A contribution to the discussion on speed sailing based on the mechanics of windsurfing.
In order to calculate the performance of a sailboat, a windsurfing board or a kite we have to look at the acting forces and moments and find the conditions where all forces and moments are in equilibrium (Newton’s law). This condition is a so-called steady state of the system which allows us to identify the speed.
The basics in aerodynamics and hydrodynamics allow us to calculate the acting forces and moments under wind conditions which are well known by theory and practical research on sailboats and yachts since long years.
Looking on a windsurf system we have the aerodynamic sail force producing a heeling moment which is balanced by the sailors weight (Fig. 1).
Fig, 1: Maximum sail force due to heeling moment compensation
The total sail force is transferred via the sailors feet to the board. The total sail force could be divided into a part which is directed into the sailing direction (course), the driving force or thrust of the sail. Then in a force perpendicular to the thrust, the side force which must be balanced by the fin. On the other hand, we have the hydrodynamic drag force of the board and the fin which are in opposite to the thrust. When both are equal the maximum speed is reached, Fig. 2, Fig. 3.
Fig. 2: Forces on a windsurfing board, side view
Fig. 3: Forces and angle definitions on a windsurfing board, top view
Due to body weight
An important result is that the maximal sail force is absolutely limited by the weight of the sailor which produces the moment by leaning out to balance the heeling moment.
Considering typical body geometries it comes out that the max sail force is about 35-40% of the weight of the sailor.
That means that under all conditions of speed, wind strength, and sail size the maximum sail force could never be greater, it is simply constant. Otherwise, the sailor would make a catapult.
Due to apparent wind angle
Well known is when sailing at a specific course and a specific amount of wind that the apparent wind angle will be reduced with increasing sailing speed, Fig. 4. This effect could be counteracted to some amount by increasing the course angle (going downwind) and by sailing under stronger wind conditions which will increase the apparent wind angle at a given sailing speed.
Fig. 4: Apparent wind angle vs speed and course
The sail force component in the sailing direction (thrust) depends directly on the apparent wind angle. The apparent wind angle is a function of the speed (Vs) to wind (Vt) ratio and the course angle. This is why for high speed a lot of wind is needed. The stronger the wind the larger the apparent wind angle and the larger the thrust. But the thrust reduction with speed is an inevitable physical effect which could not be changed and which is valid for all vessels moving under wind conditions on the water, land, snow or ice.
The thrust and side force versus speed for a constant sail force are shown in Fig. 5. The thrust reduces with speed whilst the side force increases with speed.
Fig. 5: Thrust and side force vs speed at a given course with constant sail force
Hydrodynamic drag of the board
Planing has a drag behaviour which is nearly constant versus speed. Planing drag is at first directly proportional to the total weight of the windsurf system and the angle of attack of the board independent of speed and wetted area. Secondly, we have to add some friction- and spray drag proportional to the wetted surface area which isI proportional to the square of speed. Due to the fact that with increasing speed the board is lifted the wetted surface area is automatically reduced in such a way that just the total weight is balanced. By this, the minimum drag is automatically provided at any time.
The maximum speed is reached when the sail thrust and the drag of the board are equal. This is given at the crossing point of both curves as shown in Fig. 6. The figure makes it evident that higher speeds are possible when the thrust* is increased (curve shifted upwards) and or the drag is reduced (drag curve shifted downwards). The difference between the thrust force and the drag force divided by the mass of the system represents the acceleration which is naturally zero when the steady speed condition is reached. Further, it is shown that at about 66 kts the thrust became zero.
Fig. 6: Aerodynamic thrust and hydrodynamic drag vs speed at a course of 140 deg, sail force constant Max. speed determination
As a result, the sailing speed is at first limited by the total sail force limitation due to sailors weight
and secondly by the apparent wind angle (a function of speed, wind force and course), which reduces the thrust with increasing speed.
All this could be calculated relatively easily and it comes out that the present world record of about 52 kts is just what we can get under consideration of typical sailor weight, sail size, fin size and wind conditions.
Fig. 7 shows the calculation of how fast we can go (Vs) at a course of 140 deg. downwind as a function of wind speed (Vt). Also, if there are some uncertainties due to estimated data the tendencies or relations are valid and allows us to draw the right conclusions.
Fig. 7: Maximal possible speed as a function wind speed at a course of 140 deg.
It turns out that the speed relative to the wind speed could be a factor of 2 at low speeds but nears 1 at about 50 kts. That means to go really faster much more wind force is needed. The gradient becomes very flat so that there is no much speed to gain.
For instance to get 60 kts of speed 60 kts of wind is needed.
Where can we find these conditions with flat water?
Who can handle a board under such conditions?
Increased wind speed will rough the sea and will produce additional drag.
How can we go faster?at
If we look at the drag distribution of the windsurf components at about 52 kts as it is shown in Fig. 8 we can estimate how much speed we can gain if we could reduce the drag on some components.
Fig. 8: Distribution of the amount of drag for windsurfing components at 52 kts
For instance reducing the drag of a fin by 10 % gives a total reduction in drag of about 1,1%.
1,1% drag reduction means 0,05 % speed improvement. That would be 52,26 kts instead of 52 kts also 0,26 kts more.
If we could reduce the body drag by 50% gives us a total drag improvement of 5,5%.
In speed we would gain 0,26% that’s 53,4 kts instead of 52 kts.
Only a small amount of improvements can be reached on existing windsurf boards by avoiding all adverse drag components at the sail by smoothing the sail leading edge, the boom, lines and the sailor itself.
At the board may be the spray drag could be reduced by a specific outline and other edges.
But in general, no big steps are possible.
The influence of body weight
The body weight of the sailor defines the possible thrust. The more weight the more thrust but on the other hand the more weight the more drag from the board which must lift the additional weight which is connected to more drag. But as a result, it can be calculated that
100 N more weight leads to about 2 kts more speed.
The dream of Antoine Albeau going 50 kts at 30 kts wind would mean that
he has to increase his weight by 1000 N and use a 8 m2 sail.
This is naturally quite unrealistic.
But we can go faster when we leave the windsurf configuration and use a configuration as it is realized at the Sailrocket II where the heeling moment is not balanced by the sailor but completely balanced by hydrodynamic (foil) and aerodynamic means (horizontal wing) so that the total sail force could be increased to very high values without any stability problems.
A similar solution (Fig. 9) could be an outrigger mounted on the mast with a planing device or a foil under water in order to provide a moment which at least compensate a part of the heeling moment. In this case, much more thrust could be applied and much higher speeds could be reached.
Fig. 9: Means to compensate the heeling moment for higher speeds
What about hydrofoils?
The hope to use hydrofoils in order to get higher speeds is not very realistic.
By using a hydrofoil the foil drag increases with the square of speed. This is a big disadvantage compared to a planing surface where the drag is nearly independent of speed. This effect limits the application of foils for high-speed windsurfing either we make them very small. For high-speed, the foil area has to be drag optimized for the required speed, for 50 kts e.g. it means about 100 cm2 in area. But how you can lift with such a small area at lower speeds? Further, the strut for the foil has to be really thick in order to provide the necessary stability which gives a lot of drag.
Controlling a hydrofoil is very difficult especially the altitude control is really a big problem which needs an automatic device to hold it constant and to avoid that the board touches the water surface. It would be catastrophic.
Finally, you cannot sail in shallow water conditions.
Who is willing and able to balance on an unstable hydrofoil at over 50 kts?
As a result for existing windsurf boards, much more speed could not be reached due to physical limitations mentioned above. Only little improvements at better conditions are possible: more wind , more flat water is what is needed.
Who can find and can sail it will be the new world record holder.
All that what was mentioned above is also valid for a kite. A kiter can hold much more force because the moment arms of the heeling moment are different but the aerodynamic efficiency of a kite is much more worse (more drag) than that of a windsurfing sail.
That’s why the kite record is only just a little faster than the windsurfing record.
* in the thrust curve the aerodynamic drag of the sail and the sailor is considered.