A little Math Help Please!

[daltoncalford]

Ok, after a night of no sleep, due to not being able to shut off my mind, I have lost the reasoning ability to do grade 10 math.

Here is what I am trying to do. I am trying to be able to work out volume, radius, height, width and length calculations for a variety of primary shapes.

For example, if you have the radius of a sphere it's volume would be calculated by

(4.19)*(radius^3)

Whereas, if you had the volume of a sphere, it's radius would be calculated by

(Volume/4.19)^(1/3)

The constant 4.19 is dirived from (4 divided by 3) multiplied by pi(). The exponent of 1/3 is the same as the cube root just as the exponent of 1/2 is the square root.

Now, that is all fine and dandy, but, I also need to work out the volumes of flattened spheres.

If I know the radius, I can use the above formula to find out it's spherical volume and then I multiply the result by the flatening factor (such as .5 for a sphere flattened down to a height one half of normal).

BUT, what I can't figure out for the life of me, is how to work out the radius of a flattened sphere if you already have the final volume and flattening factor.

It has been over 22 years since I dropped out of high school and I am a little rusty on my math.

Any of you math teachers??

best regards

Dalton

 

[Ptah]

It sounds like you are looking for the volume of an ellipsoid. If so, here's a link I hit right away that has the formula and a nice short explaination.

http://mathcentral.uregina.ca/QQ/database/QQ.09.99/nowicki1.html

To work out the major radius, you can back calculate the flattening factor then calculate the major radii (length and width should be the same) you need to compensate for the decrease in the height (one of the radii). Does that make sense?

If you flatten the sphere enough, you could also just treat it like a cylinder.

 

[Ptah]

BUT, what I can't figure out for the life of me, is how to work out the radius of a flattened sphere if you already have the final volume and flattening factor.

I think this portion is more easily answered than my initial post, and you already have it I believe. For a flattening factor of F caculate the radius R.

R=[(1/F)(Volume/4.19)]^(1/3)

because the flattened one radii can be thought of as equal to F*R, where R is the other two radii. Two of the radii will be R and one will be (F*R).

 

[daltoncalford]

Thanks Ptah,

I will give that a shot for the volume calculations.
I am working on the ship design system and I want to make sure the ship components are properly sized so that the system is consistant throughout.

(I caught some major gaff's in the formulas when creating my ship building software)

best regards

Dalton

 

[aramis]

Should be Ve=4/3πd²h

since area of a circle is Ac=πr², and an elipse is Ae=πLW.

(just to avoid confusion, π is pi, but in sans serif it looks poor...)

 

[Tekrat04]

Originally posted by Aramis:
Should be Ve=4/3πd²h

since area of a circle is Ac=πr², and an elipse is Ae=πLW.

(just to avoid confusion, π is pi, but in sans serif it looks poor...)

No.

Your are confusing the axis diameter and radius. It's the axis radius that are used to calculate the volume or area. Not the diameters. This applies to an Elipse as well as to an Ellipsoid or Spheroid.

 

[rhoneycutt]

unless I'm mistaken, the ratio of the volume of the ellipsoid and a bounding box it fits in, would be constant; about .524( (4*pi)/(8*3) ) iirc. l*w*h*.524 would give the volume. I think the ratio of surface areas between the ellipsoid and a bounding box would be constant too. If so, this idea could be used to figure the volumes and surface areas and frontal/lifting areas for any given hull form, once the ratios are known.

The big problem would be figuring volumes and areas for ships that combine different forms, such as the Lightning class cruisers ( box+cylinder) or the Solomani Endeavor class Patrol frigate ( wedge+3 cylinders )

not hard, but time comsuming, as it would mean figuring the hull stats multiple times and fit gear into each of the parts in a nice fashion as if making a dispersed structure ship (like the international space station) or an open frame ship with multiple modules bolted on.