theoretical wind," which seems to be what others here called "water wind." Even though older NMEA specs called this "true wind." Aaargh. I think the NMEA spec needs to create a third category, or we're going to be seriously confused here. If true wind is not wrt true North, any use of the NMEA 0183 MWV sentence in navy ships will be a risky proposition.

    4. Do you have a reference for that citation you mention. I will have a look. i am puzzled by the term "theoretical wind"... or a better put, gobsmacked.

    5. Albert, just a late note to thank you for the comment. we do not own or have a copy yet of the NMEA 4 spec but are still looking. Other work here makes us even more interested in what they are doing with these terms.

  11. David, the formula TWD = ATAN ( u / v ) will move from 0 deg to 90 deg and then make a hyper critical jump to -90 deg and moves back to zero. If you add 180 deg to the equation when v changes sign then the result makes more sense. Here is my spread sheet formula used for testing: