# 4.3 Induced resistance

If you include the finite length of the fin into your considerations, you will have to think about the flow around the tip of the fin as a consequence of pressure compensation. In reality, the flow around the fin is not two dimensional but three dimensional. The additional vortices are causing the induced resistance. Both induced resistance and lift force are correlated, the higher the lift force the higher the induced resistance.

*Figure 16: Arising of vortices in the wake of the fin*

These vortices can be visualised in a flow test quite easily. At the tip of an aeroplane wing they can be reduced by winglets.

These vortices are influencing the total performance of a fin. At the tip of the fin there arises nearly no lift and the resistance increases.

Angle of attack, twist, flex, vertical and horizontal tilt movements are not taken into consideration.

On the other hand the induced resistance is decreasing with a growing aspect ratio while the lift force is rising. That means that there has to be an ideal aspect ratio for long fins with maximum lift and minimum induced resistance.

**But it has to be said that all of these theoretical considerations are losing their practical relevance when the fin is shorter, the water surface is rougher and the more radical the sailing style is. Therefore, the practical test is of crucial importance.**

*Figure 17a: The track of the fin – hypothetical linear motion*

Assuming a totally linear motion of a fin without twist as

- the water surface is ideally smooth

- the wind speed is absolutely constant

- no disturbances are caused by the sailor.

In this situation the tip of the flexing fin would draw a straight line slightly windward of the fin root.

*Figure 17b: The track of the fin – the actual motion*

Assuming a rather linear motion of the board with disturbances from

- a rough water surface

- a gusty wind

- the sailor.

As the sideways stress is changing all the time the fin will flex in forward motion to a different extent. Therefore, the fin tip has to follow a longer path than the board, and its speed will be higher than the speed of the board. In addition, the board will tilt in various directions.

As there are so many varying influences on the fin, all the theoretical considerations have to be completed by the results of practical tests. A good fin will deliver the best compromise in a given situation.

It is the long **Formula fin** that demonstrates best the three dimensional flow around the fin and the fact that the induced resistance is a result of

**outline**(aspect ratio, taper ratio, curvature of the leading edge, length of fin, rake angle)**torsion****camber distribution**