WhistlePig Toys

The Wrights were Wrong

The Wright Brothers are justly lauded as meticulous, dedicated and skilled engineers. They were able to assimilate, collate, test, verify and falsify the disparate experiences of their contemporaries in flight. Where existing data were found to be in error, they found ways to do original research and produce their own data. They used data to bridge the gap between science and practice - to make definite predictions of lift, and drag, of strength and power. They tested their predictions, gained confidence until ultimately they were able to design the first powered, controllable airplane, and have it work as they planned.

They followed where the data led them - but sometimes it led them to dead ends. Two that come to mind are their choice to use anhedral, and not dihedral, and their belief that inherently stable airplanes were both hard to control and inefficent. We'll leave anhedral for another time, and talk about longitudinal stability.

Its important to understand the emphasis the Wrights placed on the need to effectively control the airplane. They had seen the difficulties other early aviators had and the dangers they experienced. Otto Lillienthal, an important pioneer, was killed when he lost control of one of his gliders. Lillienthal's method of control was to swing his weight to and fro to balance the plane, not unlike a modern hang glider.

The Wrights felt that there had to be a better way, by using control surfaces such as the rudder, "front rudder" (what we today would call a canard) and wing warping (similar to today's ailerons) set them apart and led them to success.

But it's clear that they felt that maintaining equilibrium, as they put it, was best acheived by the use of the controls, and not by any natual quality of the airplane. It's not that they thought it impossible to design a stable airplane, just that they felt there was a cost and that that cost was not worth the benefit.

But I wonder if they missed something about longitudinal stability.

In his address to the Franklin Institute in Philidelphia, on 20 May 1914, Orville discussed natural stability this way:

"Penaud's system consists of a main bearing surface and a horizontal auxillary surface in the rear fixed at a negative angle in relation to ahe main surface. The center of gravity is placed in front of the center of the main surace This produces a tendency to include the mahchine downwarnd in front and to cause it to descend. In descending the the aeroplane gains speed. The fixed surface in the rear, set at a negative angle, recieves an increased pressure on its upper side as the speed increases. This downward pressure causes the rear of the mahcine to be depressed tull the machine takes an upward course. This speed is lost int he upward course, the downward pressure on the tail is relieved and the forward center of gravity turns the course again townwards. While the inherently stable system will control a machine to some extent ,it depends so much on variation on course and speed as to render it inadequate to meet fully the demands of a practical flying machine."

In other words, Penaud's planes were conventionally arranged, with a big wing in front, a little wing, (tail) in back, and the center of gravity forward of the midpoint of the wing. The tail was arranged with the leading edge lowered.

One thing stands out: The idea that increasing speed is what raises the nose of an airplane disturbed from equilibrium. This is a common miscoception that persists even today. Is it possible that the Wrights didn't understand how a naturally stable airplane works?

Let's think about it a minute. Suppose the lift really acts in one place all the time on the main wing, and it's behind the CG. The lift would tend to push the nose down. The tail has lift acting downwards, which wants to lift the nose up. We can arrange things so this is in balance. What happens if it speeds up? The lift on each wing increases with the square of the speed - so each gets the same amount of additional lift - and the balance does not change.

What does happen is that the total lift, is now greater than the weight. The airplane accelerates upwards, so that the air now appears to the airplane to be coming slightly from above. This reduces the angle of attack. (The angle of attack is the angle between wing and air.) This does two things:

  1. The lift is reduced, and in fact will reduce to the point where the total lift equals weight again. The airplane, having acquired vertical speed will retain it as long as the speed stays constant.

  2. Magic occurs.

The magic is all in the natural stability of the airplane. Again, let's consider that the lift acts a fixed point on the wing. Aerodynamicists call this point the 'aerodynamic center'. It's a real thing, but a topic for another time.

The wing and tail are like a kid on a teeter totter. The main wing is a big kid, and so has to be close to the pivot to keep the balance. The tail is like a little kid, who has to be further back. The size of the kid times the distance to the pivot is called the 'moment' (or 'torque'). When the teeter-totter balances, the little-kid-moment is the same as the big-kid-moment.

For wings, instead of weight, the size of the 'kid-moment' is the number you get when you multiply:

the airspeed squared, the density of the air divided by 2 the size of the wing the distance from the aerodynamic center to the CG and the lift per degree of angle of attack times the angle of attack.

We've already seen that for balance purposes, the speed doesn't matter since any changes in speed affect wing and tail in equal proportion. Same with the density and the divide by two thing.

But the angle of attack has a profound effect. If we get rid of the stuff both the wing and tail have in common, this is what we have left:

Wing-moment: Size of wing * distance of wing * lift per degree * degrees angle of attack of wing

Tail-moment: Size of tail * distance of tail * lift per degree * degrees angle of attack of tail

Lets assume the lift per degree is the same for both wings. For fun we'll say its '1'., and that both the wing and the tail have the same angle of attack . We can see that a wing of size 2 times a length of 2 balances a tail of size 1 times a length of size 4 at angle of attack because

1 degree: 
    wing: 2 * 2 * 1 * 1 = 4 
    tail = 1 * 4 * 1 * 1 = 4

2 degrees:
    wing: 2 * 2 * 1 * 2 = 8 
    tail = 1 * 4 * 1 * 2 = 8

In that case the teeter totter is always balanced.

But lets say the tail is further away, call it distance 6:

1 degree:
    wing: 2 * 2 * 1 * 1 = 4 
    tail = 1 * 6 * 1 * 1 = 6 
2 degrees: 
    wing: 2 * 2 * 1 * 2 = 8 
    tail = 1 * 6 * 1 * 2 = 12

The tail moment is bigger and it wont balance. Or will it? What about zero degrees?

0 degrees: 
    wing: 2 * 2 * 1 * 0 = 0 
    tail = 1 * 6 * 1 * 0 = 0

There we go. However, at zero, there's no lift on either the wing or the tail, which means the airplane is balanced, but it's not flying.

Can we fix it? Sure. Lets just change the angle of the wing so what when that angle of attack of the tail is at 1 degree, the wing is at 2 degrees:

1 degree:
    wing: 2 * 2 * 1 * (1 + 1) = 8 
    tail = 1 * 6 * 1 * 1 = 6

(with tail neg incidence:)
    wing: 2 * 2 * 1 * (1 ) = 4 
    tail = 1 * 6 * 1 * (1 - 1 ) = 0

2 degrees: 
    wing: 2 * 2 * 1 * (2 + 1 ) = 12 
    tail = 1 * 6 * 1 * 2 = 12

(with tail neg incidence:) 
    wing: 2 * 2 * 1 * (2 ) = 4 
    tail = 1 * 6 * 1 * (2 - 1 ) = 6

Wait a minute - at 1 degree, it's not balanced, but at two degrees it is balanced. Even more interseting, at 1 degree, the wing moment is bigger, so the wing will want to move the nose up towards two degrees.

What happens if we get to three degrees?

3 degrees: 
    wing: 2 * 2 * 1 * (3 + 1) = 16 
    tail = 1 * 6 * 1 * 3 = 18

(With tail neg incidence; Notice that the wing is at 3, and the tail is at 2))

    wing: 2 * 2 * 1 * (3 ) = 12 
    tail = 1 * 6 * 1 * (3 - 1 ) = 12

Now it's out of balance the other way. The tail wants to push the nose down towards two degrees.

The moments due to the wing and the tail are only equal at one angle of attack - if that's not magic, it's pretty close. (and just to be totally clear - the trim angle is the angle of attack of the wings, not the fuselage.)

That special angle of attack is called the trim angle. So once the airplane has pitched to that angle of attack, the pitch will stop. If it's still going fast, the increased angle of attack will cause acceleration, which reduces the angle of attack, which cuases the nose to pitch up and so on.

If you've ever tossed a model glider really hard, you know what happens next. The airplane loops the loop, if you throw it hard enough.

Of course, in a glider, the speed doesn't remain constant. Drag will slow it down, and as the airplane climbs it will slow down too. Howver, no matter what happens to the speed, the wing and tail will seek to balance at that trim angle of attack, and the speed will adjust itself till lift equals weight, and on the airplane sails.

Watching a little balsa glider ride the air and effortlessly correct each bump truly is magical to see.

And interestingly, rather than the speed varying, once the plane has settle to it's trim speed, it remains constant, since only one combination of speed, size and angle of attack will make exactly enough lift to equal weight. Small bumps are corrected with hardly any change in speed at all. (It is true that sometimes it takes a long time for the plane to settle to its trrim speed, and it can slowly rise and fall like a roller coaster, slowing at the top an speeding up at the bottom.)

Of course, the Wrights were right that there is a price to pay for stability. Anything that makes lift also makes drag, so the tail adds to the drag of the airplane, and the more stable the plane is the larger that drag will be. Also the more stable an airplane, the more control effort is needed to maneuver it. However there is a happy medium between the extremes that most airplanes used that gives a good combination of natural stability and maneuverability. There's a whole history to how "good enough" came to be - but that's also a story for another day.