A design I've been working on...

HomeBuiltAirplanes.com

Help Support HomeBuiltAirplanes.com:

addaon

Well-Known Member
Lifetime Supporter
Joined
Feb 24, 2008
Messages
1,696
Location
San Jose, CA
Greetings. I'd like to present some ideas around a design that I've been working on, on and off, for a little over ten years now. I want to say, up front, that not a single piece of this aircraft currently exists -- some analysis has been done, but this is a pure paper design today.

The design is for a low aspect ratio, statically unstable flying wing. I'm going to talk about all three of those design characteristics in isolation first, and then talk about why I think they combine so nicely. I will defer talking about the specific mission I'm designing around until a later post; for now, we'll keep the concepts abstract. Similarly, unless necessary for understanding I'll skip numbers that arise from detailed design, although I'm glad to discuss them later.

I'm going to do this as a few posts to make reading and managing it easier.
 

addaon

Well-Known Member
Lifetime Supporter
Joined
Feb 24, 2008
Messages
1,696
Location
San Jose, CA
Low Aspect Ratio

The design under discussion has an aspect ratio of 3.0. For the purposes of discussion, I will consider this a low aspect ratio, but not extremely low aspect ratio. At extremely low aspect ratios some aerodynamic effects (such as vortex lift) come into play that are interesting, but not relevant for this design.

Aspect ratio cannot be analyzed in isolation; it is inherently related to span, chord, etc. For the design under consideration, the wing is sized based on a stall speed requirement. Although lowering the aspect ratio of a wing will lower Clmax, all else being equal, this effet is pretty minor. As a result, equal wing loadings (giving equal stall speed at equal Clmax) will be considered.

As aspect ratio of a design changes from a typical seven or eight down to three, what changes? The two main effects are a decrease in structural weight (good) and an increase in induced drag (primarily bad). How these two effects interact depend on detailed design.

Structural Weight: The decrease in structural weight is important here, and will be a recurring theme. It means, among other things, that the aircraft with a lower aspect ratio wing can also have a smaller (lower area) wing for the same wing loading. That said, this effect shouldn't be overstated either -- a well designed wing, even of high aspect ratio, can be surprisingly light and even a large decrease in wing weight is only a small decrease in aircraft weight.

Induced Drag: The increase in induced drag is similarly important, and is the obvious reason that conventional designs shy away from low aspect ratios. If the engine is sized for low-speed performance (for example, the limiting factor is climb speed rather than cruise speed), a low aspect ratio design will need a higher power loading than the high aspect ratio design. This may or may not mean a bigger engine, depending on the magnitude of the weight savings; but if it does, that will add weight both in engine size and in mission fuel load. On the other hand, if the engine is sized for cruise speed, the required power loading won't change much.

It's worth taking a digression here to talk about flying characteristics. In my personal opinion, flying a sufficiently powered, draggy aircraft is fun. More fun than flying a slippery bird. The ability to casually do steep approaches, burn off excess energy, and burn some fuel to add it back is, to me, pleasant. (I will gladly acknowledge that a variable-drag aircraft, such as a low-drag sailplane with effective speed brakes, is the best of both worlds. I will also acknowledge that I'd much rather have lower drag when the engine quits.)

There are three other effects of low aspect ratio that are normally relatively minor; one becomes quite important in this design.

Lift Curve Slope: Although a lower aspect ratio doesn't have a large effect on achievable Clmax, that maximum lift is achieved at a higher angle of attack, and the lift curve slope is shallower. This has positive effects (reduced gust loading) and negative effects (increased landing gear weights, awkward visibility at low speed). While this design will somewhat mitigate the negatives while retaining the positives (discussed later), the effects are small.

Wing Volume: A lower aspect ratio wing has a higher volume for the same wing area. Even with extremely optimistic weight savings leading to a somewhat smaller wing sizing, the wing volume is likely to increase substantially. This has obvious benefits when it comes to putting stuff (fuel, retractable landing gear) in the wing. It has somewhat less obvious benefits when it comes to flexibility on where to put things in the wing. That is, all else being equal, a lower aspect ratio wing allows the same volume of fuel to be placed closer to the target center of gravity location. Again, this is a relatively minor effect.

Flap Moment: Trailing edge surfaces on a lower aspect ratio wing act with a greater moment arm, all else being equal. This means that flaps apply a greater nose-down moment with deflection, that must be offset by a moment elsewhere, usually an increased downforce on the tail. This can limit sizing and effectiveness of flaps as high-lift devices, or increase tail sizing and weight. For the design under consideration, this is not a minor effect; instead, it is one of the primary effects leading to aspect ratio selection, as will be discussed later.
 

addaon

Well-Known Member
Lifetime Supporter
Joined
Feb 24, 2008
Messages
1,696
Location
San Jose, CA
Statically Unstable

All aircraft must be stable to fly. That is, when encountering a disturbance, it must tend to return to its previous state. This can be achieved passively, by the aerodynamics of the aircraft itself; or, the aircraft can be stable only under closed-loop control, whether by heroic efforts of a skilled pilot, or by an active control system.

The discussion here focuses on longitudinal (pitch) stabiity. The design under discussion is statically stable in yaw and has approximately neutral static stability in roll, like most small aircraft. It differs in being statically unstable in pitch.

Pitch stability is achieved when an increase in angle of attack leads to an increased nose-down pitching moment. In aircraft with a conventional tail, the lift of the wing will increase, and the lift of the tail will increase (or it's downward force will decrease), roughly in proportion of their areas (with adjustments for lift slope curve); but the moment arms must be such that the latter exceeds the former. (Wing and tail Cm also play here, but the effect is relatively small for conventional aircraft.) The placement of the center of gravity determines these moment arms.

In a statically-unstable aircraft, if an increase in angle of attack is encountered, the increased wing moment will exceed the increased tail moment, and the aircraft will tend to increase its angle of attack further. If, however, the pilot notices this happening, he can push the stick forward, increasing the tail moment and righting the aircraft. Of course, if she doesn't react quickly enough, Bad Things can happen; and if she overcompensates, the aircraft will tend to run away in the other direction.

Whether a pilot can actually fly any given statically unstable aircraft depends in large part on pilot skill. As a rule of thumb, though, a human pilot will suffer extreme workload with any amount of instability, as has no hope at all if the time to doubling (the time for a one degree pitch change to become a two degree change... to become a four degree change...) exceeds half a second. Automated control systems can handle much higher degrees of instability, but there's no magic here. To stabilize a statically unstable system, a control system (or a pilot) must recognize the change, identify the corrective action to take, and physically implement that action. For a control system, limits on sensor noise and latency, compute latency, and actuator bandwidth all limit just how much instability can be handled.

The X-29 program demonstrated control of an aircraft with a negative static margin of 35% (that is, with the center of gravity 35% of the mean aerodynamic chord behind the point where the aircraft would be neutrally stable). Required control bandwidth (directly related to time to doubling) is a function of not just static margin, but also moment of inertia. A smaller unstable aircraft needs, all things being equal, a faster control system to maintain control. Some parts of the control system (actuator bandwidths, surface inertias) scale with aircraft size, but some (sensor latency, compute) do not; so an aircraft of half the weight is, all else being equal, harder to control, but not twice as hard.

The design under discussion optimizes with a static margin around -13%, with the design center of gravity range spanning roughly -11% to -15%.
 

addaon

Well-Known Member
Lifetime Supporter
Joined
Feb 24, 2008
Messages
1,696
Location
San Jose, CA
Flying Wing

For the purposes of this discussion, a flying wing is an aircraft with only a single surface acting aerodynamically in the vertical direction -- an aircraft with no conventional horizontal tail, canards, etc. The design under discussion has a conventional vertical tail (stabilizer and rudder). This is sometimes called a tailless aircraft, but I must confess that I find the use of "tailless" to distinguish those aircraft that have a vertical tail from "true" flying wings more confusing than useful.

The appeal of a flying wing is obvious. A horizontal tail represents weight, parasitic drag, and often both induced drag and a downforce that must be countered (at the cost of more drag) by the main wing. It also represents more parts to build! Wouldn't it be nice to get rid of all those needless (and ugly!) bits?

Unfortunately, there are trade-offs. Such extreme trade-offs that flying wing designs are rare in the small airplane world.

In the previous discussion of static stability, we discussed a conventional layout where, to a good approximation, the wing is responsible for lift and the tail is responsible for stability. In a flying wing design, the wing must do both. There are two moments acting on a flying wing: the moment of the weight of the aircraft acting across the arm of the static margin, and the moment of the airfoil itself. If the static margin is positive (the aircraft is statically stable), the center of gravity provides a nose-down moment, and the wing must have a postive (nose-up) coefficient of moment. That is, when the wing increases in speed, it also tends to lift the nose of the aircraft, increasing the angle of attack, increasing lift, turning speed into altitude, and slowing the aircraft down -- providing stability.

Airfoils with positive coefficient of moment exist, but they have a lower Clmax compared to equivalent conventional airfoils. One way to think about this is that the aft part of the airfoil is producing less lift than it "should", to keep the nose up, just like the tail would on a conventional aircraft. This means that, all else being equal, a flying wing must have a lower wing loading than a conventional (or canard) aircraft, if the wing is sized for (flaps-up) stall speed.

But conventional designs are rarely sized for flaps-up stall speed. They're often sized for flaps-down stall speed. As we briefly discussed in the "low aspect ratio" section, flaps increase lift, but they also cause a nose-down moment. In a conventional aircraft, that moment is countered by the tail; in a flying wing, with nothing to counter flap moment, traditional flaps are not an option. And the wing loading of a flying wing sized for (no flaps) stall speed will be much lower than the wing loading of a conventional aircraft sized for (flaps-down) stall speed.

It gets worse! The nose-down moment of the weight of the aircraft is approximatly constant with airspeed. The nose-up moment of the wing increases with the square of airspeed. As the flying wing slows down, the coefficient of moment of the airfoil must become dramatically more positive. This is achieved by deflecting a trailing edge control surface (elevator or, when combined with roll control, elevon) upward. This acts as negative flaps, further decreasing achievable coefficient of lift. This negative effect can be minimized by increasing the moment arm of the control surface -- that is, by going to a lower aspect ratio -- but it's always significant. The Dyke Delta, a great example of a homebuilt flying wing that uses low aspect ratio to minimize the upward elevon deflection at low speed, still lands with over fifteen degrees of "negative flaps."

The final major downside of the flying wing approach is the small allowable CG range. When the center of gravity moves, the elevator or stabilator (in a conventional design) or elevons (in a flying wing) must provide a countering moment. But the moment arm of a conventional tail is much, much longer than the moment arm of a flying wing elevon. The control authority of the elevons usually limits flying wing CG ranges to a few percent at most of the mean aerodynamic chord, versus 20% of more for a conventional design. This can be countered, somewhat, by increasing the chord -- see, again, the Dyke Delta -- but remains a significant limitation.

After all this negativity on flying wings, where's the positivity?

First, the coolness factor is huge!

And second, in the next post we'll revisit these flying wing shortcomings, after mixing in the assumptions of low aspect ratio and static instability.
 

Hot Wings

Grumpy Cynic
HBA Supporter
Log Member
Joined
Nov 14, 2009
Messages
7,635
Location
Rocky Mountains
So, you want to build a forward swept clipped wing version of the Pelican?

:cool:

Other than aspect ratio you just described my vision of a modern flying machine - with a very similar logic path. That last part should cause you some concern. ;)

Nice to see a post from you again!
 

AhzeeDahak

New Member
Joined
Apr 8, 2020
Messages
2
You’ve baited and set the hook admirably. Please reel us in!

I appreciate the thought process, and am looking forward to the result.
 

BBerson

Light Plane Philosopher
HBA Supporter
Joined
Dec 16, 2007
Messages
14,727
Location
Port Townsend WA
I do think aspect ratio 3 is a sweet spot for single seat sport. I had an AR-3 model that was remarkable.
However, I don't see any major weight advantage as the AR-5 five or six can also have the same weight wing by using a somewhat thicker wing same as the low AR does.

For the "horizontal tailless" configuration, an electric powered lift jet on the front could offset the flaps negative moment for the landing and takeoff.
 

Jimstix

Well-Known Member
Joined
Sep 29, 2012
Messages
149
Location
LAS CRUCES NM
Tailless airplanes are notable for their low lift coefficients. This is usually overcome by more wing area. As for negative margin, this is a really, really bad idea. Small airplanes have low inertia anyway, and a tailless airplane is extremely low in pitch interia. Unless you have powered control surfaces and computer augmented stability (like the X-29) it is unlikely that you are quick enough or strong enough to control the airplane. That said, have you built and flow a large scale flying model of your design?
 

TFF

Well-Known Member
Joined
Apr 28, 2010
Messages
14,493
Location
Memphis, TN
What do you see the drag to be flying as unstable. As you force the nose down with the elevator, seems to me you are creating a lot more drag you have to counter with speed to stay in control, than the drag and speed if it was positive stability. Maneuverability with the negative stability will be enhanced for sure, but the augmented control has to stay up. That technology is there. Just trying to figure out the advantage of a human is in it.
 

addaon

Well-Known Member
Lifetime Supporter
Joined
Feb 24, 2008
Messages
1,696
Location
San Jose, CA
Unless you have powered control surfaces and computer augmented stability (like the X-29) it is unlikely that you are quick enough or strong enough to control the airplane.
Agreed. "Unless." (Computerized control systems for powered control surface aircraft is what I do for a real job. And one of my main accomplishments over the past ten years has been making that true.)
 
Top