IV. Results Figures show (c2
the “goodness-of-fit” better than the clutter of overlapping residuals. Tables contain the residual and percent residual statistics because these better distinguish the numerical fits. I split the Tables and Figures between the results for
I compare these various formulas in Figures and Tables. /c1
) vs r = (m1 /m2
these various formulas. Experimental test data came from the 1996 IMR Hand-
/c2
can differ by as much as a factor of 2 (0.5 or 2.0), these data are a severe test of the formulas. These data are very scattered (see Figures), because (a)
and m2 . Since m1
book [I96], which has c, m, P, and v for almost every IMR powder for each cartridge. There are 196 data pairs for a same gun and same pressure but different m1 m2
replacing a heavier bullet with a lighter one (HL), and vice versa (LH). LH fits appear better in both Tables and Figures because m2 the size of (c1 ratio (c1
), so shows more clearly the differences between
in the denominator of r is larger, which reduces /c2
) . For HL fits, the smaller m2 exaggerates the ), because this represents
Residual standard errors are about 1.3-1.4 grains, and
percent standard errors are 3-3.5 %. This means roughly that 2/3 of the estimated charges are within those ranges and that 95% are within twice those standard errors (about 2.6-2.8 grains and 6-7 %). These estimates are quite encouraging, but as always, check with loading manuals. A random sampling of a few non-IMR powders at con-
stant psi pressure gives results much like the IMR results, i.e., residuals of 0.5-3 grains. V. lImIts and QualIfICatIons /m2
A. Practical Limits to r=(m1 ) The full range of r (0.5-2.0) can lead to compressed and
these are old, were measured in different ways over several decades, and have typos; and (b) I had to make assumptions about seating depth and the volume S behind the bullet. The iterations are also scattered because of errors in the tabulated c1
the maximum range of r=(m1 /c1
a = 0.4 and 0.375) and the Barsness line lie within these data. The HL Figures 1A (.30-06) and 2A (all data) clearly and Miller r.0.4
show more clearly the scatter of experimental (c2 how well the scattered (c2 experimental (c2
/m2 /c1 show the Powley - r.0.375
Figures 1B and 2B show the same general features, but far less dramatically. Again, the r0.375
/m2
the scattered experimental data and the less-scattered iter- ated values, whereas the Barsness line becomes increasingly poor as r=(m1
the scattered experimental data and to the less-scattered iter- ated values, whereas the Barsness line is poorer as r=(m1
us to draw conclusions. A. Figures Figures 1A (HL) and 1B (LH) for just the .30-06 have ) (0.5-2.0). The fewer points ) data,
and c2 ) iterated values lie among the /c1 ) , and how well the monomial lines (with lines are closest to
) increases to 2.0. In comparison, the LH and r0.4
2A and 2B are for all 196 data pairs. Both sets of tables also compare the Barsness formula (B), the two monomial values 0.4 (M) and 0.375 (P), and the iteration (iter). These include statistics for residuals and percent residuals of (c2 residuals as (c2calc c2exptal
(m1 /m2 )/c1exptal . -c2exptal ), and percent residuals as 100 (c2calc /c1 More specifically, these statistics include (a) the mean,
which should be close to 0 if positive and negative errors balance; (b) the standard deviation, a measure of goodness- of-fit; (c) the maximum and minimum errors, which show the worst outliers; and (d) the range, which shows the combined worst outliers.
Page 172 October — December 2011
decreases to 0.5. However, for the reasons noted above, all LH results are closer together. The closer r is to 1.0 (smaller weight differences), the closer together are all predictions. B. Tables Tables 1A and 1B (.30-06) have the widest range of ) (from 0.5 to 2.0). The more complete results in Table
lines are closest to /m2
)
). I define -
. Nonetheless, comparison of these formulas allows
charges for HL or low loading densities (partially empty cases) for LH. By Smalley suggests that in these two situations it would be better to change powders to keep cartridge cases closer to full when r is outside the range 0.83-1.2. This avoids uncertainty in pressure for HL and changes in pressure and velocity with powder position for LH. However, recommen- dations from powder companies other than IMR imply that r limits within 0.67-1.5 for the same powder should be all right. With either set of r limits, the figures shows that eq (e)
with a = 0.375 (eq (a)) or 0.4 (eq (b)) are still noticeably better than Barsness’ formula.
B. What About Bullet Switching? Every gun and load is different regarding rifling en-
gagement, bore friction, core and jacket hardness, internal construction, boat tails vs. flat base, and copper-alloy vs. lead-alloy. These also affect muzzle velocity and pressure. The complete data and computations required to analyze these effects are not available to shooters. Consequently simple lumped-parameter theories (including QuickLOAD) can only approximate this complexity. These uncertainties show themselves in studies of component switching. For example, M. D. Waite [W55] studied a .30-06 with 10
bullets of the same weight but different construction. Every- thing else was the same: seating depth, powder and powder charge, cartridge cases, and primers. The results, further extensively analyzed by W. C. Davis [D86], showed a wide variation of pressures (44,510 to 51900 CUP) and velocities (2956 to 3037 ft/sec). Thus component switching, even with the same-weight bullet, can give excessive pressures. Mic McPherson has given similar results for 11 different 150-grain .270 bullets in otherwise identical loads with a pressure spread of 17,700 psi [McP96], as well as recent QuickLOAD estimates where a lighter bullet can give a greater pressure than a heavier one [McP10]. In practice, we don't measure pressures, but only as-
sume it is constant in our formulas. Therefore, a marked change in bullet type when changing the weight can give the same kind of pressure variations seen by Waite and McPherson. McPherson suggests that pressure differences will be modest and our rules will work much better if the light and heavy bullets have similar internal constructions, jacket materials, jacket thickness, and external shape. C. Effects of These Qualifications
Our simple formulas remain useful because we do get
into the right ballpark. Estimates may be off by 1 to 3 grains, but can still tell us whether the new charge won't come close to filling the case (LH) or may crush granules by excessively compressing the charge (HL). Again, with all semi-empirical
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