Math Question

W P Dixon wrote:

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

Nothing says you have to build a full size model. Make a fiberglass
model at 1/8 to 1/4 the size you SWAG, fill it with water and measure it
out. You can now scale as needed mathematically.

Don't forget to take into consideration material thickness, baffle
thickness etc as you plan.

Dan, U.S. Air Force, retired

A cad program would be really sweet, I have the Volo viewer and have not
meesed with it enough to do much but just open up a file in it! HAHA Any
good programs , cheap mind you,...I am so broke I can't pay attention!!!!
Would like to have cad prints of the finished deal. Heck I may get real
uppity and copyright my design! Volume is important in the floats because
each compartment has to be as equal as possible. And for those interested
they will be aluminum floats. And thinking of a 750 design (standard) for
small planes ultralights? And a 1000-1100 (retract gear).
Yeah yeah I could buy a kit from somewhere, or just buy them, but where
is the fun in that? Just to simple a structure to buy a set of someone
else's design . So I will make the D-750 and D-1000 model! HAHAHA

Patrick Dixon
student SPL
aircraft structural mech

Now that may not be a bad idea, and it would be pretty cool to build a RC
plane to go on top too! Dang Dan now I have to build another toy!!!!! My
wife is gonna shoot me for sure!
Seriously , that is not a bad idea, may just do that. Will check out the
math stuff first. If it befuddles me to bad I may have to resort to a plan
B, or Plan Dan!

Patrick
student SPL
aircraft structural mech

"Dan, U.S. Air Force, retired" wrote in message
news:LHOce.1573$aB.391@lakeread03...
W P Dixon wrote:

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

Nothing says you have to build a full size model. Make a fiberglass model
at 1/8 to 1/4 the size you SWAG, fill it with water and measure it out.
You can now scale as needed mathematically.

Don't forget to take into consideration material thickness, baffle
thickness etc as you plan.

Dan, U.S. Air Force, retired

Check out this site it has a bunch of volume calculators on it. This may do
the trick, especially since my math skills are in the lacking
department....from lack of
use.http://grapevine.abe.msstate.edu/~ft...vol/index.html

Patrick
student SPL
aircraft structural mech

Richard: Good post, up until the end, where you used the wrong volume
formula.

Richard Riley wrote:

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.

Good summary of the relevant assumptions!

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

(the length of one side) squared * 1.7
I used 1.7205 in my calcs, just to get additional significant digits
in the result.

Then multiply by the length of the tank to get the volume if both the
ends were the size of the large one.
So far, so good.

Then do the same thing with the small end.

Now you have 2 volumes. Add them together, divide by 2.
But this is where your formula falls down. You are basically saying
1/2*h*(B1+B2) where B1 and B2 are the areas of the bases. The correct
formula is 1/3*h*(B1+B2+sqrt(B1*B2)). There is no difference if the
two ends are the same size, and the difference grows with the size
differential between the ends to the limiting case of the tank coming
to a point (zero area "base") where your formula overstates the
correct volume by 50%.

As a "gut check", note that the volume of a cone is 1/3*h*pi*r^2.

For the pentagon examples, this breaks down to .5735*h*(s1^2 +s2^2
+s1*s2)

Average 2040

And after that, we got almost identical results. Your use of 1.7 in
the pentagon area fromula rather than more significant digits almost
exactly offset the relatively small error in the formula, with ends
this close to the same size. I calculated: .5735*24*(64+36+48)=2037.
Total 8.83 gallons.
Same
--
Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.

solid model of the tank using SolidWorks, ProE or similar. You can then

I've got solid works. Give me a yell if you want me to draw it up.

If you can find the area of the ends and average them, then multiply it by
the average distance between them, it will give you the volume. If you use
inches, dividing the total cubic inches by 231 will yield the capacity in US
gallons.




"Matt Whiting" wrote in message
...
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

Cut the shape of the tank with a piece of balsa or other solid wood. Then
place it in a tub of water until submerged and measure the volume of water
displaced. If you have something like a laundry sink, it is pretty easy
math.

Even easier is to build it into the shape that will fit into the VP and then
measure the liquid it holds and rewrite the manual.

As they proved with the Hubble telescope, you cannot really trust the math
guys, anyway.

Colin

"W P Dixon" wrote

.. 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.

Why not make it round on the ends, and just wrap it, instead of having flat
sides? Less welds to leak. That is, if you are welding each flat to the
other. If you are going continuous, nevermind! g
--
Jim in NC

Jim,
If I were welding it, it wouldn't be welded!!! HAHA It would be riveted
and sloshed. However the fellow that will be doing the welding welds at
nuclear facilities and has an xray certification. I know his work very well,
and it won't leak.

Patrick
student SPL
aircraft structural mech
"Morgans" wrote in message
...

"W P Dixon" wrote

. 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.

Why not make it round on the ends, and just wrap it, instead of having
flat
sides? Less welds to leak. That is, if you are welding each flat to the
other. If you are going continuous, nevermind! g
--
Jim in NC