Therefore, always consult loading manuals. II. EXAMPLE
Suppose I have a worked-up load for the .30-06 using
estimated new powder-charge weight c2 new bullet weight m2 bullet weight m1
. c1
=56.0 grains. Then multiplying r by itself two times is 0.5x0.5=0.25 and a third time is 0.25x0.5=0.125. Taking the square root (sqrt) once is sqrt(0.125)=0.3536, twice is sqrt(0.3536)=0.5946, and three times is sqrt(0.5946)=0.7711. Therefore c2
In our example above, r= (m1 /m2 =56.0=0.7711=43.2 grains, approximately. From eq (a), c2 The IMR data source [I96] shows 42.5 grains at a pres-
= 56.0 0.5 x 0.5 x 0.5 = 43.2 grains The second term of eq (a) also gives c2
= c1r3/8 = c1 (m1/m2)3/8
sure of 49,000 CUP. This is an error of only 0.7 grain, although errors in other instances can be up to 2 to 3 grains. Of course, one should ALWAYS check with loading manuals and AL- WAYS start with a couple of grains less. The next section is for the technically inclined. Bottom
liners can skim it. III. THEORETICAL BASIS OF NEW FORMULAS
Eq (c) and its approximations eq (a, b) come from a simplifi ed interior ballistic equation for the maximum pres-
Figure 1B Estimates of Charges when a Lighter Bullet is Replaced by a
Heavier One Keeping the Pressure Constant c2/c1 and Fitting Functions for 20 .30-06 Examples for m1/m2 = r from IMR1996
0.5 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.5
File MB4LH3006sorta.qda MB4LH3006b.qpc 7/14/10
0.6 0.7 r = m1/m2 0.8 0.9 1
c2/c1 B (1+r)/2 M r^.4 P r^.375 iter
0.6 0.7 0.8 0.9 1 1.00
M r0.4 P r0.375
Barsness 0.95 0.90 0.85 0.80 0.75 0.70
0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60
1 1 1.2
c2/c1 B (1+r)/2 M r^.4 P r^.375 c2/c1 iter
1.4 = [56.0 x (0.5)3/8 ] = 43.2 grains
a 110-grain bullet and 56.0 grains of IMR 3031 powder and a tabulated pressure of 49,300 CUP (copper units of pressure). As an extreme example, I now want to use a 220-grain bullet (twice the weight.) To avoid dangerous pressures, I need to estimate a safe, lighter charge of IMR 3031 that would keep the pressure the same. The recommended method, eq(a), in words is: Get the for the proposed and
three times, taking the square-root three times, then multi- plying by c1
by multiplying the ratio r=(m1
from the original charge weight c1 /m2
) by itself ) =110/220=0.5 and
sure P that depends on the charge weight c, bullet weight m, volume (space) behind the bullet S, groove diameter d, and a constant for each powder based on its properties [GL05,Ch08,Cl28,Co51]. This equation doesn't depend on all powder burning inside the gun. I also found that ignoring a loading-density term works better. I will consider this general case in future articles. If we assume the same powder and pressure for both
c2
loads and that small changes in seating depth don't signifi - cantly change the volume S behind the bullet, then cancel- lation reduces the general formula to eq (c), whose the right hand side contains the known-load's data and m2 is the proposed new bullet weight. We can easily solve eq (c) for m2
. However, solving eq (c) for c2 in terms of m1, c1, and m2 in terms of m1 to get c2 (c): , c1, and
gives an ugly cubic that requires many signifi cant fi gures to avoid an imaginary-number solution. However, with eq (c) rewritten, Ref. [M10] shows how with 2 or 3 iterations. The Figures and Tables below
show the iteration results, but iteration involves much an- noying arithmetic. Fortunately, a simpler monomial approximation to eq
well approximates IMR data. Good values of a are the 0.4 (2/5) of eq (b) as proposed by Miller [M10], and 0.375 (3/8) of the recommended eq (a) as implied by Powley's [P79] difference approximation to eq (5). The empirical constant a actually depends on the charge
c2 = c1 (m1/m2)a = c1
Barsness v-m formula does have a theoretical basis at constant pressure [M10]. However, his (c2
relation for (c2 velocity ratio (v2
/v1
) that he used for (v2 ) replaces (c2
/c1 /c1
) in eq (d), the resulting ) formula (eq d) does not.
/v1 Figure 2A Estimates of Charges when a Heavier Bullet is Replaced by a
Lighter One Keeping the Pressure Constant c2/c1 and Fitting Functions for m1/m2=r for 196 Cases from IMR1996
1.6 1.8 2 Barsness 2.2 M r^0.4 P r^0.375
0.90 1.00 1.10 1.20 1.30 1.40 1.50 1.60
1.2
File MB4HL196sorta.qda MB4HL196sortb.qda 9/20/10
1.4 1.6 r=m1/m2
www.varminthunter.org Page 171 1.8 2 2.2
to mass (weight) ratio (c/m) [M10,Table 1], but averages about 0.4 for most high-power rifl e loads. Barsness' new method [B10], eq (d), uses the same m ) [M10]. When the
/c1 ra (e)
c2/c1 and Fitting Functions of r = m1/m2
c2/c1 and Fitting Functions of r = m1/m2
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