I briefly talked to an aerospace engineer about tappering the wing on a plane with a small chord (about 9inches)

He told me that tapering does not have any effect on induced drag when the chord is small (i think he said under 12 inches) so a rectangular wing would be just as efficient.

However i have not been able to find any documentation supporting this.

So, does tappering have any effect on wings with small chords? Please direct me to some documentation that will explain this.


I am currently an aerospace engineering student, so i know all about the effects of drag, and tapering on a large scale.

And the reason i am asking is becasue i am on a team that designs a small model airplane.

well it would depend on the amount of taper you are using!!
and the air would slip over the wing quicker so the taper would have less of an effect than over a large chord wing because on a large chord the air is slipping over the wing for longer amount of time there for the air will start rolling down the wingi have no documentation on this but it does make sence i am lookin to get into aircraft engineering aswell.
simmo

I don't agree that tapering doesn't affect induced drag when the chord is small. According to linear wing theory, the induced drag coefficient of a configuration depends only on 1) the lift it is generating, 2) the shape of the wing's planform (including any twist), and 3) the aspect ratio. If you were to take any model and precisely scale it up or down, the planform/twist of the wing would remain the same, as would its aspect ratio (by definition). As long as you adjusted the weight (or airspeed) to keep the scale model flying at the same angle of attack, the induced drag coefficient wouldn't change. This means that if tapering at one scale reduced your induced drag coefficient by say 30%, the same tapering would reduce your induced drag coefficient by 30% at any scale.

That said, if you taper a wing with a small chord to reduce the induced drag, you could very easily increase the total drag. This is because profile drag, unlike induced drag does depend on the actual size of the configuration, not just its shape. All else being equal, wing sections with smaller chords have a smaller "Reynolds number" which CAN mean higher profile drag. I think what the engineer was trying to get across was that as wing chords start to get below about 12 inches, tapering may not be worth it. Not because it doesn't offer the same induced drag benefit as it would on a larger wing, but because it can introduce other unwanted characteristics (higher total drag being just one possibility).

Taper barely has an effect on induced drag at large scales (5%). It's used more for structural reasons, lower roll moment of inertia, bending loads, etc. The scale won't matter, since it's an energy conservation thing...

You can get much higher maximum lift coefficients out of a tapered wing though, if it is designed with the stall occurring evenly across the span.

Depending on how you taper the wing it can have a positive drag reduction at higher angles of attack. The Schumann (sp?) planform works on model sailplanes very well .

Taper in the model airplane world has to be carefully moderated overall due more to the effects of reduction in the Reynolds numbers that occur when the wing uses a strong taper. Strong in this case being in the range of 60% tip chord. Smaller amounts of taper are not so damaging. Even larger taper ratios with the tips being at 50% or less of the root require strong additions of washout to help control tip stalling at lower speeds.

There's no real numbers on all this other than what you have already available as a student. It's lessons we have learned as modelers and passed on via magazine writeups and forums such as this. The lack of hard numerical analysis comes from the fact that no lives are riding on the outcome and there's no big savings in fuel costs either. We just do not fly in a steady state for long enough for any of that to matter. Now if you are designing a micro or at least mini UAV given the reference to a 9 inch chord then this may all change.

Analysys done by unremembered gentlemen that reported their analysis in the old Soartech journals published by Herk Stokely showed that for smaller model sizes the optimum aspect ratio alters radically from sailplanes at 120 inch span and sailplanes of 2 meter span. The reason being that it was more important from a speed range standpoint to keep the Reynolds number higher by not similarly reducing the wing chord than it was to minimize the induced drag by keeping the aspect ratio high on the smaller models. Aerodynamically the former solution may be better for a craft designed to cruise at a consistent speed for most of its life in the air but from a practical RC sailplane perspective the speed range was more important as long as the overall efficiency isn't compromised to a great extent.