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Flying in a plane through turbulence can be a bit nerve wracking experience for some.

Hearing that announcement bell ring followed by the pilot calmly saying that you are approaching

“rough air”. You fasten your seat belt, the plane starts shaking, and to those who

have a fear of flying, this can be terrifying.

Knowing that the plane is specifically designed to deal with these disturbances without ANY

input from the pilot, may or may not ease your fears, but that is exactly what they

do.

Every passenger plane is designed with something called static stability. Static stability

essentially means that an aircraft, left to its own devices flying in a straight level

flight, will return to straight level flight even when it is knocked off course. This makes

them much easier and safer to fly without having to constantly adjust the control surfaces

to balance the plane.

Yet, the exact opposite is true for fighter aircraft. Any aircraft designed for air to

air battles are designed to be capable of out maneuvering their opponent, and one of

the factors that affects a planes ease of movement is how stable it is. Or in other

words how unstable it is, and thus how ready it is to deviate from a straight and level

flight with minimal force. I noticed with my recent video, detailing the physics behind

the forward swept wing, that there is a general misconception floating around the internet

surrounding the notion of instability in fighter aircraft. In my description of the X-29 I

mentioned that the plane was TOO unstable.

Which was met by a mountain of comments saying this was a good thing. The more unstable the

aircraft the more maneuverable it is, surely. That is a hot take from people who have not

studied stability and control of aircraft in depth, so let's see why this is a nonsensical

approach to aircraft design. Let's think about this with a simple analogy.

Here we have two situations, a ball placed on top of a hill and a ball placed in a valley.

If we push the ball on top of the hill, even a tiny bit, it will begin to accelerate down

the hill and will not stop until we put energy in to slow it down, AND we will need to put

even more energy in to return it to the top of the hill. This is an unstable system.

The opposite is true for the ball in the valley. Apply a force and the ball will roll uphill

and gravity will now provide a restoring force to bring it back. It may oscillate back and

forth a few times before coming to a stop, but it will eventually return to its original

position. This is a stable system.

So how does this apply to planes? Planes have three rotational degrees of freedom, pitch,

roll and yaw. Let's first approach this problem with regard to pitch stability, which

was where the X-29 was extremely unstable.

Small general aviation planes like Cessnas, are designed to be very stable, and so return

to level flight automatically after they are knocked up or down by a gust of wind, but

do they manage this?

Pitch stability is determined by 3 primary factors. The location of the centre of gravity.

The location and design of the wing, and the location and design of the horizontal stabiliser.

The centre of gravity for our cessna is located about here. This is point which all lift will

act around, it's like the fulcrum on a see-saw. Our wing is located slightly behind this,

and thus the lift it generates is slightly aft of the centre of gravity. This would force

the plane to pitch downwards without a counteracting downwards force further back on the plane,

which is exactly what the horizontal stabiliser provides, a downwards force. This force does

not need to be of the same magnitude, as it has greater control authority as a result

of it's greater distance from the centre of gravity. Once again, just like a see-saw.

This is how a plane maintains pitch stability without any outside influences, but what happens

if turbulence knocks our plane off balance. If the forces remained the same, the plane

would continue on in whatever orientation the gust knocked it into. That is not what

happens. Just like our ball in a valley example, we have a restoring force to bring the plane

back to its original position.

This is a result of how our horizontal stabilizers downforce changes with the pitch of the plane.

There are two primary factors that influence this, the first is downwash. When air passes

over the wings it is deflected downwards, this creates a downwash of air behind the

wing. This downwash strikes the top of the horizontal stabilizer, and this produces a

downward pressure.

The magnitude of the downforce on this surface is dependant on downwash, and the magnitude

of the downwash is dependant on the speed of the aircraft. The faster we go the more

air is deflected downwards, the slower we go the less air is deflected.

Luckily, our speed is also dependent on our pitch. If the plane pitches upwards it will

lose airspeed and the downforce on the horizontal stabilizer decreases. As a result, the weight

of the plane acting through the centre of gravity forward of the centre of lift, now

wants to move its nose down again.

The opposite happens when we pitch the nose down. Here we gain airspeed and the downwash

on the horizontal stabilizer increases, causing the downforce to increase. Forcing the plane

to nose up again.

This explanation is often provided as a complete explanation, but it falls apart when you consider

a t-tail configured plane where the horizontal stabilizer is lifted out of the downstream

airflow of the wing. Here our other factor comes into play, as a result of the angle

of attack of the horizontal stabilizer.

Here the horizontal stabilizer has a negative angle of attack. This angle of attack changes

as the plane pitches up or down. If we pitch it up the angle of attack decreases, and thus

the downforce decreases, allowing the weight of the nose to pull it back down. If the plane

pitches down the angle of attack increases, and increases the downforce, which forces

the tail of the plane back down.

This is an elegant solution to the problem, which is thrown out the window for planes

like the X-29.

Here we have the forces acting upon the X-29 in the longitudinal plane. The centre of gravity

and centre of lift have shifted backwards as a result of the forward swept design, and

thus in order to stabilise the plane the canards need to produce lift ahead of the centre of

gravity. This is fine in level flight with no disturbances, but what happens when if

we pitch upwards? Here there is no downwash that shifts to increase downforce on the stabiliser.

increased pitch, which increases the lift forward of the centre of gravity, which pitches

the nose up even more. And thus, for a very small energy input we could pitch the plane

a tremendous amount, just like giving that ball on the hill a little nudge.

This is great when you want to pitch the plane wildly, but that's not always the case.

To achieve level flight, the X-29s control computers had to be constantly adjusting to

compensate for little disturbances. Up to 40 times a second. This isn't a huge deal,

especially with today's computers. That is not why the X-29 was too unstable.

Let's take it back to our ball and hill analogy and think about this as an energy

problem. If we push this ball and it begins to fall. The steepness of the hill will determine

not only how quickly it deviates away from its original position, which is our analogous

for maneuverability, but it also affects how much energy we have to put in to roll it back

up the hill to return it to its original position.

This is a problem, because our original position is straight and level flight, and we are going

to want to return to it at some point. So, if we make this hill too steep, we have to

apply an excessive amount of force to get back to our original position, exactly the

problem we are trying to solve with introducing instability, where we have to apply energy

to push the ball up the valley walls.

We introduce instability to reduce the energy and time required to maneuver not increase

it, and in a worst case scenario we won't have the energy required to return to a straight

and level flight and end up in an unrecoverable situation.

In an air to air battle, energy isn't just a fuel burning problem, it's a speed problem.

Our energy source for maneuvering is our kinetic energy, our speed. To change our orientation,

we have to extend our control surfaces into the free stream. Which creates drag, which

saps our speed. Fighter pilots have a saying. “Speed is life”. Speed and maneuverability

is what wins a dog fight.

In reality, we want to achieve something between a nice level field, where the energy to shift

the ball is the same in all directions, and the ball on the hill scenario, where we don't

have to apply a huge amount of energy to get the ball to move. Visualising that with a

plane would look something like this. This line would be statically stable, where the

plane naturally wants to return to its level flight. This is statically neutral, and this

is statically unstable.

The F-16 was the first plane to enter wide service that was deliberately designed to

be unstable. Departing from many of the design principles that influenced planes like the

F4 Phantom, it's older brother. The F4 was found to have roll instability during wind

tunnel testing, so the engineers added a 12 degree dihedral to the wing tips to increase

its roll stability and the F4's horizontal stabilizer generates downforce in a similar

way to our example earlier, creating a longitudinally stable plane. The F-16 in comparison had a

noticeable straight wing, making more or less statically neutral in roll, like our ball

in the flat field.

The F-16 also shifted it's centre of gravity rearward behind the centre of lift and necessitating

a horizontal stabiliser that produced lift. Making it unstable in pitch, albeit nowhere

near as unstable as the X-29. Producing a plane that is unstable enough to allow for

energy efficient maneuvering.

This is a complicated topic, with a huge number of variables that I haven't mentioned here.

For example, the centers of lift for a wing tends to shift forward with an increased angle

of attack and with supersonic planes the centre of lift shifts as it goes from subsonic to

supersonic flight. There is a lot more to this problem than you are going to get from

a YouTube video, and many of my viewers are actually students and practicing engineers

who are likely to use this video as inspiration to go and learn more about the subject, and

to keep track of all the variables you will probably need a notebook.

While I was studying and working as a research and development engineer, I always wanted

nice moleskine style notebooks that had graph paper instead of lined pages. I could never

find one I liked, so I have decided to just make my own. The only way I could do this

without spending an absurd amount of money was to buy in bulk. I have already sold about

half of them from a community post, SO if you act quickly you can buy some of these

limited availability notebooks for yourself. I wanted to keep these a reasonable price

in relation to normal moleskine notebooks so the margin on these are small, so we may

or may not do another printing run, but if people like them and we can afford to print

a couple of thousand off we can look into it. Just let me know on twitter, which you

can find the link to below.