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Principles of Flight-3. Forces in equilibrium Newtons First Law A body at rest or moving in a straight line at a steady speed has the forces acting upon it in equilibrium.

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Principles of Flight-3

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Principles of flight 3

Principles of Flight-3

D S Puttock Based on the work of W G Scull


Principles of flight 31

Forces in equilibrium

Newtons First Law

A body at rest or moving in a straight line at a steady speed has the forces acting upon it in equilibrium.

A body at rest or moving in a straight line at a steady speed has forces acting on it in equilibrium or it requires an equally applied force to change that state.

These two statements are Newtons’s 1st Law the diagram will make it clear what is meant.

It represents a body resting on a level surface: the weight of the body presses down on the surface and the surface resists the force. If you like, it pushes back up with an equal and opposite force.

The second state referred to is a body moving in a straight line at a steady speed---which is a glider in flight.

Principles of Flight-3

D S Puttock Based on the work of W G Scull


Principles of flight 32

Forces in steady flight

The upper diagram shows a state of equilibrium. The upward force equals the downward force and these two forces are the ones acting on the glider in steady flight and even though the forces are acting up and down, the movement is taking place down the glidepath.

As we have already seen, the total reaction can be divided into two: lift and drag and this has been done in the lower diagram. This time the resolution has not been shown. Illustrated like this, the equilibrium is much less obvious. Many people are confused at the lack of force acting in the direction of motion---particularly when drag is shown opposing motion.

Principles of Flight-3

TR

W

L

D

W

D S Puttock Based on the work of W G Scull


Principles of flight 33

Forces in steady flight

What has been done here, is the resultant of L&W has been determined, giving a forward component “T”.

Remember though, we started with L,D,W, and T is now replacing L&W.

T and D are in equilibrium.

Principles of Flight-3

T = resultant of L&W

L

D

T

W

D S Puttock Based on the work of W G Scull


Principles of flight 34

TR

W

Principles of Flight-3

  • Three ways of showing the forces acting on a glider in flight

L & D together

Equal and opposite to W

L

D

D

T

W

T equal and opposite to D

TR equal and opposite to W

D S Puttock Based on the work of W G Scull


Principles of flight 35

“The ratio of lift to drag is a measure of the efficiency of a wing”

The line AB is the horizontal, and AC represents the flight path of the glider and the angle at A (BAC) is the glide angle. The point C is the point at which the total reaction acts (Centre of pressure) and the total reaction , line CT , has been resolved into its two parts lift and drag. Weight has been omitted, but acts along the line CB.

We want to prove the glide angle BAC is the same as angle LCT.

T

L

C

A

B

Principles of Flight-3

D S Puttock Based on the work of W G Scull


Principles of flight 36

“The ratio of lift to drag is a measure of the efficiency of a wing”

Consider this first

ΔLTC & ΔABC are similar triangles.

The sum of the angles in a triangle =180°

CLT and ABC are both 90° angles

T

L

C

A

B

Principles of Flight-3

D S Puttock Based on the work of W G Scull


Principles of flight 37

“The ratio of lift to drag is a measure of the efficiency of a wing”

BAC +ACB + 90°=180°

BAC +ACB = 90°

But:

LCT + ACB + 90°=180°

LCT + ACB = 90°

Therefore:

BAC = LCT

The more we reduce drag, or increase drag, the shallower the glide becomes

T

L

C

A

B

Principles of Flight-3

D S Puttock Based on the work of W G Scull


Principles of flight 38

The point through which TR acts is called the centre of pressure.

The point through which W acts is called the centre of gravity.

The centre of pressure moves as the angle of attack is changed.

Principles of Flight-3

Total reaction

Centre of pressure

Centre of Gravity

Weight

D S Puttock Based on the work of W G Scull


Principles of flight 39

The top diagram reminds you that the greatest pressure reduction is at the narrowest point of the venturi.

The 2nd diagram shows that as the angle of attack is increased the throat of the venturi moves forward.

The 3rd diagram shows the reverse is true, as we reduce the angle of attack.

So increase the angle of attack—CP moves forward, decrease angle of attack CP moves back.

Principles of Flight-3

Centre of pressure movement

AoA increased

AoA decreased

D S Puttock Based on the work of W G Scull


Principles of flight 310

This graph shows the chord-wise position of CP for the range of angles of attack. (generalisation only)

Note that the CP moves aft again at angles beyond stalling angles.

Principles of Flight-3

Angle of Attack

-5 0 5 10 15 20

20 40 60 80

% of chord

D S Puttock Based on the work of W G Scull


Principles of flight 311

This slide shows 2 situations---in the first TR and W are co-incident.

In the 2nd,the angle of attack has been increased, which has caused the CP to move forward. This will tend to cause the wing to pitch up further, which will move the CP forward again.

This shows the wing on its own is unstable, to make the glider stable we introduce the tailplane.

Principles of Flight-3

Instability of the wing

TR

W

Airflow

TR

W

D S Puttock Based on the work of W G Scull


Principles of flight 312

The purpose of the tailplane

The purpose of the tailplane is threefold

Principles of Flight-3

Balance

Stability

Control

D S Puttock Based on the work of W G Scull


Principles of flight 313

With a heavy pilot the Cof G moves forward

With a light pilot of C of G moves aft, there must therefore be a lifting force on the tailplane.

To achieve either of these effects, will need a slightly different elevator position.

Principles of Flight-3

Tailplane---Balance

Heavy pilot

Light pilot

D S Puttock Based on the work of W G Scull


Principles of flight 314

In the upper diagram TR and W are coincident.

When we increase the angle of attack, the Cp moves forward tending to pitch the glider nose up—but the increased lift generated by the tailplane will compensate by tending to pitch the nose down.

Principles of Flight-3

The tailplane--stability

D S Puttock Based on the work of W G Scull


Principles of flight

Stability

The small force on the tailplane is working at a relatively large distance.

Principles of Flight

TR

Small force

Small distance

Large distance

If the nose-down moment from

the glider is greater than the nose-up

moment from the wing, the glider is stable

D S Puttock Based on the work of W G Scull


Principles of flight 315

Principles of Flight-3

  • Test

  • Show three ways of representing the forces on a glider in steady flight.

  • Draw a diagram to show that the glide angle is the ratio of lift/drag and prove this.

  • Show why the centre of pressure moves and relate this to the angle of attack.

  • Why is a wing unstable?

  • Show how the tailplane provides stability; what other purposes does a tailplane have?

D S Puttock Based on the work of W G Scull


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