Q-talk 99 - Tandem Wing Airfoil

Design Points

When we set out to design an airplane, we first make many decisions about mission, utility, and things like that. After we decide that we want a particular seating arrangement and load capacity, etc., we start to list our wished-for performance. We make educated guesses about the reality of those wishes and use them to define a generous "performance envelope" that compares load factor to true airspeed. This V-n diagram tells us, by its corners, what combinations of speed and load factor need to be satisfied by our choices of structure and aerodynamics.

These critical points on the V-n diagram must be satisfied at all reasonable operating conditions, such as gross weight/light weight, forward and aft CG, and the settings of various deployables like flaps, speed brakes, and landing gears. For the last three, there is usually a maximum deployment speed above which we consider the device to be retracted, so we needn't worry about the high-speed points on the V-n diagram with the flaps out, for example. Or do we? For tandem wing airplanes, the elevator is essentially a flap, so, yes; we do need to consider "flap" deployment up into the high-speed range.

The V-n diagram is just one of our analysis tools, however. We also must consider the stability of the airplane at all flight and loading conditions. It is not enough just to say that the structure is strong enough to absorb the occasional gust at cruise speed; we also must satisfy ourselves that the airplane will be stable at that speed. Closely connected to stability is the controllability of the airplane and the ability to trim for continued operation in certain flight modes, such as cruise or slow flight.

The devices we use to achieve flight are simple: an engine turning a propeller, some wings to give lift, and some more, usually-smaller wings to balance the teeter-totter we make when we put a long fuselage atop a lifting wing. We talk about "planform" selection and weigh the relative merits of trying to get the balancing-wing to help the lifting-wing do its job, and eventually we succumb to the allure of sex: "I bought a Quickie because it looks way cool."

Having chosen our tandem-wing planform, we now need to know what its parts are doing to keep us from becoming lawn-darts.

Who and What

As customers who bought already-built airplanes, we trust that someone did a decent job of flight-testing and has provided us with a manual and some operating limitations. That's what the FAA requires of factories that manufacture airplanes; that's what the FAA wants us to be doing when we are "flying off the restrictions;" and that's what we should be doing to ensure the safety of our loved ones when we eventually take them up with us to share the joy of achievement and flight. Oh, yeah, I count myself among my "loved ones," too, don't you? And don't forget about our eventual customers when we do finally sell.

As customers who buy and build kits, our knowledge needs to be a little more intimate: We will be the manufacturers and test pilots, so our level of understanding needs to be about two notches higher. We must understand the functions of the various parts so that we can know what manufacturing tolerances to apply. We must also understand the functions of the various parts so that we can know what areas of the flight envelope to investigate and what outcomes to expect when we reach and exceed the limits of that "design" flight envelope.

Yes, we'll be exploring the limits, which means that we'll occasionally push those limits, perhaps beyond what the airplane is capable of,even though our theory says otherwise. We need to know and plan for what to expect when that happens. One thing we absolutely must prevent is any unrecoverable loss of control. For that eventuality, we pack our parachutes (and our prayers) and rig our canopies for quick release, hoping never to need to use these features.

As designers, we become even more challenged to know and understand the nuances of what we build, and why. Not only must we understand the functions of the various parts, we must understand the design choices that will lead us to shape a part this way as opposed to that way, and to know what design condition we chose as the critical condition for making that design determination.

We're getting close to airfoil selection; don't give up on me yet.

The final and, in my opinion, most difficult and demanding level of knowledge is required of those brave souls who seek to be modifiers of an existing design. With a clean-sheet approach to a new design, you have the freedom to set your own design goals, constraints, and conditions. In modifications, you are already constrained by the choices made by the previous designer, plus you are simultaneously trying to second-guess his design decisions while possibly expanding his design flight envelope. Quite a task! And not one to be taken without some overt arrogance - er, ah, "can-do spirit," yeah, that's what I meant to say. Not a task to be undertaken without a can-do spirit!

To give an idea of how difficult it can be to modify an existing design, consider the case of the Quickie's original Onan engine mount as supplied to kit buyers. This mount did not work. The designers apparently did not initially understand some aspect of the design and what was supplied in the kits soon started breaking bolts. These were experienced designers working on a design with which they were intimately familiar, yet it took Quickie Aircraft Corporation several changes to reach a satisfactory solution, and that was modifying their own design. (Not all of the changes were issued as QPCs; some were just newsletter comments.) And there are those among us, my arrogant self included, who still find fault with QAC's solution and have undertaken to modify it further.

Design Criteria

From here, we can't proceed without knowing the design's mission. First: what did the original designers use as design criteria? Many times I've held my breath as discussions ensued about making the Q200 a short-field airplane. Wow. I thought that was the realm of the Super Cub and the Maule Rocket. Okay, for proper perspective I'll admit that the real goal was to make it a "shorter-field" airplane; but how much shorter, and why? Would a 10% reduction in landing distance be enough? That would "only" require a 10% increase in available coefficient of lift. In our society, 10% this way or that way is so easy to achieve, we tend to discount the hard facts of nature. But the fact is that if another 10% had been available at design time, it was deliberately not used because there is a different emphasis on this design that conflicts with short-field performance goals. Specifically, the Q200 is a "fast, efficient cross-country cruiser." Most of the high-performance tandem-wing and canard airplanes of today define their brand of high performance in terms of cross-country cruising. It is equally right to speak of an Onan-powered Quickie as "high-performance" as it is to speak of a Maule Rocket as "high-performance," but the measures of performance are different. The Quickie gets its "high-performance" from the ratio of its cruise speed to the miniscule demands of its miserly little engine. The two-place tandem wing and canard airplanes all get their "high-performance" labels from this ratio. The Maule gets its "high-performance" kudos for being able to pull Bubba and his linebacker buddies out of the 200ft long fishing pond with an elk tied to each float; different measures of performance.

The airfoils on the front and back ("canard" and "main wing," respectively) of tandem wing airplanes have different measures of performance from one another, and the overall airplane has yet another measure of performance. Returning to the V-n diagram, the first interesting point on it is the 1-g stall. Let's look at the demands on the two wings and on the airplane at this point more closely.

The First V-n Point

p>At 1-g stall, we won't be defining a stall speed but solving for one. We'll look at what makes our airplane acceptable in cruise (our design condition) and relate it back to this stall speed and see if we can live with that stall speed. If we were designing a short-field airplane, we'd define a stall speed, design for that condition, and then see if we could accept the resulting cruise performance. But that's not our goal. So, we'll set a loose range for a stall speed and see whether we can stay within that range. I believe that Burt Rutan's criteria for the Vari-EZE was that he should be able to safely operate from a 2500 ft paved runway; that sounds OK to me.

Considering brake performance factors and other stuff, we'll use our scientific intuition and take a WAG (Wild "Aeronautical" Guess) and say that we want our stall speed to be below 61kts. That just happens to coincide with the number dreamed up by our friends in the FAA for the maximum allowable landing-configuration stall speed for certification of single-engine airplanes. We'll need "good" brakes to use a 2500ft runway, but not "great" brakes. (See the Mateo website for a great discussion of brake energy dissipation.)

For low-power planes like the Quickie and the small-engine Dragonfly, there is good reason to do things that will lower the stall speed based on considerations of climb performance, so we'll find ourselves with a lower stall speed in these cases. It would be much nicer to land the higher-powered two-place tandem wing planes around 50 kts, but our design criteria don't require it. What we do require is that the aft "main" wing never stalls, so now we finally get to look at what our airfoils are doing. Right after we look at wing design, that is.

Wing Design

Wings aren't straight. Taper happens, both in thickness and in planform. Wings are designed with a deliberate twist. And wings don't contribute as much lift near their tips as at their roots. Wing design is a 3-D undertaking that is well beyond the scope of this article, but it includes some key points that we must respect. Principal among those is that wings will never achieve the same coefficients of lift and drag as the 2-D airfoils around which they are constructed. That said, we can simplify our analysis of wings by substituting an "equivalent" airfoil and examining its properties, then adjusting those properties for 3-D planform effects. This "equivalent" airfoil takes account of the overall wing twist, taper, and sweep, and is called the "mean aerodynamic" airfoil section.

If we built a "perfect wing" using this airfoil that had the same area as our real wing, then the two wings would be interchangeable. However, that perfect wing would have to have an elliptical planform, so even then it would only have the mean aerodynamic airfoil section at exactly one point along its span, with larger and smaller copies inboard and outboard, respectively. However, the copies would all be operating at the exact same angle of attack, which greatly simplifies our task by eliminating taper and twist. Further, we can closely approximate the difference between a "perfect" wing's elliptical planform and that of a rectangular planform having the same mean aerodynamic airfoil by a simple formula that incorporates the aspect ratio, the ratio of span to mean aerodynamic chord length.

What all this means is that the mean aerodynamic airfoil section becomes a touchstone that we can refer to from two different directions: as wing designers, we can tailor our physical wing to yield the desired mean aerodynamic airfoil section while retaining the taper that our structure calls for and the twist that our stall behavior requires; and as airplane designers we can treat the entire wing as though it had the properties of just the mean aerodynamic airfoil section, then call for modifications to that airfoil section to meet our design goals. For the remainder of this article, we'll be looking at airplane design and leaving the icky details of wing design to the specialists.

Further, the mean aerodynamic airfoil section is usually referred to only by its chord line (don't ask me why!) which is the mean aerodynamic chord or M.A.C. I'll use M.A.C. from now on whenever I'm not talking about a specific airfoil section shape. To further standardize conversations among engineer-types, you'll note that the concepts of fuselage length and tail length are often spoken of in terms of fractional multiples of the M.A.C., e.g. "that airplane has a tail length of 3.5 M.A.C." What this means is that the quarter-chord point of the M.A.C. of the tail is approximately 3.5 times the length of the wing's M.A.C. aft of the wing's quarter chord point. More on this later.

Continued in Q-Talk issue 100

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