Need some math help

[Marcello]

I am thinking about fiddling again with SAM warheads. What I would need is some calculation, possibly not too difficult to use, to enable the compression of a variety of numbers in a 1-255scale. The lowest numbers in the new scale should be near to 1-1 conversion ratio with the old one, with the higher ones growing more slowly as they get close to 255.
Also I would need some formula dealing with blast effect: I know the the area affected by an explosion does not rise proportionally with the increase of the warhead yield but I would like to know if there is some formula dealing with it.

[Mobhack]

Originally Posted by Marcello

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Also I would need some formula dealing with blast effect: I know the the area affected by an explosion does not rise proportionally with the increase of the warhead yield but I would like to know if there is some formula dealing with it.

It is an air burst in the atmosphere so the first approximation for blast effect (ignoring air density, etc) would be the formula for the volume of a sphere. 4/3piR^3 if I remember my high school maths!.

Assume mass M1 of 1 unit of explosive creates a sphere of radius 1 unit (R1), and it will have a volume V1 given by applying the formula for volume of the sphere.

Therefore to find out what mass M2 is needed to achieve twice the radius of effect. Find V2 for a sphere of radius R2 of 2 units, and then find the ratio between V2 and V1. Apply the ratio to M1 to get M2.

Now calculate again for radius 3, 4 etc. (you could make an Excel spreadsheet for this). You now have a rough guide as to how much explosive is needed relative to M1 for twice, thrice, four times ... etc the effect.

Cheers
Andy