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Optimal Tacks

How are SailTimer optimal tacks different (and better) than traditional polar targets, VMG and laylines?

The SailTimer™ method is unique in using polar learning and tacking distances to determine your optimal tacks.  There are some similarities to traditional "laylines", the diamond-shaped outer boundaries of sailing angles between one mark and the next. But we'll show here some of the advantages of modern wireless and computing technology, compared to 1940s laylines based on VMG (Velocity Made Good) from before PCs and GPS existed. Through R&D and patenting in 2005-2006 (a few years before smartphones and apps) we developed a new approach because GPS chartplotters did not account for tacking distances when displaying VMG and ETA (Estimated Time of Arrival). SailTimer made the first GPS and later the first mobile app that accounted for tacking distances, learned polars for an individual boat, and could correctly display optimal laylines.

The logic of the SailTimer tacking results is very straightforward. It starts with the tacking distance and the boat speed, to determine the tacking time for different routes and the optimal tacks. The same as if you are wondering how long it would take to drive a car 10 miles at 5 miles per hour, you would divide the distance by the speed. 10 miles / 5 mph = 2 hours. Simple.

Since 2012, some GPS chartplotters and other apps have started to display basic laylines. There are a lot of generalizations and hype about these displays, which use a different method than the SailTimer app. Ironically, they are using a traditional method that probably dates to the late 1940s, before GPS and computers existed. The optimal tacks were traditionally determined using polar "targets" and Velocity Made Good (VMG) into the wind. They were originally (1) the domain of weather-routing software for crossing oceans. And (2) for sailboat racing where the first leg is constrained to be directly upwind, so the crew does not need electronics and can know they are on the fastest tack from the polar target speed.  What are those methods, and how clear and accurate are they? Does it make sense to use a 1940s method in an expensive new GPS chartplotter or Multi-Function Display (MFD)?

Polar plots are circular graphs such as the one below. Wind angles are shown around the outside. The boat speed is shown on the red line at different wind angles. For example, the red line shows the boat speeds at 45, 60 and 135 degrees off the wind. As sailors know, boat speed is slower when sailing close to the wind, and increases when sailing off the wind on a beam reach, which the red line shows. For simplicity, only one wind speed is shown here, although multiple red lines could be added for the boat speed at different wind speeds. There are as many different shapes of polar plots as there are boats. If you know the boat's speed from a polar plot, that helps in defining the optimal laylines.

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.

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.

The traditional method -- using polar targets to define the peak on the polar plot, which is the optimal tack with the best VMG into the wind -- is complex. There are few articles about it, and very few simple explanations. It is viewed as something that only experts can understand. The varying definitions of VMG also muddy the waters. This approach can be distinguished from the SailTimer optimal tacks based on:

a) Clarity: The SailTimer method is clear and simple, dividing the distance by the speed to find the fastest tacking angles.

b) Polar Targets: Traditionalists (or sailors and manufacturers who have invested a lot in expensive GPS chartplotters or computer systems based on the 1940s methods) may claim that any polar based on actual boat performance is suspect or improper. But doesn't it make more sense to base your optimal tacking angles on your boat's actual performance? A polar plot is just a graph in a circular shape; there is no law saying it can only display theoretical targets.

c) Tacking Distance: In the modern era, there is no reason to try to find the arrival time without using distance (except in races where electronics are not allowed, on the upwind/downwind leg). The patented SailTimer system is unique in using tacking distances with polar plots to define your optimal tacks and Tacking Time to Destination. This is a fundamental new paradigm for sailboat navigation and racing. A GPS chartplotter that measures your progress using speed into the wind rather than to a waypoint seems kind of archaic. It is an anachronism; a modern example of a horseless carriage. Or worse: using GPS technology to measure your speed into the wind instead of your speed to a GPS waypoint is actually like having a sophisticated automobile all ready, but pulling it with a horse still.

Until now, no-one seems to have considered that the 1940s method uses a complicated technique but may actually be built on fog or sand. There is no logical way to get accurate results for your optimal laylines without knowing if the theoretical polar targets for your boat fit your boat's actual performance. But that seems to be rarely verified. The polar peak method has been a handy rule of thumb for decades. But doing fancy and expensive calculations on theoretical numbers does not guarantee that they give you the correct tacking angles. Just because a new GPS chartplotter with a Multi-Function Display is expensive and displays laylines does not mean the laylines are correct or optimal. Being off by just 4 or 5 degrees could make a huge difference in your tacking distances and Tacking Time to Destination.

This is also why you need both your boat speed and the tacking distances if you want to find the optimal laylines or get there fastest (as illustrated in this case study). You cannot choose the optimal laylines first using polar targets and VMG to the wind, and then measure the tacking distances afterwards. If you do that, you'll be basing specific distances on theoretical targets that may not fit your boat's actual performance. Some of the apps and chartplotters that are now starting to display laylines and polars claim their calculations include distances for the laylines. But they don't use it to calculate the laylines; they mysteriously figure out a layline, and then measure its distance after-the-fact. But if the layline is not correct, the distance won't be either.

Finding the polar peak based on VMG into the wind was a handy visual short-cut for a navigator working with a pencil and paper in the 1940s (and for racers on the upwind/downwind leg). But it is obsolete in the era of GPS and digital electronics in wireless mobile devices and every cockpit. We can easily get actual data on boat speed at different wind angles now, and calculate actual distances to waypoints. We don't need to use theoretical targets to define optimal tacking angles. If the boat’s actual polar is not the same as theoretical targets, the optimal tacks shown based on the theoretical targets will be inaccurate.

Plus, actual data is the only way for many sailors to get their polars. Few have access to a Velocity Prediction Program. It is even questionable whether a purchase like that is money well spent now, in the absence of data showing that the boat can actually sail at those idealized speeds and angles. Garbage-in, garbage-out as computer scientists say. If your boat doesn't sail the way the idealized polars predict, you won't be seeing accurate laylines or tacking distances. So it is a lot simpler and more accurate to just use your boat's actual speeds for polars and tacking distances to calculate your optimal tacks, as the SailTimer app does.

A modified version of this was published in Sea Technology (Jan. 2017). There is also a Case Study on Calculating your Optimal Tacking Route in the SailTimer newsletter (June 2018).