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Old 08-27-2013, 06:44 AM   #21
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Originally Posted by Brian B-P View Post
The area of a circle is pi/4 or 79% of the area of a square
When I was at school (last century) the area of a circle was pi r squared.
My how thing have changed.
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Old 08-27-2013, 07:01 AM   #22
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Originally Posted by widgetwizard View Post
When I was at school (last century) the area of a circle was pi r squared.
My how thing have changed.
Just a typo - it is pi * D squared / 4
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Old 08-27-2013, 10:46 AM   #23
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Quote:
Originally Posted by widgetwizard View Post
When I was at school (last century) the area of a circle was pi r squared.
My how thing have changed.
Quote:
Originally Posted by Thomas G. View Post
Just a typo - it is pi * D squared / 4
Things have not changed, and it is not a typo. I wasn't posting the area of a circle, I was referring to the ratio of the area of a circle to the area of a square which with sides equal to the circle diameter.

area of circle: Ac = pi * r≤ = pi * D≤ / 4
area of square: As = D≤
Ac/As = (pi * D≤ / 4) / D≤ = pi/4 = 79%

... just as I said before:
Quote:
Originally Posted by Brian B-P View Post
The area of a circle is pi/4 or 79% of the area of a square.
The big difference is the first time I spent about six seconds to work it out in my head, and typing this took much longer.

I suppose it would have been more clear if I said:
The area of a circle is 79% (the value of pi/4) of the area of a square.
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Old 08-27-2013, 11:21 AM   #24
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Why would any one buy a battery with 1/3rd less capacity?
... compared to what?
A spiral-cell battery has about one-third less capacity than a flat-plate battery of the same outer package size; there is no meaningful difference in capacity for the same weight. I think in most applications, the package size is not critical.
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Old 08-27-2013, 06:06 PM   #25
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Nerd alert

Area of six circles = 6(pi(d^2))/4 = 4.71d^2

Area of a rectangle scribed around six circles (hexagonally packed) is 3.71d x 1.71d = 6.34d^2

(4.71d^2)/(6.34d^2) = .74 or 74%

Irrelevant, just an interesting puzzle.

Edit: if you connect the center of the circles you get an equilateral triangle with of course 60* angles. I used 45*. The corrected value is 72%. Of course this occurred to me in the middle of the night
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Old 08-27-2013, 06:14 PM   #26
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Brian,

Are you saying a spiral battery has a higher energy density per unit volume compared to a flooded plate battery?
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Old 08-27-2013, 06:54 PM   #27
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Originally Posted by P. Raz View Post
Area of six cylinders = 6(pi(d^2))/4 = 4.71d^2

Area of a rectangle scribed around six cylinders (hexagonally packed) is 3.71d x 1.71d = 6.34d^2

(4.71d^2)/(6.34d^2) = .74 or 74%

Irrelevant, just an interesting puzzle.


Actually relevant, as one of the Optima models does (or did) stagger the cells (maybe not all the way to hexagonally close packed) to fit one of the BCI formats (sorry, don't remember which one, but the length would have been more than 1.5 times the width).

The pi/4 (79%) factor is the ideal rectangularly arrayed case. Cylindrical (spiral-wound) cells in hexagonal boxes would hit 91%, and real battery case proportions are all going to be worse than that.

The point is just that cylindrical cells don't fit nicely in battery boxes, so the spiral-wound batteries are little bulkier (but not heavier) for the same capacity, or they are lower capacity (and lighter to match) for the same standard box size.
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Old 08-27-2013, 06:57 PM   #28
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Are you saying a spiral battery has a higher energy density per unit volume compared to a flooded plate battery?
No, about the same energy density per unit volume of working parts and - since both are made of lead and electrolyte - about the same energy density per unit mass. Since the box isn't filled with working parts, the spiral-cell battery has a lower energy density per unit of case volume, but still about the same energy density per unit mass.
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Old 08-28-2013, 02:58 AM   #29
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Originally Posted by Brian B-P View Post


Actually relevant, as one of the Optima models does (or did) stagger the cells (maybe not all the way to hexagonally close packed) to fit one of the BCI formats (sorry, don't remember which one, but the length would have been more than 1.5 times the width).
.
The optima I bought for my tractor Is configured that way which is what got me curious. The only reason I can think of for staggering is to use the same size cylinders to fit a longer or narrower foot print.
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