## Determining Aspect Ratios for a model glider

Hello, First I’m not an engineer!

I have a son who is in the eighth grade and is taking soaring lessons.

I'm asking these questions because my motive on soaring lessons is to try and introduce practical applications of math (I'm an account and out of my depth here) with the hope that it sparks an interest in engineering.

He is entering a Science Fair and would like to do a project that involves gliders/flying (really this is his idea).

So we looked though his flight manuals and we can across aspect ratios........”The ratio between the glider’s span and the mean cord of its wings. High aspect ratio in a glider is associated with a high glide ratio, other factors being equal.”

He has to let his teacher know what his project will be and I would like to have an option or two if anyone thinks this will be a project that will produce the desired outcome using a toy glider.

So I’m assuming if we were to by a cheap toy balsa glider to use as one of the Variables Held Constant (fuselage/tail assembly) and he was to make a half a dozen wings from balsa stock varying the length and cord of the wing, but keeping the surface area constant he would find a wing that provides the optimum Aspect Ratio.

I’m also assuming he/we will have to build a simple “catapult” to launch the glider so the amount of energy and the angle of attack (right term??) when launched will be held constant.

Then measure the distance the glider flew to determine the best aspect ratio………..

So what would the math be?

Is there a way to determine what the ideal aspect ratio should be?

Or should he go back to the drawing board and come up with something else?

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 I think a better idea would be to determine the wing that gives the best lift to drag ratio, for which a higher value is favoured. This wikipedia article gives you the required formula to estimate it given the aspect ratio of the wing: http://en.wikipedia.org/wiki/Lift-to-drag_ratio This forumla will tell you which wing will perform better. However, it's kind of tricky to make it a simple school project. I guess you could make some balsa models but there's too many variables that you have to keep constant, such as wind conditions to really give you accurate results. Range of an aircraft is a function of the lift to drag ratio, but in this case of a simple experiment, there's quite a few factors that will influence it. Although, this would make for a nice discussion section. I think you might find that the unless you really make the wings significantly different you won't see much of a difference over this distance. To help with these variables, I suggest attaching the wings to a water bottle rocket. This way you can keep the launch angle and propulsion the same for each test by keeping the amount of water and volume of bottle equal. You could also change the thrust and size of the bottle if you wanted to add more variables (probably not a good idea at his level of education). So basically I would: Explain the importance of the lift drag ratio and how it's usually determined (wind tunnel testing, CFD etc.) A write up of the experimental aims and procedure Discussion of the results and what they mean with comparison to the lift to drag ratio calculations. For example, what were the influencing factors (different wind conditions for eact test run, water not measured properly etc.) Make sure you graph the L/D ratio against the resultant range. Could also derive an equation relating them. This is tricky, but it's a good lesson. Conclusion (summarise the findings) I've actually done something similar, but I did it using a tonne of variables such as the number of fins for rocket stability and amount of thrust. I then used some complicated statistics to tell me the optimal combination.
 Your son picked a very complicated project! The aspect ratio affects more than drag. As a introductory example, increase the aspect ratio results in a higher likelihood of stall. A very low aspect ratio (<4) will create a tremendous amount of drag, while simultaneously gaining "vortex lift". As a project for a kid with no aeronautics background, the goal of the project should be to maximize the distance flow. Pick a 2 parameters to vary over a certain range and see what happens!

## Determining Aspect Ratios for a model glider

Yeah, I just reread what I suggested, it's probably a bit too complicated for someone in year 8. Hell, even for year 12... Although, it's a certain A if you pull it off.

 Quote by Aero51 Your son picked a very complicated project! The aspect ratio affects more than drag. As a introductory example, increase the aspect ratio results in a higher likelihood of stall.
He did some reading and related to me that high-aspect ratio wings produce a comparably high amount of lift at low angles of attack with less induced drag. So he'll need to build the launcher with a low angle of attack..........

 Quote by Aero51 A very low aspect ratio (<4) will create a tremendous amount of drag, while simultaneously gaining "vortex lift".
Ok I understand this as it applies to a delta wing but he is planning on using a rectangular wing, so won't that be minimized? He also knows the rectangular wing creates more induced drag, that's in his flight manual.

 Quote by Aero51 As a project for a kid with no aeronautics background, the goal of the project should be to maximize the distance flow. Pick a 2 parameters to vary over a certain range and see what happens!
Well, he came up with this this evening as his hypothesis; "What effect does varying a gliders wing aspect ratio have on its ability to glide?"

So should he change his hypothesis.............I guess what is happening is that; Drag is the independent variable in the L/D ratio and changes as the AR varies.

Or not and leave it and let him figure out what's happening, I'm reading his flight manual and this stuff is in there!

So if he creates a few wings sets (6 or 7) with the same surface and varying only the cord and span starting with low aspect moving onto high aspect and seeing which ones glide further..................somewhere in there he would find the "right" AR.

He's going to have to explain L/D and Drag, etc so this will be the learning thing he needs..........

I guess I can call over to the engineering department at USF and see if there's any students who might want to help him out understanding this!

Thanks!

Please let me know if the L/D and Drag thing is right that way I'll know what direction to push him.

Remember he is learning to be a pilot (glider) right now and his goal is to solo in only about 9 more months so he is going to need to understand this stuff anyway.
 That's not a hypothesis, it's a report title. A hypothesis would be - The aspect ratio that gives the highest lift to drag ratio will result in a larger flight range. I already answered those questions in my previous post. Lift and drag aren't independent, they both depend on the speed outisde the frame of reference (glider) and other things. I would just launch it at the angle that gives maximum projectile range. Like I said before, all of those will generate lift, I doubt you'll see much difference with the setup of this experiment. Especially if the weight is the same. The governing factor here will be the weight of the model, not how much lift the wing profile can generate. I must say, I hope he knows how lucky he is. I'm a mechanical/aeronautical/aerospace engineer, and I never learnt how to fly. In particular, my parents never paid for it... or were as interested in my education as you are.

I will give you the rundown as best I can:
 He did some reading and related to me that high-aspect ratio wings produce a comparably high amount of lift at low angles of attack with less induced drag. So he'll need to build the launcher with a low angle of attack..........
FOR THE CASE WHERE WING AREA IS HELD CONSTANT AND ASPECT RATIO IS VARIED: Aspect ratio does not affect lift, per-se, though it does affect the lift distribution. Increasing the aspect ratio will correspond to a decrease in wing chord, which leads to earlier stall. That is to say, a smaller chord will correspond a lower angle of attack at which the wing will lose lift. This is related to the Reynolds number, which is a ratio of the inertial forces (the force from the wind hitting you as if it was a brick) to the viscus forces (the sticky forces of the air/fluid) and flow regime (laminar, turbulent, transitional, etc). Increasing the aspect ratio will correspond to a decrease in drag at the expense of a higher likelihood of stall.

On the other hand, decreasing the aspect ratio will correspond to a much less likelihood of stall, at the expense of a dramatic increase in drag. At high angles of attack (angle of the wind relative to the chord line), a low aspect ratio wing will experience "vortex lift". Vortex lift is an amazing phenomena where the air coming over the sides of the wing rotates over the top. This rotation keeps the flow attached to the surface of the wing (when the wing stalls, we say that the flow is no longer smoothly connected to the wings surface or "attached"), delaying stall and also increasing lift. It works for any low aspect ratio wing. Delta wings happen to be low aspect ratio and be an ideal shape for supersonic flight.

 Ok I understand this as it applies to a delta wing but he is planning on using a rectangular wing, so won't that be minimized? He also knows the rectangular wing creates more induced drag, that's in his flight manual.
The answer to that question is not simple. I have no idea, I doubt it will minnimize anything as rectangular wings are very draggy.

 So should he change his hypothesis.............I guess what is happening is that; Drag is the independent variable in the L/D ratio and changes as the AR varies.
I hate to be disheartening but you wont be able to measure drag. Instead, you could measure the glide ratio, which is the ratio of how far the plane travels forward, to altitude lost in free flight. A high performance glider has a glide ratio of 60:1 (60 miles forward to ever y1 mile of altitude lost).

 So if he creates a few wings sets (6 or 7) with the same surface and varying only the cord and span starting with low aspect moving onto high aspect and seeing which ones glide further..................somewhere in there he would find the "right" AR.
For your purposes, yes. In a more general setting he is finding the right balance of wing location (related to stability), stall, drag and weight distribution.

 Please let me know if the L/D and Drag thing is right that way I'll know what direction to push him.
Stay away from L/D it really cant be measured without a wind tunnel! Go for glide ratio and remember let him be creative! Going to school for engineering tends to robs some of that valuable skill from you :(. Perhaps you can extrapolate L/D from glide ratio *hint*.

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