If I ever win the Megabucks and start my own Rocket Factory, I hope you are in need of a job.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.
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.
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.
That method is too realistic for most folks here, but exactly what I resort to, as I learned it in 6th grade.If you have the parts, then you can use the water volume displacement method.
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.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.
I have plenty of physical models.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.