Revisions for FLATNS30   17 July 2011


I found a bug in my previous FLATNS20 and FLATNS21 programs.  This is my current fix.  However, I am having a problem resolving the effects of scaling to my satisfaction, so, while this revised FLATNS30 program fits the current data (STS vs 3 from many WWII tests and WELDOX 460E vs 20mm from modern tests, assuming undamaged projectiles until full shatter sets in), it may have to have a future modification to really fit data in the middle and past each end in projectile size (as will TPFLNS20 and M79APCLC, if the required changes are what I fear they might entail).

The fix involved:

(1) changing NBL(3)/SCALEFACTOR to NBL(3)*SCALEFACTOR.  This was a very bad typo that **wrecked the updated programs for any other projectile other than 3 size**, since *increasing* the size of the projectile causes the SCALEFACTOR = [1  X*LOG(D/3)]^Y (for some positive X less than 0.5 and Y = 0.5 or 1.0) to *decrease* in value (due to the MINUS sign after the 1), lowering the NBL in step, not raising it (the reverse also applies for smaller projectiles than 3 size);

(2) deleting the (1/D)^.5 term that is used to multiply the NBL to get the final value, since it really was part of the SCALEFACTOR, which should be the ONLY scaling term in the program; and

(3) changing the formula for the SCALEFACTOR from the M79APCLC formula SCALEFACTOR = {1  [(0.04)*LOG(D/3)]}^.5 to a new formula SCALEFACTOR = 1  [(0.45)*LOG(D/3)], where the LOG(D/3) in the BASIC program is always the Natural Logarithm (Base-e or LN on all calculators), not the calculator Base-10 LOG.

This last formula, unlike the M79APCLC formula, has:

(A) no square-root around it, since the plate thickness barely penetrated is proportional to the velocity V (linear), with kinetic energy (KE = 0.5*M*V^2, where M is the projectile mass and V is the striking velocity) required to penetrate increasing as proportional to the square of the plate thickness, which means the increase in thickness penetrated with increasing KE is at the same rate as the velocity increases with KE (if T^2 increases with V^2, then T increases with V, without the square part needed), not, as with M79APCLC, the penetration thickness increasing as a function of total projectile KE, and thus a function of V^2; and 

(B) the original M79APCLC formulas scaling constant 0.04 is now the 10-times-bigger 0.41.

It is this last that worries me, since I do not see why it must be so big to fit the data, but it is, assuming there are no other factors that I am missing at the moment.  I have tried messing with the plate quality and projectile weight terms to get the correct result with the WELDOX 460E plates, but they give even more illogical results, so I am now stuck.
