Secondary Index



Aerodynamics Index

Definitions

Aircraft Axis
CG definition
Define Up and Down
Define Pitch, Bank, Hdg
Define: Lift, drag, etc.
Define Power

 

Physics Review

Newton's First Law
Newton's Second Law
Newton's Third Law
Reaction = Lift
Reaction = Drag
Conservation of Energy
What is a Vacuum
Action at a Distance

The 4 Forces

Spotting Forces & Moments

Performance

Drag Overview
Induced Drag
Induced Drag Equation
Total Drag

Jet Climb Performance
Prop Climb Performance
Range Jet
Range Prop

Forces in a Turn

Misc

Pitch Controls
Roll Controls

Configurations

Defining Center of Gravity

The simulation to the left represents an experiment that you should perform. All you need is a piece of cardboard that you will cut into a random shape, similar to the one shown. Make the shape as irregular as you like. Don't try to copy the shape in the simulation, make yours distinctive.

Once you have a random shape punch several small holes around the edges. The shape in the simulation has four holes but you can make as many as you like.

Find a place where you can put a small nail in a wall to hang your creation on.

In the simulation you can pick up the object and hang it on the "nail" by any of its holes. Try it now. [release the object when you can see the red nail through one of the four holes near the edge of the object.]

You will notice that object swings back and forth like a pendulum (because it is a pendulum.) There is friction in the system so if you wait awhile it will stop.

When the object stops the center of gravity (c of g) is ALWAYS directly below the nail. On your object you won't know where the c of g is, so use a level to draw a vertical line from the nail down the object.

Take the object off the nail and hang it up by a different hole. Then draw another vertical line.

No matter what hole you hang it on the object always comes to rest with the c of g directly below the nail. All the lines you draw will cross at one point, and that point is the c of g.

NOTE: don't press the button labeled "Hang on C of G" yet. If you did, click the "Release from C of G" button.
generic shape

The picture to the left shows the object captured in mid swing. It explains why the object swings, and why it can only stop in one orientation.

When the object is oriented so that the c of g is NOT below the nail there is an "arm." An arm is simply the distance, at right angles to the force, to the fulcrum point. In this case the fulcrum point is the nail. The object is physically only able to rotate around the nail. The force is the weight of the object, which acts at the center of gravity. Indeed, that is the definition of c of g.

Center of gravity is the point at which weight acts.

When the c of g is directly below the nail there is no arm. When there is no arm there is no moment. Moment is calculated by multiplying force times arm.

Moment = Force x Arm

It is important to realize that a moment will ACCELERATE the object rotationally. Notice that the pendulum accelerates, reaching maximum speed at the bottom of each arc and slowing to a stop at the top of each arc.

Next we will explore the situation where the moment is zero.

Pin the Object at the C of G

Return to the simulation and click the button labeled "Hang on C of G." The object is now suspended on the nail exactly at its c of g. Consequently there is NO ARM and therefore NO MOMENT.

Turn the object to any angle you like - STOP it THEN RELEASE. The object can be stopped at any orientation you desire. There is no moment, so no tendency for it to accelerate, so the rotational velocity remains zero.

Now turn the object and release it WITHOUT STOPPING it (i.e. give it some rotational velocity.) Notice that it will rotate forever (there is no friction in this frame.) A physicist would say that there is no moment so the rotational velocity does not change over time.

It is crucial to realize that an object suspended at its c of g can be oriented to any angle and will happily stay there if stopped. It is also important to note that once rotating, an object suspended at its c of g will keep rotating forever, unless you reach in and stop it.

We have seen the simulation to the left before, but it should be starting to make more sense now. The airplane is "pinned" at the c of g so that it rotates freely around that point. Grab it with your mouse and rotate it. You can stop it at any angle, or start it rotating and it will keep rotating forever.

You might be thinking that it would be better to "pin" the airplane above the c of g so that it would naturally stay level. But that would not work well at all. If you did that you couldn't climb or descend (or flare to land, or rotate to takeoff etc.) No - to fly an airplane you need the airplane to turn into the wind, as shown in the next simulation.

 

The simulation to the left shows the airplane pinned at the c of g also. In this simulation the blue vector represents the wind. You can grab the wind with your mouse and rotate it. When you do the airplane turns with the wind remaining at zero angle of attack.

You can also grab the airplane and rotate it. When you do the tail strikes the airflow at an angle of attack so a force, shown as a green vector forms. As soon as you release the airplane this force rotates the airplane into the wind.

This is the way airplanes actually fly. You may have thought that you were pitching the nose up and down with the elevators, but actually you are not. The airplane is simply turning into the relative wind, as shown in this simulation. Over the span of the next two chapters we will thoroughly explore how we actually control an airplane.

In What Sense is the Airplane PINNED at the C of G?

The final question that is likely on your mind is; in what sense is the airplane pinned at the c of g? Obviously there is no nail that the airplane is hanging on. Actually there are only four forces acting on the airplane:

  1. Weight
  2. Lift
  3. Thrust
  4. Drag

Of these we know that weight acts at the c of g. The others could act anywhere, not necessarily at the c of g. For example the thrust line might be below the c of g, thus tending to pitch the nose up. On the other hand the lift vector might be behind the c of g, thus tending to pitch the nose down. And drag might be below the c of g on a low wing airplane, or above the c of g on a high wing airplane (who can say?) The one thing we know for sure is that the sum total of all these forces must add to a moment of zero (i.e. nose up and nose down moments must cancel each other out.) If they did not the airplane would spin like a crazy top pitching faster and faster and faster. Since we know that airplanes actually stay quite nicely in a constant attitude most of the time, and obediently pitch into the wind when we climb or descend we can reason in reverse and recognize that there must be no net moment.

Think back to the first simulation, with the odd shaped object hanging on a nail. Realize that there are TWO forces at work. One is the weight, which acts at the c of g. The other force is provided by the nail. The nail provides a force equal in magnitude to the weight, but in the opposite direction (i.e. up.) The nail provides that force at the hole where the object hangs on it. ONLY if the nail is at the c of g does the object behave like an airplane. So, we are back to asking - OK, so the nail that supports my airplane obviously acts at the c of g, but what is the "nail"?

The answer is that the sum of Lift, Thrust, and Drag must add up to a force that is equal but opposite to weight, in other words they must collectively act at the c of g. When they meet this criteria they collectively are the nail.

Exactly how the Lift, Thrust, and Weight come to act just where we need them to is the topic of the next two chapters. But, before turning to that we can learn a great deal about the relationship of Lift, Thrust, and Drag if we accept that they must produce no moment around the c of g. With that in mind we now turn to the next topic.