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General comments about sweepback from Don...


Regarding the controversy about sweepback's dihedral effects:


From : Don Stackhouse

Aft sweepback DOES act like positive dihedral at positive lift coefficients. These effects disappear at zero lift. Dihedral's effects are for the most part relatively unaffected by overall lift coefficient.

Positive dihedral responds to a sideslip by altering the local angles of attack to bank the airplane away from the direction of the sideslip. For example, if a gust caused the right wing to drop, the aircraft would begin slipping to the right because of the tilt in the lift vector. The aircraft would see its "relative wind" shift so that it was coming from the right. The interaction of this with dihedral would increase the angle of attack of the right wing and decrease the angle of attack of the left wing (because of dihedral, the airflow is hitting more "under" the right wing and more "on top" of the left wing). This would cause a roll to the left, until the lift vector was tilted enough to the left to stop the sideslip.

The process for sweepback is a little different, but the results are the same. The lift coefficient of a swept wing is proportional to the cosine of the sweep angle. If a swept wing is in a sideslip, the effective sweep angles of the two sides will be different. In our example above, the sweep angle of the right wing will be less than the left. This means that the cosine of the right wing's sweep angel will be greater than the left's. For example, in a 30 degree swept wing with a 5 degree right sideslip, the effective sweep of the right wing will be 25 degrees, and the effective sweep of the left wing will be 35 degrees. The cosine of 25 degrees is .906, and it's only .819 for 35 degrees. If the lift coefficient of both wings in straight and level flight was 0.40 (which would be a baseline of 0.46 times the cosine of 30 degrees), then the right wing would now have a lift coefficient of 0.42, while the left wing would have a lift coefficient of only 0.38 . In addition, the apparent span of the right wing (measured perpendicular to the relative wind) would be greater than the left. This would cause a roll to the left until the sideslip was stopped, just like the wing with dihedral.

The increase in apparent span on one side can also be used to provide yaw stability, by increasing the moment about the yaw axis from the forward-yawed wing. Unfortunately, the increase in apparent span also improves that wing's induced drag, which could tip the balance the other way, causing yaw instability, especially at high angles of attack where induced drag is dominant.

There's an old rule of thumb that says 3 degrees of sweep is about equivalent to one degree of dihedral, but obviously this is a gross oversimplification. Sweep will act like gobs of dihedral at high lift conditions, and like zero dihedral at zero lift. The problem here is that there is a very delicate balance required between fin area and dihedral. Too much fin and not enough dihedral results in spiral instability (in a turn, the model wants to tighten up into a "graveyard spiral"). Too much dihedral and not enough fin will result in dutch roll (the model wants to wallow back and forth in both yaw and roll like a falling leaf). In the case of a swept wing, it's almost inevitably going to be more prone to dutch roll at low speeds and spiral instability at high speeds. Getting good handling over the entire speed range might be a little tricky!

As far as pitch stability is concerned, the combination of washout plus sweep will generally tend to increase it. This is one of the common methods for eliminating the need for a stabilizer in tailless aircraft. The amount of washout (i.e.: leading-edge-down incidence of the wing tips relative to the wing root) is analogous to the decalage (i.e.: incidence of the stabilizer relative to the wing) of the wing and tail.

The tail moment arm is measured from the wing's aerodynamic center (typically assumed to be at the 25% point on the wing's mean aerodynamic chord). When you add sweep, the tail boom should be lengthened to keep the stabilizer at the same position relative to the wing's aerodynamic center as before.

Fortunately the sweep angles we use on R/C sailplanes are generally so small that sweep effects are usually not a significant factor in most cases.

A good source for further info on this entire subject is "Tailless Aircraft in Theory and Practice" by Nickel and Wohlfahrt, pub. by AIAA.

Don Stackhouse
DJ Aerotech



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