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Calculus fans, come in here.....
Guys, I'm trying to calculate the area of a piston ring end cap for blowby calculations here at work....
Basically the area I'm describing is shaped like a piece of macaroni once you get down to it. I know this is an odd shape, but I figure I'll have to do a double integral to find the area. However, I'm having trouble calculating the arc lengths on the bottom and top of the macaroni shape. I know arc length is based on the radius and a radian....but what's the easiest way to get that radian? I mean we're talking about an area pretty close to around .035" based on a 3.35" bore.....The radian measurement is gonna be almost nil I'd say.... I'm just trying to get a more accurate measurement of area instead of just using a rectangular shape. |
Nevermind guys....It's gonna be so stinkin close, I think it's safe to assume it's a rectangle.....It's not worth the headache or the calculus.
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Blykins,
In case you need it again: It reduces to: Pi*(Gap/Diam)*(OutsideRadius^2 - InsideRadius^2) Think of it as two pie shapes of the same angle but different radii. Thank God it wasn't a word problem involving trains ;) Edited: Oops - forgot Pi. Ummm Pumpkin.... :D |
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Blykins, Damn, and I almost had it..... :confused: :JEKYLHYDE |
Thanks Jim. I think I'm gonna just make an assumption and get on with it. It's amazing how much information you lose when you get out of school and don't use the stuff very much....I had 4 semesters of Calc and one semester of Matrix Algebra.....I never use it and I'm reaping the results now....
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ummmm macaroni is hollow .......
that'll introduce a Diam^2-diam^2 term in there won't it ..... if it's volumn ....... which for macaroni is important (especially at lunch) you wanted the footprint of the macaroni ? in plan if I'm reading it correctly. Will need cyl. bore, piston dia., ring end gap, inner ring dia. and piston ring groove inner dia. After that it's easy. That let the range of areas be calculated. |
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Hey Jim....the shape is more like two vertical lines with an arc at the top and an arc at the bottom......both arcs facing the same way....my bad....I guess a piece of macaroni isn't shaped like that.....hehehe....
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Wow! 66 liters a minute. Makes you think more about PCV doesn't it?
Rick |
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A torque wrench that can sense bolt stretch!?!?!? Don't buy that one at the local Sears.
Rick |
I love it when you guys talk like this! Keep it up for a little while longer, ok?
:LOL: When I first read the post I thought you were wanting the volume of the partial arc ... and then you mentioned that the arc piece was to be hollow and I then started thinking about manifold surfaces and got all confused, particularly since you didn't mention the thickness of the macaroni! :) |
Yeah, I never should have mentioned macaroni. It's basically a 2D area problem.......
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Kinda like this.....vertical sides.....arcs at top and bottom......
To get the arc length though, I need the angle (theta) and I just need to know the best way to figure it...or if someone's already got a formula ready-made....that would be good too. |
good grief!
now I know why I only taught kindergarten.....
how do you spell CALCULUS??? yikes!!! I love macaroni;) kristen |
We're not to the calculus part yet.....hehhe....it may really hit the fan when it develops past trig....hehehe....
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Are you considering the whole gap, or only the part of the gap which is hanging out the ring lands?
you know the OD of the ring (bore diam) you should know the ID of the ring so calculate the area of the big circle, subtract the area of the little circle. Now you know the area of the ring. calculate the circumferance of the ring (bore), translate that into degrees by dividing by 360. Now you know how much of the circumference to use per degree. calculate how many degrees the end gap is. |
4.00" bore = 12.56" diameter = .035" of circumferance per degree
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Or....I guess I could divide the .111 in^2 by 360....get the area per degree and then multiply by the outer arc which is 2.87 deg.
That would give me 8.84e-4. I'll have to double check myself, but this sounds right too. Thanks to everyone for their help. |
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