this is a substantial piece of work. I like that it estimates strut and fuselage loads.
Be very careful just using it.
There is no listing of wing beam shear, bending moment, and torsion vs spanwise position. I was expecting those as they are the origin of loads in the struts and root mounts as well as driving spar design. I suggest that doing the calculation of shear, bending, and torsion curves while you have all the rest of this info in one place will help the designer to minimize weight. Spar weight is minimized with the strut mount further out along the span...
The assumption that the spanwise center of lift coincides with strut mount can result misplacing the strut to a place that builds in more weight rather than less.
The use of Shrenk's Approximation overestimates the loads from the outer portion of the wing. In general design, this can cause the designer to place the strut mount at a place along the wing that drives higher moments in the spar set and thus increase weight in the heaviest single item in the wing.
I also find significant that the strut tension (in positive g) and strut compression (in negative g) are not included.
Clmax and alpha as input are both insupportably high.
The removal of distributed wing weight from the root loading is more realistic than leaving it in, but neglects to add that load back into the spanwise loading, which decreases some wing loading applied to the analysis and decreases the calculated loads at the mountings...
While VsubD is talked about, I did not see the case. Maybe I missed it. Here is the problem with only doing VsubA - it is max Cl alpha, usually around 15 degrees, while VsubD is around 3-5 degrees. If you calculate I and EI of the wing rotated to 15 degrees, lifting loads perpendicular to the chord line are modestly lower, while pitching moment is relatively modest. Doing a downtown job on analysis at VsubA is the most severe cases for forward component of lift and may be the most severe for analyzing mount loads. You also need to do VsubD where you simultaneously have more load perpendicular to the chord line, much more pitching moment, and much higher inflation forces from higher q. Then there are the equivalent negative g points, which can matter a lot due to the wing-beam being asymmetric, struts are in compression, etc.
Thanks for your considered critique, Billski. The spreadsheet was an attempt to understand the calculations behind an analysis report published by Tennessee Engineering and Manufacturing (TEAM). The report describes the method in general terms and does include shear and moment diagrams but no actual calculations just the resulting loads on major components and fittings and the associated safety factors. So I turned to Hiscocks for a method this engineering dropout could follow. But my primary goal was to understand the loads on a cabane structure I had built converting my Minimax from a shoulder-wing to a parasol wing. Hence the focus on spar reactions and strut loads. My airplane has not flown in either configuration. Perhaps that should be my postscript.
My calling the spreadsheet a stress analysis is a misnomer, certainly. This is a peek at an existing design so most of the parameters are fixed while others might be somewhat "massaged" in order to fit the TEAM results. TEAM used a C˪ of 1.5 according to the report so that's what I went with. Hiscocks does make blanket statements like "all reasonable thin sections have a lift curve (C˪ v. angle of attack) slope of 0.6/radian" or 0.1/°. And the slope should be modified for "3D effects" by R/(R+2) where R is the aspect ratio. I think also TEAM was trying to make the 1100R Part 103 compliant so they claimed a 2.0 C˪ with the full-span flaps deflected. This is allowed by AC 103-7. All that leads to the drastically high angles of attack at Va (67mph). But without that high-alpha I couldn't get near the results published by TEAM. Of course one can alter the inputs and formulas any way they like. The example worked by Hiscocks also had an alpha at Va exceeding high, 23°.
I had planned to calculate the other three corners of the flight envelope but decided I could get reasonable answers simply by modifying the inputs. For example Vd loads can be gotten by decreasing the angle of attack until the airspeed matches the dive speed (110mph). Loads at G and E might be had by reversing the sense of the moment coefficient(?) and lowering the load factor (and probably selecting a more appropriate lift coefficient). Then the struts loads simply change from tensile to compressive. Or is that going too far?
Hiscocks does no calculus which is the point of his book. Maybe that explains the shortcuts and conservative choices. I imagine TEAM was conservative knowing that all manner of builders would be building their airplane.
Anyway, I hoped it might be of use if only for discussion purposes and am glad to have the opinion of a professional.
I too am building a Parasol Mini Max (VW powered variant). Wings are complete and I'll be starting on the fuselage this fall (winter project) and want to complete some analysis, such as what you have done.
Since you have already travelled a ways down this road I am curious as to any things you discovered along the way that I might benefit from lessons you have already learned.
Also, I saw your posts on the East TN Lonesome Buzzards forum for Mini Max aircraft. There you stated that you had converted a mid wing standard minimax to the parasol configuration. You also stated that a W&B check showed a "tailheavy" condition and hence you moved the engine forward.
I'm curious as to if you moved the wing "straight up" or shifted it somewhat. If you did move it straight up I am interested if you think the change to a parasol created the CG issue somehow or of you believe or know that it existed in the previous mid wing configuration.
I appreciate the info you have already provided on your project.
I supposed that since the Himax exists, a parasol should be doable. After all, remove the Himax windows and you have a parasol. But I didn't want to build a center section, so I gave up some wing span and built a root tube supported by angled struts. This was somewhat complicated because my fuselage was already covered and I didn't want to remove the covering. So the wing is simply raised straight up and doesn't affect the weight and balance very much. The plane was already tail heavy with the Rotax 277. With a 1/2 VW, you should be ok.
I was concerned about the wing root loads. Did the cabane structure have to react shear loads? What about chord-wise loads? Asymmetric lift loads? The shear and bending diagrams from TEAM indicated little shear at the root. For asymmetric lift, FAR Part 23 simplified design load criteria says to use 100% of the maximum load on one side and 70% on the other so I guess that applies to the compressive/tensile loads imposed by the wing spars. For the chordwise load, my drag truss analysis shows a 600 lb forward load in each root rib so I believe the cabane structure has to react about 1200 lbs forward (Billski? anyone?). The Himax reacts these loads with wood cabin uprights braced by angled aluminum struts. The rear pair of angled struts in the Himax are also angled forward so they can react chordwise forces as well as spar axial loads. I use a pair of struts angled forward to the fuselage longerons to take the chordwise load in compression as well as a pair of brace wires leading to the tail, a belt and suspenders approach.
Yes it should be possible - cut out the windows, as you said.
Also, the Roger Mann Ragwing Ultra Piet is a close approximation and visualizing it as a mini-max winged single seat Pietenpol indicates it is doable.
I first considered a single piece wing (like the original Pietenpol - but of minimax airfoil and "style") but decided the required building space and ease of transport made the three piece wing more practical. Also, to keep the cabanes vertical (Piet style) I opted to just build a center section. There is the option, I suppose, to keep the struts vertical AND join the wings at the Aircraft Centerline but the loads seem more complex in that configuration and I am still challenged even by simple models. So for this go at it I am looking at the "three piece wing" - even though it is like building an "extra wing".
The spreadsheet you posted, as well as your post just above, are informative (at least to a novice like me). Thanks.
I'll post back here my analysis of the strut loads on a parasol minimax - after I finish learning how to do it, a process I have learned a lot about in an adjacent thread here at HBA.