Pondering if thermal expansion can break a canopy
There has been some discussion lately on cracked canopies and some speculation on the cold weather being the culprit.
I thought I would start a new thread based on Danny Kings comment:
Danny has postulated that the difference in thermal expansion between the steel frame and the canopy is the smoking gun. I think he has hit the rivet on the head here. Danny oversized his attachment holes.. and I think he is on the right track. I have attempted to put some numbers to the problem....
Assuming a canopy built to plans we have the following numbers:
A #40 drill through the steel rail. (0.098")
A #27 drill through the canopy. (0.144")
12 " between fasteners. (Lo in the equations)
EDIT: Thanks to Alex' comments below...things have changed A LOT.
The thermal expansion Ct for steel is approximately 0.000008 in/inR
The thermal expansion Ct for acrylic is approximately 0.0000417 in/inR
I'm going to take a lot of liberties with my assumptions from here on (feel free to shoot me down)
Lets say we go flying at -5 degF outside. Lets also say that our cockpit/sun heater is able to bring the interior of the cockpit up to 32 degF for a deltaT of 37 degF as we fly around.
The expansion of a material dl = Ct * deltaT * Lo
The steel will expand by: 0.003552 inches between fasteners.
The acrylic will expand by: 0.01851 inches.
Yikes. But wait, we have some slop in the holes of 0.046 inches (#27 - #40)
So the difference in length the steel and the canopy is going to be 0.01852 - 0.003552 - 0.046 = -0.03104 in.
So, there is enough oversize in the hole to have no strain on the plexi.
If we assume we didnt drill the plexi hole in perfect alignment with the frame, (in other words, the rivet is right against one edge) there will be a maximum strain of
Well strain is deltaL/Lo = .046/12 = .00383
Stress = Youngs Modulus * Strain
Youngs Modulus for Acrylic is about 400000 PSI
So the stress rise in the acrylic is .015 * 400000 = 500 PSI
The tensile strength of acrylic is about 9000 PSI (this has a big range so I just picked one)....so we have some margin.
Now... if we increase our deltaT to 50 (meaning we managed to warm up to 45 degrees in the cockpit) the stress goes to 675 PSI.
But wait! We drilled a hole in this thing.... what did that do? Well, holes create a stress concentration.... and there's a lot of math we could go through to try to figure that out, but we will just take a shortcut, and set our hole stress rise factor to 3. (look it up)
So, NOW with a deltaT of 37 deg we have:
500*3 = 1500 PSI Still OK
Now, I have made a LOT of assumptions and taken a lot of liberty with geometry etc...
There have been a lot of comments wrt installation loading due to bending the frame to fit. But from this calc, maybe the cold differential is enough along with the preload to crack the canopy....
That being said, it looks like if you align those hole VERRY carefully during installation, you wont be introducing load due to thermal expansion.
The take away is Danny's approach looks like a good idea.
For all of us flying around with plans built canopies.... well..... I don't know the answer to that.
Except..... my canopy is still fine... and so are thousands of others..... So I have to conclude that there is some basic error in my calculations.. but, that being said, Danny's idea is still a good one.
I remember one of the first Earth Rounders writing about how firghtened he was somewhere around Greenland coming down the GS in his RV-4 in the extreme cold and watching a canopy crack begin to propagate and him wondering if it was all going to hold together.
I have had my canopy crack when moving it outside from a warm hangar into frigid temps.
Every time my overhead radiant heaters kick on and off (lots last week in the -30 to -38C temps), I can hear the canopy "pop" multiple times as it expands and contracts on the rivets and frame. My 6A is parked nearly right underneath the heaters.
Same when I roll it outside like today to fly in the winter. Built to plans, flown down to -20C sometimes, nary a crack yet after 15 years and hundreds of flights and thousands of heat/cool cycles under the heaters.
I think it also has to do with the temp at which the canopy and steel frame were also drilled. If you drilled and set the canopy in a 65 degree hangar, and it gets down cold, it throws those numbers further out of whack. I believe you have to start your calculations at the point of theoretical zero stress on the canopy (The temp at which it was drilled and attached).
Some people have gone as far as heating the larger panels prior to drilling/Cleco/riveting to reduce the chance of oil canning. After the steel cools it is drum tight with little chance of oil canning. We might have to explore just the opposite for the RV8 canopies.
+1 For stresses due to the rivets coming up too tight on the holes, you need to compare dimensions at the initial fabrication temperature to those at the current temperature. For canopies cracking on sudden removal from a heated hangar to the cold, you may be looking at the internal shear stress - the outside of the plexi is suddenly much colder than the inside, the outside shrinks and the plexi fails internally in shear, starting at some stress riser.
I do believe this is on the right trail. I have a crack in my canopy that goes from one rivet head to another where it is riveted to the front slider bow, does not extend elsewhere, just between those two rivets. I do a lot of high altitude flight and have seen temps in the negative teens on a few occasions.
I think that another consideration is an"initiating event" while the canopy is under stress. My 8's canopy cracked on a cold winter's day in Big Bear. Overnight temps were in the tens, and I rolled out to go down the hill to Cable airport. The northerly winds that brought the cold air were howling through Cajon pass, and I was descending quickly because of the altitude I had to lose, when I was hit by thee or four bumps that would have knocked me into the canopy if my five-point wasn't really tight.
When I landed, there was a neat crack back behind the passenger seat. I don't know if it would have cracked without the bumps, but my thought is that it was under great thermal expansion stress, and all it needed was a bit of a nudge to go bang.
On the opposite side of things, I don't think having it out in a very hot day with the sun shining will cause cracks. My thinking is that with the high temperature the canopy is pliable and will deform before it cracks, unlike when it is cold out.
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