I am doing a project for school and I was hoping that you could help me out by explaning to me (in simple terms if possible) how the flying wing maintains longitudinal stability. If you could it would really help me out.

From : Don Stackhouse

No problem. A flying wing does have a tail, it's just not as obvious.

First let's review the way a conventional two-surface aircraft gets its pitch stability.

As you probably already know, a conventional aircraft layout has a flying surface in front (usually the wing, unless it's a canard), and a flying surface behind (usually the horizontal tail, unless it's a canard aircraft). The C/G is placed and the incidences of the forward and aft flying surfaces chosen so that the surface in front is working at least a little harder than the one behind. Normally this means that the incidence of the forward surface is higher than the incidence of the aft surface. The difference between those incidences is called "decalage".

For example, an aircraft might have the wing set at 2 degrees nose-up, and the tail set at 1 degree nose-down relative to some reference line (typically the fuselage centerline). In this case, the difference between the incidences of the two flying surfaces (their decalage) is 3 degrees.

The airplane's weight, acting at the C/G is trying to pull the nose down, and the combined effects of the lift forces of the two flying surfaces are trying to pull the nose up. If the airplane's nose goes down a little, it starts going faster. The nose-down effects of the weight stay constant, but as the airspeed increases, the nose-up effects of the lift forces on the flying surfaces increase, which then brings the nose back up.

If the airplane noses up, the opposite happens. The weight effects stay the same, the nose-up effects of the flying surfaces decrease as the airplane loses airspeed, and the nose goes back down.

A flying wing does the same thing. There are two major types of flying wing arrangements: 1. Swept with washout. 2. "Plank" style (unswept) with a reflexed (i.e.: bent upwards)trailing edge.

In case 1, the tips are further aft than the root, and the twist ("washout") in the wing puts the tips at a lower incidence than the root. The twist acts like decalage, and the fact that the sweep puts the tips aft of the root makes the tips act like a tail. Forward-swept wings typically have wash-in, so that their tips (which are ahead of the root) are at a higher incidence and act like a canard.

In case 2, the airplane uses a special airfoil with a bent-upwards trailing edge. We call this a "reflexed" trailing edge. It can be designed into the airfoil. As an alternative, the wing can have elevators or elevons cut out of the trailing edge, and their control linkages adjusted so that they are deflected upward. The reflex in the trailing edge acts like decalage, and the reflexed trailing edge portion of the wing acts like the horizontal tail of a conventional aircraft.

Like I said, flying wings do have tails, they're just integrated into the wing itself instead of being a separate flying surface mounted at the other end of a fuselage.

In most "textbook" explanations of stability, they talk about the wing lifting upwards, the weight a little in front of the wing's lift trying to pull the nose down, and the tail way back behind lifting downward, trying to push the tail down. The tail's downward lift increases with airspeed, so that if the nose goes down and the plane starts to go faster, the tail's downward lift gets stronger. This pushes the tail down and the nose up, bringing the plane back to its original pitch attitude and airspeed.

This explanation is easy to follow, and probably representative of most airplanes in most flight conditions, but I didn't use it last night because it's not always true. There can be situations where both the wing and the tail are lifting upwards while still having positive pitch stability. In general, if the flying surface in front is carying a little more than its fair share of the load (based on the relative areas of the two flying surfaces involved), there's a reasonable chance that the plane will be statically stable. This is true whether it has a conventional aft tail, or a canard (both are just different variations of a "two-surface" aircraft, depending on whther the front surface is bigger or smaller than the one behind; if they're both the same size, it's a "tandem wing" aircraft).

For example, let's say we have a plane with a 200 square inch wing and a 100 square inch tail (total area for the two surfaces combined = 300 square inches), and a flying weight of 1 pound. Theoretically, if the forward (200 sq.in.) wing carried 2/3 pound and the 100 sq.in. tail carried the remaining 1/3 pound, then the airplane would be approximately neutrally stable. This is a GROSS oversimplification, there's a bunch of other factors that can influence the situation, but it's roughly in the ballpark for the purposes of this discussion.

Now, if we move the C/G forward so that the 200 sq. in wing is carrying 3/4 pound instead of 2/3, and the 100 sq. in. tail is only carrying the remaining 1/4 pound, the plane could have positive pitcvh stability, even though the tail is lifting upwards. Note, I said possible, I dod not say wise! The problem is that the wing is a much more efficient lift producer than the smaller tail, so asking the tail to carry part of the load is taking away work from the more efficient wing and giving it to the less efficient tail, which hurts the overall aircraft efficiency. This is one of the fundamental problems with canard aircraft; the smaller and less efficient canard has to carry a proportionally greater part of the load, so the overall efficiency of the aircraft suffers.

In general, the most efficent two-surface aircraft layout is one that has nearly zero load on the tail, and a tail that's just big enough to provide the necessary stability. Such an airplane carries nearly all of the load on the wing, which is the most efficient lift-producer on the airplane.

An additional problem with canards and lifting tails is downwash. A wing or other flying surface makes lift by grabbing chunks of air and accelerating them downwards. It's Newton's third law, the one about action and reaction. The wing shoves air downwards, and the air reacts by shoving the wing ( as well as the rest of the airplane attached to it) upwards. One of the side effects of this is that the air behind the wing is going downhill, something we call "downwash". If you have a canard in front making upwards lift, that means that the wing behind it is flying through the continuous downdraft created by the canard's downwash. This hurts the wing's efficiency, it's as if it has to continually peddle itself up a hill that the canard continuously creates ahead of it. An upward-lifting aft-mounted tail has the same problem, since the tail has to fly through the wing's downwash.

However, in the case of the more conventional downward-lifting tail, the downwash of the wing actually helps the tail's efficiency. Unfortunately, the downward lift made by the tail adds to the upward lift the wing has to make, which hurts the aircraft's overall efficiency.

The bottom line is that for a given amount of stability, the efficiency of an equivalent canard, tandem wing and conventional downward-lifting aft-tailed arrangement will all probabably be similar.

Flying wings have their own pitfalls. First let's discuss planks:

For stability, a plank needs a reflexed airfoil. That type of airfoil does not make as much lift for a given amount of drag as a conventional non-reflexed airfoil. This means that the wing area needs to be greater to lift the same amount of weight, which means more skin friction. Also, we need to consider something called "tail moment arm", which is the distance between the wing and the tail, as measured between their "aerodynamic centers" (there are some articles in the "Ask Joe and Don" section of our website that explain what aerodynamic centers are and how to calculate them). The tail moment arm is the lever that the tail acts upon to do its job of stabilizing the plane. The shorter this moment arm, the bigger the tail's area has to be in order to do its job. More area means more skin friction. It also means that the downforce of the tail has to be greater to provide the same amount of stability, which means even more positive lift that the wing has to make, which means more wing area, which means even more skin friction.

Since the effective "tail moment arm" of the reflexed portion of a plank's airfoil is about as short as you can possibly get, that means that the required area of the reflexed part of the wing, as well as the required area of the upward-lifting part of the wing BOTH need to be greater, which means gobs and gobs of skin friction drag. Also, that extremely short tail moment arm means that the allowable C/G range will be extremely small. Balance on a plank-type flying wing is among the most critical of any aircraft. One plank-type flying wing sailplane has the pilot's seat on rails. Part of the preflight check is for the pilot to slide the seat forward or back until the airplane balances on its single landing wheel. When this is achieved, the C/G is correct.

Swept flying wings can use conventional non-reflexed airfoils, so their airfoil efficiency is generally better. In addition, the effective "tail moment arm" between the wing root and the wing tips is generally much better than for a plank, although it still tends to be short in comparison to a typical tailed aircraft. As a result, the allowable C/G range tends to be better than a plank's, but still short. The real problem is with the swept flying wing's effective wingspan.

Remember how a wing makes lift by grabbing chunks of air and shoving them downward? The size of those chunks of air is a major factor in how efficiently the wing makes that lift. Bigger chunks of air means better efficiency. So how big are those chunks? Imagine a cylinder of air, with a diameter equal to the wingspan and a length equal to the distance the plane flies in one second. The mas of the air inside that imaginary cylinder is the "mass flow", or the size of the chunks of air that the wing is grabbing to make its lift from. Note that the volume of the cylinder is proportional to the SQUARE of the diameter, so even a little change in wing span can make a very significant different.

Now the problem with the swept flying wing is that usually the tips are lifting downward, just like the horizontal tails of most conventional aircraft. If the tips are lifting downwards, then the wing is not using its full span to support the weight of the plane. It has nearly all the structure and weight and skin friction of a conventional plane of the same wingspan, but since the tips are not lifting upwards, the effective wingspan (and therefore the mass flow) is less.

It is possible to design a swept flying wing so that the whole wing is lifting upwards, effectively utilizing the entire span. However, it's a rather tricky design problem. It's even more difficult to get this to happen over more than an extremely narrow range of airspeeds. It's possible to make flying wings that are more efficient than conventional two-surface aircraft, particularly if the plane spends nearly the entire flight at only one operating condition, such as cruising flight. However, it generally takes much more in-depth work by the designer for this to happen. If the plane is expected to operate at a variety of speeds, altitudes and power settings, the design problem becomes even harder. It's also possible to design a somewhat longer-span flying wing that has the same effective span as an equivalent tailed aircraft, but that has the same or less weight and skin friction. Once again, the design problems are formidable, but not insurmountable.

Don Stackhouse
DJ Aerotech