PROBLEMS WITH POLAR TARGETS
Polar plots have traditionally been expensive and difficult to obtain. Maybe a manufacturer would provide polars with a new boat. But for the price of a new boat, the manufacturer may not want to show their boat's actual performance warts and all. Plus, if you have or are buying a boat made in previous decades, it could be difficult to track down polars from the manufacturer. Even if you get the polars from a manufacturer though, you'll probably get polar "targets" that give you their boat's "ideal", not actual performance. That may be more of a marketing statement than something you can navigate by accurately.

Computer simulations have been the other main source of theoretical boat speeds on polar plots, i.e. polar "targets". For example, in 2016 and a number of years previous, US Sailing sold theoretical polar plots made with a computer simulation called a Velocity Prediction Program (VPP). US Sailing is the governing body for sailing in the USA, responsible for education, certification, officiating and national championships. You could buy a complex polar plot of theoretical targets made with a computer simulation for around $300 US, or in 2017 they sold a laminated page of abbreviated polar targets in a table for around $125 US. But as you'll see below, this cost doesn't ensure that the theoretical polars are valid.

To overcome the difficulties getting polars for your boat, SailTimer Inc. was the first company to make a GPS device that could learn the actual polars for an individual boat (as shown in our company history). Later, the SailTimer app was also the first mobile app that could learn polars for your individual boat. You don't need a sponsor to pay for this kind of thing anymore, and don't need a professional tactician on board to figure it out. The SailTimer tacking app has democratized sailboat navigation, making advanced functions accessible to all sailors and easy to use.

Sailing experts used to tell us that it is impossible to record actual data on a boat's polar plots; these are only theoretical targets that can never be measured. But you really only need wind data and boat speed. Why navigate with theoretical numbers that are generic for a model of boat or made from a complicated computer simulation, when you can navigate with actual performance data from your own individual boat? That data is now easily available.

There is an assumption that you get what you pay for: that spending thousands on a GPS chartplotter and supporting devices will somehow give you more accurate laylines than a free app. Or that buying expensive polar targets from a computer simulation can somehow be more accurate than your boat's actual performance data. Read on to see if this is true. Marine navigation is at a historic point, and we are seeing new mobile technology open up new navigation methods right before our eyes.


TRADITIONAL OPTIMAL TACKS BASED ON VMG INTO THE WIND (VMG-W)
In 1925, Dr. Manfred Curry published one of the classic texts on sailboat navigation: Yacht Racing and the Aerodynamics of Sails and Racing Tactics. The original volume and later editions up to 1948 do not appear to make any mention of the use of polar plots. The first documented use that we have seen with a graph in polar coordinates for sailboat navigation was by Frank Bethwaite, the designer of the Tasar, 49er and Laser II. He uses them as a known method from racing to a mark directly upwind, not something he invented along with the boats: “Frank Bethwaite (a WWII aviator) was using polar plots when designing racing dinghies in the early 1970s, as shown in the three books he published beginning in 1992… So before computers and GPS, the use of a polar graph to show boat speeds and the fastest heading upwind (Velocity Made Good) is probably another technology that came out of WWII aviation” (Small Craft Advisor, Issue 128, Mar/Apr 2021, p. 34-35, PDF).

The use of optimal tacks based on polar targets and VMG-W originated before GPS, PCs or smartphones existed. This method was designed to identify the optimal laylines without using distance, when there was no way to define GPS locations or to rapidly and repeatedly do trigonometry calculations on a heeling boat under sail. It is well-established among racers, but is limited to use on race courses where first mark is carefully set directly upwind.

In this traditional method, the polar plot is based on theoretical "target" speeds. Those target speeds are used to define a function like the red line on the graph above. Things can get complicated when not sailing directly upwind, but basically your optimal tack is the peak with the highest point on the red line, which is the fastest Velocity Made Good into the wind.

We have clarified some of the problems with the various terminology, measures and assumptions about VMG here. It is important to remember that the peak of the polar plot is measuring progress into the wind (not VMG to the mark, which gives erroneous results in sailboat navigation).

Since distances could not be quickly and easily obtained in the 1940s by trigonometry calculations or GPS localization, this is a vector method that attempts to identify the optimal tacking angles using speed and heading alone. Distance is not used, which means this method does not know your arrival time. Your tacking distances can be calculated after obtaining your optimal tacks, if you want to know your tacking distances or arrival time. Of course, if the theoretical estimates of your boat's performance are wrong, your optimal VMG-W will be wrong, and your tacking distances and arrival time will be wrong. And as many sailors know, a tack that is off by just 4 or 5 degrees could make a difference of many minutes for when you cross the finish line.

The polar peak method based on VMG to the wind was a handy algorithm in the 1940s. It still provides some handy strategies on the upwind/downwind leg in a race (while also dealing with wind zones, current, wind oscillations, position on the course, timing, competitors etc.). But we have GPS and computers easily accessible now on the phone in everyone’s pocket. For many situations it may be simpler and more accurate to measure your speed or progress or time to the actual waypoint, than measuring your speed into the wind.

For example, what if the wind shifts; then you may be measuring your VMG to the wind in the wrong direction. If the wind direction varies 30% of the time and you are basing your optimal tacks on VMG to the wind, your optimal tacks and their distances and completion times are going to have large errors in them. Do the existing systems account for this? Plus you may have no way of knowing how large the error becomes, or how often this happens. The one case where this can be avoided is on the upwind leg of a race, by staying within the laylines and by understanding the ladder geometry (as explained in this helpful summary). But the SailTimer tacking software can do all of this automatically, on all points of sail.

Just as the 1940s method attempts to define optimal tacks without actual distances to waypoints, it also traditionally uses polar targets rather than actual polar data. There is an assumption that theoretical data is better than actual data about the boat's performance. But in order for polar targets to give correct optimal tacks, polar targets need to be accurate. They need to actually fit your boat's speed profile. If your boat doesn't actually perform like the theoretical polar targets, the optimal tacks will be wrong. Therefore, it is essential to learn the boat's actual polars. For racers not allowed to use electronics, the polars can then be used to define target speeds on the upwind/downwind leg. But for all other points of sail and for general navigating, the SailTimer app can easily calculate optimal tacks using tacking distances and polar data now.

It is kind of funny that you can buy an expensive GPS chartplotter or Multi-Function Display (MFD) now, and instead of calculating tacking distances, which are easily available in a GPS, it uses an old algorithm from the 1940s. Isn’t it better to just measure what you really want? The traditional method is widespread, but it only works upwind/downwind, is complex, and requires expertise with geometry (as summarized with the ladder method on the link above). The SailTimer app displays optimal tacks using a fast and easy method that works equally well upwind, downwind and in all wind angles. It does not need to base your boat heading and navigation on quaint assumptions about wind direction from when your grandfather was a youngster out sailing. But in some races wireless devices and apps may not be allowed.