# Elliptical distribution

1. Jul 5, 2007

### buster

what exactly is the elliptical distribution in relation with the lift distribution along the span of a wing. i googled it but all it comes is something related to the calculus n all mathematics(lets face it, i just got rid of maths n i m happy now).
does it mean that the lift produced is max at the centre n reduces to 0 as we reach the wingtip(coz thatway wingtip vortices ll be small)??? is that why the airfoil geometry approaches symmetry about the chord line as it approaches the wingtip??

2. Jul 5, 2007

### FredGarvin

That is correct. The lift tapers off towards the tip (not necessarily zero). I can't comment on the symmetry of the at the tip though. I have some wing tips that aren't symmetric about the chord line. I always thought the ones that were were that way in an effort to reduce the induced drag at the tips. I'll do a bit of digging to see if I can find an answer to that.

3. Jul 7, 2007

### buster

one more question: which one is better to reduce wingtip vortices??
a winglet, which produces an infinite wing span effect or elliptical distribution, which theoretically would give no pressure differential at the wingtips, so no vortices(only theoretically)!!!
i guess a winglet would be better because wing would atleast give more lift(provided the wing has a uniform airfoil cross section over the entire span) than tapering it towards the end(thus affecting the lift)

4. Jul 7, 2007

### FredGarvin

Well, I guess it depends on the aircraft and it's operating regime. I would think that since we don't see a whole lot of elliptical tipped wing plans out there these days, that the winglet is the easier to utilize.

5. Jul 7, 2007

### jambaugh

Side note: The elliptical normal (or elliptical Gaussian) distribution relates to probability theory for many variables. This is what you picked up off of Google. Imagine the normal (Bell shaped curve) but as a surface over two dimensions instead of a curve over one. Depending on the scaling of the two variables you may have a "circular bell" or an "elliptical bell" shaped distribution function. Then generalize to arbitrary dimensions. This is important enough due to the Central Limit Theorem that there will be many references out there on a Google search.

So you may want to try the Google search again with "aerodynamics" added to eliminate this other meaning.

6. Jul 7, 2007