Cube Root Formula (CRF) for Armored Hull Points in NAM2

The problem

The formulas in NAM are flawed because large starships -- especially armored ones -- will have outrageously large number of hull hit points.

For instance, look at a cylindrical hull comperable to the SC stats of the Kafer Alpha.  Based on GDW's values for Signature and Profile ( from both the Radial and Lateral viewpoint) a Kafer Alpha BB:

• is 45 meters in diameter and 130 meters long
• has a surface area of 18,378 m2 ( ignoring the ends of the cylinder)
• has an interior volume of 206,756 m3
• the Material Volume ( extrapolated from the surface area) is 390!!

The formulas

The formulas, according to NAM, for an armored hull are:

• Armor Volume = MV * ( Armor Multiplier) * ( Level of Armor Protection)
• Armor Mass = Armor Volume * ( Material tons per m3)

and

• Total Hull Hits = ( Armor Volume) / ( Armor Multiplier)

Note that plugging the Armor Volume formula into the Total Hull Hits formula will cause the "( Armor Multiplier)" terms in the numerator and denominator to cancel out leaving the simplified formula of:

• Total Hull Hits = MV * ( Level of Armor Protection)

A Solution

Here is one possible fix for an armored hull's hit points.

Cube Root Formula (CRF)

I suggest taking the cube root of the Level of Armor Protection value in the Total Hull Hits formula:

• CRF Total Hull Hits = MV * Cuberoot( Level of Armor Protection)

Examples

For my Kafer Alpha BB reverse design:

• MV of 390 * Cuberoot( 9) = 811 hit points

Applying the same variant formulas to the Punyuang example in NAM, we get:

• MV of 3 * Cubrt( 2) = 3.7 >> 4 hit points instead of NAM's 6

Since the Kennedy is really armor level one, taking any root of one is still one, leaving that craft unchanged.

Cube Root Table

Here is a handy table of cube roots for armor levels 1 to 20.

  Armor   Cubroot        Armor   Cubroot
  1       1.00           11      2.22
  2       1.26           12      2.29
  3       1.44           13      2.35
  4       1.59           14      2.41
  5       1.71           15      2.47
  6       1.82           16      2.52
  7       1.91           17      2.57
  8       2.00           18      2.62
  9       2.08           19      2.67
  10      2.15           20      2.71

I think using the cube root gives a reasonable boost to any armored starships hit points, without being excessive ( like my reversed Kafer Alpha shows happening with the official NAM formulas).

P.S. For those people whose calculators don't have a cube root key, yet have a "ln" keys.

To take the cube root of X press.

1. Enter X,
2. press the "ln" key,
3. now divide by 3, and press "equals sign" key,
4. now press "e to the xth power( superscript)" key

And you now have the cube root of X.

Note the "e^x" key may require using the "inv" key on your calculator, depending how your function keys are laid out.

Also you can substitute "log" for "ln" and "10^x" for "e^x" and get the same answer.

Here is a walk through, solving for the cube root of 8.

   Enter 8,                       display reads: 8
   Press "ln"                     display reads: 2.07944 ...
   divide by 3 and press "="      display reads: 0.69314 ...
   now press "e^x"                display reads: 2

So the cube root of 8 is 2  ( since 2 * 2 * 2 = 8).

If you have any questions about the above, please email me.