# Tailless Aircraft

Northrop YB-49 Prototype, W = 192,000lbs (87,000 kg)
Range 3500 miles (5600 km) at about 390 mi/hr (630 km/hr)

As we have pointed out, a tail is not needed for stability. By locating the c.g. far enough forward, it is possible to obtain any level of stability. The tail or canard is used to provide the pitching moment needed to trim:

For stable airplanes, x/c is positive so that to trim at positive CL's, Cm0 must be positive. Typical airfoil sections have negative pitching moments, so the difficulty in designing tailless aircraft becomes that of obtaining a sufficiently positive Cm0. Since the static margin, sm, is defined as:

Trim requires that:

This can be done in several ways as illustrated by the wide range of tailless aircraft designs.

A simple means of obtaining a positive value of Cm0 is to choose an airfoil section with negative camber or with reflex. But there is a good reason that most airfoils have negative pitching moments: concentrating most of the lift forward of the airfoil's 1/4 chord point results in long, adverse pressure gradients with correspondingly low CLmax and only short stretches of laminar flow. Some recent progress has been made in the area of low and positive moment airfoil design, but there are fundamental limits as to what may be done in this area.

One example of a tailless aircraft that trims using a positive Cm0 airfoil section: the AeroVironment Pathfinder, solar-powered aircraft on a flight to over 50,000 ft (15.2 km).

Because of the degradation in airfoil performance associated with positive Cm0, other approaches to trim tailless aircraft have been pursued. One of the best involves the use of sweep and twist.

Basic lift distribution consists of lifting root, downloaded tip -> positive Cm0.

The Horten IV shown below uses a lift distribution that is actually negative at the tips. This helps lateral stability, but makes for poor span efficiency.

Of course with such a peculiar lift distribution, the span efficiency is very low. In fact, we can easily solve for the distribution of lift that minimizes induced drag while providing a given amount of pitching moment. The amount of moment can be related to the location of the lift centroid, eta_c, as indicated by the expression below. The result is that an elliptical load distribution with the lowest induced drag has a lift centroid at 42.4% of the semispan. Twisting the wing more than this to move the centroid to, say, 33% of the semi-span (as recommended by the Horten's) results in a span efficiency of 72%. In fact, the measured span efficiency of the Horten IV was about 63%.

The airplane will be trimmed when the c.g. is located on the lift centroid. Thus, the question arises: can we find a wing with the aerodynamic center at more than 42.4% of the semi-span? If so, we will have a stable, trimmed wing with minimum induced drag. The answer to the question is yes.

If the aerodynamic center of the wing falls outboard of the elliptical lift centroid (at 42.4%) the wing will be stable and trimmed. (Actually there is a slight correction due to section pitching moment, but this just moves the required a.c. a bit farther out.) A bit of analysis shows, however, that this is not so easy. The wing a.c. will lie sufficiently far outboard of the 42% point for reasonable stability levels only when the wing aspect ratio, sweep, and taper ratio are sufficiently large. In practice this means aspect ratios greater than about 8, sweep greater than 25° (a bit lower for very high AR), and taper ratios in the range of 0.75 to 1.0.

At first, this swept, slightly tapered wing seems very inefficient. Most textbooks suggest that taper ratios of 0.25 to 0.3 are more conducive to low induced drag. The reason that this design works out is that the basic lift distribution carries the lift far inboard while the additional loading is far outboard. The result is a case in which two wrongs make a right.

One of the difficulties of tailless aircraft is associated with their controls. The Northrop flying wings had some problems in this area. In order to nose the aircraft up, a positive pitching moment must be introduced. This may be done by reducing airfoil camber or increasing the washout of a swept-back wing.

Both of these methods are used when elevons are deflected.

Elevons have several problems, however:
• They initially decrease the wing lift when used to increase the trimmed angle of attack.
• They are located in the wing tip region where spanwise boundary layer flow can be a problem
• They require mixing so that the same surfaces can be deflected symmetrically as elevators or antisymmetrically as ailerons. This reduces the maximum control effectiveness.

A design incorporating some of these ideas was designed at Stanford as a foot-launched sailplane. The SWIFT is a swept wing with an inboard flap for trim. The flaps extend over almost half the span and can be deflected as much as 50° for approach and landing. With its clean, laminar flow design and lightweight composite construction, it outperforms other foot-launched aircraft by a wide margin. It has been flown to altitudes over 15,000 feet (4600 m) over distances of 140 miles (225 km). About 150 of these aircraft have been produced. Click here for a short QuickTime video clip of the Swift.

One of the recent motivations for tailless aircraft is associated with reducing radar cross-section. The B-2 aircraft illustrates how active controls and an unconventional design can provide an acceptable compromise between aerodynamic efficiency and low observability.

B-2 Photo courtesy Northrop-Grumman Corp.