Echo (Ultralight Self-Launching Sailplane)

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peter hudson

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174
Hello all,

I’m designing an electric ultralight self-launching sailplane called “Echo”.

This project log is intended to share with you the long process of designing, detailing, testing, and building a design from scratch. Or at least my approach to that. If I’m realistic you can sit back and enjoy the ride for somewhere between 6 and 10 years. I encourage PMs discussing details and will always consider suggestions whether they influence changes or not. If a topic bears open discussion we can do that in the open forums here: Discussion: Echo (Ultralight Self-Launching Sailplane) design

I expect a reasonably active post schedule at first, while I catch you up. But after that? Well...things move pretty slowly in the “one person, one-off” design world. Hopefully, your patience (and mine) will be rewarded.

Here’s how she looks today...
ISO_trans.png
Enjoy,
Peter Hudson
 
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peter hudson

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Messages
174
Hi All,

I thought I should start, as most do, with defining missions and establishing a basic configuration. And then , also as most do, I’ll change it to be what I want now.

Some History...

In fact, before I move on I want to stress that the biggest challenge me as a home designer is not to define a mission per Raymer’s or Roskam’s methods, but to settle in on what I really WANT... Want so bad in fact that I can spend many years on it without changing direction or motivation. I’ve sketched a lot of airplanes that, in the end, I didn’t think I could see all the way through. Often because there are so many similar airplanes out there. And nothing really special or challenging in designing another one of my own.

Which brings up the second biggest mental challenge. Anything you want to design and build is probably already closely represented out there, and perhaps for sale cheap. So WHY are you wanting to do it from scratch?

In my case, even as a boy I found that designing, building, and testing my own model airplanes was the part that I loved. Flying them (once all sorted out) only held my interest until the next concept pushed it’s way into my head. Most of my education and career choices revolved around acquiring the skills and knowledge to do it full size. I’m ready. It’s time to realize that kid’s dream and design my own. No one else’s design can scratch that itch for me. OK I’m in, so back to question #1 what do I really want to design and build.

My original mission statement:
Design Concept: Self launching ultralight sailplane. A one-off, just for me, but maybe plans. The mission is more about fun soaring than serious cross countries, or any sort of competition. Considering I think soaring a paraglider is fun, I’m willing to sacrifice some performance for ease of building, simplicity, and some wind in my face. As a light weight, fairly efficient aircraft that only needs power for a few minutes, it opens up to electric propulsion without it being too heavy or expensive.

Some motivating thoughts at the time: There are many ultralight gliders from Super-Floaters, Bugs,and the several Sandlin designs that are all pretty close already, BUT with composites and a little more engineering I could get a lot more span, and span is king. Also, with planning for some electric self-launch, I can move the pilot forward for good visibility and use aft mounted motors for balance.

Here’s a earlier version (OpenVSP model): 15m span, 12m2 area, 109kg (240 lb) empty , 200kg (440 lb) MTOW
Echo-130.png

It assumed composite D-tube spars: fabric aft covering, and very little laminar flow past the thick point. Straight, constant taper surfaces and the tail the airfoils are symmetric (and the same mold used for fin and stabilizer.) A "Marske Monarch-like" fuselage but with a “tent like” carbon pole and rip-stop nylon pod (paraglider influence?) Also a pretty high lift, unflapped low speed airfoil (Eppler 748).

It’s sort of fun for me to dig this design back out now, and review it as “future me”. I’m not disappointed, and it’s still interesting, but after a lot of math and soaring I realize how much value there is in L/D along with the light wing loading. And it posed the challenge I was looking for…

“Is it possible to home build a 15m ultralight sailplane with extensive runs of laminar flow, and keep the structural weight under a couple of hundred pounds? “

In my recently departed career, I was a “structures guy” so I feel and up to the challenge, and excited by it. So it’s revised:

Design Concept: Self launching ultralight sailplane. A one-off, just for me, but maybe plans. Mission is more about fun soaring than serious cross countries, or any sort of competition. Performance should only be traded to make weight, or if creates an extra ease in building that makes the loss of performance something I am OK with (and will be over the years).

P.S. I think I'll follow Topaz's lead and start a thread in the aircraft design forum for discussion.
Discussion: Echo (Ultralight Self-Launching Sailplane) design
 

peter hudson

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May 24, 2020
Messages
174
Gross weight and wing loading.
After defining my mission, my next task is to estimate the empty and gross weight, and then the wing loading. The wing loading will be needed to lay-out the flight envelope, establish load cases and therefore will drive a lot of structural design.

Based on my mission, I’m planning to be able to operate under the FAR part 103 rules which defines my upper weight limit as 254 lbs. (and up to 24 lbs more for a recovery system) so 278 lbs. There is a similar category in Germany that is 120kg (265 lb which is slightly less and, I believe, includes the recovery system) so these are good limits. It’s pretty common to come in about 10% heavier than your target, so I should really aim for around 230 lbs empty weight.

But, for the sake of design flight envelopes, and loads, I’ll use the max structural weights in case I really do go past my target. As far as pilot weight I could use my 180 lb self and some water. Or comfortably set it at 200 lbs. If my structural weight comes in lower, then that can be added to the available pilot weight. In practice, once the airframe structure is designed and tested, then some of the available margin may allow for even bigger pilots.

So my max design weight is 265 lb + 200 lbs pilot or 465 lbs total (211 kg)

To calculate the wing loading that I want requires some trades. I want good performance in light lift which requires low wing loading. Or, more accurately, low span-squared loading for climb performance. On the other hand, higher wing loading is better for upwind legs, penetrating out of sink, and just moving around to the next heat source. Just going with the maximum wing area I can afford by weight is not a good bound.

One of the less obvious considerations is that, for laminar flow surfaces there is a far amount of weight involved in the skins. Different skin options I’ve considered, range from 0.18 to 0.33 lb/ft2 (880 to 1610 gsm) with finishes, so 20 extra square feet of wing area adds 7 to 13 lbs to the wing and another 1.4 to 2.6 lbs more for bigger tail surfaces just for the skin, not counting any other extra structure and mass balances. It adds up fast. So I’d like to go with the smallest (lightest) wing I can, which will be defined by the part 103 stall speed requirements.

AC 103-7 allows for satisfying the stall speed requirement by using the charts in the appendices. It also allows for using an aircraft total Cl based on the wing type. For my double surface wing with more than 50% flaps I can use a Cl of 2.0. And based on the graph in appendix 2, I can go as high as 3.9 lb/ft2 (at 254 lb with a 170 lb pilot, and no chute) and meet the 24 knot stall speed requirement.

stall.png
So, 254 lbs plus 170 lb pilot = 424 lbs at 3.9 lb/ft2 and I need a minimum wing area of 109 ft2 (10.1 m2). I’ll round up to 110 ft2. That satisfies the stall requirement but at gross weight it is higher.

My design wing loading becomes 465lb/110ft2 = 4.23 lb/ft2. (20.7 kg/m2)

So that’s settled and I can work the design envelope next. But I do have to keep in mind that It will be less than that, most of the time, so I should explore the minimum wing loading too when, for example, I'm looking at gust loads, or determining speeds to fly. That will be as a glider (with the pod removed), and me on a diet, and I forgot my water. glider empty weight isn't known yet but the target is 200 lbs. plus a 20 lb chute so 390 lb/ 110 ft2 = 3.5 lb/ft2 (17 kg/m2).

Thanks for following along!
 

peter hudson

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Messages
174
Flight Envelope(s) and the Basic Glider Criteria Handbook

With wing loading established, I next define my operational flight envelope(s). This will determine a number of structural design load conditions and therefore plays a big role in the structural design and analysis to come. I suggest that there are more than one envelope with my “(s)“ because I do need to look at it when flown light as a glider, and again with flaps deployed.

The basis of how this envelope is constructed comes from the FAA’s Basic Glider Criteria Handbook. I won’t describe the details, since the handbook is pretty clear, and has examples. What I will do for you, is attach the spreadsheet I made to allow quick generation of the graphical envelope. This will let you play around with the effect of wing loading, aspect ratio, and wing lift coefficient on the envelope for your design. It will determine for you, the recommended minimum design glide speeds Vg (the peak speed for which gust loads are calculated) and a lower bound on design dive speed Vd. I’ll apologize to all our metric brothers and sisters, but since the handbook is in pounds, feet, and MPH so is this spreadsheet.
env_1.png
You do have to make some choices. The minimum design glide speed from the handbook is a minimum but you can choose to make it faster. Also the design dive speed can range from Vg to 1.2*Vg (your choice). Vne (not shown in the chart) must be 0.9Vd (or slower...your choice). In the chart above I used the minimum Vg but set Vd a little faster at 128 mph. I may not keep that faster Vd if it adds too much structural weight. But, I liked the option. Speeds pick up fast when the nose is down, and, as an untested design, there is potential for that to happen unintentionally at first. Also, the maximum allowable Vne is set at 0.9 Vd =115 mph or an elegant 100 kts on the ASI!

My minimum acceptable design envelop (Vg at minimum and Vd = Vg) looks like this:
min_env.png
I could then set Vne to no more than 102 mph (.9*Vd) or 88 kts. I CAN set Vne even lower but it doesn’t relieve the need to design the structure for Vg and Vd.

Another optional parameter is the design load factor N. The charts above are using the minimum from the handbook (+5.33g/-2.67g) but, I could choose to set it higher. Maybe I’m thinking some loops and rolls would be fun, and I would feel better with the FAA part 23 rules for aerobatics (+6g/-3g).And I should keep my higher 100 kt Vne since I know my nose would be down!

env_3.png

Note that the positive gust load is now lower than the design load factor. Also note, that If you just looked at the handbook values of +5.33, and designed your structure to that ,you would be under-designed for the gust load factor. This is common with light wing loading. In fact the lighter the wing loading the more pronounce the gust load.

With Echo, as a glider (no pod and light payload) my wing loading was 3.5 lb/ft2 (but keeping the same Vg and Vd to avoid confusing the pilot about Vne) the envelope looks like this:

env_4.png
Note the jump in gust load factor to 6.3gs! But, 6.3 gs at the lower weight requires fewer pounds of lift from the wings than the 5.6gs gust load at gross weight, so the wings are fine. Other things like fuselage bending, mounts for instrument batteries etc. need to address those higher gs.

I plan to use the first envelope unless I find It’s driving too much structural weight, in which case I’ll back off to the the minimum (2nd) envelope.

Some last comments:
Flutter may limit Vne to something below these minimums, but it makes more sense to just fix the flutter issues, and keep these structural limits which are based on historical information on how fast you might need, want, or accidentally go.

I hope you enjoy the spreadsheet!
 

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peter hudson

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Lift Distributions (part 1)

There are plenty of sources discussing planform choices and resulting lift distributions. Those choices are as much about fabrication and tooling as they are about aerodynamics. I want to talk about lift distribution prediction methods. The distribution will affect loads, strength, and stall behavior so It’s pretty important to get right, and with some confidence.

A multi-tapered planform is something I’ve decided to use. And I expect some twist, whether from built in washout, or from deflections due to aerodynamic forces. I will, therefore, need to iterate a few times to get the behaviors I want, and I will sometimes want to include flap settings, and I want to consider the planform’s affect on stall progression, So I’d like to compare tools and settle on which I find to be easiest to use and to iterate, and it must include features like multiple tapers, flaps, aspect ratio effects, and twist (and maybe spoilers?).

The easiest to use method is probably Shrenk’s approximation. It can easily be implemented with a spread sheet. Another benefit is it handles generic planforms like multi-tapered ones easily. There are some limitations; it does not fully account for effects of aspect ratio, and it doesn’t change with airfoil camber (flaps etc.).

One can go further back and look at the more general Fourier solution that Glauert developed for generic planforms and twists. His examples only looked at 4 span-wise locations, and fit curves to those 4 points,which is OK for straight linear changes, but it needs more points for a good distribution with multi-tapered wings. I like the idea of expanding it, but I don’t want to spend a lot of time writing code to solve for so many coefficients as functions of wing shapes.

Anderson did just that (solve Glauert’s equations for a lot of coefficients) for straight tapered ,and twisted wings, and it retains the aspect ratio effects. Those tables are presented in Theory of Wing sections among other places. So this is accessible, and close to what I want, but he didn’t address multi-tapers and variable airfoils either in those solutions.

Prandtl, Glauert, and Anderson’s work all relied on horseshoe vortices as the fundamental basis. With that in mind, the vortex lattice methods codes should produce similar results for those classic cases, then It can extend into the special cases I want to consider like partial span flaps, twist, (perhaps non-linear) etc. Plus there are vortex lattice method codes available open-source, which means I can work on wing design rather than program development.

All of the above vortex based solutions assume thin airfoils (at small angles of attack). But, panel method codes account for airfoil thickness and flow effects from adjacent bodies (fuselage) etc. So I will consider those too.

I’m really most interested in lift distribution at maximum Angle of Attack (AoA) which is where both the stall occurs, and where maximum structural loads occur. All of the above codes do not address separated flow which is just beginning to occur at Maximum AoA. To capture a very accurate lift distribution one really needs a full blown Navier-Stokes based CFD code (there are some open source versions of them like OpenFoam) . But I feel that’s too much to learn, and to slow to use, for me, for this stage in the design. Maybe later.

Shrenk’s Approximation:
There already some handy spreadsheets for Shrenk’s approximation. It’s generally considered acceptably accurate for strength work. I wanted to build mine around expecting multi-tapered panels and twist that may not be constant across the whole wing (perhaps only twisting the outboard panel for example). Another feature I wanted to include was that, with twisted wings, the “basic distribution” of the zero lift wing gets added to the “additional lift“ of the wing at CL=1. And, if scaling the overall lift distribution, only the additional lift gets scaled per Shrenk’s approach. This allows me to scale the wing Cl to max for the airfoil sections in question.

A side effect of keeping non-liner twist across the whole wing is that the determination of the zero wing lift angle is not able to be calculated without an iterative approach to the root angle of attack for zero wing lift. I considered writing a macro, but I wanted to share the spreadsheet with you readers. I don’t usually trust macros from other sources, so rather than ask you to trust me, I require you to use the “goal seek” spreadsheet tool instead.

Here’s a sample of a double tapered wing (plus small center section and wing tip) with a 1 degree washout across the inboard panel and 2 degrees across the outboard panel.
shrenk_1.png

For Echo’s wing I don’t plan to have twist built into the wing, and I want very close to elliptical distribution when in the faster cruise configuration. But, in thermal/climb flap configurations I believe I can rely on the “effective twist” that can be achieved with having the inboard flaps be deflected a little more than the ailerons. Even more so, in landing mode, with more inboard flap deflection. For my planform without twist my distribution is:
shrenk_2-png.122920

Shrenk’s approximation is accepted and robust, but to add several sections with different flap configurations by altering the zero lift angles of those sections so severely, is farther than I feel comfortable extrapolating. So I want to compare Shrenk’s results to some tools that do allow for those changes an a way that is consistent with those tool’s methods. That is, the open source vortex and panel based codes of OpenVSP and XFLR5. I’ll verify them against Shrenk without flaps then add the flap deflections for the other two configurations. But, I’ll save that for the next post.

Spreadsheet is attached if you want to play!
 

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peter hudson

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Lift Distributions (part 2)

OpenVSP has two built in methods for aero analysis: the vortex lattice method (VLM), and a panel method. Here, I’ll compare both sets of results for Echo’s untwisted, double tapered wing from Shrenk’s approximation.

There are some things to note: First, is that it’s easier to build the wing geometry and change it in OpenVSP than in the spreadsheet and the visual representation of the wing prevents entry mistakes. Second, is that the results aren’t in exactly the same format for comparison. Third, is that some iteration is required to get the angle of attack to produce the wing Cl you want.

I looked at Cl = 1 first, since that is an assumption Shrenk used to solve the distribution prior to scaling the additional lift component. Then I used the scale in the spreadsheet to get the wing Cl of 1.2 which is about stall in my flaps-up cruise configuration. I then had to sweep through alpha in OpenVSP to find the alpha to achieve the same 1.2 wing Cl. The OpenVSP results for both AoAs is shown below:
open_vsp_results.png

As you can perhaps see (if you squint) that the load distribution is presented as cl*c/cref vs span whereas the Shrenk’s approximation spreadsheet is cl*c (not scaled by the MAC reference chord). Fortunately for a number of reasons, the numerical results are output in a text file with a [filename].lod extension. From there, it is easy to load into a spreadsheet and manipulate the results. In this case just multiplying the cl*c/cref value by cref and scaling the span location to go from 0 to 1 as in the spreadsheet.

Here’s how the VLM and Panel method compare to the Shrenk’s approximation at CL=1.2
openvsp_dist.png
and here’s the local Cl comparison:

openvsp_local_cl.png
These results look pretty good to me , I feel confident I can start lowering flaps and drooping ailerons. One thing that I did see was that the AoA for the VLM method was about 1.4 degrees higher than the panel method for the same wing CLs. I don’t have a good explanation for that, but perhaps it’s a result of actually including the airfoil thickness in the panel method. It’s something to remember when working on setting the wing incidence.
 

peter hudson

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Lift Distributions (part 3)

XLFR5 has 4 methods from which to choose. 1)lifting line theory, 2) horseshoe vortices (VLM1) 3) ring vortices (VLM2), and 3D Panels. There are some things to note:
First, similar to OpenVSP its very easy to input wing geometry and validate it visually. There are a few more options for the way one might sweep through an analysis such as constant lift, constant speed etc which will be handy later when creating polars. (a sweep with fixed lift but different speeds and Re)
xflr5_wing.png
Second, unlike OpenVSP, it first requires a sweep of analyzing the 2D airfoil through the range of lift coefficients and Re Nrs that might occur in the lift distribution analysis. I believe it only uses this data to filter out the unrealistic conditions where you exceed the possible Cl for that section at that Re. At any rate, that becomes the effect. You won’t get results past Cl max for the airfoil or if you are outside the pre-analyzed Re in the analyses. Which is a nice safety feature.

Also similar to OpenVSP, the XLFR5 panel method required about 1 degree less AoA to achieve the same wing lift coefficient. (I'm still not sure exactly why). Output is a little less accessible (at least at first glance) but graphs can all be exported as .CSV files for further manipulation.

xflr5_vlm1.png

Again the load distribution is presented as cl*c/cref vs span whereas the Shrenk’s approximation spreadsheet is cl*c (not scaled by the MAC reference chord).

Here’s how they all compare at CL=1.2
xflr5_lift_dist.png
and here’s the local Cl comparison:

xflr5_local_cl.png
So for our purposes they all work well for unflapped wings. I can see that both analytical tools have different strengths and weaknesses when it comes to: data extraction, including bodies, creating drag polars etc. so I’ll plan to keep models in both tools. Besides, the comparisons will show me when I make mistakes and give more confidence when they agree. So now I’m on to looking at including flap settings and considering different design conditions on the flight envelope.

Thanks for following along!
 

peter hudson

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174
Stall behavior (clean)

This one is about using lift distribution results to estimate stall behavior.

In my clean wing configuration (without flaps affecting twist and stall behavior) I need to provide a small but comfortable tendency for the stall to progress from the root towards the tip. While this flap configuration is intended higher speed cruise there may be sometime that a stall might occur in flight. We all know that a big untwisted rectangular wing stalls nicely.
And a highly tapered wing without twist stalls out at the tips in a nasty way.


rect.png
pt2_taper.png
But in my case I want to flirt with the elliptical lift distribution which stalls all at once. I do design my tapered sections and chords to provide a slight tendency to stall inboard but is it enough margin?

echo.png
While I’ve seen this discussion before, I’ve never seen a recommendation for how close one may come to elliptical and still have something considered nice to fly. So I’ll do what any right thinking engineer would do and see what everyone else does.

Fred Thomas “Fundamentals of Sailplane Design” has a very nice collection of statistical information on a lot of sailplanes. From this data I can select the wings with double tapers and compare those local Cls with mine.

The eight sailplanes I use for comparison (from among many) are based on whether they had double tapered wings, the root and tip airfoils were available to me online (so I can predict aerodynamic twist) or, if the same airfoil was used for the whole span (then I didn’t need the airfoil data). I could have had a lot more comparisons if companies were more sharing with their airfoil data :)

It was interesting to note that wing twist in the pre-1980s birds tended to be around 2 degrees of washout, but after the eighties the trend was for no twist at all. Of the eight sailplanes I compared, only the ASW 20 and ASW 24 had twist, the other six have untwisted wings with constant airfoils. The ASW 20 has 2.5 degrees of mechanical washout but a positive 1.5 degrees of aerodynamic wash-in. (so an effective twist of 1 degree washout). The ASW 24 had the same airfoil along the span (no aero twist) but 1 degree of mechanical washout.

So here are the results:
local_cls.png
It looks like I fall comfortably in the middle of the pile of past experience, so I’ll consider my stall behavior likely to be no worse than that other high performance sailplanes when running around clean.
 

peter hudson

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174
Airfoil Choice:
The next thing to do with the lift distribution, is size the wing structure. The wing structure estimate is needed in order to predict wing bending and torsion under loads. In my case, it will likely results in positive twist which moves the lift distribution outboard and therefore I’ll need to re-assess the lift distribution (static aeroelasticity). If it results in negative twist (washout) then I can ignore it and use the first estimate of lift distribution as conservative. That twist will also affect stall behavior.

The torsional stiffness of Echo’s wing is largely dependent on the composite skin. The airfoil shape will be needed to predict that torsional stiffness, and the shear center of the wing (when treated as a beam) and the spar cap sizes and wing bending stiffness will also depend on the airfoil thickness. So it’s time to broach this topic.

Choosing an airfoil for your project, is like choosing a wife:
You want something reliable, predictable, and that behaves well even when pushed to it’s limits. You want it to be a bit hotter and sexy, maybe a bit newer, and with curves in all the right places. Some might argue for selecting an older one that many others have already used, which seems OK depending on what you like. Sometimes they are a little too sharp, and bit unstable. The thing is, when you choose one, you have to live with it. (though you might be able to swap it out later at great expense, and with a sense of failure). Where the analogy breaks down for me, is that I want it to be available online for anyone to use.

So I have one picked out. It’s a modern low speed sailplane airfoil, which means she’s a bit thinner and designed for 15% flaps/ailerons. I haven’t learned of any sailplanes that currently use it, but I expect that’s because most sailplanes firms now are using their own proprietary airfoils, or not talking about it. She looks very much like some of the newer DU airfoils. I have had one or two other sailplane designers suggest it’s a good one, which may be all I really have to go on.

So here she is:
ah93k131.png
I expect there will be some heated debate over whether this airfoil is a good choice, since, in HBA, there is always a heated debate over anybody’s airfoil choice. Well, I think my choice is pretty sexy, in an Uma Thurman sort of way, which will be pretty hard to talk me out of!

I haven’t yet gotten a hold of the reference for it mentioned in the UIUC airfoil database:

“Althaus, D., "Niedriggeschwindigkeitsprofile," Friedr. Vieweg &
Sohn Verlagsgesellschaft mbH (publisher) Braunschweig/Weisbaden,
Germany, 1996, 591 pages. ISBN 3-528-03820-9”

So if anyone has a link, or a copy, I’d love help getting a look at it. Otherwise, for design, I’ll be using XFOIL data. I did see a copy on Ebay from Germany for about $650, but for that price, I’d want to flip through it first, to see if it has what I want. (laminar flow wind tunnel results for this airfoil.)

Next, I can get into the wing structure...
 

peter hudson

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Wing Structure as a Beam (Part 1).
When faced with not knowing something that you think is important to know for your design, what do you do to keep moving forward? Well, for me, the answer is usually to do some analysis, and get estimates of that thing. I may learn it’s not so important, and can be safely ignored, I may learn it’s crucial, and I need to refine my analysis, or change my design. At any rate, these places that stop you and require you to learn something in order to press on, are a part of the design process. On a project I worked on in the past, they were referred to as “knowledge points” which I think describes the situation nicely. It’s the point at which you go from being unsure about a potential issue, to knowing enough about it to make a decision and move on. These knowledge points may come from completing an analysis, performing tests, comparison with similar art, or even a decision to accept some risk and wait until later to learn what you need to know.

This post is about wanting to quantify my wing deflections and learn how much I care. For Echo, I anticipate a few degrees of forward sweep to keep the pilot in front of the spar enough for good visibility. This is largely because it’s such a light airframe compared to traditional gliders. I also know the combination of forward sweep, and a wing with full chord wing skins (moving the elastic center aft of the center of pressure) will cause a positive twist (wash-in) that will move the lift distribution outboard. That will increase root bending loads, and affect the stall behavior by increasing the angle of attack of the outboard part of the wing. So for this knowledge point, I’ll analyze my wing deflections, redefine/reiterate the lift-distribution and bending loads, look at the potential stall behavior issue, and decide whether I need to change my wings built-in twist.

For this level of knowledge (just wing bending and torsion deflections) it is appropriate to model the wing as a beam. A more detailed model than that is not needed yet, and should wait until things are better defined. Since my wing has a double tapered planform, and since my spar cap area will change along the span it seems easiest for me to build a simple finite element analysis (FEA) beam model. I can set up a spreadsheet to generate the wing section properties for different chord lengths and spar caps areas for the beam elements along the span. Then I can apply the span-wise loads from XLFR5 and read the resulting bending and twisting results.

The FEA code used for this is one I’m comfortable using, and is available free and open source! It’s been developed since the 60’s, lots of tax dollars have gone into improving it. Many companies have since developed it with more features and charge dearly for them. It’s very well known for the robustness and accuracy of its structural elements. Have you guessed yet? That’s right it’s NASTRAN! [GitHub - nasa/NASTRAN-95].

For the bending and torsional beam section properties calculations I refer you to Bruhn’s “Analysis and Design of Flight Vehicle Structures” and I discretize the airfoil based on the airfoil coordinates. Here’s a picture of the basic approach.

section_props.png
table.png
Once the section properties spreadsheet was set up, I just changed wing chord and cap areas to get the sections along the span. The sharp reader may notice I left out any torsional stiffness from the spar web, that will be a little conservative as it will twist a bit more than if I included it.

But wait. I need to know what my spar cap area is along the span before I can build this beam model. Another knowledge point! And this new one needs to be answered first.
 

peter hudson

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Wing Structure as a Beam (Part 2).

Calculating the spar cap area required along the span of the wing was done by taking the loads from XLFR5, rotating them into the wing reference chord line coordinates (from the airflow axes so lift and drag become X and Z direction forces for the model and align with the section property data.)

I do this for four points on my design flight envelope. I’ve updated that from the earlier posts to 485 lbs gross and I’ve limited the Vne to be equal to Vg at 115 MPH to reduce the number of corner points I need to analyze. Those points are referred to as “conditions” in the Basic Glider Criteria Handbook as shown here in red.
envelope.png
As you might expect, Condition III drives the highest bending moment and sizes the spar caps. I do keep the other conditions around in my analyses since they may drive other things later.

So for Condition III I’m at 5.5 degrees alpha for the wing, and 51.4 meter/sec (115 mph) and the XLFR5 results for that condition give me loads along the span in terms of lift, drag and moment coefficients in the coordinates of the airflow. I convert those to loads by multiplying by that wing segments area and dynamic pressure Q (which I scale to net the desired Gs) I also subtract the estimated weight of that section of wing (times those gs) from the load due to the inertial response, then rotate the loads into the wing coordinates.

Now I can integrate those loads into shear and moments along the span. If I assume the spars are the only resistance to bending moments, and I know the spacing of the caps based on percentage of chord and the chord length at a particular span location I can back out the spar cap area required at each span location.

Of course, I also have to know the strength of the spar cap material. I’m using carbon pultruded rods (who isn’t anymore?) and there are numbers out there suggesting from 325ksi tension and 270ksi compression (from Marske’s book for “graphlite” rods) down to maybe 200ksi as Marske suggests “to be on the safe side”. Boku suggests he’s getting similar numbers for some other sources of rods. For my initial calculations I use 100 KSI since my loads are limit loads, and I want a factor of safety of 2 for ultimate on my composite components.

This method results in needing 0.373 in2 per cap at the root (which is 24 of Boku’s 2mmx5mm rods) and a total of just under 1000 feet of those rods for the whole wing. But there is another consideration. Another “knowledge point” and that is “what is an allowable wing deflection?”

A basic hand calc of spar bending (per Marske’s book) comes in at 16.4 inches per “g” And he states his preference is less than 1/30th of the cantilevered semi-span per g which is 9.8 inches for my 15 meter wing. I would have to assume an allowable of only 60ksi to get beefy enough caps for 9.8 inches per g. (caps about .622 in2 at the root and 1500+ feet of rod) now that’s only another 5 pounds of rods, but it’s more work and more money too.

It becomes apparent that the strength of the pultrusion isn’t too sensitive for my long skinny wing design, but stiffness is. And it’s hard to quantify how flexible is TOO flexible. I can start by looking at the deflection of my NASTRAN wing beam model since it’s going to be a little stiffer with skins than a spar alone. That model with spar caps based on 100ksi (limit) pultrusions only deflects 13.5 inches at 1g which is less, as expected, but still over Marske’s published preference. His wing test data in that book showed 12 inches per g for the genesis wing test (same 15M span as mine) so maybe I’m close enough.

Looking at similar art is appropriate, but difficult. Boku says he looked a lot of pictures of sailplanes in flight, estimated the deflections per g, and aimed for the middle. I’ve also looked at some of the very long span examples which seem to allow more deflection per span. But, it’s hard to quantify the deflections in pictures and separate the dihedral and curved wing panels etc. from the deflection under load and it’s hard to know the load factor when the picture was taken, I doubt I could tell the difference between 12 inches per g and 13.5 inches per g based on this approach. And in the end is that what really matters?

There are also 2 benefits to a more flexible wing: gust load relief and ride comfort in turbulence. I’m not planning to to do rigorous aeroelastic gust load analysis but rather just trust the envelope prediction method, so that is still no new info for me. And the ride comfort is definitely not an analysis worth attempting.

Thinking more about it, there are 3 main risks to living with the higher deflections: 1) flutter, 2) control surface stress/binding from wing bending and 3) spoiler box and spoiler design to accommodate the bending. Flutter is not really addressable in earnest until structural dynamics can be measured or at least accurately predicted which doesn’t happen until later in the project. But, at least for the classic wing bending/torsion flutter, keeping the bending more flexible for a lower frequency (and keeping the torsion freq higher) is better, since the separation of those two modes is what you want. The spoiler box design will be a design based solution that I will have to do later. As for the control surface stresses; consider the condition when the wing is bent up into a radius, then the control surface is deflected down. That puts the surface aft of the hinge line back to the trailing edge in tension, and anything in front of the hinge-line in compression (for example the balance weight of the aileron). And, It will put loads into the hinges to bend the control surface. That applied strain is in addition to stress from air loads and control rod forces.

So I have a new knowledge point to deal with. “How bad is the stress in the flaps and ailerons from wing deflection and should it drive the wing bending limits?” So next I’ll look at predicting control surface stresses under the bent wing conditions and see if I learn what I need know to move forward. Then I can set my spar cap areas, and then I finish the wing beam model work!
 

peter hudson

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174
Flap Finite Element Analysis. ( a wing bending interlude!)

So I left off the last post with the question: “How bad is the stress in the flaps and ailerons from wing deflection and should it drive the wing bending limits?” For me, the easiest approach to answer that question is to build a simplified finite element model (FEM) of a portion of the flap (long enough to include 4 hinges) then force the deflection of the flap from curvature of the wing, while also forcing the flap into a deflected down position with a pushrod, AND applying the limit air loads from the basic glider criteria handbook.
loads.png

One of the trickier bits of doing this kind of model is that the flap skin is a +/- 45 degree only composite. It is much stiffer in torsion than in the “along the flap direction”.

PCOMPS and orientation dependent stiffness :

There is a potential for major misrepresentation of stiffness when it comes to non-quasi-isotropic composites. The properties of a shell element MAY be treated as a single isotropic material but only if the lay-up is quasi-isotropic. In my case the skins are just +/- 45 degrees. NASTRAN shell elements [PSHELL entry] allow for different material stiffness properties to be used for membrane, bending, bending stiffness parameter, transverse shear, transverse to membrane thickness ratio, and membrane bending coupling. While it’s possible to populate all of those variables through laminate plate theory and lamina test data, there’s an easier way through using the PCOMP property entry.

PCOMP allows the user to input each layer’s orthotropic material properties and define each layer’s thickness and orientation. NASTRAN does the laminate plate theory and creates a PSHELL that represents the lay-up.

So that problem seems solved, but there is another pitfall. The way orthotropic stiffness properties for fabric composites are generally reported, they don’t account for the change in modulus “around the clock” from 0° to 90° they typically only give the 0° and 90° (1 and 2 direction) moduli, and using them as the orthotropic properties in a PCOMP entry (or PSHELL) won’t result in the desired behavior of the modulus being high when aligned with the fibers and much lower at +/- 45. My skins should be “soft in bending” and “stiff in torsion” for this structure. For example:
modulus_variation.png modulus_variation2.png
One work around is to model the +/- fabric as two orthogonal (half thickness) layers of unidirectional layers with a modulus “tuned” to result in the desired 1 and 2 direction laminate modulus values. Testing the validity of this “cheat”, along with assurance that I’ve defined the element material directions correctly in the input files, and the importance of this to accurately predict loads and stiffness suggests an FEM “coupon test” is in order.

NASTRAN fabric modulus coupon test:

This is a single NASTRAN CQUAD4 shell element with properties defined by a PCOMP entry.
If you’re not into this sort of thing skip ahead to the graph of results.
For the uniaxial properties I need an initial estimate for a unidirectional carbon (modulus in both directions) AGATE-WP3.3-033051-101 shows a E1 as 18.8 MPSI and in E2 as 1.26. Marske’s composite design manual shows carbon UNI TAPE at 17 MPSI so that’s consistent enough. For my first cut I’ll use E1 as 17MPSI and E2 as 1 MPSI. And, to keep it similar to my wing skin, I’ll assume a 2 layer of 6 oz carbon plain weave laminate thickness of .024 in.

The single element coupon looks like this:
coupon.png
my orthotropic material estimate is:

MID E1 E2 Nu12 G12 G1z G2z Rho
MAT8 1 17.0+6 1.0+6 0.32 0.60+6 17.0+3 17.0+3 0.00014

The transverse shear moduli (G1z and G2z) are not good guesses, but set very low to not contribute much and for thin skins it will have little effect. The units are pounds and inches and Rho (mass density) is in slinches (Sorry to all the purists it’s just what I’m most used to using)

The laminate assumes each fabric layer is really two orthogonal layers at .006 in each. Like so:

PCOMP 1 -0.012 0.0 +comp1
+comp1 1 0.006 0.0 1 0.006 90.0 +comp2
+comp2 1 0.006 90.0 1 0.006 0.0

The -.012 offsets the reference plane to the bottom surface of the .024 laminate.
The 1 in each layer entry is just referencing MAT8 number 1 from above.
Running a static load case with the unit load shown above, results in these deflections

D I S P L A C E M E N T V E C T O R

POINT ID. TYPE T1 T2 T3 R1 R2 R3
1 G 0.0 0.0 0.0 5.030161E-22 5.471115E-21 0.0
2 G 4.607568E-06 0.0 0.0 -2.318719E-21 -2.028998E-21 0.0
3 G 0.0 -.638247E-07 0.0 -5.107694E-22 -3.728907E-21 0.0
4 G 4.607568E-06 -1.638247E-07 0.0 2.344531E-21 2.932575E-21 0.0

So our laminate’s axial modulus in the 0° direction [E1] is the stress over the strain. Stress is our 1 lb load on the .024 inch thick, 1.0 inch wide coupon and strain is the average displacement in the X direction (T1) of the corners [grids 2 and 4].
equations.png
Note that Marske’s composite manual has an axial modulus of 8.2 and 8.9 MPSI for plain weave and 2x2 twill carbon laminates respectively. I’m happy so far BUT, now I modify the input file so the layers are rotated from 0 °to 45° (in 7.5° increments) and plot the modulus results.

coupon_results.png

I think that worked pretty well! To be fair, I’ve done that test before. But, its very important for internal loads models, component models like the flap, and for structural dynamics models so I wanted to document it here. The axial modulus of the unidirectional material could be reduced maybe 10% to account for fiber waviness of a fabric and the results would line up well with several sources for woven carbon fabrics.

So having addressed that issue we can look at the results of the flap model. The deflected model (with a 1.0 scale of the deformed results) looks like this:
deformed.png
The stresses tend to be highest at the hinges and where the flap section is thickest but the tensile stress along the training edge is less than I imagined probably since the ends of the trailing edge aren’t restrained. The max values of stress along the stress major axis is shown here. And at this limit load condition are only a little over 4 ksi.
stress.png

I assume that if I modeled a full length flap, it would like the middle part of this model over and over until reaching the ends of the flap where the bending stresses unload as they do here. The stresses are pretty low, and again I’m driven more by handling, damage and skin minimum thickness goals than stress from air loads and wing bending. So for this knowledge point “How bad is the stress in the flaps and ailerons from wing deflection and should it drive the wing bending limits?” I now can say the stresses in the control surfaces are not forcing a limit to my wing deflection. That doesn’t give me a number to shoot for but it relieves the angst about it.

So here’s my [probably] final thought on wing deflection limits...Back when looking at design envelopes I looked at the gust loads when lightly loaded (6.3 g) and that was going to size some components but not the spars, I also considered setting a 6g limit so Conditions I and III had the same load factor (just slightly different angles) and to be more confident in doing some light aerobatics. I chose the lower limits (5.33 at condition I and 5.7 at condition III) to avoid designing in unnecessary spar weight. But, it looks like using just enough pultrusion to meet those (with a low assumed ultimate strength of 200 ksi and a factor of safety of 2) results in a slightly soft wing in bending. It doesn’t appear TOO soft for the controls, and there are some advantages to soft. So I think I’ll make the final choice to design the spar caps for 6g and live with the resulting stiffness.

If you made it to here, WOW, thanks for following along. I'm finding it helpful for me to write down these decisions and processes as I go. It keeps me better focused, and forces me to error check myself more. Hopefully, some of you are enjoying the ride.

-Peter-
 
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peter hudson

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Messages
174
Wing Structure as a Beam (part 3).
I was getting ahead of my posts here, and as sometimes happens I got “wrapped around the axle”. Since writing about it seems to help me re-focus, I thought I’d catch you up.

Wing beam FEM :
So I was attempting to predict wing bending and torsion of my forward swept wing, and back in part 1, I had calculated the wing section properties, then reworked the spar cap sizing in part 2, and addressed wing deflection limits with a flap FEA and some comparisons. I could then just finish a simple NASTRAN beam model and check my deflections:

Results:
11.5 inch deflection at 1g (best L/D) and about .32 degrees wash-in
68.8 inch deflection at 6g (condition I) and about 1.9 degrees wash-in


I started to reconsider the lift distribution at best L/D. Maybe I should build in that much wash-in to get the flat wing I want at best L/D (or running fast at 1g). For strength, it would still require redefining the lift distribution at condition I to account for the more outboard resultant from the wash-in (bad for loads). I next started to think about an accelerated stall condition (say a 6g emergency pull-up) with almost two degrees of twist moving the stall initiation out towards the tips.

Before using this analysis to base significant (and undesired) changes to the wing design need to double check my work.

Thought experiments:
Of course, those results seemed reasonable, but part of checking ones work involves thinking about it from a few perspectives. With a beam model as an effectively cantilevered beam, how much does the forward sweep play a role in the twist? I expect an aft swept wing to develop more wash-out and a forward swept wing more wash-in with bending. But does a beam model capture that? If I change the sweep in the FEA global coordinate system, I'm still applying the same lift and moment forces. The wing gets the same loads and since the end is fully constrained it gets the same deflections AND TWIST. My loads were based on the undeflected wing so it can’t capture the effect of the sweep without re-running the loads with that nominal twist and wing bending (and iterating until converged! And for each condition!). The twist I got was not from being forward swept, but just that the wing section’s shear center was aft of the center of pressure. The bending is where the extra effective twist from sweep is hiding, and adding that bent shape to the XFLR5 (or most analyses) is tricky. And all that twist will be noticeably more than the "results" above.

Another thought experiment was that; if I applied vertical loads at the shear center of an outboard section of a swept wing it should produce twist but by definition, my beam model won’t...it’s not getting a moment applied, and the load is on the section’s neutral axis. In fact, the difference between a section’s shear center, and a beam’s neutral axis, and the definition if the beam is swept (and twists with load because of sweep), has now got me “wrapped around the axle”.

So I do some more reading...
This one turned out to be of the most help:

“On the interpretation of bending-torsion coupling for swept, non-homogenous wings”
by Olivia Stodieck, Paul M. Weaver, Je Cooper

I especially enjoyed the list of papers, definitions used therein, and the inconsistent usage of: Shear center, flexural center, center of twist, torsional center, elastic center, reference axis, elastic axis, flexural line, and flexural axis.

This paper delves into the idea of swept wings having a difference between section properties, flow alignment, bending deflections, and the location along a span one can place loads without effectively changing the angle of attack (twist) anywhere in the wing . And defines a sort of “global flexural axis” or line along a span that a load produces no twist. They present a method for analyzing this for preliminary design that is slightly less than the full FEA mesh approach it wants to replace, but it is still a significant stiffness/matrix method. On the other hand, for me, it does mean that creating a full 3D wing FEA model and applying pressure loads from XFLR5 will capture the twist from sweep as well as geometry.

Like an X-29 but slower:
I was still in the same place of having to consider building in a small twist for good glide performance, and having to beef up structure for wash-in at 6gs (and still uncertain what I thought about all that wash-in and accelerated stall behavior at that condition) and having to iterate the analyses for convergance of deflections and loads.

It occurred to me that if I go to the trouble of building a full 3D FEA with upper and lower wing skins and everything, so I can apply pressure loads, I have the analysis I would need to get tricky with my composite lay-up. In the last post I talked about PCOMP cards in NASTRAN. They allow me to easily change lay-ups and note the change on the wing’s deflection.

Consider the X-29: It’s most famous for having forward swept wings, and getting away with it by clever use of the composite materials in the wing to create bending torsion coupling, and effectively undoing the twist under load of being forward swept. Can I do that on Echo?

Also consider that my wing skin thickness has been driven by handling rather than air loads, I might be able to take out some of my +/- 45 degree layers and replace with unbalanced (upper to lower surface) uni-directional layers that negate my twist (with no extra weight penalty!) If the torsional deflections can be reduced to very small or negative, then I don’t have to attempt to capture the static aero-elastic problem of converging on an amount of twist and bending with load for each condition. That's a pretty exciting idea to me.

I guess I learned something from my beam model...just not what I planned. So perhaps doing a full 3d FEM and some composites tricks can get me OUT of an analysis black hole, AND avoid building a twisted wing, AND keep my existing spar cap sizing, (AND assure a 6g pull-up is not likely to snap roll?) Ok, I'll try it!

I’ll save that analysis for another post...
 
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peter hudson

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Messages
174
Stall Behavior (revisited)
I was thinking about the local lift coefficient approach I’d used to satisfy myself I would have reasonable stall behavior. It revolved around having somewhat lower local lift coefficient requirements at the ailerons, and similarity with other sailplanes. I started to think about the fact my Re, near stall at the tips, is only around 500,000 and that where this airfoil’s performance starts to really drop off. Clmax at the 500,000 Re at the tip is a fair bit less than Clmax at 1,000,000 Re at the root. That isn’t really comparable to other sailplanes which fly a fair bit faster. So time for a session with XLFR5 here’s how my planform and it’s local lift distribution looked in XLFR5:
xlfr5_1.png
The thing I like about doing this with XLFR5 instead of my spreadsheet is that I can choose a “constant lift” type of analysis so that for each angle of attack and resulting Cl the speed is set to produce the same amount of lift. (aircraft weight in this case) and more importantly, XLFR5 uses Xfoil profile data at the resulting local lift coefficient and local Re for each condition/AoA to predict the drag. Now I don’t care about the drag really, but the benefit to me is that if the airfoil section data can’t achieve the required lift coefficient for a part of the span, at that part’s Reynold’s number at stall speed It produces an error. The log file looks like this:
xlfr5_2.png

This was for the planform I thought would be OK, but it went from all sections OK at AoA = 9.0 degrees, to every section out to 6.56 meters (of my 7.5 meters semi-span) exceeding Clmax! That sounds like a little too abrupt with no inboard to outboard stall progression.

So, after a lot of iterations I’ve homed in on a new planform using this method as a check. Here’s the new log file.

xlfr5_3.png

You can see that at AoA of 9 degrees, the part of the wing from 0.0 to 0.94 m semi span can’t achieve the required Cl. So an inboard stall first, and even at the next higher AoA the outboard 1.5 m is still flying. That new planform and lift distribution look like this:

xlfr5_4.png

The new planform is a little more comforting. In reality, the airfoil’s stall behavior is probably at least as important as the planform. Also, I have a less elliptical distribution but the XLFR5 predictions only show about a 2% drop in wing L/D which I’m willing to accept for a possibly better stall progression. The 20% increase in wing tip chord (and therefore Re) improves the airfoils performance at the tip, and reduces it’s requirements to perform.

I wanted to share these thoughts, since we often talk about low Re on high aspect ratio wing tips, XLFR5 made it pretty easy to see the effect it has on our potential for tip stalls due to small chord wing tips.

So another iteration under my belt for this aircraft here’s how she looks now:
3view.png
 

peter hudson

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Like an X-29 but slower

A couple of posts ago I decided to look into an asymmetric layup for the wing skins in order to generate some bending-torsion coupling that would give my wing some wash-out under load DESPITE having forward sweep and a shear center aft of the center of pressure. This required a more detailed finite element analysis. Here are those results:

The original wing skin was 2 layers of .012 inch thick stitched carbon biaxial cloth. In order to accommodate a third layer without increasing skin thickness, I would have to use 2 layers of .008 thick biaxial carbon and find a .008 inch thick unidirectional carbon. This makes the skin layup a little more effort and a little more expensive but it’s the same weight and thickness as before and it fixes the wash-in under load concern. And I can find sources for those weight materials.

What angle to place the uni-layer (sandwiched between the two +/45 layers) was a quick study by re-running the model with changes to the PCOMP cards that define the upper and lower wing skins.

The load case I’m using is the condition I corner of my envelope (Va; max AoA at 6g has the biggest load and the most forward center of pressure) and I use the flaps set at there “reflexed” negative position which has the furthest forward center of pressure. This will maximize the wash-in or “bad” twist of the wing. The pressure loads are taken from the panel method runs of XFLR5.

So here are some pictures!
mesh.png pressures.png def.png results_twist.png
So if I use the optimum of about 24 degrees for the uni-layer I can get a small and favorable wash-in of about 0.4 degrees under a 6g load. It still has about 72 inches of deflection for 6 gs, but that is consistent with sailplane wings. I may still play with other layups using a single +/-45 and a single uni-layer but I’m encouraged that I can avoid the static aero-elastic iterations needed design for the worse load distributions of the wing with the original layup (and the extra weight to manage the increased bending loads). If I come up with a better lay-up I’ll make another post about it.
 

peter hudson

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174

Stability and Control (Part 1)

Wow, moving takes a lot of time...not so much the shifting of boxes from one house to the next, but all the sorting, organizing, home improvements, etc. It really halts the progress of a solo aircraft design effort. Still, I’m looking forward to setting up my new shop. I stole some time to work on this for my mental health, enjoy.

For these next few blogs I want to assess Echo’s stability and control; at least at the preliminary design level. More refined analysis requires reasonable inertia properties which won’t be available until more structural detail design is much more complete. But, I can consider tail volumes, roll rates, pitch trim ranges, and crosswind slips to get a good initial feeling about how she’ll handle.

Tail Volumes:​

For tail volume comparisons I reference “Fundamentals of Sailplane Design” by Fred Thomas. It is an excellent reference, with lots of numbers from a wide range of successful sailplanes. Really, if I land in the middle of those, I’ll probably be fine. As you can see from the graphs, I have tail moment arms and tail volumes that fall nicely among the rest of the pack.
tv1.png tv2.png

Static Margin:​

For refining the horizontal tail size I used OpenVSP’s panel method (which includes the fuselage effects). I define my aft CG limit at 50% MAC, and minimum static margin of 10%, so in OpenVSP I place the CG reference at 60% MAC then play with the horizontal tail size until the Cm/Alpha curve is relatively flat. In OpenVSP the curve has a bit of...well...curvature so it’s only approximately flat and I round up a little on the required area. The 50% MAC aft CG limit was Fred Thomas’ recommendation. I’m designing to that but I’ll probably limit my aft CG to 40% MAC for a little extra margin.
60percentCmy.png

Pitch Trim:​

The tail volume and static margin above doesn’t say quite enough about the elevator’s pitch authority. I next looked at the pitch trim settings for a variety of conditions. For this I’ve used both XLFR5 and OpenVSP but using the vortex lattice method in OpenVSP allows for easier control surfaces definition.

The first case I considered is forward CG limit (25% MAC), “thermal” flaps settings (which are also my max flaps), and the speed and alpha for Cl max. this should require the maximum up elevator to trim. I enter those flight conditions and run the “steady” stability type analysis. I can get the pitching moment (Cmy) and the pitching moment due to elevator deflections (CMm wrt my elevator control group per RAD) from the ##.STAB file (or just Cmde to everyone else!). The results are 7 degrees of up elevator deflection to trim that condition. That still leaves a lot of throw for maneuvers and gusts. I looked at lots of CGs, flap settings, and speeds. My worst down elevator trim condition was also with thermal flap settings but aft CG (50% MAC) and Vne (104 mph). Which required 11 degrees of down elevator to trim which is about half the usable throw. (XFLR5 produced similar results for confirmation). Trimming the pitching moment from the power pod during climb requires some elevator too. That coefficient is defined as:

1659047129617.png
where:
Offset is from the thrust line to the CG
q = dynamic pressure
s = wing area
c = reference chord (MAC in my case)

So I can balance that with the my elevator (Cmde) as before. It takes a whopping 11 degrees of up elevator to trim out the offset thrust from the pod during climb. It’s workable, but that does cost some drag that puts climb energy to waste. I’ll still consider a pair of pods mounted much lower as an option that reduces the offset term a lot. That would be better for climb but probably worse for the majority of the soaring flight. It may be worth considering the trade between a smaller somewhat less efficient prop vs reduced trim drag due to less offset.

There are other things like maneuvering flight conditions I could explore but you get the idea. It looks pretty controllable in pitch. Next time I’ll look at roll authority.
 

peter hudson

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Messages
174

Stability and Control (Part 2: roll rate)

In this one,I will generate the roll stability derivatives with, and compare results from, XFLR5 and OpenVSP. I’ll calculate roll rates and check them against the recommended minimum for sailplanes.

XFLR5:
First I’ll use XLFR5: my model doesn’t have a fuselage (per the recommendations in the documentation) but, for roll especially, it will make little difference. I chose to use the 3D panel method for check against the VLM method I’ll use with OpenVSP. When defining the wing for the panel method, I use flapped airfoils all along the trailing edge, as it allows XLFR5 to mesh the controls deflected position nicely. But I do have to add 0 length wing segments where I want a deflected surface and undeflected surface to exist at the same wing station like where the tip and the outboard aileron come together. (see the XLFR5 docs if you want more!) Here’s the setup:
roll_setup.png
The definition of the control movement needs a little explanation. All the wing flaps are numbered from left to right. So I have the left wing tip “flap 1” (which doesn’t move) set to a gain of 0. next from the left is flap 2 which is the left aileron. I am putting in a right roll command so it gets a gain of 1 (positive is TE down in XLFR5 and most other definitions). Flap 3 is the inboard part of the left flaperon so it also gets a gain of 1. Flaps 4 and 5 are the fixed center section through the fuselage so a gain of 0 for them. Then 6 and 7 are the movable flaperons on the right side which get a trailing edge up value of -1.

When I define the stability analysis I only need to run the control parameter from 0 to 1 and the results will include the stability derivatives including those from that control deflection.
results1.png
When the run is complete XLFR5 pops up a window with the results. There will be some error messages about not calculating eigenvalues since I don’t have rotational inertia defined, but the derivative results are valid. The values of interest for roll are the roll damping, which is the moment coefficient resisting roll from a giving roll rate (rad/sec) labeled “Clp” and for Echo it is -0.733 and the moment coefficient for a unit deflection of my flaperons (in radians) labeled “Clde” which for Echo is 0.527. The negative Clp means if I’m rolling right the damping produces a “left roll” reaction moment. The positive value of Clde means a right roll command is producing a right roll moment.

With these two coefficients we can calculate the steady state maximum roll rate (when the roll moment from controls equals the resisting roll moment from damping). Here’s the equation:

1659376460746.png
where:

Wx = steady state roll rate in rad/sec
V = velocity
b = wingspan
Clde = roll moment coefficient per rad of control deflection
Clp = roll moment coefficient per rad/sec of roll rate.
Defl = control deflection in radians (note that if you use differential ailerons it is usually defined as the average deflection but it depends on how you defined the gains in XLFR5)

The velocity term means we will have different roll rates at different speed, as expected, but for what speed should I check it? Well the only reference I have that recommends numbers for minimum roll authority is the “Sailplane Rule Book” from EASA which states:

Using an appropriate combination of controls it must be possible to reverse the direction of a turn
with a 45° bank in the opposite direction within b/3 seconds (b is the span in metres) when the turns
are made at a speed of 1.4 V S1 with wing-flaps in the most positive en-route position, air brakes and,
where applicable, landing gear retracted and without significant slip or skid.


For Echo with flaperons set to thermal position (which is their maximum) the stall speed, when light with aft CG is 15 meters/sec and this roll recommendation speed is 1.4 times that, so 21 meters/sec. (I’m picking the slowest condition) The other thing to note is that without roll inertia well defined, it’s not possible to calculate the steady state 45 deg to steady state -45 deg time since I can’t determine the acceleration and deceleration terms, but for preliminary design those parts of the maneuver are considered small enough to ignore. If I ignore them, then the above criteria says I need to roll 90 degrees in b/3 seconds. For my 15m span that’s 5 seconds so I have a recommended minimum of 18 degrees per second at 21 meters/sec (but I want a little more to account for the missing acceleration and deceleration lags).

The other thing I need to define is my maximum control surface deflection. It’s common to assume a maximum control surface deflection of +/- 25 degrees for ailerons but I have two things going against me on that. With flaperons I have already given up some of the down deflection, and at these low Reynolds number I may have more trouble getting the flow to stay attached at that 25 degrees. I do plan to use some differential ailerons so 12.5 deg down and 25 deg up is equivalent to 18.75 degrees of throw. I’ll reduce that to maybe 15 degrees average to minimize the concern over early flow separation. (and 15 deg = .26 rad) I can, and probably will go back and redefine the XLFR5 wing flap gains to reflect the differential but for now I’ll leave that alone and consider +/- 15 degrees without the differential.

So for Echo (according to XLFR5’s panel method) I have:
1659376542066.png
Which is 30 degrees per second steady state roll rate which makes me pretty comfortable.

OpenVSP:
Let’s do that again but with OpenVSP…
OVSP_setup.png
In this case I have the controls defined as subsurfaces on the wing, fin, and elevator. I tried a run where I combine the ailerons and flaps into a control group and gave them all the correct gains but the runs did not produce a .stab file. After quick help from the OpenVSP team (they are very responsive!) I found I needed to redefine the ailerons so that control group only included a right and left aileron that ran the full span of my combined flaperons. So the new control inputs look liked this:
ovsp_controlgroup_2.png

Notice that the gains are both positive in OpenVSP. The little arrows show the positive deflections and they are opposite across the centerline rather than TE down for all. Also important is that using subsurfaces currently only works with the VLM method but it does include the fuselage panels. To get the stability derivatives after the run, you open the ###.stab text file:

ovsp_results.png
The stability derivative nomenclature is slightly different the roll damping moment coefficient is called CMl wrt p per rad and the roll moment per unit deflection of aileron is Cml wrt ConGrp_1 per rad. Notice the sign for roll authority is different than with XLFR5 but the roll moment about x per deflection is positive (dotted circle). So our derivatives (translat
ed back to XLFR5 nomenclature) are Clp =-0.745 and Clde = 0.495

And the results for Echo are:
1659376762657.png
Or 28 deg/sec, so I’ve got good agreement between two different codes using two different methods, and they both show a reasonable margin over the recommended minimums.

Next I’ll check the rudder authority by looking at a slip for a strong crosswind.
Thanks for following along!
 

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peter hudson

Well-Known Member
Joined
May 24, 2020
Messages
174

Stability and Control (Part 3: cross-winds and slips)

How much rudder is enough? I think it It depends on how much cross-wind you want to be able to handle with a slip. Also I need to check it for enough authority to counter adverse yaw with a hard over stick deflection. For design guidelines I again look to EASA’s “Easy Access Rules for Sailplanes” (also referred to as the Sailplane Rulebook) which states:

"With a crosswind component of not less than 0.2 V S0 or 15 km/h, whichever is the greater, it must be possible to perform normal approaches and landings until the sailplane comes to a stop, without exceptional piloting skill and without encountering any uncontrollable ground-looping tendency."

My lightest slowest stall speed (Vso) is 15 m/s and 0.2*Vso is 3 m/s (10.8 km/h) so 15 km/h (4.17 m/s) is greater. And I have an approximate touchdown speed of 1.2*Vso (18 m/s). So my slipped condition is a forward speed of 18 m/s and a crosswind of 4.17 m/s or about 13 degrees of slip angle to keep my wheels line up with the runway.

Side Slips (OpenVSP this time):​

I want the effects of the fuselage since there is so much more fuselage side area in front of the cg than there is behind (owing to the typical sperm shaped sailplane fuselage). Plus I can easily set up the different control surface deflections and yawed flight conditions in OpenVSP, so it seems ideal for this analysis.

The plan is to establish what steady state yaw angle I need to maintain (13 degrees) how much rudder it takes to maintain it, and what aileron deflection and roll angle I need to to balance that rudder, and all the yaw roll coupling from dihedral and stuff. So yes, it will be an iterative process. When I can get the roll and yaw moments near zero (steady state flight condition) while maintaining the required yaw angle, I’ll get a feel for how much rudder authority/margin I have.

After a several iterations I had determined the control positions that resulted in basically 0.0 values for roll, pitch, and yaw moment coefficients while maintaining the 13 degree yaw angle.
slip.png
So a slip to align myself with the runway against a 15 km/h cross wind requires 13 degrees of rudder (and a couple of degrees of aileron to resist yaw roll coupling.) That leaves me with a fair amount of margin for gusts and things.

Coordinate a turn:​

Next I set up runs with no yaw angle but hard over (18 degree average) ailerons, then played with how much rudder I needed to result in basically a zero yaw moment coefficient (the rudder countering the adverse yaw moment of the deflected ailerons). Again it was done through iteration. I know I could have predicted it with the stability derivatives, but this goes really fast so I just ran a bunch of rudder settings. Here are those results:
coordinate.png
So hard over ailerons required about 10 degrees of rudder to coordinate the turn (maybe ½ my total deflection) which seems pretty reasonable for a sailplane to me.

In the last three posts I’ve tried to get a warm feeling about roll, pitch, and yaw control authority. There is much more to be done with stability and control but I needed to lock in these control surface geometry to continue to work on loads, strength, and structural design. At this point in time I feel that this current geometry is looking pretty good from a stall behavior and handling point of view so I can return my attention to structural design.

Thanks for following along!
-Peter-
 

peter hudson

Well-Known Member
Joined
May 24, 2020
Messages
174

Composite Design Allowables (Part 1: Is guessing OK?)

This topic borders on being a moral dilemma for me. There have been many times in my working career when I insisted on seeing b-basis material characterization for material properties used during a design review. After all, if your guessing at material strength, your really guessing at your margins of safety. Now, as a designer of an experimental homebuilt aircraft, I clearly don’t have the resources or time to do coupon level testing with statistical numbers of samples, at varieties of temperatures and absorbed moisture. Some of the test matrices in CMH-17 (the gold standard for testing composite materials) suggest that, for prototype airframes, a reduced set of tests (as few as 1 batch of 6 samples per property) might be OK. But that still adds up fast with several materials and many properties per material. Also, the test methods and fixtures are quickly beyond the scope of a home designer/builder. So I’ll be guessing at my material properties. This post will talk about how I might make an educated guess, and what I plan to do to manage the risk that guessing imposes.

AGATE database:
A few decades ago (1990s) NASA teamed up with the FAA and many companies in the aviation industry to try to address the decline in general aviation. Many of the projects were sponsored under the umbrella of “Advanced General Aviation Transportation Experiments” or AGATE. Part of the “problem” was that certifying advanced composite materials was beyond the scope of small businesses that might otherwise introduce some exciting new aircraft. A consortium of material suppliers, test houses and aviation companies posited that a freely available set of material properties for advanced composites should exist so that a new design project only needed to prove their internal material processes produced “equivalent” material properties (a much much smaller set of tests). And the consortium set out to do just that. The results of that project are at AGATE since then, that idea has been transitioned to Wichita State University under the name National Center for Advanced Materials Performance (NCAMP) which you can check out here: National Center for Advanced Materials Performance

There is a challenge to this idea of a freely available database. These materials quickly become unavailable, manufacturers change hands (and processes). New materials get adopted over old ones, some chemicals and resins become unavailable...in short this database has a shelf life. So we homebuilders are going to order composite materials from what’s available now, and affordable, and it won’t be the same stuff from year to year.

What’s a good guess?:​

The above implies that we can’t really use the full strength and advantage that high performance composites offer, but should use reduced strengths to account for material substitutions, process variations from builders, etc. Is there already a standard list of reasonable design allowables for composite homebuilders for different materials? I haven’t found one, especially one that includes any supporting data. There are a number of sources that do list some strengths that are worth reviewing such as the “Composite Design Manual” by Jim Marske, I also like to compare to the AGATE database for similar materials. For example I have a skin using +/- 45 degree IM7 biax with epoxy resin infusion; I can expect it to be similar to (if not a little better than) the AGATE laminate design allowables for wet lay-up of T300 3k plain weave carbon fabric with E765 epoxy resin.

Coupons → Sub-component → Full-scale test:​

The typical approach to using the statistical amounts of coupon data is to then do just a few sub-component tests for things like stiffened panels, joints and fittings, spar sections, etc. These explore the more complex 3D interactions of the materials when used to build something. It helps to identify places where that build process reduces the material properties or finds failure modes not really addressed by little coupons. I think this is the key to the homebuilders “equivalency” testing. If a particular design has a bit of structure that is critical, then I propose a set of plans needs to include a sub-component test article that stresses all the elements of the test component to the design allowables assumed. It should be similar to the actual structure but designed to be broken. The builder can load to “limit” then “ultimate” (2x limit) then on to actual failure to confirm his material choices and shop practices get the strength the airframe needs. It would likely require several different test components to cover different structural details, joints, other materials in the design etc. but it should be within the scope of maybe 10 to 20% of the total build time and material costs. These broken components provide the bulk of the confidence in the airframe, but it wouldn’t relieve the need to proof load the actual structure you intend to fly. Proof loading is typically 1.1 X limit load but I’m not sure I think that is enough with all the guessing that has happened. Metal components should be capable of at least 1.15 limit load without yielding so, if there are metals in the load path, there may be a practical upper limit for a proof test of the airframe. I may go to 1.25x limit load I don’t know yet, At any rate, the designer should define the recommended proof loading test(s) for a builder to perform.

Sub-Component Example :​

Here I’ll work though an example for the materials/concept I’m using for my wing spar. In order to keep the component reasonable small, I’ll design something to represent the spar out towards the middle of the wing. There are a number of limits and structural details I want to test with one component. Primarily the test should validate:

-Web shear strength
-Pultruded spar cap strength
-Hard-point bearing strength

Now since this is my first structural test for this design there are some other things I want to check with this sub component, such as:

-How well resin infusion works with a stack of pultruded rectangles (flow between rods)
-How well resin infusion works with the foam core (if I use one)
-Web buckling (just confirm it’s not the failure mode)
-Spar cap buckling (just confirm it’s not the failure mode)
-Pultrusion drop-off issues

Conceptually, here’s the test component:
spar_test1.png
It’s the same height as the spar in the constant chord section of my wing. I’ve shown it without foam core or the 2nd layer of carbon fabric. It’s a beam in a 3 point bend test. I can pick the load P to produce the shear stress I want, and the distance will determine bending moment in the middle to produce the spar cap stress I want. The hole diameter in the middle can be sized to produce the bearing stress I want. Here are the shear and moment diagrams:

s&m.png

Web shear strength:

The design allowables I’ve found for web shear strength vary considerably. Marske’s “Composite Design Manual” shows a plain weave carbon fabric and epoxy laminate as having 40 ksi shear strength for +/-45degrees. However, the AGATE data for 3K plain weave carbon, wet layup with epoxy (MGS 418) shows an F12SU of 14.1 ksi (B-basis RTD). But F12SU isn’t really the way we use it since the web gets laid up at +/-45 deg. Several sources show the relationship between shear strength and orientation of fabric based composites such as:
shear_orient.png

Note this shows a shear strength at 0/90 deg (basically F12SU ) of about 14 ksi and when used oriented at 45 deg it’s up to 24.0 ksi. (a 1.71 factor increase!) This data is for 7781 e-glass fabric but basically its the same F12SU numbers that AGATE shows for the T300 plain weave. Which implies it would be 24 ksi for the carbon fabric at +/-45 deg. I don’t expect myself, or most home builders, to have the same level of consistency as what went into those test coupons, and there are variations from resin and fabric substitutions, and other factors so I could set my design allowable to 20ksi in shear (for +/-45 deg) to cover those.

So I want to produce 20 ksi in my test component shear web. It’s two layers of fabric, 0.024 inch total thickness and 3.8 inches tall.
1662589237274.png
So: P = 1824 lb (and 2P = 3648 lb). Note these are “ultimate” loads to reach the material ultimate strength.

Pultruded Spar Cap Strength:

Marske’s strengths for “Graphlite” pultruded rods are claimed to be 325 ksi tension and 270 ksi compression. I’m currently planning to use the 2mm x 5mm “Sparlite” which is a Chinese pultrusion imported by HP aircraft. (Boku!). Bob did some compression tests and suggest they are “similar” to the Graphlite properties but it’s really up to me to set the design allowable. If I used a very optimistic number like 270 ksi my wing is a bit too flexible. I was happy with the wing bending prediction if I increased the spar cap area to a value that produces 100 ksi at limit load or 200 ksi ultimate which seems like a reasonably conservative knock down to cover unknown suppliers in the future. The 2x5 mm rods have 0.0155 in2 area. And I want to test a small stack of them to get a first look at infusion to bond them together. At 200 ksi (ult) my wing spar ranges from needing 24 rods at the root, down to not even 1 at the tip. It needs five rods about half way out the wing panel so that seems like a reasonable test number.
1662588803854.png
So I want a cap load of 15500 lbs. My cap centers are 3.36 inches apart so I need a moment of 52080 in-lb. From the S&M diagram the moment is P*l and P is now 1824 lbs so the length is 52080/1824 = 28.5 inches.

Hard Point Bearing Strength:

My hard point plan is to use ¼” “Garolite” or G-10 or FR-4 or equivalent. I’ve found a few sources for tensile and compression data but none for bearing strength. The AGATE data for 7781 laminate with equal parts 0/90 and +/-45 layers might be close. It shows 33.8 ksi for single shear and 65.3 ksi for double shear. Marske suggested 25 ksi for the “Rutan” fabrics. I honestly expect the G-10 to be quite a bit better than that, and I may get into testing it at a coupon level. I really only have a few places that get hard points but they are critical! So I’ll use 25 ksi as bearing ultimate for design.
1662588825049.png
So I need a hole diameter of 0.584 inches to hit my design allowable for this test.

What does the test really mean?

I plan to set up the test using an hydraulic engine hoist to apply load and use a 0-5000 lb load cell to record the load data. The 3648 pound load represents an ultimate load. If my properties were all perfectly correct, then the component would fail in web shear, cap compression, and hard-point bearing all at once. What it really means is that if I reach ultimate load then my materials and processes would be adequate for the real aircraft. Then, hopefully, I can continue the test to failure if that happens below my load cell limit.

This sub-component test also gives me a look into other failure modes such as buckling. I may need to add some ribs and skins to the test article if it fails due to cap or web buckling. It will also confirm the transfer of load from the G-10 to the web and into the spar caps. Also, there is a stiffness discontinuity from the hard-point which was superficially addressed by shape, but not through any analysis. Lastly, this sort of “hand calc” analysis misses lots of real world interactions of this 3-dimensional, multi-material, hand-assembled component, and this test may show me areas that need a more careful analysis.

Well I still have a lot of work to do getting my shop set up after my move, but I'm eager to build this component and break it!

Thanks for following along!
 
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