# Volume?

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#### MClark

##### Well-Known Member
Does Open Rocket or other program have the ability to give the volume of the airframe?

M

TRF Supporter
L*Pi*r^2

#### timbucktoo

##### Well-Known Member
Staff member
TRF Supporter
Global Mod
If you google "volume of cylinder", a calculator will be the first search result.

#### MClark

##### Well-Known Member
I was wanting the volume of nose cones, (elliptical, ogives, V Karman), tail cones.
Cones and cylinders I can do.

M

#### timbucktoo

##### Well-Known Member
Staff member
TRF Supporter
Global Mod
You said airframe in the OP. That's what you got!

#### MClark

##### Well-Known Member
I call the nose cone, tube and tail cone the airframe
M

#### blackbrandt

##### That Darn College Student
So, to do a volume calculation will require a bit of calculus. Attached is a copy of a paper I wrote for a class I was in. On the second or third page, there's a list of the nose cone shapes and the equations for the cross section. Essentially what you have to do is calculate the value of the equation of the nose cone revolved around the axis. This is done with some calculus.

Let's look at the equation for an elliptical nose cone.
y=R*sqrt(1-[x^2/L^2])
Where
x=distance from tip of cone
L=Total length of cone

Plug in lengths and values for what you know. Let's do a 1" wide nose cone 3" long.

y=0.5*sqrt(1-[x^2/3^2])

y=0.5*sqrt(1-x^2/9)

This is the X/Y coordinates of any point on the side of the nose cone. To figure out the volume, we use calculus.

The equation for the volume of a solid revolved around the x axis is the integral from 0 to L of the equation squared times pi.

This math will be as follows:

Integral from 0 to 3:
0.0833333*Sqrt[9-3^2] + 0.75 ArcSin[0.333333*3]-0.0833333 * Sqrt[9-0^2] + 0.75 ArcSin[0.333333 0]

This equals approximately 0.927.

pi*integral from 0-3 squared:

3.14*(0.927^2)=2.69 cubic inches.

View attachment Fletcher Cd Optimization.pdf

#### MClark

##### Well-Known Member
BB, thank you. This is why I was hoping a design program could give the numbers I need. To do multiple rockets in the field would be a real task.

M

#### markkoelsch

##### Well-Known Member
Mark, Rocksim does not provide volume. I do not know about Open Rocket, but I doubt it would give volume.

#### TopRamen

##### SA-5
I've never seen it as an observable parameter in Openrocket.
I'm developing a system for molding things, and knowing the volume of rocket shaped things might be helpful. but I'm going to make the first mold blocks regardless as I already see them in my head, and that's good enough for me.

Truley impressive Matt..
You are a very bright young man indeed...
You've got the potential for some incredible future....

Be very careful making choices in life ....

Teddy

#### TopRamen

##### SA-5
So, to do a volume calculation will require a bit of calculus. Attached is a copy of a paper I wrote for a class I was in. On the second or third page, there's a list of the nose cone shapes and the equations for the cross section. Essentially what you have to do is calculate the value of the equation of the nose cone revolved around the axis. This is done with some calculus.

Let's look at the equation for an elliptical nose cone.
y=R*sqrt(1-[x^2/L^2])
Where
x=distance from tip of cone
L=Total length of cone

Plug in lengths and values for what you know. Let's do a 1" wide nose cone 3" long.

y=0.5*sqrt(1-[x^2/3^2])

y=0.5*sqrt(1-x^2/9)

This is the X/Y coordinates of any point on the side of the nose cone. To figure out the volume, we use calculus.

The equation for the volume of a solid revolved around the x axis is the integral from 0 to L of the equation squared times pi.

This math will be as follows:

Integral from 0 to 3:
0.0833333*Sqrt[9-3^2] + 0.75 ArcSin[0.333333*3]-0.0833333 * Sqrt[9-0^2] + 0.75 ArcSin[0.333333 0]

This equals approximately 0.927.

pi*integral from 0-3 squared:

3.14*(0.927^2)=2.69 cubic inches.
If I ever win the Megabucks and start my own Rocket Factory, I hope you are in need of a job.
I do appreciate and respect those that can master it though.

#### dhbarr

##### Amateur Professional
Treat 'em as cones-on-cylinders, should be pretty close.

If you need finer tuning, maybe do it in the lab and write the results on the shoulder?

#### BLKKROW

TRF Supporter
It can be done using a triple integral, using software the integral should be easy.

#### Buckeye

##### Well-Known Member
TRF Supporter
If you have the parts, then you can use the water volume displacement method.

#### Reinhard

##### Well-Known Member
You can use a little trick, to get the volume out of OpenRocket. Instead of the correct wall thickness, use the option "Filled" to generate a non-hollow part. Then, you can divide the mass of the part by it's density, to get its volume - or, even easier, you can create a custom material with a density of 1 in your preferred unit system. You can directly use the mass value then. One needs to pay attention, to not double count internal parts of the rocket - e.g. the shoulder of the nose cone in addition to the surrounding body tube.

Reinhard

#### MCriscione

##### Well-Known Member
Integrals? Yuck. If you know the cross-section area and the centroid of the area you can find the volume using Pappus&#8217;s Centroid Theorem with much simpler math. You just take the swept area and multiply by the distance the centroid of that area travels.

This assumes you know the cross-sectional area of the nose cone volume, and can plot or sketch it on some cardboard. First, take your area and half it, to get the swept area. Then take your cardboard cutout and cut it in half too, along the center axis. Find it's balance point (centroid) and measure the distance to the center axis. Then apply the following formula:

V=2*pi*D*A

Where:
A = Cross-sectional area of the revolved solid. (area of the cutout)
D = Distance from the centroid to the axis.

That's it. Works easily for simple geometry and great even on more complex stuff. I recently used it to estimate the fluid volume change for a replacement reactor vessel head I'm designing for a nuclear power plant. Came out to within 1% of the Solidworks estimate.

#### TopRamen

##### SA-5
If you have the parts, then you can use the water volume displacement method.
That method is too realistic for most folks here, but exactly what I resort to, as I learned it in 6th grade.

Folks want virtual garbage or over-complicated innuendo to fulfill there lack of common sense skill sets nowadays.

It's probably a bad idea if your rocket is made of conventional materials, but with CA and Epoxy Saturated composite, you can dunk them all day long with no distortion.

Last edited:

#### Steve Shannon

##### Well-Known Member
TRF Supporter
That method is too realistic for most folks here, but exactly what I resort to, as I learned it in 6th grade.

Folks want virtual garbage or over-complicated innuendo to fulfill there lack of common sense skill sets nowadays.

It's probably a bad idea if your rocket is made of conventional materials, but with CA and Epoxy Saturated composite, you can dunk them all day long with no distortion.
But it requires you to have a physical model. It's useless for virtual simulations which is a valid method for optimizing designs. Each has its place.

#### TopRamen

##### SA-5
But it requires you to have a physical model. It's useless for virtual simulations which is a valid method for optimizing designs. Each has its place.
I have plenty of physical models.
Why would you not have a mock-up physical model to use for test purposes???
I even have a few "Physical Models" in my trash bin.

It would be great to create everything in virtual limbo word, but jeez! Can't anyone create real life anymore?
I rarely even discuss Mindsim anymore, because not many understand that it is real, but my launch videos speak for themselves so $%^& anyone who does not think I can make an airfram and wings/fins fly in a stable fashion. I'm working on something new and crazy right now, and it will not be discussed here nor will there be a "Build Thread" for just that reason. Saran Wrap and 3M "Scotch" Permanent Double Sided Tape will let you make your volume observable. If you are even worried about things like this, you can certainly afford$3.50 worth of materials and the second order to BMS if you get your precious one off build wet.

#### Steve Shannon

##### Well-Known Member
TRF Supporter
It's kind of like the difference between a typewriter and a word processor. [emoji4]

[emoji1010] Steve Shannon [emoji1010]