Ok. So I have a math degree from MIT. That doesn't mean dookie - it was my wife who was more helpful in calculating these numbers that I'll get to in a minute. Just because I could implement fast fourier transforms 15 years ago doesn't mean I can do anything useful today. But still, my point is that I'm not a freakin' moron. So let's get to the topic of discussion.
My wife and I have been trying to get our chimney lined for about 10 months now. The short version of the story is that the cross sectional area of the chimney liner needs to be sized relative to the opening of the firebox (aka, the fireplace in your living room.) You need a certain number of square inches in the cross section of the chimney liner (which is a flexible steel tube, essentially) to get the proper draft and airflow so that smoke goes up the chimney instead of coming out into the room.
Well, the first liner that was installed was too small (we need roughly 60-65 inches of cross sectional area). Smoke billowed out into our room. We did the math to show the chimney guy this fact. The liner had started life as a 10 inch round tube, and had been "ovalized" to fit our chimney flue. The problem is that it had been ovalized too much - squashed down too much so that the cross sectional area was too small. We had a discussion about this, and although I don't think I actually convinced him that an oval does NOT have the same cross sectional area as a circle (seriously - he didn't/doesn't believe me), he knows it didn't work as it was. So now we're still talking to the guy about putting in a new one.
He has proposed that they will try an eleven inch round liner, ovalized down to 5 inches. I think the company he is talking to is using this chart. You can see from the chart that if you take an 11 inch round and ovalize it down to 5 inches, that, by definition, implies a major axis length of 14.8 inches, which my wife and I agree with. (Interestingly, we don't quite agree with the other numbers in that chart - but the 11 inch --> 5 x 14.8 actually matches up with what we calculated for that specific scenario).
NOW - the chart on the top of that page I just linked above also has cross sectional area for each scenario, and we simply can't figure out how they get to 65 square inches here. This is where you math super-wizards come in.
For area, if "a" is the minor axis and "b" is the major axis of the liner, we're using [a/2 * b/2 * pi]for the area. In this case, it comes out to 58, which is a far cry from the 65 in their chart.
My chimney guy actually told me that the ovalized liner would be 5 inches by 16 inches (yielding a cross section of 63 inches). I explained that I didn't think that was possible - my wife designed a spreadsheet showing the major axis length implied by each minor axis length (after all, circumference doesn't change), and 5 inches implies 14.8 on the other axis - which is what the chart shows. Of course, when I told the guy that I didn't think it was correct, it didn't go over too well. We (my wife) used ellipse math to calculate the implied dimensions of the cross sectional axis, starting with a circle of fixed diameter, and assuming the dimension of the minor axis.
So there are two issues. 1) I don't understand how they get from an 11 inch circle to a 5x16 oval. and 2) even if they get to a 5 x 14.8 inch oval, how do they calculate 65 inches of area?
Thoughts? Anyone? Is there somehow a problem in the ellipse assumptions? (And yes, we know that all ovals are not ellipses)