Air is invisible. An airplane moves through the air. So you can see that an airplane is moving – relative to you – but you can’t see how it is moving relative to the air.

Actually, you can. But it takes a bit of work. You have to stare at the airplane and mentally take a video of its motion. Then your brain can compare frames of the video. Mentally, you draw a line joining all the positions of the airplane, and project that line ahead to see where it is going.

But is that the same as where the airplane is pointing? No. Almost never. There’s the rub.

What do the flying surfaces do?

• the wing generates lift

• the horizontal tail generates lift (usually downwards. This gives the airplane stability.)

• the vertical tail (and the horizontal tail) are like tail feathers on a bird or a dart. They keep the nose pointing forward

What do the controls do?

The stick, or the control yoke or control wheel, controls lift:

• where the lift is pointing

• the amount of lift generated

The rudder pedals:

• steer the airplane on the ground (with the help of linkages to nose/tail wheel)

• allow the airplane to fly slightly sideways when necessary (or correct to fly straight)

The throttle (gliders don’t have one):

• controls how much energy is added to the system (the flying airplane)

Equilibrium

Remember the four forces? And how when thrust = drag, and lift = weight, the aircraft is in equilibrium? Crazy though it may seem, the airplane can be in equilibrium (that means the forces are balanced) in a climb or a descent or a glide, as well as when flying straight and level. The secret is this:

No force, no acceleration

That’s Newton’s first law, which says:

A body in motion will remain in motion in a straight line, unless acted on by an external force.

So as pilots, what can we learn from this that is of practical use?

If we are happy with what the airplane is doing, don’t change anything.

In other words, keep the forces balanced. Stay in equilibrium. That will ensure that the airplane flies in a straight line, whether it is climbing or gliding or staying at the same altitude.

The Flight Path Vector

Here is where we have to start thinking about stuff we can’t see. We have to see in our heads (imagine) where the airplane is going and how fast. Here is an example (in 2D) of a jet on final approach. It is pointing slightly down (maybe 1°) but its flight path is three degrees lower than that. The pilot sees that in her head. She knows the airplane is pointing almost level, but that it is descending a slope toward the runway, represented by the arrow.

That imaginary arrow is called a vector.

A vector has both speed and direction. A long arrow means fast; a short arrow means slow. In each case the arrow is pointing somewhere in 3D. Straight up. Straight down. Or, more usually, parallel to the earth’s surface (OK, tangent to it) in some direction (North, East, etc.). Pilots call this the flight path vector. In equilibrium, this vector does not change. Why? Again, Newton’s First Law: there is no force acting on the vector. (True, there are four, but they are balanced).

So as long as we are happy with where the airplane is going, we don’t have to change anything. But we have to imagine where it is going, because we can’t see that directly. We have to watch the scene change (a video, not a snapshot) to get the idea.

Potential Energy and Kinetic Energy

A theoretical digression is in order here. But why? What does it do for pilots?

Well, we are flying an airplane which is:

• moving fast, and
• suspended above a large body (earth) to which it is being attracted (gravity)

A body that is moving is said to possess kinetic energy. It took energy to accelerate it to that speed, and that energy is still there.

A body that is in the gravitational influence of another (larger) body is said to have potential energy. It took energy to move away from the larger body (climb), and that energy is still there. Without lift, the airplane would fall to the ground, accumulating more kinetic energy as it fell.

There is a principle here that is very useful to pilots: kinetic energy can be traded for potential energy, and vice versa. And it is the pilot who controls the trade.

Becoming a glider

A case comes to mind where the pilot has no choice but to make that trade: engine failure.

The engine quits, and the thrust vector (yes, forces can also be depicted as vectors) disappears. Obviously (in the equilibrium diagram above), if nothing is done drag will slow the aircraft. And since lift depends on speed (the square of speed, actually) lift will decrease and gravity will pull the airplane down.

That’s OK as far as it goes – as long as it descends under control and not too fast. But here is where we have to use our imagination again to see the invisible: how the airplane is meeting the air. The airplane is still level (long axis parallel to the horizon) but it is descending. There is a difference between where it is pointing and where it is going.

You can see that the air is meeting the wing at a large angle. This angle is called the Angle of Attack. We remember (from How an Airplane Flies) that as angle of attack (AoA) increases, so does lift – up to a point. That point is about 16°. Here is the lift vs angle of attack diagram:

You can see that the jet airplane in the picture above is meeting the air at an angle well above 16°. It is falling, not flying. The wing is creating mostly drag. That is what happened to Air France 447 over the Atlantic Ocean. Its AoA was more than 40° – well off the above chart.

So with our engine failure, what do we do? What is the solution?

We point the airplane down. We point it closer to where it is going. We make the AoA less than 16°. The airplane is now flying again, and sliding downhill. Gravity is being used to overcome drag. We are using some of our potential energy (altitude) to maintain our kinetic energy (airspeed). We have become a glider.

(To be fair: most airplanes have longitudinal stability. In the above situation they would nose down on their own. The pilot in this example obviously made a mistake by trying to hold the nose up. In real life this has happened in three famous accidents: Colgan 3407, Air France 447, and Asiana 214.)

There is a lesson here:

To control the airplane, point it in the right direction.

Acceleration

What if we want to change where the airplane is going? Another way of saying the same thing is: how do we change the aircraft’s flight path vector?

You won’t be surprised to learn that Isaac Newton has the answer: you apply a force. He derived the equation, too: F = ma. That says that the force required is the product of the mass of the object (airplane) and the acceleration required.

Acceleration is defined as change in velocity. (This is a consequence of the Calculus,invented independently by Newton and Leibniz.)

But velocity can be changed in different ways, depending on how the force is applied. If you think of the flight path vector, that arrow in 3D, imagine a force applied along the axis of the arrow: that will change the length of the arrow (the speed). But if the force is applied at an angle, it will change the direction the arrow is pointing. In both cases, the force is producing an acceleration.

An acceleration can be either a change of speed or direction. In vector representation, a speed change is a change in the length of the arrow. A change in direction is represented by a curved arrow.

Why do pilots have to know all this math? Well, perhaps we don’t, but we do have to know this:

These are the vectors representing a turning airplane. The white vector is lift (it is supposed to be at right angles to the wing). The orange vectors are components. You add vectors by putting the tail of one on the tip of the other. So the white vector is the sum of the orange vectors. The meaning of this diagram is that the pilot is using lift, the largest force he has at his disposal, to turn the airplane. He tilts the lift so some of it is acting sideways. Of course, if he doesn’t make lift larger, the airplane will descend. He has to make the vertical component of lift the same as it was before the turn began: equal to the weight of the airplane. So he pulls back on the stick to make lift larger.

The yellow arrow is the flight path vector. It is curved, because the airplane is changing where it is pointing. It is changing heading. It is no longer in equilibrium. It is accelerating.

Oops – a complication . . .

The complication is time. One of the things the Calculus is good for is depicting changes over time. In the above diagram, the sideways component of lift is acting on the aircraft’s flight path, changing its heading. As long as the airplane is banked, tilting the lift, the airplane will keep turning. Mathematically, as long as the force is applied the flight path vector will keep changing. There will continue to be acceleration.

I know that seems strange, because we associate acceleration with flooring the gas pedal in a car. But if we drive a car at high speed around a bend, we will be pushed sideways in our seats. That’s acceleration, too.

But with any acceleration the airplane is no longer in equilibrium. As long as the force is applied the flight path vector is in flux.

The change, though, takes time.

The result of a large force is usually obvious. A smaller force (say, a change in thrust of 5%) is less noticeable. We have to be watching for the change, expecting it. Because it doesn’t happen immediately.

This is a reproduction from my favourite book on flying: Stick and Rudder. It was written the year I was born – 1944. This illustration says better than thousands of words something basic about flying an airplane.

There are short-term and long-term results from moving the controls.

The practical question, though, is: How does a pilot learn what those long-term results will be?

The short answer is: trial and error. After all, that’s how the Wright brothers learned to fly. And even to this day, there are very few texts which address the issue.

Attitude Flying

If you don’t want to spend expensive hours learning by trial and error, the answer is attitude flying. Watch any good, experienced pilot, and it will seem like nothing is happening. The airplane will be rock-steady, as if on rails. Even (or especially) in bumpy conditions, if a gust lowers a wing or raises the nose the airplane will magically return to where it was before the gust. Watch an inexperienced pilot and you will experience the sensation of wandering vaguely.

Why is this happening?

The inexperienced pilot doesn’t know where to look. When a gust lowers the left wing, he doesn’t notice. The tilted lift vector tugs on the flight path vector, bending it to the left. After a while, the pilot says – hey! I’ve got to turn right!

He was watching heading, not attitude. The turn has surprised him. What is the takeaway?

Keep the wings level and the airplane won’t turn.

It is amazing how many low-time pilots don’t understand that.

. . . . . . . . . .

Part of the problem is that we don’t do much hangar flying anymore. Hangar flying is hanging around the airport and listening to the old guys’ stories. Some of those stories were pretty wild, and their basis in fact could sometimes get tenuous. But there were countless valuable nuggets, nonetheless. And listening to them was a lot cheaper than listening to inexperienced instructors at $$$/hour.

My old buddy and mentor (rest in peace, Dan) liked this version of a common nugget. He would giggle both at its bathroom humour and its fake math:

P + P = PP

Translated, that means:

Pitch + Power = Predictable Performance

This technique appears in many guises. In his book IFR: A Structured Approach, John C. Eckalbar calls it flying by the numbers. He advocates memorizing, for your airplane, a pitch attitude and a power setting for each of the phases of flight: climb, cruise, descent, approach, etc. This (recommended – see bibliography) book is about instrument flying. But the good news is that the technique is equally applicable to flying in visual conditions. The only change is that you look out the windshield to gauge pitch attitude.

We’ll explain attitude flying in the next article.