How to calculate wing deflection? 5

[oriolbetriu]

Hi!

Albeit I studied aero engineering, I never finished my studies. I have been lately reading Timoshenko, to learn some beam theory basics. I can calculate deflection for a single beam, but I do not know how to calculate deflection for the whole wing? In fact, I can not even tell how to calculate deflection for the two spars, at once?

I am guessing that, I can calculate deflection of each spar independently, and then make both have the same deflection, to avoid internal stresses inside the wing structure. Another option would be, to calculate Moments around both spars, and thus obtain a single Moment equation for both spars, that can be integrated to obtain deflection. This can be achieved, since both spars have the same Young Modulus.

This all makes me wonder about, how to calculate deflection of a cantilever composite spar? That is, what happens if the materials that make up the wing section, have different E and G values? Like a full wing section, D-tube plus spars plus shear webs etc.

Any comments will be greatly appreciated!

Oriol

 

[rb1957]

A wing, especially a cantilevered wing, is just a fancy beam. The loading is not simple, but aero load is typically considered a distributed load. The Moment of Inertia of the "beam" is also not simple, but changes along the span. Typically a wing is solved piecewise, 1 rib bay at a time ... a simple analysis with loads from the outbd portion, and loads from the rib bay under consideration adding together to give loads on the inbd side (which is the outbd side of the next rib bay). One thing is to consider that aeroloads are not in the same reference system as the structural axes of the wing.

There should be plenty of references of this analysis online, look for hobby or kit planes, maybe "Part 23".

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[oriolbetriu]

Thanks rb1957!

To make things easier, I am considering a flat lift distribution, and a constant spar and wing section/rectangular planform. I have calculated the moment of inertia of the different parts that make up the wing section, and located the resulting airfoil centroid, but I do not know how to move any further? Once I have mastered the method for this basic problem, I will change the conditions to improve the analysis.

I have searched online for references without success. If you have any book recomendation, or link I will appreciate it!

Oriol

 

[SWComposites]

you cannot analyze the spars and skins separately. you need to analyze the whole wing box as a beam with moment and torsion loads applied.

Get a copy of Peery, Aircraft Structures. Or a copy of Bruhn.

 

[oriolbetriu]

Thanks SWComposites!

I will finish Timoshenko's, and then start with one of the aero structures books you mention.

Oriol

 

[rb1957]

You can certainly simplify the problem ... simple loading, simple structure. I'd go with a single spar wing ... the simplest is to say "ineffective skins" (like the old fabric skins of WW1 planes); then the spar is the structural element. Adding "stressed skins" was a development in the 30s. Adding a structural "D-nose" skin would increase the torsional stiffness (which your problem may or may not excite).

If you can handle it Bruhn would be an excellent text for this ... he does all this stuff by hand.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[oriolbetriu]

Hi rb1957!

I am working on an example of a self designed wood glider wing, which has a D-tube plywood and two spars, the ribs are mostly covered by fabric, that is ineffective skin or non structural skin. So far, the reference books I have used are Stelio Frati's The Glider, and Timoshenko's.

With some very helpful guidance, I have ellaborated a spreadsheet, in where the D-tube has been defined, using the NACA coordinates, as small rotated rectangles with the skin thickness. Using Mohr's circle for Inertia, I have obtained Ix and Iy of each small rotated rectangle. I have sized all the elements separetely, and now I want to see how they interact together? Among other things, I want to calculate deflection?

I have seen an example in Bruhn's (A19.13) in where the author, analyzes the bending longitudinal stresses of an aluminum tapered cantilever wing. The problem is that all the elements in his wing, are probably made of alu 2024; they all have the same Young modulus. Instead of calculating the whole wing deflection, the author analizes bending stresses in different stations. So I guess that, I have to break the wing in sections and analize each one, and then add the resulting deflections. That is more or less what I did, for calculating Phi/Torsional stiffness.

In my example, I can get values for EI of each element, but I do not know how to consider them together? Most of the classic aero structure books, are focused in alu, so it is hard to figure out how to proceed with different values of E? Perhaps I can transform the airfoil section elements, as if all had the same Young Modulus? This is something usually done, when analizing composite beams with axial loads.

Any advice will be greatly appreciatted!

Oriol

 

[WKTaylor]

I was going to suggest trying a classic structure-stress analysis procedure... such as from Bruhn... for hand analysis of the wing Assy, within elastic deformations.

HOWEVER... wood aircraft structure is a 'vwery-vwery-vwery-twicky' analysis... due to the very 'nature' of wood... and little current engineering expertise.

Strongly suggest that you gain access to legible copies of these documents...

ANC-18 Design of Wood Aircraft Structures [1951 or 'later']

ANC-19 Wood Aircraft Inspection and Fabrication [1951 or 'later']

NACA TR-84 Data on the Design of Plywood for Aircraft

NACA TN 296 Bearing Strength of Wood Under Steel Aircraft Bolts and 'Washers and Other Factors Influencing Fitting Design

Army TM 1-414 Aircraft Woodwork [1942+/-]

USG FPL-GTR-190 Wood Handbook - Wood as an Engineering Material [current]

FAA-H-8083-31B Aviation Maintenance Technician Handbook—Airframe
Chapter 6 - Aircraft Wood & Structural Repair

Regards, Wil Taylor
o Trust - But Verify!
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation, Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", HBA forum]
o Only fools and charlatans know everything and understand everything." -Anton Chekhov

 

[rb1957]

there is a standard analytical approach for sections with multiple Es ... research "rule of mixtures". It's in Bruhn ... what it says is convert the section to 1 value of E by adjusting the element areas.

So your wing is a plywood D-nose and a spar of a different material ?

Since this is "just" an analytical exercise the values you use are "arbitrary". Yes, you calculate bending stresses, based on the local moment. For deflection you are using the beam equation ... d[sup]2[/sup]y/dx[sup]2[/sup] = M(x)/(E*I(x)) ... I'm assuming your wing tapers (if I is constant then things are much easier). With simple (UDL) loading the resulting deflections for a constant section cantilever is in every text.

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[oriolbetriu]

Thanks WKTaylor for the links!

There were some of the documents on the list, that I did not knew about!

Yes, wood is tricky. However you can run the calculations, with some estimative values gathered from ANC-18, or Frati's book etc. The most important thing to me, is to have a working method to perform the analysis, the data can be improved later, but yes obtaining accurated data on wood is a job on itself.


Thanks again rb1957!

I will learn about "rule of mixtures". I think this is what I need, to complete my spreadsheet. Bruhn seems quite readable, the examples are very hands on. There are plenty of books, they all have something to learn from.

The wing I am using for my analysis has a plywood D-tube, and a wood fir spar. It is very similar to the structure analized in Frati's book, it was the standard construction for wood sailplanes, before composites became mainstream. I am hesitating about covering the ribs with fabric, or using a very thin plywood skin. I am still hesitating about the overall configuration of the glider? But having a working structure analysis system, helps me studying the pros and cons of the different possible configurations?

Thanks guys for your answers, those are very helpful!

Oriol

 

[rb1957]

BTW, your approach is very "analysis intensive". A general wing section with stringers and spars and such would assume point areas and build the section MoI from that. Your section is more easily considered as a section in total ... a D shape has an easy to calculate MoI. The other option would be subdivide the D into small areas (and not worry about the self MoI of each detail small area). Maybe this is a learning exercise ... so include the self MoI (as you have) then consider the section MoI without these small self MoI and see the difference (it should be small compared to sum A*y^2)

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[oriolbetriu]

Hi rb1957!

The person that has been guiding me, has told me what you said; that some engineers skip analizing the rotated rectangles, and only use A*y^2 of parallel axis theorem.

By creating this spreadsheet I have learned to work with Excel. I learned to program during my studies, but I never used after. In short, once the program runs the numbers, it all becomes automatic; it is perhaps analysis intensive but not labour intensive for the user. In any case, excel can manage this amount of data. Also, calculating the MoI of the small D-tube rotated rectangles, has allowed me to learn about Mohr etc. I really did not knew much about structures theory before, even though I weld. I guess that this analysis technique, can too work well to model a composite wing, made of superimposed plies.

I have been surprised that the examples of wing box beams on the books, use very basic shapes. I sarted modelling the D-tube as a half ellipse, using the basic formulas for torsion in Timoshenko, but as the spreadsheet progressed the model incresed its fidelity. I do not know much about what is a standard analysis practice? I am just learning as I progress, with the books and the internet!

Cheers,

Oriol

 

[mfgenggear]

There is a beautifully done you tube video.
Review at your own discretion. Always verify.

It's called exoskeleton wing design , how carbon fiber makes it possible.
For GP I would recommend viewing it.
Why use wood when carbon fiber is possible.

 

[mfgenggear]

Ori
The above video the channel is dark aero
There is a ton of helpfully information. They even have membership and classes in Aero design. Might be helpful for small aircraft.

It is helpful for this old g

 

[oriolbetriu]

Hi mfgenggear!

Thanks for the links! The internal structure of the Darkaero wing is very original. I just saw the video about it, the idea of cutting all the internal parts using a CNC machine seems wise.

I have started building wood RC models to experiment. Wood is less messy than composites. I can work at home, without anyone complaining about the smell. Jim Marske says that building a mold pays off, if you are about to build three airplanes. So for a one off, or at least for building models, wood is better. OTOH, I build bicycles, and share my shop with carpenters, so starting with wood is the natural thing, because its ecologic etc.

Besides the above, yes composites is very interesting and worth learning! Talking about learning, I still need to finish reading Timoshenko's, and build a couple more models to test ideas, finish other projects etc. So, I realize that there is a long road ahead, but it is OK. University was a sort of torture, but reading and learning for pleasure is very rewarding.

Cheers,

Oriol

 

[mfgenggear]

Orio
Glad it was helpful, when I was young, as young
Manufacturing engineer, I was given the task of liason for the entire manufacturing floor, of General Dynamics Convair Division, what
Fun that was. I was like a sponge. Trying to learn as much as humanly possible. What an experience that was. Some of the methods were still WW2 style manufacturing. I learned a bunch of assembly methods with aircraft.
Composites was in its infancy. I was just introduce to stealth technology.
The stealth cruise missle. It was top secret then. MD 10, then known as the KC10, the
Mid fuselage, the space shuttle mid fuselage.
So this series of videos is a refresher, and more learning on Composites. I as well find it very entertaining. I guess a nerd always a nerd lol

 

[oriolbetriu]

Hi mfgenggear!

It seems that you had an engineering career that many dream of! In my particular case, I really enjoy the freedom of experimenting on my own in the shop, but I also admire the craftmanship and quality of certified aircrafts.

Cheers,

Oriol

 

[oriolbetriu]

Hi!

I have a fundamental doubt regarding deflection on a 3D beam/wing. Given that Timoshenko only covers deflection for 2D structures. I am guessing that perhaps, you can calculate deflection in a 3D wing, as if it was a 2D structure. Once the values of EI are known for the beam/wing section, you can draw the deflection diagram and the wing lift distribution, both located on the centroid of the wing section. Would that approach be valid, is it that simple?!

Any comments will be greatly appreciated!

Oriol

 

[rb1957]

that's a starting point, but issues arise if you go beyond the structure's elastic limits. If webs buckle (under compression or shear) then assuming the structural properties apply at the centroid would not be correct.

Why do you say Timoshenko only applies to a 2D structure ?

"Hoffen wir mal, dass alles gut geht !"
General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

 

[oriolbetriu]

Thanks rb1957!

As a starting point, I am trying to calculate a moderate deflection, within the elastic range. Instead of the original cantilever wood wing, I have come up with a tube and fabric braceless structure, similar to that of the Goat homebuilt glider, which can be analized as a truss. In that case, assuming no buckling etc, the simplified approach might work.

Otherwise, in the case of high deflection beyond the elastic range, I guess that you have to work using FEA.

Sorry, it was confusing to say that Timoshenko only covers 2D deflection. The wing that I am analizing, has two struts, one for the forward beam/tube, and another one for the rear beam/tube. Therefore, if we want to assume, to calculate deflection, that the load is concentrated in the wing's centroid, the struts are creating a downward force, that is not applied at the centroid, but to the forward and rearward beam. But since this is a simplified approach, we can consider that the struts reaction is applied to the wing centroid. I was worried about neglecting the deflection created along the wing's chord, between lift and the struts. But I guess that in that case, we can consider this deflection to be negligible, so that the problem is 2D; we only analize deflection along the span. Is that a valid simplification?

After calculating deflection created by Lift, I will superimpose Drag deflection, which would very small, because the wing section is much bigger in the horizontal axis, than in the vertical axis, and Drag <<<< Lift. Next will be, superimposing Torsion etc.

In the particular example I am working on, I am considering a wing with rectangular planform. So, I am intrigued about how to calculate deflection for a taper ratio wing? I believe that it might be possible to do so, by cutting the wing in numerous sections, and analixing deflection in each section, by considering the section to be constant; equal to the average section between the stations. Then all the small deflections between each section, can be added to obtain total deflection. Is that a valid simplified approach?

Just for clarity, attached is the example with both a spreadsheet and a doc explaing all the steps. I still have to compute buckling in the struts, and of course deflection.

Thanks a lot for your help, I really appreciate it!

Oriol