America's Cup 2013 - About Polar Plots: CupStats

Other Pages: 2013 Louis Vuitton Cup: Louis Vuitton Cup Results | LVC Final Race 7 Stats

Polars: What are they?

In sailboat racing, a “Polar Plot” is often used to illustrate the performance of a sailboat as it varies with different combinations of sailing direction and wind speed.

The true wind direction is represented by convention as 0 degrees, oriented to the top of the plot. The speed of the boat is plotted as distance from the center of the circle, and at the angle representing the boat's heading relative to the wind direction. This is the True Wind Angle, abbreviated TWA.

Any data with a direction and quantity could be plotted in this manner, but for sailing there are very specific uses of polar plots.

A single point on the plot represents the speed of the yacht when sailing at the angle shown.

While a collection of these points on a polar plot may simply just describe the recorded boat speeds at the angles and conditions mentioned, it is also possible to stratify the data according to windspeed, which opens up some useful applications for sailors and designers.

Most commonly for sailboat racing, the data points are filtered to group points that were recorded at the same given wind speed, and the boats peeds at that particular wind speed are then plotted as a line on the polar axes. Adding this third aspect means the relationship between boat speed and wind speed at a given wind angle can be studied. And possibly multiple groups of wind speeds might be plotted on the same graph.

The information can be helpful in showing the expected performance for a particular set of conditions, for one example, and as sailing conditions change, the sailors can adjust sails and other trim to try to reach the speed potential predicted by the polar data for those conditions.

Another common application, after testing with several different sails, might be a polar plot that indicates which sail selection is fastest for a particular windspeed at a particular wind angle, and the crew can make sail changes accordingly.

In a one-design or production class, data gathered from other boats of the class can be a guide toward optimizing an individual boat, trying to reach the performance others have been able to find.

Yacht designers in very high-budget projects might use predicted polars as part of a Velocity Prediction Program (VPP) to evaluate how a new design balances upwind and downwind performance around the expected courses. America’s Cup designers have done versions of this since the 1970s.

In the 2013 America’s Cup, the predicted polars were used to enforce on-the-water penalties. Based on the conditions at the time that boat was flagged by the umpires, a penalized boat was required to slow down until they had lost a calculated time and distance relative to the progress of an unpenalized (but virtual) boat, as indicated on the polar plot of a hypothetical average AC72 yacht. (The polars of the virtual yacht had to be revised during the regatta as the real yachts continued to get even faster.)

These sorts of calculations require a data gathering project that records the raw data; processing to calculate any angles and speeds not directly recorded in the raw data; and steps to filter or stratify the data points for plotting.

Without some processing of this kind, whether done by the data gathering devices or via post-processing of the data points, the raw data alone is not likely to be of much use, except as a scatter plot of a particular time period.

The 2013 America’s Cup Polar Plots

The diagrams shown on CupStats for the 2013 America's Cup aren't the same thing as the diagrams often referred to in performance racing circles as "Polars," which is usually a shorthand for performance plotted in a similar looking radial configuration.

The typical "Polar" might be more accurately described with the unwieldy title "A Polar Plot of Boatspeed at Given Wind Angles, stratified by Wind Speed."

The 2013 information presented via the links at the top of this page for each race is along the lines of “A Polar Plot of Average Boatspeeds Recorded during the Race at Given Wind Angles.” Significantly, the data in these plots is not stratified by wind speed.

Below is a comparison of these Recorded Data Polar Plots with Data Stratified by Windspeed:

The red and bright blue lines represent actual recorded data points for the two competing yachts during an official race. This is the recorded data set for Races 1 and 2.

The green, purple, and light blue lines represent estimated performance, in terms of boatspeed, for a hypothetical AC72 yacht in windspeeds of 12 knots, 16 knots, and 20 knots, respectively, as computed by America's Cup Race Management (ACRM). The race officials used the estimated performance curves at those windspeeds to apply penalties during AC72 races.

The red and blue recorded data is not exactly "raw data" in this case. Data points were recorded multiple times per second for both boats. For these plots, all of the points gathered at each wind angle were averaged together.

(Visually this can be confirmed by observing that the plotted lines are smoother near the wind angles the boat sailed most often, where a range of readings at adjacent angles averages out closer to the same value. Other portions of the lines are more jagged, where fewer readings produced more variation from angle to angle.)

Another divergence in plotting this data, compared to the typical performance polar plot, can be seen as the true wind angle approaches zero, or directly into the wind. The boat could not sustain sailing directly into the wind for an unlimited amount of time, but the angles between 30 degrees and zero degrees TWA here represents the speed of the America's Cup boat as it tacked, turning through the eye of the wind. Boat speed did decrease as the boat turned through the wind, but the momentum of the boat continued to maintain enough fraction of full speed to complete the tack. Incidentally, this aspect of the AC34 plots offers some hints regarding tacking techniques, which became a critical element of the match.

Though the AC34 polar plots shown here are not stratified by wind speed, and for that reason not suitable for some of the typical polar analyses described previously, they are useful as a comparison between ETNZ and Oracle Team USA’s AC72 yachts, race by race.

There are many limitations to the data, among the most singificant being that the wind speed and wind direction were not recorded on the race yachts themselves. And any attempt to apply analytic data from a yacht race needs to give due consideration to the unfolding of the particular race, any points at which unusual circumstances such as tactical actions, penalties, gear malfunction, and other incidents that don't represent the normal sailing manner, might affect the data for one or both yachts.

Taken as a whole race, though, given the pretty narrow and restricted courses, the boats generally sailed in similar conditions, even more so on the downwind legs. So despite the obvious caveats, the polar plots of the race data have proved to offer valuable insight into the fascinating historic match-up of the 2013 America's Cup.