# How does an aircraft tailplane work?

How does an aircraft tailplane keep the aircraft stable, and prevent it from tipping over? Also, how does the lift generated by a tailplane compare to that generated by the wing?

• A question from the early days of this site, many answers could do with an update. References to having to have negative lift should be passé by now. – Koyovis Aug 19 '19 at 6:27

For conventional designs, the tail is composed of two parts: the horizontal tail and the vertical tail. They play a role in the trim and the manoeuvrability of the aircraft but at different levels. The horizontal tail is mainly used for longitudinal stability (and trim) while the vertical tails used for the lateral stability (and trim).

It is possible to talk of stability only after having defined an equilibrium point around which the stability is studied. An aircraft is in equilibrium if the forces and moments it experiences are balanced. Using a simple model for the longitudinal analysis, it can be decomposed in three relations called the trim equations. In order to keep it simple, it will be assumed here that the angle of attack and the flight path angle are zero. (Note that the same reasoning can be achieved with non-zero values but the equations then become quite messy.)

### Longitudinal Equilibrium

These three equations are:

$$L=mg$$ $$T=D$$ $$M=0$$

where $L$ is the total lift, $mg$ is the weight of the aircraft, $T$ is the thrust, $D$ is the drag and $M$ is the pitching moment around the centre of gravity of the aircraft. The second equation won't be studied further since it does not help to understand the role of the horizontal tail and its influence. Looking at the following picture, one can see that usually, the centre of gravity and the point where the lift applies (called the aerodynamic centre) are not the same. This means that the lift generated by the wing creates an induced moment around the centre of gravity that one should add to the already intrinsic pitching moment due to the main wing (usually a pitch down moment for conventional airfoils).

Knowing that, it is possible to rewrite the two equations of interest including the contributions from the main wing and from the horizontal tail.

$$W+L_t=L_w$$ $$M_0+bL_t=aL_w$$

From these equations and the figure, it appears that the horizontal tail is used to generate a lift which induces a moment helping to balance the moments equilibrium and thus prevent the aircraft to spin on itself (pitchwise).

### Drawback and Solution

From both the figure and the equations it turns out that the lift contribution from the tail is usually negative, meaning that more lift from the main wing is needed to keep a trimmed (or balanced) aircraft. This drawback can be overcome by the use of a canard configuration instead.

### Lateral Stability

The same can be done for the lateral equilibrium and stability but there it is the vertical tail that is used. It is symmetrical so that there is no yaw induced and if there is some side force experienced, it will create a moment in order to reduce the side-slip angle.

### Comparison of Lift Created by the Tail and Main Wing

For a trimmed configuration, it is easy to see that the lift created by the main wing is more or less the one created by the tail plus the total weight of the aircraft, which gives an idea of the difference between the two forces.

There is nothing really wrong with the existing answers, but I feel that they don't really dig down to the core of the issue. But it is actually not so complicated ...

All that is required for static longitudinal stability is a lower lift per area on the horizontal tail than on the wing. Downforce on the tail helps, because then the lift at the tail is obviously lower than on the wing, but is not necessary. What counts is that the relative lift change at the rear lifting surface due to a change in the angle of attack of the whole airplane is higher than the relative lift change on the forward lifting surface. The mechanism is the same for conventional configurations, canards or even flying wings.

Say the airplane flies at the angle of attack $\alpha_1$ and is disturbed by a gust or a sudden control input, such that it assumes a higher angle of attack $\alpha_2$. Due to camber and a higher incidence, the lift curve of the wing (blue line) is shifted up relative to that of the tail (green line). Also, the downwash effect and the lower aspect ratio reduce the lift curve slope of the tail relative to that of the wing.

Now assume that the aircraft was trimmed in state 1, such that the moment from the small tail lift was equal to the moment of the much larger wing lift around the center of gravity. In state 2, the absolute lift change ∆L on the wing is much smaller relative to the lift at state 1 than on the tail, such that the resulting moment change produces a pitch-down moment. The same happens with a reduction of the angle of attack in state 2, only in reverse.

$$\frac{∆L_{Wing}}{L_{Wing}} < \frac{∆L_{Tail}}{L_{Tail}}$$

If the lift ratios would be equal for wing and tail, the balance of moments would not change between state 1 and state 2. But since the tail experiences a higher relative lift change, a moment change follows which works against the change in angle of attack.

This effect also works for a canard, where the lift per area on the foreplane needs to be bigger than the lift per area on the wing. For a flying wing the the lift per area of the forward part of the wing needs to be bigger than that on the rear part of the wing, and still static stability is possible.

A wing with a conventional aerofoil profile makes a negative contribution to longitudinal stability. This means that any disturbance (such as a gust) which raises the nose produces a nose-up pitching moment which tends to raise the nose further. With the same disturbance, the presence of a tailplane produces a restoring nose-down pitching moment, which may counteract the natural instability of the wing and make the aircraft longitudinally stable (much the same way a windvane always points into the wind). (From the Wikipedia page on tailplanes)

The tailplane does not produce any lift. You could say it produces a 'Negative Lift'. The reason many early aviators were killed is because the tailplanes produced lift in order to help the plane fly which would result in unrecoverable nose-up tailplane stall. Most modern aircraft are designed so that when the airflow decreases, the effect/momentum produced by the tail surface is decreased as to prevent the previously mentioned condition

• According to a book about the Wright Flyer, early planes were deliberately designed to avoid having them nose-down into a stall; that meant that stalls could not be recovered in the air, but tended to limit the speed at which the planes hit the ground. The first air fatality was a result of a broken control cable, which caused the plane to nose down into the ground, hitting it quickly, rather than stalling and hitting the ground slowly. – supercat Feb 28 '15 at 15:24
• @supercat: The first air fatalities were Pilâtre de Rozier and Pierre Romain. The first heavier-than-air fatality was indeed caused by a stall and the Wrights chose the canard configuration in the mistaken belief this would make just this kind of stall impossible. – Peter Kämpf Aug 13 '16 at 22:48
• according to how it flies, sec 6, the tailplane does not necessaraly produce "negative lift". It only needs a lower AoA. – Manu H Aug 14 '16 at 8:01
• @PeterKämpf: You mean it would make "nose-down" stalls impossible? The book suggests that they recognized that their design would create unrecoverable stall situations, and stalls were a frequent occurrence, but the first (and I think only) fatality in a Wright plane of that design occurred when a control linkage broke (which would be bad news in a plane of almost any design which lacked redundant control mechanisms). – supercat Aug 14 '16 at 19:08
• @supercat: No, it does not make "nose-down" stalls impossible. What prevented them from happening to the Wrights was their choice of the center of gravity - all early Wright flyers were statically unstable, and stalls would first occur on the main wing. By quickly commanding a nose-down moment with the unstalled and fully functional canard they could recover every time. – Peter Kämpf Aug 15 '16 at 5:48

The wings(which has a aerofoil cross section ) produce lift (basically a force that acts opposite to weight) which act at a distance from center of gravity (C.G) so the force gets transferred to C.G. as a force and moment(in clockwise direction) which lead to pitch up movement

To balance that moment tail are used the tail produce lift (small compared to that produced by wings) so if we transfer it to C.G. an force and moment (since it produce less lift it should be placed far from C.G) this moment acts in anticlockwise direction thus neutralizing the moment due to wings ...Thus making the aircraft stable ...

The absolute value of the lift generated by the tailplane varies and depends on the phase in which your plane is in that moment:

Takeoff (flaps extended): high drift
Climb (no flaps): mostly lift (not much)
Cruise (no flaps): drift
Landing (flaps extended): high drift

Due to the fuel consumption the weight of the plane reduces while flight. This may change the position of your center of gravity and this in turn will affect the absolute value of your lift/drift. Usually |drift| increases, in other words, while flight the lift of the tailplane decreases.

Some words to stability: Just think about equilibrium of moments.
The center of gravity is near the main wing. The high lift of the main wing is very near to c.o.g., the drift of the tailplane is rather far away from it. The sum of all moments equals zero, they will balance the plane if there are gusts etc.