How does speed and angle of attack affect pressure distribution at the wingtip?

Question

So I was wondering how speed and AoA affect lift distribution at the tip of a wing. For example, if you are flying level and at a high speed, does that mean your wing has more even lift distribution at the tip? (meaning instead of lift decreasing and pressure decreasing as you move toward the tip, it stays more even). Also if you're flying slow and at a high AoA, how does that affect lift distribution?

And how exactly would AoA affect the pressure distribution in those circumstances? (All of this ignoring the effect of tip vortices)

Thanks!

Answer 1

It sounds to me like you aren't firmly separating flight path angle from angle of attack.

The aerodynamics of the wing can be scaled (non-dimensionalized) such that the airspeed does not matter when considering the lift distribution or pressure distribution.

On the other hand, if the aircraft is in level flight (zero flight path angle), then the total Lift is equal to the weight.

So, if you're talking about an airplane (not just an aerodynamic calculation or a wind tunnel model), and you're interested in level flight (L=W), then you can't consider speed and angle of attack separately. If you start with a given airspeed, then the aircraft must fly at the angle of attack that provides L=W.

Hopefully you're totally OK with the fact that to slow down, you must increase AoA -- and to fly fast, you must decrease AoA. The exact values of corresponding AoA to Vtrue will depend on altitude (and weight), but that is why we often work in equivalent airspeed.

So, if I interpret your question as "what happens to lift distribution of a wing as I change angle of attack", then the answer is "it depends"....

In aerodynamics, we sometimes introduce the concepts of the 'basic' lift distribution and the 'additional' lift distribution. Unfortunately, there are slightly different definitions of these used out there, so while the idea remains the same, the details can differ.

The basic lift distribution is one of:

1. The lift distribution at zero alpha
2. The lift distribution at zero lift

The additional lift distribution is one of:

3. The change in lift distribution for one degree alpha.
4. The change in lift distribution for a unit change in CL.

1 & 2 will differ in shape and magnitude.

3 & 4 have identical shapes, but one is scaled by the lift curve slope of the wing.

For this discussion, I will use the definitions as 1) and 3). They are the easiest to work with.

You can think about basic and additional lift distributions as a 3D extension of the idea of superposition in thin airfoil theory (where we decompose an airfoil into a flat plate at angle of attack, a camber line, and a thickness distribution). This idea falls apart when the wing is stalled.

Using the basic and additional lift distributions, we can write the total lift distribution as a linear combination of the basic and additional (times AoA):

$l(y)=l_b(y)+\alpha\,l_a(y)$

The basic lift distribution depends on the wing planform, twist, and camber distribution. If the wing has zero twist and zero camber (i.e. the lift is zero for all sections at zero angle of attack), then the basic lift distribution is zero.

The additional lift distribution depends on the wing planform. It does not depend on the twist and camber distributions. Recall that variations are sometimes called 'aerodynamic twist', this is because camber can play such a similar role as geometric twist.

So, the answer to your question "What happens to the lift distribution as you change alpha" -- the answer is "It changes by the additional lift distribution" (which only depends on the wing planform).

If you were looking for a simple answer like (it increases at the tips, or it decreases at the tips), then you'll be disappointed because it is more complex than that. Sometimes it increases, other times it decreases. It depends.

However, the great news is that it only depends on the wing planform.

So, fire up your favorite VLM type solver (VSPAERO, AVL, XFLR5, etc). Put in the wing planform you desire, zero camber, zero twist. Run a single case at one degree angle of attack. The result is the additional lift distribution for that wing.

Tada!

So, if you know the basic and additional lift distribution for a wing, you can very quickly calculate the overall lift distribution at any angle of attack.

There are lots of cool conclusions that can be derived from these ideas.

For example, if you want to achieve an elliptical lift distribution at a certain angle of attack (or any other targeted lift distribution shape), then for a given wing planform, you achieve the target lift distribution by changing twist and camber. In fact, if you know the target lift distribution and the additional lift distribution, you can back out the required basic lift distribution.

Or, if you calculate the bending moment of the basic and additional lift distributions, then you can quickly calculate the bending moment of a wing at any angle of attack.

And so on...