'taking a break here...

I see that no one has responded, perhaps due to the amount of recent material on this topic posted here and on SSWF. However, the question merits attention, and I'll try to briefly (Edit: Ha, Ha, Ha, Ha-ha-ha-ha-, Ha,...!) outline what I think, mostly from theory, but with a bit of practice thrown in.

Does anybody have firm ideas on the optimal wing taper ratio for our models? John Havel mentions that the Speed King wing is more tapered than most at about 0.5 but I don't have a feel for whether there is an optimal figure.

"Optimal" taper ratio has to vary with flight conditions and model size, among other things. Most taper ratios seem to fall around .7, +/- .05, and I think that these are mostly based on compromise and aesthetics. Since most designers in stunt's evolution apparently didn't sit down and study aerodynamic centers (neutral points), some of this probably came about in tailoring area to chosen span. Others probably worked it from the other direction, perhaps choosing tip shape or l.e. sweep first. You'd have to ask them. Despite being an enthusiast of theory in optimizing things, I really don't feel (and this has been discussed recently here) that tip shape and taper are as important as span loading, wing loading, other proportions, and power - on our models. That doesn't mean that it isn't worth doing "right", but it does mean that they are not as influential on models as on full-sized aircraft. That's because of the air not scaling as the plane (Reynolds Numbers). However, for just this reason, tip chord may make a difference among different classes (sizes) of model. Well, that verbage is my disclaimer.

Very Late Edit: ...also because weight doesn't scale the same as wing area: wing loading is better in models, reducing vortex energy.

In short, for gusty weather, you want greater taper, and for all-around performance, you need that compromise. If you like harmonious lines, my opinion is to go with the compromise. Hershey-bar wings seem to fly "OK" on "Twisters" (some taper from flaps) and "SkyRays." Elliptical planforms, where the taper varies continuously are pretty close to optimum, with straight trailing edges being about 8% more efficient, but tail moments suffering. These have the furthest inboard lift concentrations of most often used planforms. Their a.c.'s are at about 42% of the halfspan, as compared to 46-48% for most common tapered wings in use. For comparison, the most inboard possible position is at 1/3-halfspan for pointed or delta wings.

I've re-posted two illustrations below. The first shows the straight taper necessary to achieve the same inboard lift center as on an elliptical wing of the same span and area (therefore same aspect ratio). The second is an internet photo of Brian Eather's "Firecracker", probably the most radically tapered of all successful modern stunt designs. On it is superimposed the outline of the taper you'd need to get the lift center of the elliptical wing illustrated above it. Regardless of span, that taper ratio is always .376. The "Firecracker" competes in Australia's windly conditions, and the inboard a.c. reduces the leverage lateral gusts have in upsetting the model.

So for gusty weather, that extreme taper may be "optimal." Reduced tip Reynolds numbers from the short tip chords may reduce efficiency, while the elliptical tips control tip vortices better than straight tips. I really liked my short-lived, high-aspect-ratio wing with rearward raked tips (aft span greatest) and a taper ratio approaching .5 (last photo). The high aspect ratio seemed to be at least somewhat compensated by the extreme taper, but it never had a harsh test, before the pilot ruined things. It was supposed to get stationary flaps and a reduced stab. Still, it flew nicely in the rounds, wing-overs, inverted...just never tested corners much, other than on the wing-overs. I would have eased the points chordwise on the tips.

I think that optimally, I'd go with the 5.5 aspect ratio (or lower) at a taper ratio of about .7 - .75,  compensating for any further increases with greater taper. Remember though that increasing A/R also increases the lift-curve slope - more lift for same pitch angle or speed. That makes the plane more gust sensitive. An important consideration stressed by others here has been the greater importance of trim and especially of power available. Other than possible vortex danger in calm weather, I think the engine is more important than wing efficiency these days on the top winners, and high-aspect-ratio gust sensitivity may not be what you'd like to risk, when you have the power and stall resistance of thick, lower-aspect-ratio wings. (Edit: As has also been mentioned often, the more efficient wings lose some of their allure, when one considers that the "normal" stunters already corner as hard as reflexes allow with smooth recovery)

I referred to the data that I have accumulated on the Shoestring racer and found that it has a Taper Ratio of .57. The Shoestring also has an Aspect Ratio of 5.5 which is the figure Ted Fancher says is optimal. Other designers have suggested to me that an aspect ratio between 5.0 and 5.5 is the target so 5.5 works for me.

Some nice stunters have had aspect ratios under 5.0. I'd be aware of the performance changes that may result from tip shape, so that when you try for a taper ratio on a Shoestring wing, you're careful to compensate in some way for the rounded and raked tip. .57 sounds sort of low to me, from what I remember of its appearance.

I'm thinking about typical lift diagrams and pondering ways to make the entire wing area work at its optimum. Does anybody have any thoughts?

Just that, although I always try for "the optimum" in my own flights of fancy, I'm very aware that wing efficiency (L/D) is no longer of the same importance as in the Fox .35 days, when building light and wind "penitration" so critically demanded efficient wings. Of course, I usually have designed around smaller powerplants.

Edit: The "Firecracker" photo was from Dallas Hanna. From measuring it, the "Firecracker's" taper ratio seems to be about .5, which would put its a.c. about 44.4+% from the root. 'neat plane!

SK

Thanks Serge.

I may have made a mistake in my assumptions but, to allow for the tip shape and area, I substituted Ct (the tip chord) in the area calculation to arrive at λ = 2S/bCr where S is the area, b is the span and Cr is the Root Chord.

This gave me 0.573 for the Shoestring. By ignoring the radius on the thick tip ribs on the Twister, I calculated 0.885 for the Twister. Using my formula, I also obtained a figure of about 0.43 for the Speed King because John Havel cites the chord lengths only.

Thanks again for the contribution.

Geoff

Ooh, I love to dance a little sideslip, now they see me and now they don't.. ;->

L.

"Gentlemen, you can't fight in here! This is the War Room." -President Merkin Muffley

I once ate dinner in one room of Edna's Chicken Ranch,  This was the real name of the best little w.......  To explain this was after it had been dismantled and reassembled as an upscale cafe in North Dallas. 

Thanks Serge.

I may have made a mistake in my assumptions but, to allow for the tip shape and area, I substituted Ct (the tip chord) in the area calculation to arrive at λ = 2S/bCr where S is the area, b is the span and Cr is the Root Chord.

This gave me 0.573 for the Shoestring. By ignoring the radius on the thick tip ribs on the Twister, I calculated 0.885 for the Twister. Using my formula, I also obtained a figure of about 0.43 for the Speed King because John Havel cites the chord lengths only.

Geoff-

This is an interesting way to look at it. So if a rounded wing were to have a tip chord, this would be it. I think however that in posting, you left out a term that you actually used in your computations. I get "2S/(bCr) - 1". You must have done the computations right, since without the "-1", the printed expression would give a minimum taper ratio of 1 (rectangular) for a pointed wing.

I tried this equal-area assumption on an elliptical wing and got a taper ratio of pi/2 - 1 or .5707. As mentioned above, to get a straight tapered wing to have the same spanwise MAC position as an elliptical wing of the same span and area, the taper ratio would have to be .376. That's for a wing with the same area and span, but larger root chord. Perhaps the more the tip shape varies to vary the taper, the further from an equivalent wing you get with equal root chords??? I'm thinking about this.

SK