Message-Id: <3.0.3.32.19980926051927.006b9bac@mail.digital.net>
Date: Sat, 26 Sep 1998 05:19:27 -0400
To: lancair.list@olsusa.com
From: John Cooper <heyduke@digital.net>
Subject: fiberglass & carbon fiber
Mime-Version: 1.0

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OK, you guys have me a little concerned about how I chose to address what I
perceive to be a weak area on the two-place Lancair fuselage. But not
concerned enough to prevent me from flying as-is when the time comes. At
least if I have an in-flight breakup in turbulence, the failure mode will
be well-documented <G>.

First, let me say that I and several other people have inspected an L-320
fuselage which failed in the critical area directly over the main spars.
(The aircraft made an emergency landing off-airport and hit a pile of dirt
with the inboard part of the right wing, spinning the plane so that the
left wingtip stuck into the ground like a spear. The pilot was killed, the
passenger walked away).

When I inspected the wreckage, I saw that the longerons had failed in
tension where the holes had been drilled in them to attach the forward
canopy parallogram mechanism (ironically, these holes were unused, since
the builder later decided to go with the forward-hinged canopy). The ends
of the wood fibers were not bent at all as they would have been had they
failed in bending, the longerons had simply pulled straight apart, IMO.
From where the longerons failed, the sidewalls ripped down through the NACA
vents down to the wing root then down and around to where the fuselage
attaches to the bottom of the main spar. The entire front of the aircraft,
including the engine, firewall, header tank, and forward-hinged canopy
separated from the main spar forward.

I realize, of course, that the Lancair was never designed to withstand an
80mph impact with a pile of dirt. What I saw got me to thinking, though. I
got out my calculator and did some rough calculations - very rough -
assuming that the forward fuselage was a simple truss structure with the
weight of the engine cantilevered out in front of the main spars. I can't
remember the exact figures I used, but the CG of the engine is something
like 40" in front of the main spars, and the longerons are something like
17" above them. You can measure this yourownselves, easily enough...

By summing moments, one can see that the tension in the longerons is
multiplied by the spar-to-engine distance divided by the spar-to-longeron
distance, or 40/17 if you use my numbers.  If the engine weighs 300#, say,
then the tension in the longerons is 706# at 1G, or 353# per longeron.
Since the cross-sectional area of the longerons is .75x.75" or
.56sq.in.(assuming you did NOT drill any holes in the longeron), the stress
in each longeron comes out to something like 627psi/G. If you DID drill
that .188" hole in each longeron, then the numbers come out 835psi/G, a 34%
increase!

The "elastic proportional limit" for spruce is listed at 8000psi in my
Seely's "Resistance of Materials", and the "modulus of rupture" is listed
as 10,000psi. My construction books allow a working load of roughly 2500psi
for spruce used in building construction. So if your longerons have holes
drilled in them, they should start to fail at 9.5 Gs and separate for sure
at 12G.
Good design would dictate some kind of a safety factor. Using the 2500psi
figure would result in a working limit of only 3Gs for longerons with
holes, and 4 Gs without holes.

I originally thought that not taking credit for the strength of the
fuselage sidewalls was probably way too conservative until I considered
that the NACA vents destroy much of this strength if installed in the
critical area above the spars. I also noted in the Neico promotional video
on the L320, there was a photo touting the Finite Element Analysis of the
airframe by the "best engineer in the country" (done by Martin Holliman I
assume). You can see right on this video that the area of the longerons
directly above the main spars is bright red surrounded by yellow, in
contrast to the rest of the airframe which is green. I am guessing that
this particular "picture" was of stress. If so, I also noted that
consideration of the NACA vents was NOT included in this particular mesh. I
have always wondered if these vents were modeled when Martin did the
original FEA.

------------------

OK, I have spelled out my reasons for beefing up the longerons and not
drilling any holes in them, and not putting the NACA vents in the
sidewalls...now on to how I chose to "strengthen" my airframe. (Strengthen
in quotes because I admit the possibliity that I weakened it in another area).

I placed a 5" wide layer of unidirectional carbon fibre on the outside of
the fuselage on either side, from the top of the longeron down. These ran
from the firewall back to the rollover stucture. On top of that, I placed
another 5" layer with one-third folded back upon itself so that the final
buildup was in three thicknesses. First one layer, then two, then
three...with the three layer thickness abeam the longerons. On the inside,
I placed another 5" folded into thirds in the recess underneath the
longerons and about 2" down the inside.

So basically I've now got 6 layers (or 0.12sq.in cross sectional area) of
450,000psi carbon fiber in parallel with my longerons, or enough to carry
the whole load. However it will only carry that portion of the load
proportional to it's stiffness and cross-sectional area according to the
formula:

P ~ AE/L  P=stress  A=area  L=length

"A tension or compression member may be made up of parallel elements or
parts which jointly carry the applied load. The essential problem is to
determine how the load is apportioned among the several parts, and this is
easily done by thye method of consistent deformations. If the parts are so
arranged that all undergo the same total elongation or shortening, then
each will carry a portion of the load proportional to it's stiffness..."

	--Formulas for Stress and Strain, Roark, 1943

Since we are dealing with a tension member made up of three materials:
spruce, glass, and carbon, we can estimate the proportion of the load
supported by each. Let's assume that the area of the both the glass and the
carbon is 0.12sq.in, and the area of the spruce is 0.56sq.in. Let's also
assume that the carbon is three times as stiff as the glass, which in turn
is 7 times as stiff as the spruce.

AE(spruce) = 1x0.56
AE(glass) =  7x0.12 = .84
AE(carbon) = 21x.12 = 2.52
sum of above = 3.92

So therefore the percent of load carried by each material is:

Spruce .56/3.92 = 14%
Glass .84/3.92 = 21%
Carbon 2.52/3.92 = 64%

For the original configuration (without carbon fiber):

Spruce = .56/1.40 = 40%
Glass = .84/1.4 = 60%

-----------------------

To continue this missive, the only thing that I really nead to worry about
is where the carbon stops and the other two materials assume the whole
load. Back near the canopy rollover, I stopped the second and third layers
of carbon several inches ahead of where I stopped the first layer, so as to
provide a gradual transistion back to the strength of the glass. Since
there is only one layer of carbon back in that area, the load percentages
in that area would be:

AE(spruce) = 1x0.56
AE(glass) =  7x0.12 = .84
AE(carbon) = 21x.04 = .84
sum of above = 2.24

Spruce .56/2.24 = 25%
Glass .84/2.24 = 38%
Carbon .84/2.24 = 38%

In retrospect, I probably should have used E-glass, or nothing at all.

As Forrest Gump said, "That's all I have to say about that"...