rect is rectangle, tri is triangle.  What I do is calculate the area of the rectangle between any two of the ribs and then the area of the (2) triangles (treating is as a single triangle), then I calculate the centroid individually, and the the centroid of them combined. The shear is then the total area times the wing loading and the moment is the total shear times the distance to the combined centroid from where the section cut is made. Once you have the moment, you just divide by the spar cap height (center of cap to center of cap dist) to get the cap load. Of course, once you get that you divide by the load/rod to get the number of rods. Marske did his at 8 Gs, but I think I've seen some 6g gust loads and since people in sailplanes are actually looking for strong thermals, and the rods don't add that much mass, then I don't see any reason to not go the 6g/9g route.

Again, if you make the spar symmetric, just size the flange with the compression allowable for the ultimate load, and use that for the lower (tension dominate) spar so they are both the same.
Kenny


--- On Mon, 10/3/11, Philip Lardner <This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:

From: Philip Lardner <This email address is being protected from spambots. You need JavaScript enabled to view it.>
Subject: RE: [Carbondragonbuildersandpilots] Re: Wing calculations
To: "'Kenny Andersen'" <This email address is being protected from spambots. You need JavaScript enabled to view it.>
Date: Monday, October 3, 2011, 8:53 AM






I presume Marske's rod numbers are at 8g, but - wow!
 
I'm still working my way through your spreadsheet (thanks for that by the way) and comparing it to my numbers (and trying to figure out your column headings!) but at +8g I was getting 5 rods on the top cap and 3 rods on the lower cap at -4g, totalling 104.25ft of rod for both wings (see
attached.) I'll get a bit more time to work on it tonight. The different numbers we're getting for our cap loads (you: 9826lbs - me:19226) is significant!
 
Phil.



From: Kenny Andersen
[This email address is being protected from spambots. You need JavaScript enabled to view it.]
Sent: 03 October 2011
14:16
To: Philip Lardner
Subject: RE:
[Carbondragonbuildersandpilots] Re: Wing calculations







Just ran across this
statement about the Monarch, Marske's sail plane with almost
the same span I was looking at the
the number of rods tracks pretty close to the solution I got 9see below).
 The next step is looking at and sizing the spar webs.  I was
looking for a hand method to do the webs, but it doesn't look so good
(easy).  However, I do have tools at work that I can use (FEM stuff).
 Maybe Timeshanko has something, but they are always really complex
(IMO).

The new Monarch G, a 42.6 ft span sailplane, uses
only four rods (.092 x .220) in each spar cap. Enough rod for one wing
panel (upper and lower caps) requires 112 ft. That amounts to 1.44 lbs of
rod per wing spar. The total weight of the completed wing spar is 7 lbs
which includes blocking for root and strut fittings.

--- On Sun, 10/2/11, Philip Lardner
<This email address is being protected from spambots. You need JavaScript enabled to view it.> wrote:


From:
Philip Lardner <This email address is being protected from spambots. You need JavaScript enabled to view it.>
Subject: RE:
[Carbondragonbuildersandpilots] Re: Wing calculations
To:
This email address is being protected from spambots. You need JavaScript enabled to view it.
Date: Sunday, October 2, 2011, 5:59
PM



Hi Kenny,
 
I'm sending you the attached pages
of Marske's manual (off-list, as it is copyright material) so you can
see how I am arriving at the figures in my spreadsheet and other pages
of notes.
 
I'll leave off asking any questions
until I've had a chance to see your spreadsheet and the numbers you're
using... but I've already got a few!
 
Glad you're on the
mend!
 
   
Phil.



From:
This email address is being protected from spambots. You need JavaScript enabled to view it.
[This email address is being protected from spambots. You need JavaScript enabled to view it.] On Behalf Of
Kenny
Sent: 02 October 2011 13:14
To:
This email address is being protected from spambots. You need JavaScript enabled to view it.
Subject:
[Carbondragonbuildersandpilots] Re: Wing
calculations


 



OK, I FINALLY got a chance to go over the calculations (the
bronchitis is down to a dull roar) . I don't have Marske's book, so it
was hurting my brain trying to figure out how he did everything, so then
I thought, I'd just do it the 'real' way (LOL). so I just made my own
spreadsheet and ran the numbers for the wing I was thinking of it.
Calculate the area, the wing loading and then the moments and cap
(flange) loads. Our solution tracked OK until you go to calculate the
load in the flange. The load in the flange is just the moment divided by
the height.

At the root for 8gs you got a moment of 112,951 in-Lb
(I got 109,000). The height of the outer contour is 11.75 at the root,
but I used 11.5 to account for any offset

The cap load is then:
113000/11.5 = 9826 Lb
you got 19226 Lb

One thing I did to
make sure I didn't get confused is I kept all the units in inches. I
upload my spreadsheet once I get my wing straightened out. I put the
standard wing on page 1 and I'll put my wing on page 2. I'm
using:

pilot weight 220
parachute 25
air frame weight
155
wing weight -75

I'm using 6g limit, 9 g ultimate (that's
the same as an F-16! -- I think it will be enough!)

A word about
sizing the wing. There is a couple of things that we can do to simplify
the analysis and that is a decision to keep the upper and lower wing
spar sizing symmetric. It won't cost much weight due to using the carbon
spar caps. We do that and the centroid is in the middle and we can use
P_cap = M/h to calculate the load in the cap (easy-peeze).

So you
size just one spar for ultimate load, and that's good enough. because
carbon fails catastrophically, there is no need to be concerned about
limit load. Limit load is only used to check for yield. For virtually
all aerospace-grade aluminum (other than 6061) , and graphite limit
checks are not necessary.

Also, I'm going to be a bit more
sporting than my buddy and use 150,000 psi for compression in the carbon
rod [rather than 100,000] and just make damn sure I pack everything
right into the corner. Between using the lower allowable and making the
wing cap sizing symmetric, it should be plenty conservative. Check your
spreadsheet for that cap load.
Kenny

--- In This email address is being protected from spambots. You need JavaScript enabled to view it.,
"Philip Lardner" <philiplardner@...> wrote:
>
> Ok,
I've updated the Excel spreadsheet in my files directory with a
new
> sheet detailing the Rib Stress Analysis for each of the ribs
in the main
> wing.
>
> Phil.
>
> _____

>
> From: This email address is being protected from spambots. You need JavaScript enabled to view it.
>
[This email address is being protected from spambots. You need JavaScript enabled to view it.]
On Behalf Of Philip
> Lardner
> Sent: 28 September 2011
16:25
> To: This email address is being protected from spambots. You need JavaScript enabled to view it.
>
Subject: RE: [Carbondragonbuildersandpilots] Re: Wing
calculations
>
>
>
>
>
> Hi
Folks,
>
> I've uploaded another few pages of calculations
(Page-20 to Page-23 in the
> 'Phil Lardner' files directory)
covering the rib layout and stress analysis.
> I've used the root
rib as a worked example and will upload the numbers for
> the
other ribs when I get them finished.
>
> I discovered a
few more numerical typos in Jim Marske's text - confirmed by
>
him. The text could also be a little clearer when describing how the
rib
> panel centroids are arrived at. I mistakenly used the
formula on pg D-1 of
> Marske's manual to calculate both centroids
and got answers different to the
> examples in the text. It took
me a while to discover my error - the
> centroids are being
measured left and right from the spar location and not
> just from
the left as on pg. D-1 - hence my drawing on Page-21 showing the
>
graphical method of finding the centroids!
>
> Comments
welcome...
>
> Phil.
>


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