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Twist

Now things get serious. Wel will now twist the foil. Why ? Because if we don't twist it, each profile will have a different 'angle to the tow point' (draw a line between the Xcp and the tow point, and measure the angle between this line and the chord). By 'tow point', I mean 'meeting point of all secondary bridle'. There are two tow points for a foil, one for each half of the foil. As there are symetric, we can consider there's only one tow point. Here's a small case to illustrate this :

The red line connects the two tow points (in white). Each line starting from the Xcp to this line should be perpendicular to the chord of the profile. You can see that this is not the case. Here, the Xcp is at 25% of the chord (the black dot on each 'profile'). The Xcp's describe a curved line, (the more the leading edge is curved, the more this line is too), so the tip profiles could have a real tow point far from 25%. As a consequence, you'll get a foil that's very prone to luffing (starting from the tips). To avoid that, we will twist the foil so each chord will be perpendicular to the line connecting the Xcp to the tow point.

Notice that this is the way *I* think this should be. If you think I'm wrong, you can skip this section and go to the next page. You will be able to correct this 'on the beach' later if your foil finally requires twist, anyway. But in this case, I don't know where to put the tow point, you'll have to figure it out yourself.

This is a little bit difficult, so be patient and accurate. I love 'geometric' methods, so there's no trigonometric computations in this part. If you want to compute an angle for each profile, and then apply the corresponding rotation, it's exactly the same.

First, we draw a line between the two tow points. We take the center profile as a reference. An important parameter to set now is the total length of the bridle. If you want to change it later, every angle for every profile will change, so you'll have to restart everything from now. Notice that the longer the bridle is, the lesser are the angles ; but the bridle will become more sensitive to tune, and the drag will be higher. Here, I'll take (arbitrary) 70% of span. On the next picture, I've hidden useless layers at this stage. I draw a vertical line (length=70% of span) from the Xcp point of the center profile.

Then, I copy the span line at the end of this line, including the positions of the profiles (pink points).

Now, for every profile (except the center profile which position is already correct), I draw two line, each starting from the pink dot on the 'tow point line' : a vertical line, and the other connected to the Xcp line (purple) on the corresponding chord. This way, I get for each profile the twisting angle. With this small example, I get 2.75 for the tip profile. You may think it's not a lot, but for very curved foils, with short bridles, you could easily get 4 or 5. A profile usually fly from 0 AoA to 15 AoA, so 3 really is a lot. On the next picture, the vertical lines are in black, for readability.

Now we have to rotate the profiles. I usually choose the center of the chord as center of rotation, because I get more smoother leading edge and trailing edge, but you could choose another point if you want. For each profile, move the two lines from the 'tow point line' to the center of the rotation. Here, this is really easy, as the centers of rotation are aligned, so I just have one copy operation to do. You'll get something like that :

Obviously, if you have a more complex shape, you could have to move each angle one by one. This is not so much more work.

Now, lock the layers that must not be rotated (all layers that do not contain elements of the profiles), then select all parts of one profile, and apply the rotation defined by the two lines, the center of rotation beeing the intersection of these two lines. Be careful to the orientation of the rotation : on the pictures, from the black (vertical) line to the pink line. You'll end up with :

You can clearly see the chord are no more aligned. Very good.

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