Induced drag confusion - More than one cause?

[scanwinder]

Hi,

I'm a bit confused by induced drag on an aerofoil and hoping somebody can clear it up for me.

I understand that as air slips around the edges of the wing due to the pressure differential between the top and the bottom surfaces, the angle of attack at the ends of the wings is effectively reduced(as the air is being deflected downward).

What I'm unclear about is, some sources seem to state that component of lift opposing motion is the induced drag(i.e. if the wing is at an angle with respect to the airflow, the wing generates a force perpendicular to it, and a component of that is lift and a component of that is drag)

Below is an image illustrating the latter:
http://selair.selkirk.bc.ca/training/aerodynamics/images/induced-definition.gif

So my question is, is induced drag due to downwash from wingtip vortices, or the rearward component of lift since the force the wings generate isn't directly upward. Or is it a combination of both of these things?

 

[boneh3ad]

Induced drag is sort of a catchall term for the sources of drag that are unavoidable on anybody producing lift, for example the drag as a result of the wing being at an angle of attack and the drag associated the wingtip vortices. In short, the answer to your question is "both of these things".

 

[scanwinder]

Thanks for that, I thought that would be the case. It just seems that most textbooks explain one or the other but not that it's the combination of both. The derivation in the text I'm reading makes a whole lot more sense now that I realize it's a combination.

 

[rcgldr]

Is induced drag due to downwash from wingtip vortices, or the rearward component of lift since the force the wings generate isn't directly upward. Or is it a combination of both of these things?

For an ideal or perfect wing, using the wing as a frame of reference, this ideal wing diverts the relative air flow by only changing direction and not speed, so that there is no change in energy of the affected air. The change in direction means the "forwards" component of the momentum of the affected air is reduced, while the downwards component is increased from zero. The decrease in the forward component of momentum corresponds to the drag component of impulse, which is force x time. Induced drag can be calculated based on the angle of diversion and lift. If I did the math correctly, and defining θ as the angle of diversion, I get induced drag = lift (1 - cos(θ)) / sin(θ).

My math (induced drag calculated so that it's a postive number):

f = force
i = impulse
m = mass
v = velocity
t = time
θ = angle of deflection

i = f Δt = m Δv
f = m Δv / Δt

lift = m Δv / Δt = m v (sin(θ) - 0) / Δt
induced drag = m (-Δv) / Δt = m v (1 - cos(θ)) / Δt
lift / sin(θ) = m v / Δt
induced drag = lift (1 - cos(θ)) / sin(θ)

 

[PJC01]

Hi there,

Induced drag can indeed be caused by more than one factor. The two main causes are the downwash from wingtip vortices and the rearward component of lift. Both of these factors contribute to the overall induced drag on an aerofoil.

The downwash from wingtip vortices is created by the pressure difference between the top and bottom surfaces of the wing. As air flows over the wing, it creates a low pressure area on the top surface and a high pressure area on the bottom surface. This pressure difference causes the air to flow from the high pressure area to the low pressure area, resulting in a downward flow at the wingtips. This downward flow creates a vortex, which in turn creates a drag force known as induced drag.

The rearward component of lift is also a factor in induced drag. As an aerofoil generates lift, there is a component of this force that acts in a rearward direction. This rearward force is a result of the angle of attack of the wing and the shape of the aerofoil. This component of lift also contributes to the overall induced drag.

So, to answer your question, induced drag is a combination of both downwash from wingtip vortices and the rearward component of lift. These two factors work together to create the drag force that we call induced drag. I hope this helps to clear up any confusion you may have had about this topic. Keep exploring and learning about aerodynamics!