Aspect Ratio and Taper Ratio

[Cost Index]

Ok, I've been reading Aerodynamics for Naval Aviators and I have a few questions but first few things which I believe are correct.

A high aspect ratio wing, winglets, raked wing tips are good as they help reduce tip vortices, this reduces downwash behind the wing and hence reduced induced drag.

A highly tapered wing (taoer ratio 0 - pointed tip) and sweepback have high local tip CL's.

A rectangular wing (taper ratio 1) has has higher CL's inboard and less at the tip, hence stall progresses from inboard to tip (I've known this is good especially for trainers) HOWEVER according to ANA it has higher downwash near the tip.

Sweepback is meant to act like taper right? Taper is meant to have very little downwash near the tip but it says that a swept wing has a large amount of induced drag.

Now a highly tapered wing has very little downwash at the tip but has higher local CL's at the tip but less induced drag near the tip! What the?!

This is what I've always believed: I thought higher downwash always results in higher CL's near the tip and hence higher induced drag?! Is there something to do with spanwise flow i'm not reading?

Everything seems to be conflicting! :confused: I'm after explanations of induced drag, downwash and local lift coefficient of lifts with regards to aspect ratio, highly tapered wings, swept back wings and rectangular wings.

Someone please explain. :confused:

Cheers

[Mad (Flt) Scientist]

I think the problem is that some of the "has higher downwash" statements aren't related to the same baseline. You're looking at a number of effects - aspect ratio, taper ratio and sweep. Lets look at them in isolation first, for a wing of constant area.

A wing with higher aspect ratio will be more efficient - that is, will generate less drag for a given lift coefficient. This is because the tip - which is the most inefficient part of the wing (in a classical elliptical spanwise distribution, the tip generates no lift at all, at the limit!) - is a less significant proportion of the wing - consider the extreme case of an infinitely long wing - the tip has an infinitely small impact on the rest of the wing. The actual TOTAL downwash is the same - you're generating the same amount of lift, after all - but it's more evenly distributed, which is helping the drag. The section CLs are lower - more span to spread the lift over.

Now, taper ratio for wings of constant aspect ratio. If we compare the two extremes of TR=1 and TR=0, the pointed wing is having a similar effect to high AR, in that we're moving the bulk of the wing area further from the tip. So that should help efficiency. But we're also making the chord very short NEAR the tip, which means that although the absolute amount of lift distributed in a spanwise sense is small, it's on a small chord too, so the local loadings may be high. Which brings both inefficiency and potential stalling issues. (Commonly you'll have washout to help with this, but that also can make the tip less efficient)

Finally sweep: the wing becomes less efficient in terms of CD for CL due to three dimensional effects - spanwise flow. This becomes more pronounced outboard. There'll be less downwash outboard because the wing's not as good at generating lift outboard - but that means more drag for the same total CL.

I think the problem may be that you're trying to relate downwash and CL too closely; just because the tip CL is low, and hence the LOCAL downwash is low, doesn't mean the overall drag is low - if it's just that the outboard wing "isn't working" then you'll actually get more drag overall - you end up making the inboard wing work harder to compensate.

If you like, think of an aircraft with tip ailerons. If I place the wing at a given AoA and obtain a given CL, then deflect the ailerons trailing edge UP to obtain near-zero lift over the outb oard section of the wing, I do get less drag - but also less lift. And if I increase the AOA to get the lift I originally had, while using the ailerons to continue to zero-out the tip lift, I'll actually end up with the same overall wing CL and MORE drag than originally - even though the tip is unloaded.

[barit1]

MFS touched on the subject of washout in his last paragraph. Planes with fabric-covered wings and separate lift struts for the front & rear spars can be rigged with a bit of washout (decreased incidence at the tip). This tends to improve roll control at the stall by forcing the wing root to stall first, at the possible sacrifice of a bit of cruise efficiency.

Rigging airlerons (symmetrically) high can achieve the same thing.

[XPMorten]

Many wings also have a different incidence on the wing root and tip
to complicate things a bit :)

M

edit: barit mentioned that already - sorry!

[Cost Index]

Help.
I just wrote a big speel and the web page deleted it all for me because I hadn't logged in. :mad: Not happy. Now to re-write the general emphasis of it all.

1) I need to refer to constant area and thus constant lift when comparing everything, right?

2) Is it the higher local lift relative to chord that produces the variations in lift across the wing even though the total lift is the same?

3) Thus anything that produces higher local tip coefficients at the tip compared to the total will have higher induced drag? I.e. Taper and Sweep.

4) Is it the higher local tip coefficients compared to the total that produces the higher vortices?

5) For a constant area irrespective of aspect ratio, taper and sweepback the downwash will be the same over the whole wing?

6) What happens to downwash in the local areas (root and tip) for higher aspect ratio, higher taper ratio and sweepback?

7) You say that a high taper ratio is similar to having a higher aspect ratio wouldn't this suggest that a higher taper ratio would therefore have less induced drag? I thought Taper was similar to sweepback and had higher induced drag?

8) If there is higher local tip coefficients at the tip for taper, then wouldn't this suggest higher induced drag for this design? Or is that although the taper ratio acts like a higher aspect ratio wing the fact it has higher tip CL's means that these cancel each other out?

9) What happens to the tip coeffients of lift for taper and sweepback?

10) Is it just the spanwise flow that causes tip stall for sweepback or is the higher local tip coeffiieicents as well?

I'm just after a simple rule of thumb to remember this all. :ugh:

I'll be honest, I didn't really follow your previous post that well, my bad.

Help!