Math Question

Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will see if
yall can come up with it. Yes I did check on the web, but did not see the
formula I need.
I want to figure the volume of a gas tank that will not be round or
square, It will have five sides and then the two ends of the tank. With one
end being larger than the other. I would give exact measurements , but being
as I don't know what they will be yet I can't:} I need to find the right
volume in order to get the right measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do this!


--
Patrick Dixon
student SPL
aircraft structural mech

sounds like you will need to just fill the tank and measure the output.

Dave

W P Dixon wrote:
Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will see
if yall can come up with it. Yes I did check on the web, but did not see
the formula I need.
I want to figure the volume of a gas tank that will not be round or
square, It will have five sides and then the two ends of the tank. With
one end being larger than the other. I would give exact measurements ,
but being as I don't know what they will be yet I can't:} I need to find
the right volume in order to get the right measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!

W P Dixon wrote:

Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will see
if yall can come up with it. Yes I did check on the web, but did not see
the formula I need.
I want to figure the volume of a gas tank that will not be round or
square, It will have five sides and then the two ends of the tank. With
one end being larger than the other. I would give exact measurements ,
but being as I don't know what they will be yet I can't:} I need to find
the right volume in order to get the right measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!


Depending on how irregular the tank shape is, you may have to solve this
using numerical integration. However, if the tank shape is the same in
at least one axis (say z or vertical), then figure the area of the shape
in the x-y plane and then simply multiply times the height, z, and
equate that to the volume you desire. Then solve for z.


Matt

Matt Whiting wrote:

W P Dixon wrote:

Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will
see if yall can come up with it. Yes I did check on the web, but did
not see the formula I need.
I want to figure the volume of a gas tank that will not be round or
square, It will have five sides and then the two ends of the tank.
With one end being larger than the other. I would give exact
measurements , but being as I don't know what they will be yet I
can't:} I need to find the right volume in order to get the right
measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!


Depending on how irregular the tank shape is, you may have to solve this
using numerical integration. However, if the tank shape is the same in
at least one axis (say z or vertical), then figure the area of the shape
in the x-y plane and then simply multiply times the height, z, and
equate that to the volume you desire. Then solve for z.


Matt

That would work if it had the same cross sectional area along Z. He says
otherwise. This leaves to 3 solutions: 1) build it, fill it and measure
the volume coming out, 2) calculus which would be quickest and easiest
or 3) draw a diagram, cut it into solids you can calculate, then add up
the volume of the solids.

If the small end isn't very much smaller than the big end go ahead and
do it Matt's way and add a fudge factor.

Dan, U.S. Air Force, retired

Hee Hee,
No simple answer huh? Thanks guys, I looked more on the web late last
night and I do think I will have to make the shapes into smaller measureable
shapes and add the totals. I do think figuring up something before you
actually build it is alot cheaper,...you don't have to build it but once.
Well we all hope anyway!
Also planning to build a set of floats and that's where the volume
formulas really get funky. I would sure hate to spend a grand just to fill
it with water and say, well not right can't use it. Heck my old lady would
kill me if I wasted 200 bucks on a ruined gas tank! HAHA
It won't be to bad figuring it all up "cutting it into basic shapes" ,
just will take some time. For the gas tank, it will be in a VP-1. I am
welding aluminum instead of using the fiberglass. An old high school buddy,
certified nuclear welder is going to weld it up for me. So I need to send
him a drawing of it, thus the need for getting it right. That math stuff is
pretty cool when you can remember the formulas ain't it? So for the gas
tank, I just wanted to see how much fuel a aluminum tank would hold with
alittle mod. But the floats , I definitely have to know the volumes of each
compartment before I even think of starting the build there.

Patrick
student SPL
aircraft structural mech

W P Dixon wrote:
Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will see
if yall can come up with it. Yes I did check on the web, but did not see
the formula I need.
I want to figure the volume of a gas tank that will not be round or
square, It will have five sides and then the two ends of the tank. With
one end being larger than the other. I would give exact measurements ,
but being as I don't know what they will be yet I can't:} I need to find
the right volume in order to get the right measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!


Depending on the shape of the tank, you can divide it into prisms (the
area of a triangle, multiplied by the height) and add them up.

This method should work for any tank that can be composed of
non-overlapping easy-to-calculate volumes. Or, if they are overlapping,
you can subtract the intersection betweeen the two overlapping volumes
-- but that starts getting a little hairy, since negative volumes make
my head hurt when I'm working with something real. :-)

If that doesn't work, I'm with the guy who suggested integration. I
would try regular calculus first -- I would use the
rotate-around-the-axis trick (if you've done it, the previous phrase
should make sense?), and then subtract off any volumes that aren't
there. After that, I'd try for for a numerical solution. A program
like Mathematica (http://www.wolfram.com) can make the plug&chug parts
easier -- especially for a numerical solution.

The complexity really depends on how irregular your tankis. If your
tank just has an irregular footprint but is the same height all-around,
(a puzzle piece that is 10" thick), all you need is the area of the
footprint and the height -- multiply them together and you're done.

I hope this helps,
-Luke

P.S. I am not a math wizard! But, I do drink beer with math wizards... :-)

W P Dixon wrote:
Also planning to build a set of floats and that's where the volume
formulas really get funky.

I just got my seaplane rating. I spent some time looking at the floats
-- it looks like the only way I could calculate the volume of the floats
I was looking at would be a double-integral. Elegant, but could still
be tricky.

One thing to keep in mind is the place where the float will contact the
water at various attitudes. If the contact-point is too far forward
(either because of the attitude of the aircraft or because of the design
of the float), you're flying a taildragger in a soft-sticky-massive
substance that is many times more dense than air... Scary!

Also, floats a have many effects on the aerodynamics of the aircraft.
The side area of the craft is different when it has floats -- a lot more
aerodynamic stuff happening in front of the CG, which can require a
bigger rudder. Also, the instructor told me that in a plow turn, the
change in the amount of the float exposed to the wind was one of the
things that makes the aircraft turn downwing. Lastly, the mass of the
floats would probably change the CG around a bit too.

-Luke

"Richard Riley" wrote in message
...
On Sat, 30 Apr 2005 00:26:32 -0400, "W P Dixon"
wrote:

:Ok Guys and Gals,
: I do not remember the formula for this to save my life, so I will see
if
:yall can come up with it. Yes I did check on the web, but did not see the
:formula I need.
: I want to figure the volume of a gas tank that will not be round or
:square, It will have five sides and then the two ends of the tank. With
one
:end being larger than the other. I would give exact measurements , but
being
:as I don't know what they will be yet I can't:} I need to find the right
:volume in order to get the right measurement . Oh the dilemma !
: Be gentle math wizards it's been 25 years since I have had to do
this!
:

I'm not engineer, and I'm not currently playing one on TV, but I think
it's straightforward. Just so we're clear, I'm assuming -

Each end is a pentagon, each one of *it's* sides is equal length. The
two ends are parallel to each other. One pentagon is larger than the
other. They are perpendicular to a line drawn from the center of one
to the center of the other.

First, find the area of the large pentagon. The formula is

(the length of one side) squared * 1.7

Then multiply by the length of the tank to get the volume if both the
ends were the size of the large one.

Then do the same thing with the small end.

Now you have 2 volumes. Add them together, divide by 2.

So, if one end is a pentagon with sides that are 8 inches long, and
the other has sides that are 6 inches, and it's 24" long

Area of end one - 108.8
Area of end two - 61.2

Volume 1 2611.2
Volume 2 1468.8

Average 2040

Total 8.83 gallons.

This looks like the winning formula to me.

Dan, U.S. Air Force, retired wrote:
Matt Whiting wrote:

W P Dixon wrote:

Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will
see if yall can come up with it. Yes I did check on the web, but did
not see the formula I need.
I want to figure the volume of a gas tank that will not be round
or square, It will have five sides and then the two ends of the tank.
With one end being larger than the other. I would give exact
measurements , but being as I don't know what they will be yet I
can't:} I need to find the right volume in order to get the right
measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!


Depending on how irregular the tank shape is, you may have to solve
this using numerical integration. However, if the tank shape is the
same in at least one axis (say z or vertical), then figure the area of
the shape in the x-y plane and then simply multiply times the height,
z, and equate that to the volume you desire. Then solve for z.


Matt


That would work if it had the same cross sectional area along Z. He says
otherwise. This leaves to 3 solutions: 1) build it, fill it and measure
the volume coming out, 2) calculus which would be quickest and easiest
or 3) draw a diagram, cut it into solids you can calculate, then add up
the volume of the solids.

If the small end isn't very much smaller than the big end go ahead and
do it Matt's way and add a fudge factor.

I'd find an ME student at a local university and have them create a
solid model of the tank using SolidWorks, ProE or similar. You can then
get an accurate volume with the press of a key. And you can play "what
if" with the design until the cows come home.


Matt

Matt Whiting wrote:
Dan, U.S. Air Force, retired wrote:

Matt Whiting wrote:

W P Dixon wrote:

Ok Guys and Gals,
I do not remember the formula for this to save my life, so I will
see if yall can come up with it. Yes I did check on the web, but did
not see the formula I need.
I want to figure the volume of a gas tank that will not be round
or square, It will have five sides and then the two ends of the
tank. With one end being larger than the other. I would give exact
measurements , but being as I don't know what they will be yet I
can't:} I need to find the right volume in order to get the right
measurement . Oh the dilemma !
Be gentle math wizards it's been 25 years since I have had to do
this!


Depending on how irregular the tank shape is, you may have to solve
this using numerical integration. However, if the tank shape is the
same in at least one axis (say z or vertical), then figure the area
of the shape in the x-y plane and then simply multiply times the
height, z, and equate that to the volume you desire. Then solve for z.


Matt



That would work if it had the same cross sectional area along Z. He
says otherwise. This leaves to 3 solutions: 1) build it, fill it and
measure the volume coming out, 2) calculus which would be quickest
and easiest or 3) draw a diagram, cut it into solids you can
calculate, then add up the volume of the solids.

If the small end isn't very much smaller than the big end go ahead and
do it Matt's way and add a fudge factor.


I'd find an ME student at a local university and have them create a
solid model of the tank using SolidWorks, ProE or similar. You can then
get an accurate volume with the press of a key. And you can play "what
if" with the design until the cows come home.


Matt

Or a cad student if all you want is volume. I use Micro Station 95 left
over from my old collitch days and what he descibes is simple.
Engineering types can do all kinds of neat analysis so they can make
constructive hints. Just bear in mind most engineering students have no
background in auto repair or similar so their grasp of reality may be
limited. When I was going for my EE (I dropped out in 3rd year) in the
1990s I ran into a bunch of kids going for the "big fix."

Dan, U.S. Air Force, retired