Calculating Cross Sectional Area

[coulterracn]

yes, that is correct.

If you are using a drill bit it would be easier to use the diameter, less math.

Ray

[86rocco]

Here's the shape we're interested in.


Let's first consider this shape,

The area of the red sections are the same in both pictures but it's easier to calculate in the second pic, it's simply the area of the square minus the area of the circle.
Area of square= 1.25*1.25= 1.5625
Area of circle= pi*0.625*0.625=1.2272
Red area= 1.5625-1.2272=.0.3353

So going back the the first shape.

Area= 2.57*1.91-0.3353=4.5734

[Flash]

how did you come up with the 1.25

Area of square= 1.25*1.25= 1.5625

I get the math how its done above, but trying to apply it to a smaller radius, like 1/4 or .25

[coulterracn]

Gorden
If your corner radius is the same radius as a 1/4" drill bit then your square would be 1/4" X 1/4".

.25 x .25 = .0625
3.14 x .125 x .125 = .0490
.0625 - .0490 = .0135
Subtract .0135 from your total and that will be your port CSA

My intake port has a 5/8" radius or .625".
.625 + .625 = 1.25
1.25 is the diameter of the circle and the length of the square on all four sides
Ray

[86rocco]

how did you come up with the 1.25

Area of square= 1.25*1.25= 1.5625

I get the math how its done above, but trying to apply it to a smaller radius, like 1/4 or .25

1.25 is just twice your 5/8 radius.

I'll make the math a bit more generic so you can plug in whatever numbers you like.
Consider this diagram:


Area in red = area of square - area of circle
= 4*R² - 3.1416*R²
= (4 - 3.1416) * R²
= 0.8584 * R²

So, for a rectangular port with height H, width W and corner radii R
CSA = H * W - (0.8584 * R²)

[Flash]

OK, i know I'm being an annoyance here,and I'm sorry for that, but, if i can't trust the math.......well it's not worth the paper i printed it off on.

here is the problem, if I us Rays last example, then verify it with Stan Weiss calculator, AND use the "Diameter" choice, they both come out the same at 2.2365 or 2.24

If i use 86rocco math, i get 2.19635 or 2.20. Using Stan's Calculator, its also Right.
"IF" I us the "Radius" option......................

so is it 2.20 or 2.24?
Not trying to cause trouble here, just wanting to know.

O almost for got, the port is 2.25" by 1" = 2.25 right?
1/4" drill bit fits in the 4 corners of my intake port.

and here is the link to Stan Weiss calculator.
http://users.erols.com/srweiss/calccsa.htm

NOTE: I'm entering .25 in to the 4 corner spots

Thanks to every one that has posted up so far

[coulterracn]

The radius of a 1/4" drill bit is 1/8" or .125"

With Stan's calculator, diameter would be .25 for all four corners, radius would be .125 for all four corners.

If your corner radius is the same radius as a 1/4" drill bit then your square would be .25 X .25
.25 x .25 = .0625
.0625 is the area of the square

The radius of the 1/4" drill bit is .125
3.14 x .125 x .125 = .0490
.0490 is the area of the circle being subtracted from the square

.0625 - .0490 = .0135
Subtract .0135 from your total and that will be your port CSA

2.25 x 1 = 2.25 - .0135 = 2.2365

2.2365 square inches is the cross sectional area of your port

Ray

[coulterracn]

Here's the shape we're interested in.


Let's first consider this shape,

The area of the red sections are the same in both pictures but it's easier to calculate in the second pic, it's simply the area of the square minus the area of the circle.
Area of square= 1.25*1.25= 1.5625
Area of circle= pi*0.625*0.625=1.2272
Red area= 1.5625-1.2272=.0.3353

So going back the the first shape.

Area= 2.57*1.91-0.3353=4.5734

This is an excellent visual aid.

[86rocco]

Hi Gordon,
When I use Stan's calculator, I get the same results that I do using my own calculation.

I think you were just getting radius and diameter confused, a 1/4" drill bit has a 1/8" radius so you would use 0.125" for the value of R in my calculation.

BTW, I've got a bachelor's in mathematics, even though university was a long time ago, I'm still supremely confident in my ability to do computations of this nature, I trust my math.

[Brucepts]

One of you Excel gurus out there should come up with a spreadsheet