okay, so here's a question I've been hung on for some time now... I want to tune and balance a virtual explosion on my computer via a multivariable mathematical function.
If angles, spheres and big numbers make your head hurt, do not read any further; otherwise, bear with me.
now that you have been sufficiently warned, here's the problem as I envision it:
We're going to explode a virtual bomb in a zero-G vacuum, which will fragment into d number of pieces, all of equivelent mass and velocity, and travel off into space on uniform vectors (not realistic, I know, but it doesn't have to be - its a math problem)
The net terminal force of each fragment, we will call n.
A target of a size (profile area, in square meters) will be placed r meters from the center of the bomb.
The number of fragments to strike the target, we will measure as h
The first objective is to build a function which for a given a, r and d, we can calculate h. (this will require a formula for finding what the uniform spherical vector for d is - something I haven't figured out yet)*
Note: although the target cannot be hit by a fraction number of h, a fraction value is acceptable, since we want a probable average number of h for any position on the r radius
The second objective is far easier... it's basically just multiplying n by h to get the total force exerted on the target (f)
The third objective is where it all comes together... if given a and r, we want to solve for f in terms of d and n. This part should be a farily simple matter of rearranging the problem variables.
So basically, we want to take a specific-size target, and set it up a specific distance from the bomb, then test it with various numbers of fragments (d) and energies per fragment (n) until we are satisfied with the total force that hits it (f).
We then want to be able to change the distance from the bomb, to see how it is effected nearer to and further from the bomb.
for an example, let's start by working with
r = 200
a = 20
and shoot for
f ≈ 2,000
to make things work out, we want to constrain d and n to
30 < d < 100
n < 2,000
Anyone care to take a crack at making it work?
if you do give it a try, please build the equation first with JUST the variables, and THEN plug in the numbers to solve, so I won't have to keep coming back to ask you repeatedly what the heck it is you're doing... there's a chance I could fint it hard to follow, thanks.
* by uniform vector, I'm saying that if we have d number of objects travelling out from a point in 3-dimensional space, they will at any given time constitute points evenly-spaced around a sphere (like electron pairs in molecular geometry).
~Mobius
If angles, spheres and big numbers make your head hurt, do not read any further; otherwise, bear with me.
now that you have been sufficiently warned, here's the problem as I envision it:
We're going to explode a virtual bomb in a zero-G vacuum, which will fragment into d number of pieces, all of equivelent mass and velocity, and travel off into space on uniform vectors (not realistic, I know, but it doesn't have to be - its a math problem)
The net terminal force of each fragment, we will call n.
A target of a size (profile area, in square meters) will be placed r meters from the center of the bomb.
The number of fragments to strike the target, we will measure as h
The first objective is to build a function which for a given a, r and d, we can calculate h. (this will require a formula for finding what the uniform spherical vector for d is - something I haven't figured out yet)*
Note: although the target cannot be hit by a fraction number of h, a fraction value is acceptable, since we want a probable average number of h for any position on the r radius
The second objective is far easier... it's basically just multiplying n by h to get the total force exerted on the target (f)
The third objective is where it all comes together... if given a and r, we want to solve for f in terms of d and n. This part should be a farily simple matter of rearranging the problem variables.
So basically, we want to take a specific-size target, and set it up a specific distance from the bomb, then test it with various numbers of fragments (d) and energies per fragment (n) until we are satisfied with the total force that hits it (f).
We then want to be able to change the distance from the bomb, to see how it is effected nearer to and further from the bomb.
for an example, let's start by working with
r = 200
a = 20
and shoot for
f ≈ 2,000
to make things work out, we want to constrain d and n to
30 < d < 100
n < 2,000
Anyone care to take a crack at making it work?
if you do give it a try, please build the equation first with JUST the variables, and THEN plug in the numbers to solve, so I won't have to keep coming back to ask you repeatedly what the heck it is you're doing... there's a chance I could fint it hard to follow, thanks.
* by uniform vector, I'm saying that if we have d number of objects travelling out from a point in 3-dimensional space, they will at any given time constitute points evenly-spaced around a sphere (like electron pairs in molecular geometry).
~Mobius