Sailing and Maths - do they fit together?

The answer is simple: Yes they do! Julia G., a German high school graduate, proved this when she wrote her term paper with the title: "Mathematical and Strategical Observation of the Up and Down Regatta Course".

Here is the result of her term paper, which received the highest marks. Julia's teacher, Dr. Katrin F., explained the reason for this decision as follows: "Right from the start Julia's approach to the final presentation was obviously clear. The quality of the software she was using to full capacity, was going to be very valuable. Even at her intermediate result she convinced me, and her fellow pupils, that this presentation was going to be remarkable. In her paper, different start situations were mathematically evaluated several times." (e.g.: see the above coloured line diagram)

In the spring of 2018, Dr. Katrin F., wrote to inform us that Julia wanted to use the "Tactical Sailing" programme for her forthcoming term paper. The leadtopic of the Science Propaedeutic Seminar was "Physics and Mathematics in Sailing". Julia is an active sailor who, up to about five years ago, sailed regularly and took part in Optimist regattas on the Altmühlsee. Since then she has her "SBF" licence and will do her "SKS" in Portoroz (Slovania) this summer. The theoretical knowledge for this assignment of task was partly conveyed to Julia in a seminar given by Dr. F. Not only that, Julia also reads specialist literature* on this subject and sails every summer.

Julia's subject focussed on "Regatta Strategy", which is why she was interested in "Tactical Sailing". Through empirically creating multiple diagrams, under set conditions, it should be possible to determine how to be first on reaching the leeward mark. Here shows a simulation of "Tactical Sailing's" software, which can be adapted to specific regatta situations by using the "Coach's Toolbox".

Is it possible to calculate a "regatta strategy"? Yes, Julia did it by determining the optimal ratio of the sailed distance to the speed of the boat. Anyone who drives a car knows how to work out this simple formular: How long will it take from Munich to Berlin (600km) when the average speed of the car is 120km/h? Answer: in 5 hours will the destination be reached. "Regatta sailing strategy" is similar - but a little more complicated! Here there are two deciding "parameters" which influence when the sailor will reach the finish line. These are: "wind shifts" and "top speed on the course".

Distance: Shortening the sailing distance between the down - and upwind marks. With help from a 10 degree "wind shift" at the starting line, an "upwind advantage" can be obtained which shortens the sailing distance on the "long leg" tack.
Boat Speed: When a boat is optimally trimmed, there is usually no problem regarding the speed of the boat. But are there other causes that can effect a boat's speed (Velocity Made Good against the wind (VMG)? The maximum speed of a boat on a certain course is made visible here in the "polar diagram" (VPP). The exact "Close Haul Course" between 35 degrees and 50 degrees, and the "Down Wind Course" between 135 degrees to 195 degrees meet exactly, being theoretically fixed by the "polar diagram" (VPP). This, however, must be trained in practice to optimise the boat speed. Whoever masters these subtleties on water will be faster to pass the finish line.

Of course Julia also understands the limitations of these calculations. "The 3-dimensional chessboard of a regatta is variable and can never be exactly calculated. However, experienced sailors can anticipate wind changes and react accordingly by optimising every new situation. Although small variations of maximum speeds between 90 degrees and 270 degrees are typical of the 470 dinghy, the experiment shown here demonstrates a conventional strategy with possible alternatives. These possible alternative options could, within seconds, determine the final outcome of the race".

"After analysis and evaluation of various regatta situations, an origin of tactics can be seen in certain given facts through the physical construction of the boat. Whereas, strategical rules can be traced back to geometry on the regatta field."

Dear Julia, our "Tactical Sailing" team wish to sincerely congratulate you on the success of your highly esteemed term paper. Also, we wish to extend our grateful thanks to Dr. Katrin F., for using "sailing" as the key aspect of her 2018 seminar. We are grateful to her that abstract mathematics has been made practically recognisable. We are also delighted that "Tactical Sailing" was of use in this academic excursion.

The Tactical Sailing Academy will continue to offer seminars in 2019. If you are interested in a further education as a member of a sailing association, club or association: Please send an e-mail to

If you already have a license key for Tactical Sailing, you can download a free update to the latest software here. The Tactical Sailing Software can be downloaded directly from the net (39 €), or with extension Trainer-Toolbox (+20 €), "All in One" (59 € ). It runs on almost every computer (Windows, Linux, Mac). See the features at and order the game on the website as a download

Sources: Seminar Paper Julia G., Mrs Dr. F., Erlangen (Germany).
* Specialist literature: e.g. Tilo Schnekenburger: "Die Geometrie des Regattasegeln" (eBook or paperback)