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

Definitions of Relative Wind, Lift, Weight, Drag, Thrust, and Side Force

The five aerodynamic forces acting on an airplane are:

  1. Weight
  2. Lift
  3. Drag
  4. Thrust
  5. Side force

To define these terms we must first define another term called Relative Wind.

 Airfoil

Relative Wind

All motion of an airplane that is relevant in aerodynamics is motion through the air. The air itself may be moving over the ground, and that is called wind. But the airplane does not experience wind. An airplane is like a fish swimming in a river, or lake, or ocean. If the water is moving the fish does not know that, it just drifts along with the current. The IFR navigation section of ProfessionalPilot.ca has some interesting simulations that further clarify this point.

When a model airplane is placed in a wind tunnel a fan is used to blow air over the model. The model itself does not move. When an airplane flies through the sky the air as essentially a stationary gas (it is recommended that you completely forget about wind) through which the airplane moves. But from the airplane's perspective the situation is just like the wind tunnel. The air appears to flow over and around the airplane in EXACTLY the opposite direction and speed to the direction and speed of the airplane's motion. This apparent airflow is called the Relative Wind.

All of aerodynamics depends on the relative wind. The relative wind is always equal to the true airspeed (TAS) but in the opposite direction. I have heard many amusing arguments as pilots try to convince each other that groundspeed is the proper measure of energy, but this is totally wrong. All energy measurements are relative to a frame of reference. When you drive a car the frame of reference is the earth, because it is the earth that supports the car and from which friction is used to move and stop it. We don't expect to have worse accidents if we crash going eastbound than westbound even though we could say we are driving backwards when eastbound, due to the earth's rotation. Similarly the airplane does not climb faster, or carry more weight with a headwind. It is an AIRplane, and as such its motion must be measured relative to the air. The only time groundspeed matters is for determining range, or when crashing (because at the moment of the crash the AIRplane stops flying, and becomes a GROUNDplane - so, don't ever crash with a tailwind.)

In summary then:

Relative wind is the airflow opposite to the direction of flight and equal in magnitude to the true airspeed.

Weight

Of the five forces above two are defined by their orientation to the relative wind, and two by their orientation to the aircraft axis. Only weight is is defined relative to the earth. Weight is by definition the force caused by gravity, and it therefore acts directly toward the center of the earth. The words up and down are also defined relative to the direction of gravity. Therefore we can say truthfully that weight always acts down.

Weight is calculated as: W = mg [m is the mass the airplane, and g is the acceleration due to gravity.] As anyone who took high school physics knows g changes with altitude, but the value of g changes only minutely between sea level and 100,000 feet. Remember that the radius of the earth's sphere is over 24 million feet, so flying at 50,000 feet doesn't change the force of gravity significantly (less than .01% change in your distance from the center of the earth.) We will therefore assume that airplanes have a weight that does NOT change with altitude. The only thing affecting the weight of an airplane is the load of fuel, cargo, and passengers.

In summary then:

Weight is the force caused by gravity acting on the mass of the airplane. It is calculated as W=mg, and acts downward, toward the center of the earth.

Lift

The lift force acts in the plane of symmetry, as defined on the previous page. By definition lift is the force acting at right angle to the relative wind.

In the simulation to the left the airplane is exactly in level flight. We know that by the blue relative wind vector, which is horizontal. If the airplane was climbing or descending the relative wind vector would not be horizontal. Always remember that the relative wind is exactly opposite to the direction of flight.

You can cause the airplane to pitch nose up or down using the up and down arrow keys - just like an aircraft joystick. Assume that the power is adjusted for you. The simulation shows the airplane speed up and slow down, but it ALWAYS flies level. I.E. the relative wind vector never changes from horizontal. Therefore the lift vector never changes.

Lift is defined as the force that acts perpendicular to the relative wind, and in the plane of symmetry.

Drag

In the simulation to the left you can speed up and slow down using the up and down arrow keys, just like the simulation above.

The black arrow represents the drag, which is proportional to true airspeed squared. The drag vector is NOT to scale, as you will see in the section on thrust below. The important thing to note here is that drag is always parallel to the relative wind, which means it is perpendicular to lift.

Drag is defined as the force that acts parallel to the relative wind. That is to say opposite to the direction to flight.

Thrust

The simulation to the left shows the relationship between thrust (black vector with white outline) and drag. It also shows that thrust provides some lift as the airplane slows down.

The engines are usually mounted parallel to the longitudinal axis, as shown in the simulation . This way the thrust vector will be exactly level when the airplane is in cruise (Pitch = 0.) When the airplane slows down the thrust vector is tipped up slightly helping to support the weight, reducing the amount of lift the wings must produce. The simulations above do not take this effect into account, but the one to the left does.

You can increase the angle of attack(AOA) using the up and down arrow keys. Notice the readout of weight, which remains constant at 1860 lb and notice that as AOA increases a small amount of thrust helps lift the airplane.

The horizontal black line marks the starting lift, which equals weight at 1860 lb. You can see that the reduction of lift as the airplane slows down is NOT significant. If you watch closely you will see that the minimum drag occurs at AOA=3.5 deg. At that AOA lift due to thrust is only 8.3 lb. Notice also that total thrust at 135.8 lb is only 0.2 lb more than drag. Later, in the performance chapter, I will ask you to accept the simplification that thrust equals drag, and lift equals weight. Neither of these is strictly true, nor are they acceptable as definitions, but as this simulation shows they are sufficiently good approximations for most purposes.

 

NOTE: In the simulation the thrust and drag vectors are multiplied by a scale factor of five, otherwise they are so small you can hardly see them. Use the button at the lower right to change to true scale to see how small the thrust and drag vectors are compared to lift.

By definition:Thrust is the force produced by the engine(s).

Because the engines on almost every airplane are mounted in or parallel to the plane of symmetry we can assume that thrust acts in the plane of symmetry. (In reality the engine is often mounted a degree or two out of alignment with the plane of symmetry, especially in single engine propeller airplanes. This is done to help counteract the asymmetric thrust and slipstream effects that tend to make an airplane turn when power is applied. We will discuss these factors in the final page of this chapter. The extent of any side force created by this small misalignment is so minor that we will consider it to be zero.)

Note that when an airplane has more than one engine these are almost always distributed symmetrically about the plane of symmetry (i.e. one left and one right engine equidistant from the plane of symmetry) so that the sum of their thrust vectors act in the plane of symmetry. When an engine fails on a multiengine airplane the thrust vector is no longer in the plane of symmetry, but it is still parallel to it. However, when the pilot uses the rudder to counteract the resulting yaw moment a sideforce is created (by the rudder.) We will look at sideforce next (and this will be a major point of our discussion in the multiengine chapter.)

 

Side Force

Previously we defined Lift as acting in the plane of symmetry. We also said just above that thrust acts in the plane of symmetry also. It is important to note that drag is defined as acting in the direction opposite to flight, so if the airplane is flying sideways through the air there is a component of drag acting across the plane of symmetry, i.e. a sideforce. The resultant flight path is called a sideslip.

In a bank there is obviously a component of gravity acting as a sideforce, but in a normal turn the centripetal force exactly counteracts that gravitational force resulting in no net sideforce. In other words, when we make turns in airplanes we want the situation to be like riding a bicycle, where we are in balance, not like a car, where passengers are pushed to the outside of the turn.

99.9% of the time we do NOT wish to slip. In other words we don't want there to be any sideforce. When there is a sideforce you can feel it "in the seat of your pants." You feel yourself being pushed sideways (left or right) in your seat. If you have done any amount of flying you know that to create this feeling you use (or misuse) your rudder pedals.

In the simulation to the left the A-key and D-key are the rudder pedals. If you use them you can create a sideforce.

You can also use the left and right arrow keys to roll into a bank.

The picture to the left shows a slipping turn. The pilot has rolled into a right bank then applied left rudder (opposite to the direction of turn) so that the airplane turns more slowly than it would with no side force. The green vector represents the sideforce. The orange vector is the actual force produced by the wings. Remember that lift is defined as being in the plane of symmetry (i.e. parallel to the normal axis) therefore the red vector is defined lift. The sum of lift and sideforce is the total force actually produced by the wings (i.e. the orange vector.)

 

The picture to the left shows a skidding turn. Can you see the difference between this and the slipping turn shown above?

The key to remember is that the orange vector represents the total force. In this case the total vector is tipped more than the lift vector. This pilot is applying rudder in the same direction as the turn (a very dangerous thing to do.) The result is called a skid.

You can explore all these situations with the simulation above.

The picture to the left shows a forward slip. In this case the pilot has rolled in 30 degrees of bank but applied enough opposite rudder so that the net force is vertical. The result is that this airplane isn't turning, it is just slipping forward through the air.

This technique can be used to lose altitude because drag is increased substantially. It it also be used to land with a crosswind. We will discuss this more in the drag chapter.