Lift and Drag component question

In summary, on page 20, the Lift and Drag components are geometrically explained. The symbols below are used: A=axial force and N=normal force. \alpha=angle of attack. L=N\cos \alpha - A\sin \alpha D=N\sin \alpha + A\cos \alpha I am having trouble understanding why this is true, and why they put the +/- where they did. I see that N\cos \alpha is equal to L, so why are we subtracting the A\sin \alpha ? Same goes for the equation for D. I am sure I am overlooking something very obvious here, but id appreciate
  • #1
NBAJam100
146
0
Hey guys,

I current picked up Fundamentals of Aerodynamics by John D. Anderson Jr. and am having a little bit of trouble understanding some of the equations i am given. This is the first aero book I've picked up so I am not too familiar with aero concepts or terms yet.

On page 20, they break down the Lift and Drag components geometrically. The symbols below are as follows: A= axial force and N=normal force. [tex] \alpha = [/tex] angle of attack.

They have:

[tex]L=N\cos \alpha - A\sin \alpha [/tex]
[tex]D=N\sin \alpha + A\cos \alpha [/tex]

I am having trouble understanding why this is true, and why they put the +/- where they did. I see that [tex]N\cos \alpha [/tex] is equal to L, so why are we subtracting the [tex]A\sin \alpha [/tex] ? Same goes for the equation for D. I am sure I am overlooking something very obvious here, but id appreciate someone helping me see it.

Thanks.
 
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  • #2
NBAJam100 said:
… I see that [tex]N\cos \alpha [/tex] is equal to L, so why are we subtracting the [tex]A\sin \alpha [/tex] ? …

Hi NBAJam100! :smile:

(have an alpha: α :wink:)

No, Ncosα is not equal to L, it's only the component of N is the L direction.

cosα -sinα
sinα cosα

is simply the transformation matrix for a rotation (from axes x,y to x',y') …

it converts the pair N,D from coordinates fixed in the aeroplane to horizontal and vertical coordinates. :smile:
 
  • #3
tiny-tim said:
No, Ncosα is not equal to L, it's only the component of N is the L direction.

cosα -sinα
sinα cosα

is simply the transformation matrix for a rotation (from axes x,y to x',y') …

it converts the pair N,D from coordinates fixed in the aeroplane to horizontal and vertical coordinates. :smile:

Hey Tiny!

Ahh! now that you point that out i see that is the transformation matrix for CCW rotation.

Now i understand that, but when you say it converts the pair N,D from coordinates fixed in the aeroplane to horizontal and vertical coordinates, do you mean it converts the pair N,A ... or am i missing something completely?

So regardless, the basis for doing the CCW rotation is rotating the 2 target vectors by the angle of attack (which would make them match up with L and D) hence giving us the components of L and D?

[Edit] Wow! Now that you pointed out at CCW thing that i was neglecting, everything else in the chapter seems to make so much more sense when i look at it!

Thanks a lot Tiny!
 
Last edited:
  • #4
NBAJam100 said:
Hey guys,

I current picked up Fundamentals of Aerodynamics by John D. Anderson Jr. and am having a little bit of trouble understanding some of the equations i am given. This is the first aero book I've picked up so I am not too familiar with aero concepts or terms yet.

On page 20, they break down the Lift and Drag components geometrically. The symbols below are as follows: A= axial force and N=normal force. [tex] \alpha = [/tex] angle of attack.

They have:

[tex]L=N\cos \alpha - A\sin \alpha [/tex]
[tex]D=N\sin \alpha + A\cos \alpha [/tex]

I am having trouble understanding why this is true, and why they put the +/- where they did. I see that [tex]N\cos \alpha [/tex] is equal to L, so why are we subtracting the [tex]A\sin \alpha [/tex] ? Same goes for the equation for D. I am sure I am overlooking something very obvious here, but id appreciate someone helping me see it.

Thanks.
the (rather rough) sketch should help clear up ur doubt-just resolve forces vertically and horizontally
 

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1. What is the difference between lift and drag components?

The lift component is the force that acts perpendicular to the direction of motion of an object, while the drag component is the force that acts parallel to the direction of motion. In other words, lift is the force that allows an object to move upward, while drag is the force that opposes the motion of the object.

2. How are lift and drag components measured?

Lift and drag components are typically measured using a wind tunnel or through mathematical calculations. In a wind tunnel, the forces acting on a model are measured using sensors and then converted into lift and drag components. In mathematical calculations, the lift and drag components can be determined using equations that take into account factors such as air density, velocity, and surface area of the object.

3. What factors affect the lift and drag components of an object?

The lift and drag components of an object are affected by various factors such as the shape, size, and surface texture of the object, as well as the velocity and density of the air surrounding it. These factors can be altered to change the lift and drag forces and affect the motion of the object.

4. How do lift and drag components affect the flight of an aircraft?

The lift and drag components play a crucial role in the flight of an aircraft. The lift component creates an upward force that counteracts the weight of the aircraft, allowing it to stay airborne. The drag component, on the other hand, slows down the aircraft and must be overcome by the engines to maintain a steady flight path.

5. Can the lift and drag components be manipulated?

Yes, the lift and drag components can be manipulated through various techniques such as changing the shape or size of the object, using different materials or surface textures, and altering the angle of attack or velocity of the object. This is often done in the design of aircraft and other vehicles to optimize their performance and efficiency.

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