Today's Message Index:
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1. 07:55 AM - BPA ressurection (Douwe Blumberg)
2. 07:49 PM - Re: Riblett to Spar Fit (taildrags)
3. 07:56 PM - Re: Ragwing Ultra-Piet (taildrags)
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Subject: | BPA ressurection |
Hey Pat,
Not sure what may come out of it, but there is a lot of good stuff and a ton
of great photos/info already on westcoastpiet.com run by Chris Tracy. He's
a good guy, maybe the two sites could collaborate, share info etc? it's
ready-made content if you can work something out with him for the greater
good
Douwe
Message 2
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Subject: | Re: Riblett to Spar Fit |
Terry, Brent-
I am an engineer, so I can get carried away with numbers and formulas, but usually
when that happens people just quietly walk away and leave me muttering to
myself, so it's OK if you do too ;o) When we talk about a spar being "strong",
we have to define what kind of strength we're talking about. I'll be over-simplifying
here, but when it comes to beams (like our wing spars), there is bending
strength and there is shear strength. We are interested in bending strength
so let's look at our Air Camper wing to see what's what.
Structurally, there are three elements to our wing. Simplifying, of course. The
centersection is one element, the section of the wing outboard from the cabanes
to the lift strut attach points is another, and the part outboard of the
lift strut attach points is a third. Of those three, the centersection is the
most lightly loaded and the easiest to analyze structurally because it is supported
and restrained at both ends by the four cabane uprights. The next section,
from the cabanes out to the lift strut attach points, is more heavily loaded
than the centersection but it, too, is restrained at both ends (by the cabanes
at one end and by the lift struts at the other). The outboard-most section
of wing is the part that has to work the hardest because it is only supported
at the lift strut end and the other end is cantilevered out into thin air.
That part of the wing is what needs the most strength in bending, because that's
what it has to work hardest at.
The heavies that Terry flies have wings that are completely cantilevered out from
the fuselage, so when you are at maximum takeoff weight with full fuel, pax,
and baggage and you pull that baby into climb attitude on takeoff, the wings
bend gracefully in an upward sweep out at the tips as they do their hardest work.
In a spectacular example of this taken to the extreme, check out the 787
Dreamliner's wingtips bending upward about 25 feet at the tips (during testing,
of course), here:
https://www.wired.com/2010/03/boeing-787-passes-incredible-wing-flex-test/
The bending stress is at its maximum at the wing roots of a cantilevered wing,
diminishing as you go out spanwise to the tips, where it is zero. So, in theory,
we can save weight by tapering the wing spars to follow the profile of the
diminishing stress as we go out to the tips, but that adds complexity to the
spar construction, and if we also taper the wing chordwise like the heavies are,
it means every rib is different from its neighbor and everything is harder
to make. So, we build our wing Hershey bar-style with a constant chord and constant
spar size for simplicity and ease of construction. Consequently, the wing
centersection is very much overbuilt, the section from the cabanes to the
lift struts is still plenty overbuilt, and the outboard section is probably just
about right but progressively more and more overbuilt as you go from the lift
strut attach points out to the wing tips where the bending stress is (theoretically)
zero.
Bottom line, we analyze the forces in an Air Camper wing where the bending stress
is the highest: on the outboard section, where the lift struts attach. Inboard
of that, the spars are restrained from deflecting in bending and outboard
of that, they are not.
Now for the math. Feel free to leave the room quietly ;o)
The bending stress in a beam (which our wing spars are) is calculated by knowing
two things: the moment (which is the product of the lift force on the wing times
the distance where it acts on the wing), divided by the section modulus.
Forget about two of those things for a minute because we are looking for the
maximum "strength" of our wing and we know the properties of the wood (or metal)
that the spar is made of so we know its maximum allowable stress, and we also
know the lift forces on the wing because we are designing it for a certain
maximum gross weight, G-force, and safety factor. That just leaves the section
modulus, which is a property of the beam section. It's different for a tube,
a rod, an I-beam, a C-section, rectangle, square, bar, whatever. In the case
of a typical rectangular-section wood beam, the section modulus is equal to
the width (thickness) times the height (spar depth) squared, divided by six.
As H. Ross Perot used to say during his talks, "stay with me now..." ;o)
The amount of stress that the wood in our spar is able to take without failing
is essentially constant and is a property of the wood. So, the larger we can
get the section modulus of our spar to be, the "stronger" it is (the more bending
stress it can take, which means higher Gs or a higher gross weight, or both).
So, lets look at the section modulus. We have two things we can work with
to determine it: the thickness and the height. If we double the thickness,
we also double the section modulus but if we double the HEIGHT, we increase the
section modulus by a factor of FOUR because the height gets squared in the equation
(2x2 = 4). Since we're trying to build our spars as light as we can,
why make the spars twice as thick to double the section modulus (but double the
weight), when we can do the same thing by simply increasing the spar depth by
about 2 and the weight only goes up by about 40% instead of 100%? In resisting
bending force on the spars, you get more bang for the buck by going taller
rather than fatter.
So (and this has nothing to do with where you slept last night), your example of
a spar that is 1" thick and 5" tall means that its section modulus is about
4.17 but if we make it 3 times that tall, 15", its section modulus skyrockets
to 37.5 and the spar isnt 3 times stronger, its 9 times stronger in bending than
the 5" tall one. There's that squaring effect at play.
But wait, because there are many reasons why it would be impractical to actually
build something like that due to buckling from "slenderness" and fiber shear
in the web, twisting, and other things. However, the point is that in a wing
spar that is subjected to bending loads, depth is everything. I'm not certain
of the Riblett airfoil nomenclature, but if the 612 has 12% thickness and the
wing chord is 60", the airfoil would be about 7.2" tall at its maximum thickness
so maybe 7" at the main spar. (Terry, how tall are the metal J-3 spars?)
For a 1" thick rectangular Riblett 612 spar, the section modulus might be 8.17.
The stock unrouted 1 thick Piet spar is 4-3/4" tall so it might have a section
modulus of 3.76 and the deeper 612 spar, if it's a rectangular shape like
the Piet's, is then theoretically competent to take more than twice the bending
stress than the stock Piet spar, so maybe (to temper what Wese said about
the Air Camper wing spar), maybe the 2-G Piet becomes a 4-G "Super Piet" ;o)
All of this is theoretical and none of the above should be taken as a rigorous
analysis of either spar, or of the wing, or anything other than a general discussion
to point out that calculated design can sometimes beat eyeball engineering.
On the other hand, many things that are exquisitely designed, cannot readily
be constructed on the floor of a wooden barn using hand tools. Thus we have
the timeless and understated technical elegance of the Pietenpol Air Camper,
which does what it does very well and without a lot of analysis or re-engineering.
If you choose to depart from Mr. Pietenpols design, take your time analyzing
what you do.
--------
Oscar Zuniga
Medford, OR
Air Camper NX41CC "Scout"
A75 power, 72x36 Culver prop
Read this topic online here:
http://forums.matronics.com/viewtopic.php?p=466620#466620
Message 3
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Subject: | Re: Ragwing Ultra-Piet |
Not building one, but I do have a set of plans! Very nice airplane, but when I
studied the plans it seemed like just as much work to build one as to build a
full-size Air Camper.
--------
Oscar Zuniga
Medford, OR
Air Camper NX41CC "Scout"
A75 power, 72x36 Culver prop
Read this topic online here:
http://forums.matronics.com/viewtopic.php?p=466621#466621
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