Spar question for the structural engineers

[DICKEYBIRD]

I am re-designing the wings on a lightweight biplane I did a few years ago and was wanting to change the spars to a tapered cross section to reduce the stress concentration at the root. Is there a rule of thumb that would help me to decide what the difference between the spar height at the root and tip would be?

I'm only planning to taper the height only, not the width. Also this design has only one spar....on the bottom! I know, I know....it's very wrong structurally but my goal was to keep the top surface as smooth as possible to help reduce drag.

[Ollie]

The spar design depends on how the loads are applied. If the spar is unsupported except at the fuselage (cantelivered beam) with no working inter plane struts or guy wires, then the bending load is zero at the wing tip and increases as the second, third or fourth power of the distance from the root to the tip, depending on the lift distribution. Under lift distribution loads, the spar top is in compression, the bottom is in tension and the material in between is in shear.

The lift distribution depends on the planform, twist(washout) and angle of attack. It is practical to save half the weight of the spar by tapering it from full depth at the root along a straight line to nearly zero at the wing tip. Such a spar will still fail at the center of the wing and be overdesigned between the root and tip for almost any ordinary lift distribution.

The spar design would be much different if there were point loads by struts and by bracing wires.

A biplane with interplane struts and flying wires, has the top wing spar in compression, the bottom wing spar in tension and the flying wires in tension carrying the shear load. the landing wires are slack until the wheels hit the ground or the plane flies upside down.

[DICKEYBIRD]

Thanks Ollie; I have saved your learned response in my "neatstuff" folder. :) I was thinking that a straight line from the root to the tip, tapering down to a height that would allow enough gluing area to hold the rib upright would suffice in my application and your response makes me more comfortable.

[BMatthews]

Further to Ollie's last bit on proper biplane rigging....

In a biplane the spars are in effect acting like the upper and lower flanges in an I beam with the rigging acting as the web. So since the two wings in concert make up a locked structural cell then I would think that the upper and lower spars are largely seeing the same loading along their entire length between the roots and the outer struts. Only the tips hanging out beyond the struts should be tapered in this case. On top of that the spars between the root and stut locations are being subjected to a normal supported at both ends loading that, for upright flight, is trying to bend them upwards in a arc between the root and the strut support points.

So, assuming we ARE talking about fully functional biplane rigging here, I'm going to go out on my limb and say that in this case we want to see constant spar sizing out to the struts and only then should it taper to the minimum consistent with gluing.

Not so?

[Ollie]

DB,

Do you know that the spar crossection at the root is strong enough from past experience? If not, then you need to beef up the root end of the spar.

[DICKEYBIRD]

Bruce, that do make since don't it.....thanks!

Ollie, so far the wings have held up well under the flight loads imposed upon it with me flying but when I hold it up by the wing tips and bounce it up & down, the wings flex a startling amount. I'm working on a magazine construction article and am sorely afraid of the consequences when built and flown by someone that might throw a lot more speed and G's at it. I built it to cruise "on the wing" at 1/3 power and pushed the design envelope toward the big, light, fragile side.

I'm thinking the final version will have the ubiquitous upper & lower spars method with crossgrain balsa shear webs between them. The extra drag caused by the spar protrusion on the top surface probably won't hurt it that much. Matter of fact, I might put an another one forward of the main spar on the top only to add a turbulation effect. Any guesses as to where it should go (% wise) on a thinned (9%) Clark Y?

[Sparky Paul]

Full-scale design and construction practices fail for models in one area at least!
We use wingtips as landing skids!
A tip designed to the gnats eyebrow for flight loads will crumple when intercepting Ma Earth, as it is destined!
A little more beef than full-scale is required for tips.

[BMatthews]

DB, how wide is the chord? You may want more than one turbulator spar.

As a guide I've done a few wings that way and I don't like to see more than about one inch between the spars if I expect the covering to be decently suported. On some of my free flight models I've gone as tight as 1/2 inch.

But in any event I like to bias the turbulator(s) a little more towards the leading edge to better support the covering in the usually more critical first 20 to 25% of the airfoil.

[DICKEYBIRD]

The chord is 4.5" Bruce....you're probably right about adding 2 spars instead of one.