Mathemeticians... Need some Geometry Help... Surface Area of 3 Cone Filters...

[TROLL]

If anyone knows the equation to figure out surface area of a cone (not including top and bottom) please let me know what the surface area is of the following three filters:

#1) Base: 6.5", Top: 4.5", Height: 5.5"

#2) Base: 6.5", Top: 5", Height: 6.5"

#3) Base: 6.5", Top: 4.375", Height: 7"

Trying to figure out which has more surface area, and also which will actually fit in my engine bay :)

[Gaze]

No guarantee because i didnt know if your measurement was referring to the actual height from top to bottom or length of the side of the filter but here's what i came up with:

112.25"
132.67"
142.87"

Regardless of the actual numbers, the 1st is the smallest and 3rd is the largest.

[ I came to these numbers by finding the perimeter of each end of the cone and using it as the top and bottom of a trapezoid. From there it's pretty simple to find the area of a trapezoid ]

[willthethrill]

No guarantee because i didnt know if your measurement was referring to the actual height from top to bottom or length of the side of the filter but here's what i came up with:

112.25"
132.67"
142.87"

Regardless of the actual numbers, the 1st is the smallest and 3rd is the largest.

[ I came to these numbers by finding the perimeter of each end of the cone and using it as the top and bottom of a trapezoid. From there it's pretty simple to find the area of a trapezoid ]
Wouldnt you need to then subtract the base area of the cone since it does not play a part in the filter area?

[TROLL]

height was the length of the side... can you write down the equation you used? not sure how a trapezoid can really help find the surface area of a cone.
my best guess is since the cone does not come to a point at the top, i would have to take the area of a cone from the base to an imaginary top point, then subtrace the area of a cone from the top to an imaginary point. without the radius i'm just not sure how to do it though...

thanks!

edit: i mean since its flat on top and doesnt come to a point like this:
http://www.gomath.com/geometry/cone.jpg

the surface area i'm looking for is for something shaped like this: the top and the bottom do not count, only the surface of the side... and yes i am assuming that the folds are uniform on each filter, because there's really no way to account for all of that, haha.
http://www.envyperformance.com/images/products/sum-239301_w.jpg

[Driven]

edit: i mean since its flat on top and doesnt come to a point like this:

You're correct.

The imaginary point heights that you are refering to are:

H1 = 17.88
H2 = 28.09
H3 = 21.41

This assumes the height you gave is the vertical height though, not the angle height. The difference will be small though.

[TROLL]

the height i gave was marked "s" on the diagram listed above, i assume that is angle height since it is not vertical.
driven, sounds like you might have a good start on this, can you confirm the numbers posted by gaze, or did you come up with something different? thanks...
bryan

[Gaze]

The easiest way to measure SURFACE AREA of a cone is to act like you sliced the cone open and unraveled it into the shape of a trapezoid.

Take your cone filter... measure the diameter of the top and the bottom of the filter and either the actual height of the filter, or the distance down the side of the filter.

Using P=2piR where pi = 3.14 and R = radius of the top of the cone (1/2 the diameter)
your "P" is the length of the top of your trapezoid.
Do the same for the bottom to find the perimeter and that number is the bottom of your trapezoid.
From there, you can use your other dimension (overall height or length of side) to determine the 3rd and 4th sides of your trapezoid. You shoudl be able to find are from there.

For Instance, Filter 3:
Ptop = 2*(3.14)*(2.25) = 14.13
Pbottom = 2*(3.14)*(3.25) = 20.41

Now, the easiest way to find the area of your trapezoid (which is essentially the surface area of your cone filter) is the following formula:
A * B + [(C - B) * A]
Where A = Actual height of cone, B = top, C = bottom

= 5.5 * 14.13 + [(20.41 - 14.13) * 5.5]
= 77.715 + 34.54
= 112.255

Now the number you gave me for height is actually the diagonal side of the trapezoid, the number is a little high but i could figure it out if you want.

[willthethrill]

you would probably be better off getting the area of a cylinder for something like that if it where smooth. However because of the pleats the surface area is dramatically increased. You would be better off finding the surface area of a single pleat and then count them all up.

[Driven]

The numbers posted by Gaze are wrong. Use this site to finish up your calcs: http://www.webcalc.net/calc/0040.php

All you need to do is take the height I posted and that will get you A1, subtract your height from the height I posted and that will be the top cone, A2. A1 minus A2 is the area you're looking for.

If you want to calculate new heights since I didn't do it 100% correct (misread your post), use:

Base * Tan(arc-cos(((Base - Top) / 2) / height)) = total height

[Driven]

The easiest way to measure SURFACE AREA of a cone is to act like you sliced the cone open and unraveled it into the shape of a trapezoid.

Thats all well and good, except that a cone doesn't unravel to become a trapazoid. The math is more complex than you're making it to be.

[TROLL]

ok gaze i see what you're saying, but you're not right... you're assuming that if you flattened out the surface area of the cone it would look like a trapezoid, but it wouldnt. the top and bottom will have a curve to them if it was 'unravelled', kinda like this photo, except with the top portion of this point cut off, leaving another curve similar to the one on the bottom
http://mathcentral.uregina.ca/QQ/database/QQ.09.99/frothy1.2.gif

[Driven]

Brian, did you follow what I posted? I ran through the calcs once but I mis-read your post before doing them. I don't really feel like doing them again.

[Gaze]

yeah... im realizing that now... geometry was a while ago and im trying to do this without looking it up online... I'm taking another stab at it.


BTW, thanks for the entertainment for the day!!

[TROLL]

ok thanks driven... based on your heights, which may be slightly off... i came up with:

ex: (area of cone from base) - (area of cone from top) = (area of 'flat' cone filter)

#1: 185.5 - 127.4 = 58.1 in^2

#2: 288.7 - 221.5 = 67.2 in^2

#3: 221.1 - 147.9 = 73.2 in^2

so since we used vertical height instead of side height i guess this is slightly off, but i dont have a scientific calc handy and i hated cos and tan and all that bs, so i think this is close enough :)

[Gaze]

meh, close enough... i told you the right order...

[TROLL]

and i'd just like to add that i think k+n and other filter manufacturers should list surface area of their filters along with the bajillion other specs they give, dont you? after all, it is certainly a performace aspect to consider. i'm trying to stuff the largest filter i can into my engine bay, which is the reason for all of this... looks like #3 is the winner as long as i can get it to fit :)

[TROLL]

the interesting part is all of your answers were proportional to the actual area... although the actual numerical value was way off, they were all between x1.92 and x1.96 of the 'correct' answer.

[Gaze]

It definately should be listed on the box. though I'd be curious to know how many 1/10ths of a HP you get for each Sq Inch too!

[willthethrill]

and i'd just like to add that i think k+n and other filter manufacturers should list surface area of their filters along with the bajillion other specs they give, dont you? after all, it is certainly a performace aspect to consider. i'm trying to stuff the largest filter i can into my engine bay, which is the reason for all of this... looks like #3 is the winner as long as i can get it to fit :)
They wont do it because it will take to long for them to figure out :rofl:

[teh DIRT]

They wont do it because it will take to long for them to figure out :rofl:

....and its pointless




i think.

[Gaze]

your car can only suck in so much air so at a certain point, increasing filter surface area would become pointless.

[teh DIRT]

exactly.

[S4toSTI]

This entire thread was about how much something can suck. I am happy to see some people remember their math. I totally forgot the equation for it and had to look it up. I remember in high school the trick was remembering the equation not doing the actual math i guess my memory suck, or i just never thought i would be asked the surface area of a cylinder again.

[wgknestrick]

How deep are the folds?

Troll, I can calculate an exact measurement using Solidworks at work. It would even calculate the fold radii area.

[TROLL]

....and its pointless
your car can only suck in so much air so at a certain point, increasing filter surface area would become pointless.
so both of you are saying that efficiency on the intake side doesnt affect performance? might as well route your intake through a drinking straw then. why do race cars run huge inlets or even nothing at all? the least resistance the better, regardless... and more surface area on a filter will help achieve that. efficiency is key... and that applies to pretty much everything.

How deep are the folds?

Troll, I can calculate an exact measurement using Solidworks at work. It would even calculate the fold radii area.
well beyond the dimensions above, the rest would just be guessing. all of the folds should be the same depth though so the numbers posted above should be a pretty good indication, relative to each other at least. thanks for the offer though... i am planning to give you a call tonight by the way.

and for anyone interested, i'm not even sure i can fit any of the filters listed above under my hood at all. a slight miscalculation on my part that may force me to revise my entire plan for my intake... kind of frustrating, but it could be worse.

bryan

[cravej]

the least resistance the better, regardless... and more surface area on a filter will help achieve that. efficiency is key... and that applies to pretty much everything.But there is a point of diminishing returns. If you put an enormous filter on your car, there will be a section that collects more dirt, because that is the path of least resistance & that is where most of the air is flowing through. The clean part of the filter isn't doing a whole lot.

[teh DIRT]

But there is a point of diminishing returns. If you put an enormous filter on your car, there will be a section that collects more dirt, because that is the path of least resistance & that is where most of the air is flowing through. The clean part of the filter isn't doing a whole lot.

im with this guy. then again i dont use a filter so i should be quiet.

[TROLL]

i agree, but what is that point? you're comparing open exhaust pipes and a turbine spinning at 150k rpm to a filter, which obviously does not flow as freely pound for pound. i agree that you'll reach a point of diminishing returns but i do think that filter size should be considered when piecing together a setup.