Designing from scratch: wing taper ratio

In all the sources I could get my hands on (previous threads on this forum, old Stunt News, etc) there was quite a bit of discussion on various wing properties (aspect ratio, airfoil thickness, LE radius a.k.a. blunt leading edge, flap chord and area, etc). But I couldn't find a reference to the role of the taper ratio (root chord / tip chord) on wing characteristics. Especially as applied to CL stunt flying, where we turn at near-stall speeds and angles of attack.
A couple of related questions: 1) how is taper ratio calculated for an elliptical wing? 2) Why do most people taper wing chord at one ratio, but taper airfoil thickness at a much smaller ratio?

First, I'm far from an expert on this, but do know a few things on this subject.

Swept back leading edges act similar to diehedral on a straight wing and offers stability to the plane, esp. in the wind. There have been designs using from no sweepback, to the extreme.
Constant chord wings are examples of no sweep back, where Curtis Comers Classic design, "Cloud dancer", and the Australian design "Firecracker" are examples of the extreme.

Depending on the half span, the most often seen sweepback is between 1.5 to 2 inches. A true elyptical wing uses no sweepback as it is incorportated in the wing layout already. A modified elyptical planform, such as the T-Bird will sweep back straight to the point where the tips take on the elyptical shape.

As for your question regarding chord and percentage rates between the root and the tip, most designers use a few more percentage points thickness at the tip to help reduce tip stalling in manuevers. There have been occasional succesful departures in this practise, most notably Berringers World Champ winning Stunter from last years competitions.

There are shapes, though not truly elyptical, that offer many of the advantages of that planform, and are easier to build. Most of our wings designed for stunting conform to one of these shapes.

John Miller

John, I read that an extreme sweep, as in GMS's Magnum, resulted in the CG being moved too far aft and made the plane very difficult to balance in flight. With the low speeds of the typical PA model, what little sweep used is enough to maintain stability. If they were to go into the mach numbers, then 33 degrees would be ok, but the landings would have to be fast also. Do you agree on this? Ty

That should be GMA's Magnum. It was based on a racing plane, the Flokerts Special I believe.

Mike,

I'm certain that there have been many places where such information has been discussed, but I just happen to have just finished reading Ted Fancher's two part article on designing the Imitation, wherein he briefly discusses leading edge sweep and its effects, among other design criteria. It was published in the September and October 1979 issues of Model Aviation. Copies should be available from PAMPA. I would make copies of my copies and send them to you but for the fact that my copies are several generations removed from the originals and barely legible themselves.

As I wrote previously, I'm certain that there has been a lot of information written on this subject. Possibly someone else can come up with a better example.

I recently read a statement in an old British magazine, made by someone I had heard of, that a wing with a 5 degree leading edge sweepback had the lowest drag configuration. It escapes me at the moment where I read this, but maybe I can find it again and be more detailed.

I do know that stunt airplanes with parallel chord tend to bounce around more in the wind than similar airplanes with tapered wings.

I have always been interested in the extreme taper, low A/R wings of many Aussie stunters, including Paul Turner's Wind Wizard and predecessors, and the aforementioned "Firecracker". I believe the reasoning is for improved windy weather performance, as Australia is known to be a windy continent. Note, however, that the hinge line is swept forward. Mr. B-17 cautioned me that this made for extreme difficulties in trimming, however I have not figured out why's or how's. At least one of Bill Werwage's designs had swept hingeline, plus Walt Pyron's P-39, various Jack Sheeks designs, Bernie Ash's Supersonic Stunter, Grogan's King Sweep, etc. I'd love to see an article in Stunt News about why it does whatever it does. Steve

I measured several designs and found that the LE sweep was anywhere from 4 1/2 to 5 1/2 degrees. Looks like 5 degrees is right in the ballpark.

>I have always been interested in
>the extreme taper, low A/R
>wings of many Aussie stunters,
>including Paul Turner's Wind Wizard
>and predecessors, and the aforementioned
>"Firecracker". I believe the reasoning
>is for improved windy weather
>performance, as Australia is known
>to be a windy continent.
>Note, however, that the hinge
>line is swept forward. Mr.
>B-17 cautioned me that this
>made for extreme difficulties in
>trimming, however I have not
>figured out why's or how's.

Paul can give his theory, but I have imagined that the deflected flaps with a forward hinge sweep was unstable/reduced the stability in yaw

Bobby Hunt has a couple of designs with a swept forward flap line and thinks they work just fine. In theory the center of lift can remain more true with a swept forward flap line.

However, I am with Paul in thinking it can cause trim problems. My theory is that if the plane starts to yaw in any direction, whichever way it yaws that flap is going to be squarer to the "wind" than the other side and present more drag with flaps deflected. This will then add to the yaw, which adds to the drag which...

In extreme situations I could see the thing wiggle waggling all over the place.

This is a question whose time I'm not sure has come. Taper ratio (and, yes, I've used the term) is nothing more than a ratio between the root and tip chords of a wing. For most straight winged or straight "tapered" wings the ratio is not much more than a numeric description of that ratio.

Probably the only important thing to note about it is that a tapered wing is more closely configured to the classic lift distribution of any wing wherein the lift generated is biased toward the root due to the existence of spanwise flow of the airstream as it works towards the tips. It is probably true that a tapered wing makes more efficient use of its area than does a constant chord wing. Whether this is of particular importance to a stunt ship is questionable and probably ranks around the priority level of equal vice assymetrical wings and front and or back up lines. At our scale the issue is very much overwhelmed by proper trim and pilot skill.

It might be correct to state that, if tapered, a wing should probably not have a very (whatever that means) short chord at the tip since efficiency is reduced greatly as Reynolds numbers are reduced by such a configuration. It is also probably true that tapered wings are less susceptible to buffeting and rolling in crosswinds than are tapered wings...although tip configuration probably enters into that scenario as well.

Suffice to say that I consider it just important enough to make one of my design criteria for a competitive flapless stunter (which demands more efficiency by default) will be the use of an elliptical planform (with clipped tips to deal with the Reynolds number issue) to, at least theoretically, make the most efficient use of the wing's area.

Back to the original question, the real issue involved with the question is one of aspect ratio which has a very real effect on lift performance and, thus, efficiency. The more a wing of given span and root chord is tapered, the greater the aspect ratio and, therefore, the more lift will be generated from a given angle of attack.

FYI, the more the wing is tapered the more important the question of Mean Aerodynamic Chord (MAC) vice "Average" chord for design and trim considerations. Technically the MAC is the point on the halfspan whereat half of the area is inboard and half outboard to that particular chordline. Thus, if the wing is of an unusual planform (all taper in the leading edge; all in the trailing edge; swept forward or aft, etc) it becomes more important to accurately determine the MAC as the basis on which CG locations (and, thus moment arms) are determined.

In the final analysis, the taper issue is probably more of an aesthetic consideration that a performance one at all but the very highest levels of competition. Frankly, the reason the clipped tip ellipse appeals to me is because it'll frankly look cool as heck!

>...Frankly, the reason
>the clipped tip ellipse appeals
>to me is because it'll
>frankly look cool as heck!
>
>
>Ted

Ted, let's get honest now. You are just clipping the tips so the plane will fit in your car.

Hee-hee-hee, I like Leonards' comment on the TRUE reason for clipped tips. But if we're talking about fitting it into your minivan, the beast must have a 120-in span!!!

Seriously, Ted, every time you post an article like that, I feel like I just got so much stunt-wiser. I had no idea about the span-wise airflow, but now it makes sense.
I agree that the taper ratio is of secondary importance to the wing performance, compared to factors like aspect ratio, airfoil shape and thickness, flap parameters (or no flaps at all?). I had both kinds of wings (high and low taper ratios), and didn't notice a big difference, hence was my question.
You made a comment on how much more efficient are wings with high AR (aspect ratio). Why, then, I don't see any designs with AR=7 or 8? Over the past 30 years, stunters have averaged AR=5, based on my data. There must be a limiting factor, that compromises a different aspect of flight. Is it stability? In a Russian article I'm about to publish in SN, the author (Valentin Salenek, frequent Russian national F2B team member) mentions that high AR wings seem to be prone to strange oscillations in level flight. Any clues?

An afterthought to my previous post. I forgot to thank eveyone else for their valuable comments. Sorry guys.
I believe it is through this kind of exchange of information and opinions that this wonderful sport (lifestyle for many of us!) grows better and stronger. Everyone's input is valuable, whether it's based on personal opinion, empirical data, or theoretical knowledge.
Thank you all!

Hi Mike,

This is off the subject but nevertheless I feel it to be important. I was looking at a picture of your 99 Intrepid X/L on the back of Stunt News the other day and I had an opportunity to look closely at the picture. That plane was/is? gorgeous! If the opportunity comes up I beleive that you would be a most valuable finnishing editor for Stunt News! Give it some thought please.

Jim,
great thanks for the compliments on my finishing abilities, but there must have been a confusion. I've never built an Intrepid XL in my life, and probably never will! Not because I dislike Randy's design, but because I take pride and joy in designing my own (exception: Classic and OT). I can't recall any typos in captions in Stunt News, either. The planes of my design that were published in SN were: Quickie (.40 profile, MonoKoat), Quickie II (.40 profile, white-and-blue simple dope finish), and Super Quickie (ST51, white-yellow-silver-black dope finish). The Super Quickie fuselage might resemble that of Intrepid XL (not intentionally), and it indeed was published on the back (color) page of SN.
As to the quality of finish, it was the LAST row finish at '2001 Brodak, along with peeling repaired MonoKoated jobs. It hurts, but what can I do. I'm not a great finisher at all, although I'm striving towards perfection, and hope to show continuous improvement. Just a month ago I bought my own air compressor and a used DeVilbiss spray gun. Two of my previous planes were sprayed by Les Nering of Kent, OHIO.
So, I doubt I currently qualify for a position of the finishing editor at SN. But, like I said, I'll take any compliments I can.
--Mike
P.S. See my post on appearance judging in the thread on that topic.

As Ted pointed out a tapered wing is more efficient due to better usage of the spanwise flow of air. It probably handles turbulence better simply because the smaller tips give nasty air less leverage on the wing as a whole. Like any of these considerations there is a point of diminishing returns. Pushing out the ratio to 7 or 8 would probably increase the wing effiency marginally but the long lever arm of the wing, even with the skinny tips, might actually decrease the wings resistance to tubulence. Also it's a heck of a lot harder to make a long skinny wing structurally resistant to twisting than a short one. Even a small bit of in-flight twisting could aggravate those funny oscillations.--Mark

>You made a comment on how
>much more efficient are wings
>with high AR (aspect ratio).
>Why, then, I don't see
>any designs with AR=7 or
>8? Over the past
>30 years, stunters have averaged
>AR=5, based on my data.
>There must be a limiting
>factor, that compromises a different
>aspect of flight. Is it
>stability? In a Russian article
>I'm about to publish in
>SN, the author (Valentin Salenek,
>frequent Russian national F2B team
>member) mentions that high AR
>wings seem to be prone
>to strange oscillations in level
>flight. Any clues?

Great question, Mike, and probably worthy of at least one separate thread of its own.

The efficiency of a high aspect ratio planform is subject to qualification considering just what task you are trying to accomplish. Thus a a sailplane and a jet airliner, both of which want to get the most of out the least...the glider to set records, the jetliner to make $$$$$ by burning less fuel...can utilize high aspect ratio to their advantage.

If you want to go fast or roll rapidly or pitch dramatically you're better off with a planform/aspect ratio which is less "efficient" but more suited to the task. Ergo, supersonic fighters have very low aspect ratios which go like stink flat out but require very high angles of attack and tons of power to fly slowly as well, as on landing approach. As a glider it sucks and as an airliner...well, let's just say the cost per passenger mile is prohibitive!

Aerobatics, more or less what we do, is somewhere in between and, not surprisingly, we utilize planforms/aspect ratios somewhere in between as well. Here's a few words on why.

There have been a number of higher aspect ratio stunters built and flown by many innovative designers...including myself. The driving force is almost always the recognition that long wings make more lift for a given angle of attack than short stubby ones of the same area. The aeronautical expression for this sort of thing is L/D or the ratio of lift to drag.

Crudely stated (and, of course, subject to a lot of "yeah, but what ifs...), a wing of given area and airfoil can be configured in a variety of planforms all of which are roughly capable of producing the same amount of lift at a given speed. In general, the high AR version will develop that lift at a "lower" angle of attack and produce "less" drag by so doing. Thus we think of gliders as "high L/D" machines.

The low AR version will produce the same amount of lift but at a "higher" A of A and produce a lot more drag in so doing. Thus a stubby winged fighter requires such a high angle of attack and develops so much drag on approach that it takes nearly as much thrust to maintain flight as it does at high mach cruise. These machines are pretty much the ultimate in LOW L/D.

Note that, for their defined purpose, both machines have wings which are appropriate for their tasks...notwithstanding that one is technically much less "efficient". The fighter flies at such high speeds when doing its "designed thing" that little angle of attack is necessary to produce the lift necessary and the resultant drag is minimal and mostly consists of parasitic or form drag. Thus a short stubby wing at speed is much less of a drag producer.

Lets' leave these and get back to what's appropriate for stunters. What we've demonstrated is that the most appropriate planform for a given task is seldom the most "efficient" in terms of L/D.

In good air...almost calm to gentle breezes...a high aspect ratio stunter can be delightful. Because of low induced drag (the kind of drag which results from the production of lift and, thus, what we talk about in terms of our L/D discussion) such a stunter maneuvers very easily, is difficult to even think about stalling and creates so little drag that engine power is seldom an issue (thrust must overcome drag and if your induced drag component in maneuvers is minimized the need for raw thrust is much reduced). If we always flew in ideal conditions I think the average stunter would have evolved more in this direction than the classic five to one AR you've so correctly alluded to.

Where the difficulty arises is in bad air, either turbulence and/or high winds. Here's why:

One of the verities of high aspect ratios is that for a given increase in angle of attack the the increase in lift produced is greater than in the same area at lower aspect ratios. In addition, the lift thus gained comes with much less drag baggage. The net result is that when flying in winds the effects of winds on the flight path and speed of the airplane is much greater than with lower aspect ratios. Since, by definition flying on a tether, wind speed is constantly changing at the airplane the effects of increased angles of attack and effectively increased airspeed (flying into, along and downwind at various times in the same maneuver) the amount of lift is constantly changing and flight path adjustments must be made to counteract the lift component's changine effect on the vertical axis of the airplane throughout the maneuver.

Unless very precisely placed with respect to the wind the result will almost always be a significant wind up with the ship going faster and faster and the lift trying to tighten up the radius at one point requiring less elevator and vice versa at other points.

We had a combat flyer in the Bay Area years ago who loved to build very high aspect ratios combat ships...like 10 to one. Several times while doing the classic combat macho dance (how many loops can you do in "X" seconds) I saw him simply blow the wings off these ships as the loops got tighter and tighter. Impressive...and, instructive.

Much lower aspect ratios...like the one to one ratio flying saucer types that were popular as sport types when I was a kid...are the reverse. They develop so much drag in maneuvers that the engines of the day didn't have enough thrust to maintain speed at all and they would just sort of flop around...not unlike the Bi-Slobs we all get such a kick out of watching...but probably wouldn't enter in Expert stunt!

Other issues also mitigate against extremes in ARs. Structural integrity is an issue with very long wings at high G conditions. Simply getting a 70+" stunter into the Toyota could cause a lot of scratched hairs to come up missing, etc!

Modern powertrains are likely to have some effect on ultimate determination of aspect ratios. Very constant RPM stuff with lots of torque and low pitch props can handle lower aspect ratios without the loss of airspeed typical of a similar platform with a Fox .35 and six inches of pitch.

On the other hand, the speed control capabilities of those same powertrains make the feasability of competitive unflapped designs more viable. The use of higher aspect ratios on unflapped ships is very attractive due to the ability to get a lot of lift with modest angles of attack and at slower speeds. The problem, as previously addressed, is that of speed build-up in bad air...potentially much worse than a flapped ship because you don't have the flaps making the nice clean symmetrical airfoil a cluttered up draggy cambered one. The ability to put a very constant speed set-up (tuned pipe at near maximum length for the revs desired to maximize braking when the ship tries to wind up; or a four stroke propped for max revs) with a large diameter low pitched prop could well provide adequate speed control to allow the use of the more efficient high aspect ratio wing.

Another postitive of the high aspect ratio for an unflapped ship is the ability to get the lift required from a smaller overall wing which would also help to mitigate wind up and turbulence effects.

Whoo, enough. I'm sure I've missed something but even I'm bored writing it all.

>There must be a limiting
>factor, that compromises a different
>aspect of flight. Is it
>stability? In a Russian article
>I'm about to publish in
>SN, the author (Valentin Salenek,
>frequent Russian national F2B team
>member) mentions that high AR
>wings seem to be prone
>to strange oscillations in level
>flight. Any clues?

Oops, forgot all about this last item re Salenek's mention of instability.

As I mentioned briefly in the long post, one of the characteristics of "high" aspect ratios is their ability to create "more" lift with small angle of attack changes. This is a major consideration in the design of ultimate performance sail-planes with huge aspect ratios. These ships are so sensitive in pitch that elevator control is often damped somehow, usually mechanically to prevent inadvertent and potentially destructive large and/or rapid elevator inputs.

You can easily see how a long wing with controls set up for flying stunts might well be unacceptably twitchy in pitch because tiny changes in either angle of attack or airspeed (into and/or out of the wind in our circle) can change lift enough to make the ship try to either climb and or dive. this would result, of course, in the need to compensate with opposite control which could arguably result in phugoid types of oscillation which would be very tiring to manage.

"Modern" stunt design with larger tails and aft CGs would mitigate this effect quite a bit by reducing or eliminating the download on the tail required by "classic" forward CG locations and their resultant couple between the aerodynamic center of the wing and the CG.

Hi Crist. The 5 1/2 degrees might be the maximum considering the aspect ratio we tend to use. GMS's Magnum had a sweep of over 6 degrees, which probably put it past a stable point in the overall scheme. Just a thought.

Ted,
once again, thank you so much for enlighting all of us. Everything you've said made perfect sense, and all but completed the the big "stunt puzzle" in my head. What you and other leading members of this community are doing to help the less skillful/experienced of us is unprecedented in the history of stunt, and has a tremendous impact on this sport in the USA. The value of sharing knowledge specific to our application goes far beyond satisfying someone's curiosity or helping one or two guys. It keeps this sport alive. Well worth the effort!

It is now getting clear to me that the collective knowledge and (most important!) UNDERSTANDING of the majority of factors involved in the type of flying we do has reached the critical mass, at which it is sufficient to design the "ultimate stunt machine".
The EMPIRICAL knowledge might have been there long before ("this plane flies great, but don't ask me why" -kind of knowledge), but few have been able to draw up a set of plans, predict the flying characteristics of the plane with a high probability of success, and further trim the actual airplane with a clear understanding of the consequences of each trim change.
In this tread, as well as the Doctor and other articles, you've given a pretty comprehensive picture of the wing behavior and the parameters influencing it. The Trivial Pursuit article had an explanation of the "aft CG - large tail" concept and its advantages. Brett "the rocket man" has posted a nice long piece elsewhere on this forum on the moment arms (especially the tail moment arm). All this, combined with a virtually infinite pool of knowledge on the powertrain setup, and the building art demonstrated by Windy in his videos, gives an average Joe like myself a great chance to take a peek at the "stunt nirvana". How can I not be grateful for that?!
--Mike

Ted: Terrific, instructive thread. We learned a lot.

By the way, I have been experimenting with rather high ARs on scratch, profile bipes, in the area of 8 to 1. Sort of the opposite of a BiSlob. I put the struts right at the wingtip, which is squared off. This gets the leadouts as far away from the fuse as possible, which is an attempt to reduce the yawing you see on bipes.

The problem is weight, since I have been using balsa sheeted foam wings. But yes, the plane is pretty maneuverable, given the wing loading. The other issue is correct trim, which I will attack once the snow is gone.

The next step is to build one with conventional ribs and silkspan, and get the weight down. Currell

thanks for the nice words, Mike. Looking forward to seeing you again one day, by the way. Maybe get you a chance to fly the Doctor with the four stroke.

Just reread your original post and saw I missed the question regarding elliptical wings. Here's a couple words on that.

The elliptical planform is a pretty good example of just why taper ratio isn't a particularly useful aerodynamic term. It's descriptive, to be sure, but doesn't tell us much about the airplane it alludes to. Just think a taper ratio of say 70% on a 60" span ship is one thing, but the same root and tip chords on a 30" wing are still a 70% taper ratio but the resulting wing is quite a different animal!

This is why it is much more valuable aerodynamically to talk about aspect ratios and, there, the ellipse fits right into the mold. We commonly think of aspect ratio as being derived by dividing the wing span by the average chord. This works just fine for constant chord or straight tapered wings but falls apart when we start dealing with an ellipticl planform which may have one ellipse ratio for the leading edge and another for the trailing edge and finding the "average" chord is a difficult task.

When you realize, however, that the technical means of determining the aspect ratio is to divide the square of the span by the area of the wing the whole thing falls into place. (Although I'll not address the issue of determining the area of an ellipse). Thus we find that truly important and useful aerodynamic information can gleaned from an awareness of aspect ratio and that we can concentrate on that parameter when we design our ships knowing a great deal about what the performance of the resulting whip will be like.

>Hi Crist. The 5 1/2
>degrees might be the maximum
>considering the aspect ratio we
>tend to use. GMS's Magnum
>had a sweep of over
>6 degrees, which probably put
>it past a stable point
>in the overall scheme. Just
>a thought.

Hi Ty,

I know that GMA felt that way about the original Magnum but Frank McMillan several years ago built one for VSC and worked diligently to trim it properly...specifically locating the CG in terms of the MAC rather than at the fuse and adjusting leadout position accordingly. I was pleased to get a chance to put several flights on Frank's ship and must report it was one of the best flying Classic Era ships I've flown. It ranked right up there with Bobby Hunt's Mackey Lark and Frank's earlier Tucker Special.

There isn't much inherently "out of the envelope" with the Magnum, it's just that at the time George built the original there were some "conventions" regarding trim that prevented the builder/flyer from "going where he hadn't gone before"...which is what the design needed.

As an aside, one of the things we probably should alter in our stunt lexicon is our tendency to define wing "sweep" by how much the leading edge tapers. A much more accurate definition would be to determine the fore or aft sweep of the quarter chord point of the airfoil (the generally accepted Aerodynamic Center of a symmetrical airfoil).

It is entirely possible for a wing to have "zero" aerodynamic sweep even when the leading edge bends aft from the longitudinal centerline. If the trailing edge is swept forward an equal amount the net sweep measured at the quarter chord (or any constant chord location) will be zero. If the leading edge is swept back one inch but the trailing edge is swept forward three inches the net sweep at the quarter chord point is "forward"!

This is one of the reasons that many good stunters have most of their taper in the leading edge (at least why mine are that way!) because the resulting slight aft sweep is stabilizing...like just a touch of dihedral that works, however, both upright and inverted.

Thanks Ted. One more "old" concept blown out of the water. Now I feel better about the plane I'm designing.

Ted,
I'll try to make it to the Nats this year, with or without a plane (my old ugly rig, that is), so I'm sure we'll see each other again. Can I fly your Final Edition?... Kidding, kidding!

Guess what - with your last post, you just set yourself up for more questions. OK, why does an aft wing sweep (yes, aerodynamic sweep, not just leading edge) act like a dihedral to stabilize a plane? What direction does it stabilize in - pitch, roll, yaw? Assuming it's pitch stability, can too much aft sweep make a plane so stable it wouldn't want to turn a sharp corner?

Also, why do you West Coast guys have high AR wing (5.2) and low AR tail (4.6 is it?). Why is your stabilizer/elevator area ratio 60/40, as opposed to older conventional tails with 50/50 or even 40/60 ratios? I suspect someone wrote about this before, but I can't find references. A couple of brief sentences, please?
I agree to be billed for the time you've spent answering my questions.

Another piece of information for this thread. Just came back from flying my F-86D profile to prepare for the P-40 profile meet next week. These ships have sweptback wings, both LE and TE of approximately 15 degrees on the LE and they will turn as good a corner for me as any of the normal configuration ships I have built and flown in the past, hence I would say design your wing platform as you desire, it should fly just fine if all else is right.

Don (When I get old I will build a conventional model!)

I saw Don's late F-86 fly. It flew really well.

Two points regarding stability in wind. The low aspect ratio has more of the wing in the same air. The high aspect has the tips moving at a greater speed difference, "Magnifying" lift differences and causing the bobble in still air loops.
I fly the same structure and weight planes, one has 5/1 ar the other is a Half Fast with 14% center airfoil and 18% tip airfoil. Tye 5/1 ship is cleaner on the third turn, the HF will fly right thru the long wing plane. I prefer the Half Fast, I can get more in the car and they look good.MM