Spanwise Lift force distribution?

[ken]

Hi

I wanted to get clear on this conclusion of lift distribution along the span of a wing.

Graphs in texts show that for constant chord wings, Cl distribution along the span is eliptical.
Conclusions:
1.Induced incidence is greater towards the tip.
2.Lift force at the root is PI/4 greater than mean and as local chord is a constant, lift force falls away in the same eliptical relationship as Cl toward the tip.


Now take an eliptical wing plan form. Texts show that CL is constant almost to the tip. Conclusions, except right near the tip:

1. Induced incidence is constant across the span.

2. As local lift force is a product of Cl and local chord and Cl is constant, the lift force distribution follows the same eliptical relationship as the chord.

The two plan forms result in the same eliptical lift force distribution along the span. Now logic would seem to dictate what defies common sense and seems to be way too easy but could it be that wing taper does not effect the distribution of lift force along the span. Is this conclusion correct or are the texts incorrect?

I can so only these 2 possabilities.


Regards,
Ken

 

[enigma]

The most efficient lift distribution is elliptical. (unfortunately, doing space track work, I don't remember why or exactly what the efficiency is a scaling of)

For real wings, there is typically a fudge factor thrown in for non-optimal sections of the wing (Due to wing twist, chord length variations, etc). Calculating the actual lift distribution is nasty to the upteenth degree without some sort of CFD software (and even then...)

 

[ken]

Hi Enigma

Your reply, is really not exactly what I am after here.

I am not trying to determine this to a high accuracy. Rather the graphs for various wing plan forms all strongly suggest that the distribution of lift force along the span is eliptical or at least as near as can be determined from the graphs.

That seems way too convenient to trust my interpretation.

What I am after is an idea of how correct this conclusion is.
Is it completely wrong or close?
If close, then how close for say a constant chord and an eliptical wing?
Is the variance within say, 30%, 10%, 5% etc.

I really just want to check if I am understanding this correctly or not.

Regards,
Ken

 

[selfAdjoint]

Anecdotal observation.

In 1958 I attended the British air show at Alderburgh. It was a moist day and as a new RAF light bomber came toward us, head on, a beautiful elliptical pattern formed from one wingtip to the other, formed of water droplets that had condensed out in the lower air pressure over the wing. It was a SEMI-ellipse, of course!

 

[paults2]

That's due to the wing vortex, which is a result of the lift distribution. Often the tip vortices are more noticeable than the wing vortex.

http://home.flash.net/~lauras34/sav15a.jpg

 

[cptcolo]

Ken,
Spanwise lift coefficient is what you multiply the local CL by. An elliptical wing is 1 across the entire semi-span (root end to tip). Most wings have taper and are defined by a taper ratio (tip end cord length/root end cord length).

For most straight wings the spanwise lift coefficient is given as a function of the fractional semi-span distance (x):
1. Taper Ratio = 1
From x= 0 to 0.86
= -1.3474x3 + 0.8774x2 - 0.2469x + 1.1736
From x=0.86 to 1
= -36.7776x2 + 63.5583x - 26.7419

2. Taper Ratio = 0.5
From x= 0 to 0.65
= -0.43567x2 + 0.39804x + 0.97582
From x=0.65 to 1
= -5.51768x3 + 7.29061x2 - 2.31958x + 0.97582

Please note for both of these the real life spanwise lift coefficient does not really ever drop below 0.6. You will have to make that adjustment when x gets high (for an approx sol you can ignore this)

 

[micromass]

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