LAA Schrenk Approximation

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imamac96

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May 10, 2018
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Hi All,

I'm trying to learn a bit about Schrenk's approximation.
There's a great little document from the LAA on Schrenk Approximation (http://www.lightaircraftassociation.co.uk/2010/Engineering/Design/schrenk approximation.pdf), which I'm trying to emulate.
I've gotten consistent results with them so far, but I'm very stuck once I get to their section on Wing Root Reaction.
I should understand this stuff from Statics/MoM, but I can't quite figure out where they pull numbers from.

They say in the second to last paragraph on Page 11:
"Hence in this example case, the constant ultimate bending moment across the centre-section can be assumed to be 116596 lb in. The root shear reaction can be assumed to be (2575 - -731) = 3306 lb per side."

I have absolutely no idea where these (bolded) numbers are coming from. They're not listed anywhere else in the spreadsheet. There are no calculations for these described.
Is anyone familiar with this document? Would it be possible for anyone to describe this calculation?

I'm not sure if -731 is calculated or specified, but it is in the spreadsheet to represent the reaction at the wing root joint.
I have absolutely no clue where 2575 came from.

My work so far is here if you'd like to inspect: Schrenk

Thanks,
Connor
 

imamac96

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May 10, 2018
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North Texas
Bilski, I checked before posting. HotWings cited the LAA paper awhile back. That's the only mention. The work for Schrenk's distribution has already been done. This is more of a reaction force question. I finally figured it out after being stuck on this today.

As the paper states, "Hence, at station 15, the total shear reaction must equal the shear at the aircraft centre-line. This will result in zero shear at the aircraft centre-line...". Newton said that every action has an opposite and equal reaction. The lift of the element assigned to station 0 is 487.08 lb. The reaction force is the same magnitude but in opposite direction, so it's -487 lb. The spreadsheet matches the LAA spreadsheet now.

Spreadsheets are not always so great and can be brutal to follow. The changing of sig figs here really messed with me.
I hope that if anyone else is ever stuck on this, they'll find the answer here.

-C
 

plncraze

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If I remember this correctly the paper has a short version of the spreadsheet and then an extended version of the same listed below. I believe the short version is pretty much as it appears but the extended one below this has some cell which are manually entered and this is briefly mentioned in the text. You can find the NACA paper by Schrenk with a search. I hate it when there is a change that is given in the text but not explicitly mentioned near the copy of the spreadsheet given in the paper.
 
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I have absolutely no clue where 2575 came from.
It gets kind of 'lost' due to the example having landing gear adding to the bending moment and wing weight subtracting from the ultimate bending and shear. Also the numbers in the text appear to be a mix of limit and ultimate.....not the easiest to follow. My calculator gave me 3312.75 (ultimate) for the root shear using napkin grade math..........compared to the example (2575+731=3306)

This kind of illustrates why sharing spreadsheets has limited value. Unless you understand how the sheet was built it can be pretty hard to follow/figure out just where the numbers come from.

^^Ditto what plncrazy said
 

imamac96

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Joined
May 10, 2018
Messages
33
Location
North Texas
Hot wings, You are a lifesaver. I was still lost at that. Thank you so much to you both! Yes to plncraze, it starts with a basic Schrenk approx and then builds on it. The beginning stuff is pretty easy to follow.

It’s not impossible to be successful when sharing a spreadsheet, but the steps aren’t all explicitly explained along the way. The use of column numbers in the math steps had me lost for quite awhile until I realized that they were column numbers. This is really unconventional to me.

-C
 

plncraze

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Check out the beam shear spreadsheet that wsimpso1 did. That gives you sort of the same thing explained a different way. I find three or four different explanations of the same thing are more valuable than the standard textbook descriptions.
 
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