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Some questions about wing torsion

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Arfang

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Good day,

I have some difficulties understanding the way torsion is created by the wings and how to design the wing structure accordingly and I wondered if someone could shed some light on the subject.

  • I found this formula posted by wsimpso1 on another thread to determine wing torque: dynamic pressure * moment coefficient * chord * projected area. Probably a silly question but by ''projected area'' are we talking about the entire wing area?
  • I've read explanations describing a center of ''rigidity'' or center of torsion and the lift force resultant times the distance between the two being what creates torsion. Is that a viable method and what exactly is this center of ''rigidity''?
  • One book I found says that skin along with the shear web is designed to carry torsion loads and is sized using Bredt's formula. Another source states that when using an airfoil for which the center of pressure doesn't move significantly with AOA, the spar alone could be enough, when properly designed, to resist torsion loads. Are there certain conditions that would make one choose one option over the other?
  • If the spar is resisting all bending and torque loads, what is left to the rest of the structure? By that I mean if the skin isn't carrying torsion loads then what are you basing your calculations on?
  • Also, if the wing creates torsion, should the wing attachment points at the fuselage be designed to resist that torsion?
  • Let's now assume that I have a solid D-tube made in one piece with no separate skin, ribs or core, like an extrusion if you want, and that D-tube is designed to resist torsion loads. Would treating it as a beam in bending and torsion be the correct way to proceed?
  • Following that, if I wanted to build and load-test a sample wing using different building methods, what method should I use to ''simulate'' both torsion and bending at the same time (can it be done with sandbags?) and what indicators aside from plastic deformation and cracks should I look for?

I realize now that's a lot of questions but I'm happy with whatever bit of information you want to share, I'm here to learn. Thank you in advance.
 

wsimpso1

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You are starting from scratch. Theory of Wing Sections First chapter is required reading.


This is the starting point for all things airfoil and control surface related. Wing projected area is the area of the entire wing as viewed in plan view, that is from above. Use all of the wing area, including the part "buried" in the fuselage. Yes, the air behaves like all that area is there, and this is a Stanard Calculation.

Next topic is you will have to learn some beam thoeory. You need a Mechanics of Materials reference. There is a lot in there... I like Timoshenko, it too is listed in the thread mentioned above. Everything has a bending stiffness and a torsional stiffness, and there is a center of it called a shear center on any structure. Wings have spars and skins all contributing to the torsional stiffness. If the skin is fabric, you end up assuming all bending and torsional stiffness comes from the spar set. Anyway, there are methods for computing the shear center. Then there is shear stress at any spot along the wing from two main sources, one is the accumulated lift outboard of any spot along the wing, and the other is from torsion accumulated from outboard of any spot. You are talking about the torsional source.

Tau = Tr/J where Tau is shear stress in psi, T is torsion applied to the wing at that spot, r is the radial distance from shear center to the spot you want to know the shear stress of, and J is the second area moment of inertia about the shear center. The spar and skin (if structural) contribute to this. Piece wise numerical integration is a straightforward way to calculate shear center and then second area MOI. More stuff for you to learn. Then to get deflection, you integrate pitching moment divided by GJ from the tip to the place along the span you are interested in... G is the torsional modulus of the material your spar set and skin are made of. this is a documented number for metals. If you are working in say aluminum, this is easy as aluminum alloys all have about the same G, but airplane plywood on the bias as used in wing skins is substantially lower than Sitka spruce as used an oriented for spars.

You might check out:


For beam threory without all that confusing math. Want to get into materials with differing characteristics? Check this out:


If the idea of all this math scrambles your eggs, I will suggest that you stick to building an established design with known good structures and known good flight characteristics. Build the design to the plans, and be happy. This works really well for a lot of folks. Sorry, they do not hand out engineering degrees in Crackerjack boxes, there is years of dedicated study behind every BSE degree. Now if this excites you, we can start working you through the curriculum...

Billski
 

Dana

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Good day,

I have some difficulties understanding the way torsion is created by the wings and how to design the wing structure accordingly and I wondered if someone could shed some light on the subject.

I found this formula posted by wsimpso1 on another thread to determine wing torque: dynamic pressure * moment coefficient * chord * projected area. Probably a silly question but by ''projected area'' are we talking about the entire wing area?
For the torsion at any given point along the span, it would be the projected area outboard of that point.
I've read explanations describing a center of ''rigidity'' or center of torsion and the lift force resultant times the distance between the two being what creates torsion. Is that a viable method and what exactly is this center of ''rigidity''?
Never heard it put that way, but it's the centroid of the beam (wing structure) cross section.
One book I found says that skin along with the shear web is designed to carry torsion loads and is sized using Bredt's formula. Another source states that when using an airfoil for which the center of pressure doesn't move significantly with AOA, the spar alone could be enough, when properly designed, to resist torsion loads. Are there certain conditions that would make one choose one option over the other?
For the spar to handle torsion loads it would have to be a tube. A flat spar with a shear web isn't very good for torsion, but combined with a sheet metal leading edge, it forms a D-tube which will resist torsion.
If the spar is resisting all bending and torque loads, what is left to the rest of the structure? By that I mean if the skin isn't carrying torsion loads then what are you basing your calculations on?
It depends on the structure.
Also, if the wing creates torsion, should the wing attachment points at the fuselage be designed to resist that torsion?
Of course.
Let's now assume that I have a solid D-tube made in one piece with no separate skin, ribs or core, like an extrusion if you want, and that D-tube is designed to resist torsion loads. Would treating it as a beam in bending and torsion be the correct way to proceed?
Yes, a beam with a distributed load.
Following that, if I wanted to build and load-test a sample wing using different building methods, what method should I use to ''simulate'' both torsion and bending at the same time (can it be done with sandbags?) and what indicators aside from plastic deformation and cracks should I look for?
Static testing, whether with sandbags or something else, is of limited value. It has its place, often as a gross sanity check, but it really only verifies the structure's integrity under that specific loading condition.
 

BBerson

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The wing when bending from lift will twist around what is called "centre of flexure" (in the UK).
Explained in his very readable book STRUCTURES, by J.E. Gordon.
 
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Arfang

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Thanks a lot everyone!

Dana: Your comments are much appreciated, thank you. Straight to the point and simple enough for me to get a picture.

wsimpso1: No scrambled eggs here. I'm pretty confortable with beams in bending, shear and moment diagrams, planar statics, I also had the chance to learn about shear, pressure/ Hertzian contact, but mostly applied to things like injection mold design, milling, stamping and bolted joints. I also studied torsion but applied to engine shafts for instance. Non-engineer level, pretty basic stuff.

Here's where my problem lies: it's ''easy'' to see where the load comes from and why shear modulus will be taken into account when calculating angular deformation of a shaft for instance. But in the case of a wing I'm unable to figure how torsion loads are created (I'm guessing Cm comes into play) and how it translates to the wing structure design.

Looking back, I feel like I didn't ''do my homework'' before posting. I'll go back to reading and if that's okay I'll come back in a while with more specific questions.
 

Norman

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Here's where my problem lies: it's ''easy'' to see where the load comes from and why shear modulus will be taken into account when calculating angular deformation of a shaft for instance. But in the case of a wing I'm unable to figure how torsion loads are created (I'm guessing Cm comes into play) and how it translates to the wing structure design.
This might help you visualize where the torque on the wing originates:
 
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plncraze

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Sometimes context helps to understand where forces come from. Check out this book for the aero and structural from a designer who has done this for a while. The title is "Flying on your Own Wings" by Chris Heintz. He covers pitching moment of an airfoil and designing a metal wing to handle these loads.
 

BBerson

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Aileron deflection twists wings. Flutter is probably the biggest reason to build the wings stiff in torsion.
 

wsimpso1

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Here's where my problem lies: it's ''easy'' to see where the load comes from and why shear modulus will be taken into account when calculating angular deformation of a shaft for instance. But in the case of a wing I'm unable to figure how torsion loads are created (I'm guessing Cm comes into play) and how it translates to the wing structure design.
Cm is the dimensionless term we determine for the twist. All aerodynamic force on the wing are summarized with Cl, Cd, and Cm. The wing causes changes in momentum of the airflow. The change in momentum in the direction of travel is drag. The change in momentum normal to the direction of travel is lift. And much of that lift is generated in downward moving air over the aft part of the foil, producing a nose down pitching moment.

You can hang a torsional moment anywhere on a beam cross section, and it will result in a torsional deflection about the shear center of the beam. Lifting forces that are not be aligned with the shear center also produce moments. Most foils we use in airplanes have the lift and drag pretty well centered close to the 1/4c point, and the pitching moment moves very little too when measured at the 1/4c. Pretty convenient really.

Billski
 
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Arfang

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You're right Norman, thank you. But when read this part again:

the c.p. is not mentioned because it's obsolete. The reason it was dropped from the polar charts and replaced with Cm is that at zero lift there's still a pitching moment implying a moment arm of infinite length ie a moment arm of finite length can not produce a torque without a force acting on it. So the pitching moment is a couple produced by the pressure forces acting on the top and bottom of the airfoil, not a torque produced by a single lever.
I can't help but to think about why there's a moment without force. To sum it up: the vertical component of the force created by air acting on the wing, lift, is moving forward and aft as AOA changes. That force times the distance to the AC creates a pitching moment. But when lift equals zero there's still a moment. Now when I look at the picture below, I note that most vectors have a horizontal component (drag) and a sum vector just like lift is the sum of all vertical components. Can't it be that the moment at zero lift is due to the sum of all horizontal vectors acting at a distance from the AC? After all, there's a zero lift angle but never a zero drag angle.

center_of_pressure.png

Sometimes context helps to understand where forces come from. Check out this book for the aero and structural from a designer who has done this for a while. The title is "Flying on your Own Wings" by Chris Heintz. He covers pitching moment of an airfoil and designing a metal wing to handle these loads.
Thank you, glad you mentioned that book. I was re-reading it the last couple of days and there are some points I can't wrap my head around:

The simplified formula on page 168 is: M0.25=q * Cm0.25 * deltaS * chord
And on page 243 we read: Mt=Cm0.25 * q * chord^2 * half span * n (dimensionless, section position from root) * 1.5
But on the next page: Mt= Cm * q + chord^2 * half span * n * 1.5, now there's is a plus sign after dynamic pressure? And how come chord is squared in one formula but not in the other?

Cm is the dimensionless term we determine for the twist. All aerodynamic force on the wing are summarized with Cl, Cd, and Cm. The wing causes changes in momentum of the airflow. The change in momentum in the direction of travel is drag. The change in momentum normal to the direction of travel is lift. And much of that lift is generated in downward moving air over the aft part of the foil, producing a nose down pitching moment.

You can hang a torsional moment anywhere on a beam cross section, and it will result in a torsional deflection about the shear center of the beam. Lifting forces that are not be aligned with the shear center also produce moments. Most foils we use in airplanes have the lift and drag pretty well centered close to the 1/4c point, and the pitching moment moves very little too when measured at the 1/4c. Pretty convenient really.

Billski
Thank you, I will have to do some research about a moment not being aligned and still producing a moment around the shear center. But just thinking aloud: what prevents us to do the following for a particular station along the wing: determine the shear center position, resulting lift force position then use lift force * distance between shear center and cp position to find the moment around the shear center?

Thank you all for your help!
 

Norman

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I can't help but to think about why there's a moment without force. To sum it up: the vertical component of the force created by air acting on the wing, lift, is moving forward and aft as AOA changes. That force times the distance to the AC creates a pitching moment. But when lift equals zero there's still a moment. Now when I look at the picture below, I note that most vectors have a horizontal component (drag) and a sum vector just like lift is the sum of all vertical components. Can't it be that the moment at zero lift is due to the sum of all horizontal vectors acting at a distance from the AC? After all, there's a zero lift angle but never a zero drag angle.

View attachment 107640
There is force just not lift. If you view the pressure on the bottom separately from the pressure on the top surface you'll see that they couple to create the pitching moment about 25%c. When the pressure pulling down is equal to the pressure pulling up there's no lift but the couple is still there. Pressure drag also exists but it never has a long enough arm to make a significant contribution the pitching moment.
 

wsimpso1

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+1 on Norman.

Do you have a copy of TOWS? If not, get one. That book is the starting point for everything airfoils. Then go through it. If your foil has low drag at cruise it has nose down pitching moments. Want to get no moment? You can do it, but you will have more drag when making lift. Does the tail have some drag nulling out that pitching moment? Sure it does, but usually the tail nulling out pitching moment is less draggy than the drag of a symmetric airfoil making lift without pitching moment. Yep. And you can not avoid that phenomenon anyway, because we all like our airplanes stable, and stability happens when we intentionally add some more pitching moment by putting the CG ahead of the Neutral Point, which we also have to null out with the tail.

When we use symmetric foils that have no sweep and no control surface deflection, no moment occurs. When we decide we want to minimize drag while getting lift, we go for a cambered mean line. This shifts the min drag spot of the airfoil to a place where we have some lift, and in so doing makes the pitching moment happen. That is the trade... In the foils that work well on airplane wings, the forces end up centered at or close to the chord line at the 1/4c position. Lift, drag, and nose down moment centered at spot darned close to the 1/4c point.

Now please, no more arguing about reality. This is not a philosophical discussion. We are talking about what it actually does and has been documented thoroughly over more than 100 years. We can help you with concepts and how to apply math to all this. You asked some questions, we answered, you can look at the plots for any family of foils and see this - go ahead, open your copy of TOWS - and see what we are talking about.

Billski
 

plncraze

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Heintz is a difficult read because he will show something once and then use it as an example later. Moment is discussed early on and then brought up again later. If I understand the formulas you are talking about then the one on page 243 is a good example. MT1 is "moment torsion 1" which represents the moment and torsion at the inboard portion of the wing. The ending subscript tells where Heintz is talking about. When reading Heintz it is a good idea to find the initial reference to what he is discussing and then find the details of the latest example in the text. It takes time. I spent a morning, before the caffeine wore off, trying to find some justifications for some of is numbers.
 

Arfang

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Thank you both, and actually TOWS is also listed as a reference in Mr. Heintz book. So, I'm going to read TOWS I guess!

wsimpso1, I hope you're not upset by my questions, if that's what the comment about philosophy refers to. It was not my intent by any means. But as a machinist, being considered philosophical is a compliment I guess.
 

wsimpso1

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This is not philosophy, it is engineering. The world behaves as it does, and learning that has way more value than thinking it should behave some other way.

What is disturbing is :
Folks talking about issues like this is a menu in a Chinese restaurant;
Folks arguing about things that show up clearly in the references we recommend;
A lack of respect for folks sharing knowledge for free that normally costs money to get.

In the real world, the variables interact, and multiple responses have covered how the inputs affect the outputs. Then we ask folks to go look at TOWS. Yes it is a big book, but most of it is a catalog of airfoils. Insights can be gained pretty easily in most chapters and a review of the various airfoils.

Responses that clearly indicate no insight and/or that are arguing with us as to how the physics works gets ... tiring. These members and the moderators are volunteers and worth way more than you are paying them, so going to the existing literature, showing insights and thanks, and bringing something back to the table to keep them interested is usually worthwhile.

Billski
 

Arfang

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My comment about philosophy was an attempt at humor, I tried to de-escalate because it seemed something I wrote upset you. I don't know what could be considered philosophical in my post and I don't even know exactly what philosophy is, I know that I don't know. It was just humor trying to de-escalate, please don't be offended.

I never tried to argue, if that's the way you interpreted it then sorry. I merely asked a question based on what I found in a book where there's a wing design example using the distance between cp and shear center, so I asked people who know. See, when someone asks: 'why does it work like this and not like that?' It is not lack of respect, I call it 'trying to understand' or 'questioning'. And it was questioning after reading a book, like you recommended. Maybe my choice of words or something I wrote seemed disrespectful but I can assure you that it was not my intent.

I wrote that I will start reading TOWS and I'm currently at page 22. So I listened to your advice about going to the existing litterature, said thank you and asked a couple more questions. If that's considered disrespectful then again, sorry if you took it that way.

I understand that internet communication can lead to misunderstandings but saying that I'm disrespectful to others and arguing and whatnot about some chinese restaurant (as long as they don't serve bat soup...*) is a little too much in my opinion.

*another attempt at humor
 

plncraze

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Another helpful book is Richard Hiscocks' Design of Light Aircraft. There should be a copy for about $100 bucks online.
 
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