Andrew Jaremkow

THE FORMULA Since the users of the formula have so far declined to either post it, or give reference to where in the Ordnance Board report the equation is, I thought I'd take a stab at identifying it. That way we can all apply the appropriate data and draw conclusions, rather than simply taking the blanket assurance being offered to us. As far as I can tell the equation being discussed is the National Physical Laboratory Formula for Normal Attack, described in Chapter 2, Section 4 of the report. It comes in the form (here modified for angled impact): (Wv^2)/d^3 = {[43.4*B^0.5*(t/d)*sec 3/2 theta]+747-[54000/Bo-B]-[182theta/(65-theta)]}^2 where: W = shell weight v = shell velocity d = shell diameter t = plate thickness theta = angle of impact B = plate hardness (Brinnell) Bo = limiting hardness The limiting hardness can be derived with reference to the standard 2 pdr shot used to derive the equation, using the following formula. Bo = 500 - 160 log(d/d2) where d2 = 1.565 inches, the diameter of 2 pdr shot. The model is considered to apply for A.P. shot up to 6 inches being fired against homogenous armour in the 200 to 400 Brinell range, at angles up to 45 degrees. The model was first developed from 1942 firing trials of 2 pdr shot (1.565" dia), and later expanded with 1943 and 1944 testing of three subscale AP rounds of the 2 pdr shape (0.990", 0.540", and 0.296" dia). Shots were conducted against 3% Cr.Mo. steel plates up to 2 diameters thick, and ranging from Brinell 250 to 450. Later on, in work that continued into 1947, trials were conducted with 6 pdr, 17 pdr, and 3.7" shot, and these confirmed that the model was generally accurate for AP shot. The formula's accuracy was found to be better than 2% velocity (roughly 21 f/s), so long as the baseline 3% Cr.Mo. steel was being used, but when other types of steel were used as a target the formula's accuracy dropped, and deviations of as much as 150 f/s were noted. The model has several limitations. It can only compensate for mass, diameter, and velocity of the projectile, and hardness of the target plate. It cannot distinguish between rounds with different nose shapes, different hardnesses, and different materials, nor does it predict the angle-dependant performance of features such as armour piercing caps. It does not predict the performance of face hardened armour. Its correction for angled armour is a fairly clumsy fit (sec 3/2 theta) when you compare it to charts of penetration vs. angle, with their complex curves. If this is the wrong equation, I apologize, but I suspect it's the one. The only other options are modified DeMarre formulae, which seem even less likely to provide good results across the board. Limiting Velocity The report has the following to say about definitions of penetration: "The term "perforation" cn be defined in many ways, according to the stage at which defeat of the plate is considered to have occurred. Thus the "ballistic limit" of a plate is that velocity above which a given shot will produce a cracked bulge, and below which it will produce and uncracked bulge. The "critical velocity" used in this chapter, however, is that corresponding to exact perforation with no residual velocity after the shot has perforated the plate, i.e., the minimum velocity at which the shot passes clean through the plate." (Emphasis mine) 88L71 vs 88 L56 I'm not an expert on WWII shells (I usually concentrate on modern ammunition), so, like some others here, I was wondering if someone could post details of the size, shape, composition, hardness, etc. of the shells for the L71 and the L56. Are they identical shells, or was there a significant difference between them? If the shells were identical we should be able to plot a penetration vs. velocity curve (not range) for both guns, AND THEY SHOULD MEET AND OVERLAP. If the curves do not overlap, then there are obviously discrepancies between the two sets of data. Of course, if the shells are of different designs we cannot do this, since each shell will behave differently at the same speed. Does anyone here have the data to check this? [This message has been edited by Andrew Jaremkow (edited 08-26-2000).]