FAQ: Polar Diagrams

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Subject: RE: "Polar Diagram"
Don, what is a "polar diagram"? Thank

Hi Pops,
Well, I'll give it a try.
Different boats, of course, have different performance characteristics. These characteristics depend such variables as hull design, keel design, rigging, sails, etc.

What is not so well appreciated is that different boats perform quite differently on different points of sail. Sure, we all know that some boats point better than others, but what about other points of sail?

Further, the performance differs depending on wind strength, and wave action, and other factors. For example, a light displacement hull may have problems cutting through chop that would not seriously delay a heavier boat.

Many years ago (perhaps 20-25 years) some folks realized that a mathematical simulator could be designed to predict boat performance on different points of sail and different wind velocity, based on the characteristics of the boat. These folks designed a mathematical simulator called the Velocity Prediction Program (VPP). The VPP has as input a wide variety of yacht characteristics. The output of the VPP is a set of tables showing predicted yacht speed at different points of sail, at different wind velocities, and different water conditions. (There are a lot of other tables produced - stability of the boat, best heeling moment, etc. - but these do pertain to your question.) The VPP has become increasingly sophisticated, and changed from a "free" service to a "for fee" service offered by US Sailing. In fact, perhaps 20 years ago the VPP code was available on a BBS, and I think I saw a version published in Sail Magazine or somewhere. Anyway, the current availability is through US Sailing as a part of their "performance package" on a fee basis. Serious racers usually purchase the performance package from US Sailing, since the package is specific to their boat. When I say "specific" I mean that you provide US Sailing with a lot of details that are unique to your specific boat (rather than characteristics of the boat type). For example, you provide such details as whether you have a fixed, folding, or feathering prop - regardless of how the boat was equipped when it came from the factory. When I purchased the performance package about 15 years ago for Carpe Diem (my Kalik 33), I believe the price was $250-$300. A "polar diagram" is a visual that can be created from the output of the VPP. Picture a set of concentric circles drawn on a page, with the circles radiating out from a center. Each circle corresponds to a wind speed, with the center being zero and the outer-most circle being perhaps 20-25 knots (depending on the normal expected maximum wind the yacht is to be sailed in). At the top of the page is an arrow pointed down, depicting wind direction (that is, heading directly up the page would be directly into the wind, while heading to the bottom of the page would be directly downwind). With me so far? Now, around the circles are lines radiating out from the center, representing degrees: directly into the wind would be 0 degrees, directly downwind would be 180 degrees, etc. That is the basic polar diagram foil. On the polar diagram foil can be drawn the predicted yacht speed at various points of sail and wind velocity. Of particular interest is the velocity made good (VMG) toward a mark either directly upwind or directly downwind. For a particular yacht, the VMG differs based on both the point of sail and the wind velocity. For example, for a wind velocity of 25 knots, you may be able to head almost directly downwind for the best VMG (this is the best run VMG for Carpe Diem at 25 knots of wind), while at 20 knots, you might have to sail at 175 degrees for best VMG. The polar diagram might show that at 5 knots of wind, you may achieve the best VMG downwind by sailing at 150 degrees off the wind. These sorts of findings are often counter-intuitive, but are crucial, particularly when racing. (As a side note, one result of the VPP results has been the use of asymmetrical spinnakers in the racing circuit.) The same concept applies when beating, of course. Some boats point higher than others, while some boats achieve best VMG to an upwind mark by footing off slightly. A Catalina 25 tends not to point quiet as well as some other boats I race against unless the wind is above 15 knots. At that point, TNT seems to be quite happy as I feather to wind with a 155 - depowering to compensate for the otherwise overpowered conditions and pointing quite well compared with the fleet. The output from the VPP (and the polar diagrams created from the output) must be validated, as simulations are not always accurate. However, once the numbers are validated, they can be used with good success. Many racers use the output quite extensively, and you may have heard the phrase "target boat speed" used by serious racers. This is simply the expected speed from the VPP of the boat based on wind velocity and point of sail. For example, I suspect that the skipper of Prada knew that he had a problem with something on the keel by comparing target boat speed with actual speed, rather than him simply "knowing that my boat is a bit slow". Hope that this brief explanation helps.

Subject: RE: "Polar Diagram"
Hi Bo,
Be careful using polars that are not specific to your boat. And I mean *your* boat, not just C-30. The output from the VPP (and the corresponding polar diagrams) will vary considerably depending on the input provided.

Notice that the C-34 Polar Diagram at the referenced site was for a C-34 (non-spinnaker, 150 jib, feathering prop). The Polar Diagram likely would be quite different if the boat were equipped with a spinnaker, would be different if the boat were equipped with a 135 furling jib, would be different if the boat had different prop, etc. I expect that the optimum run angle would be more like 150 at 8 knots with spinnaker, rather than the 162 degrees shown. If memory serves me correctly, the optimum run angle for Carpe Diem at 5 knots wind is 144 degrees with spinnaker!

Probably the biggest difference between polars for different boats within the same class/length/keel will be spinnaker/non-spinnaker, and the size of the jib - but I don't know what effect other things would have on the algorithms.

This is just a "heads-up" to be careful, as you might not get the effect you expect if you don't look at a polar that is for *exactly* the same boat as yours.

FYI, you can create your own polar diagram quite easily by using the VMG function of GPS. Just remember to periodically hit the GOTO/ENTER sequence, as the stupid GPS algorithms do not update the VMG to a mark, but calculate it based on a vector established at GOTO/ENTER time. (That is a sore subject with me, as I've had some spirited discussions about this failure with engineers at both Garmin and Magellan - their basic answer "that is the way it is designed".)

Oh yeah, don't take the polars as gospel that should always be used to control your course. You will find that there are a lot of other factors (current and expected wind at different parts of the course come to mind) that would cause you to ignore the optimum run angle.
Regards, Don Deese, Carpe Diem (Kalik-33) and TNT (C-25/TM)
Chesapeake Bay (Carpe Diem) and Potomac River (TNT), cpexpert@ibm.net

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