More ANSYS runs

Using the 75/25 load split between LE and TE, and with the addition of the forward sweep cable, I re-ran the 6g loading case on my Goat wing.  Not altogether different, as you might expect.  The bowing shape is still roughly the same.  The maximum stress is roughly the same.  At first glance, the results are pretty equivalent.

 Maximum stress is still in the leading edge tube between the jury strut attachment and the wing root pin joint.  There is still some bowing of the main struts upward as the jury struts are pulled on by the main spar.  
Do note that these deflections are listed as approximately 0.5 inch.  With such a low-fidelity FEA, I'm expecting somewhere between 3-12 inches of actual deflection during the load test, but the point is to say that the shape shown in the analysis is scaled to be visible.  ANSYS has a true-load deflection option and it shows essentially no discernible deflection.  Beware of length scaling.



To answer a few other questions:

• I am too far into the build to change the main strut attachment location to the wing spars.  So, what you see in the FEA is what I have to work with.  Potentially I can add additional sleeve length or inner sleeves to the jury strut location or also change where the jury strut attaches to the main strut.
• I am not using Schrenk's approximation or an elliptical load distribution.  Instead, this loading comes from the AVL model, which is likely better than Schrenk for arbitrary wing planforms.  See a previous post to learn more about the AVL work.
• I have so much margin left in the wing structure near the strut attachment that I'm not going to run the asymmetric aileron loading case.  The FEA in my mind was more concerned with showing how much margin to yield or ultimate load that I had, rather than doing the detail-work checking for aeroelastic effects.

Finally, I'm thinking it's worth moving onward with the construction.  Additional sleeving can be added at the jury strut attachment location without invasive surgery, so it doesn't hurt me to continue on.  There is a kitchen renovation in my near-term future (July), so the time is ticking away before another major delay!  Ack!

I should probably add that I'm narrowing in on a decision to load-test to 4G's.  According to the FEA, this should be well below where I'd anticipate any yielding and is more than I plan on pulling (no loops, heh).  A cohort at work has even suggested it will be difficult to pull that many G's in the airchair, considering the high drag count and low-performance airfoil.  Self-limiting is good in this case :-)

Detail work on structures analysis

Among a bunch of great questions/suggestions/feedback, I took a look at the fore/aft distribution of forces on the two spar tubes.  The previous analysis ran a simple 50/50 split of the wing total forces to get things started.  What is better?  AVL can help provide the answer.

Under a 7g (using this now instead of 6g) load case at CL of 1.5 (assumed CLmax), the element forces can be plotted (seen above).  This gives the distribution of CP along the airfoil chordwise and showing the distribution of force.  For the root, here is the element force distribution:

 Strip # 25     # Chordwise = 10   First Vortex =241
    Xle =   3.16670    Ave. Chord   =    5.0000   Incidence  =    1.7500 deg
    Yle =  -0.59947    Strip Width  =   1.20000   Strip Area =    5.999976
    Zle =   4.03135    Strip Dihed. =   -2.9939

    cl  =   1.56703       cd  =   0.73643      cdv =   0.67992
    cn  =   1.66386       ca  =   0.47903      cnc =   7.78287    wake dnwsh =   0.10109
    cmLE=  -0.55324    cm c/4 =  -0.13727

    I        X           Y           Z           DX        Slope        dCp
  241     3.19462    -0.59918     4.03134     0.17282     0.28424     5.05604
  242     3.41428    -0.59918     4.03134     0.37261     0.14534     2.82108
  243     3.83407    -0.59918     4.03134     0.54628     0.08312     2.09844
  244     4.41670    -0.59918     4.03134     0.67141     0.03037     1.77600
  245     5.11040    -0.59918     4.03134     0.73689    -0.01091     1.54034
  246     5.85353    -0.59918     4.03134     0.73689    -0.04508     1.32883
  247     6.58005    -0.59918     4.03134     0.67141    -0.06874     1.10233
  248     7.22542    -0.59918     4.03134     0.54628    -0.08517     0.86729
  249     7.73230    -0.59918     4.03134     0.37261    -0.09597     0.62162
  250     8.05563    -0.59918     4.03134     0.17282    -0.10036     0.35427

The X position does not start at zero because I use the nose of the glider as the origin location.  An X position of 3.1667 is the LE at the root if you were curious.  Plotting the X position vs the dCp value gives the distribution of pressure along the airfoil chord.

Now some simple statics can give the force distribution between the LE and TE.  Assuming each CP acts like a force on a beam, the component of load carried by the LE and TE can be found by multiplying the force by a ratio of distance to the beam length.  The beam looks like this:

Component of force F acting at a distance xa from simple support A is given by: F_a = F * xb / (xa + xb).  Carrying out this algebra using the CP distribution from AVL along the root chord gives 74% on the LE and 26% on the TE.  Note that different airfoils and loading conditions will have different CP distributions, so don't use this approximation for any other purposes.  Also, this force split does not account for a tilting of the lift vector due to pulling angle of attack, but I will be considering this split sufficient for a static loading case.  This is certainly more representative than 50/50...

Note from the AVL plot that the root airfoils are working harder than the tip airfoils, with regard to a CP peak at the LE vs more evenly distributed along the chord.  Using the force distribution at the root (75/25) should provide a conservative estimate of the LE spar loading out toward the tips.  I may also run 100% on the LE just to see what that looks like.

Structural analysis preliminary results

Alright, I stayed 1.5hr after work and made a huge dent in the structural work.  Thanks to Trent for helping me get set up on ANSYS.  Here we go...

The primary wing structure was input as BEAM188 elements with a tube shape of varying wall thicknesses.  This includes the LE, TE, and struts.  Where the sleeves are installed inside, the element thickness was increased to match the total wall thickness (no-slip as if it was machined). 

The compression ribs, cables, and jury struts were treated as LINK180 elements with the cables as tension-only elements.  Note that the cables connect across the rib bays as they connect in the real aircraft.

The loading case chosen was a 6g load of a 300lb AUW airframe.  AVL gave the loading distribution across the span, which you'll note tapers off somewhat elliptically from the root to the tip.  To note, the tip sees very little actual loading and the majority is probably the center 1/2 to 2/3 of the wing.

Load was split up 50/50 between the LE and TE, which may not be exactly fair, but is a good first pass.  14 discretized loading locations represented the full half-span of load, some 938lb (conservatively including interpolation error) spread along the rib connection locations.

The LE and TE constraints are pins, fixed in x/y/z space and allowed to transmit moments only in the drag-direction (z if you're counting).  Similarly, the strut connection to the fuselage carry-through tube is set up the same way.  Furthermore, the strut to LE connection can only transfer forces, no moments, which reasonably represents the pinned connection out there.

Do disregard the stray line in the above screenshot; it was taken early while I was still cleaning up the element numbering.

Now the fun stuff... solving the FEA.  The right wing is shown.

Looking at von-Mies contour plots by element starts to quickly illuminate some unexpected results!  First and foremost, the cantilever portion of the wing tip isn't bowing up.  To the contrary, there is hardly much deflection out there at all, and it's ironically down.  That's explained by the significant loading on the inner portion of the wing bowing UP.  Yup, for a positive loading on the wing, the middle of the wing bows up.

Looking at the bottom of the spars shows the maximum stress concentration in the trailing edge.  This is a compression stress.  Turns out that the jury strut connection areas are the most stressed in the wing.  What else is important to note is this location is where the 12' tube meets the 6' tube.  There is only actually a sleeve there.  That is going to change.

This view also shows the minimum stress is at the leading edge attach point.

What you should also be seeing is the struts themselves are bowed.  A lot.  Hm.

I'll be taking another look at the Euler buckling criteria to ensure the relatively smaller strut tubes aren't being pushed to the limits.

Oh also, check out the maximum stress: 8500psi.  According to matweb and wikipedia, the yield stress of 6061-T6 is approximately 35,000psi.  The fatigue limit is 14,000psi.  Meaning, occasional pulls of 6g aren't appreciably fatiguing the structure and we're looking at a safety factor of 4 prior to yield, let alone ultimate.  Take this with a grain of salt ... FEA is an approximation.  But seeing such large margins of safety is really making me smile :-D

Last screenshot is a closeup of the underside of the wing.  Just because electrons are cheap.  And I thought it was a cool picture.

There are several uncompleted tasks / unanswered questions, namely:

• more fidelity in how the load is split between the leading and trailing edges,
• better representation of the spar to spar joint with inner sleeve, now that we know that's an important location,
• what is an appropriate sleeve arrangement for the jury-strut attach point?  This ventures from analysis into design changes.
• check into buckling.

I'm happy to take suggestions or feedback.  I'll post the model in a few days.

Disclaimer: This is not considered structural advice; I consider this post (and all) my personal notes and rhetorical discussion.  This analysis is only for my implementation of a design I found online and does not constitute engineering advice for your project.

Cable

I was short some thick washers, so thought it would be a good time to get the cables:  3/32" Stainless Steel 7x7 control cable.  I estimated 120ft was 15% more than I needed.  This stuff is pretty hefty... Aircraft Spruce lists 920lb strength.  The structural analysis I'm working on includes a cable member so we can get an idea of the loading in the internal bracing.

The structural analysis is still ongoing.  It's slow working for ten minutes at a time before/after work.  The simple quick tests that my coworker has shown me look absolutely fantastic, so I'm hopeful for good results.  My plan, I believe, is to run the structure that I'm building to:

1. Find the loading for yield/ultimate.
2. Figure out the first component to fail (which joint is most stressed).
3. Decide on any changes and rerun the analysis.
4. Get tip deflection numbers to anticipate during the load test (if they are within 15% and I would feel pretty awesome about the analysis).
5. Based on the analysis and load test, make a V-n diagram that I can hold myself to... this should also help justify the "has not been known to fly faster than 45mph" Vne.

What I'm really looking for in the structural analysis is a warm-fuzzy that the structure can carry me without breaking.  Beyond that is gravy.

Encouragement video

The Yando Goat is doing some more flying this autumn (southern hemisphere) season.  I thought this would be worthy of posting as encouragement for myself, as well as showing the structure actually has flown.  If you're interested in the structure of the Yando Goat, join the airchair yahoogroup.