A dram is a unit of weight just
slightly larger than 27 grains. (1 dram = 1/16 of an ounce or 27-11/32 grains or 1/256 of a pound) It was the stan- dard measurement for black powder. Today, powder is managed differently, and there is no known method to safely weigh or measure smokeless powder and be sure to have a dram equivalent. It would be necessary to know the char- acteristics of the powder and how many grains would give the same pressure as the dram of black powder. (1 grain = 1/7000 of a pound). All units used in a problem must
be consistent. This is a frequent cause of wrong answers, and we all make this mistake on occasion. If we are lucky, it will be by such a huge amount that an error is obvious. If the formula calls for grains, pounds will not work. If yards are needed, feet will not give the correct answer. A fast way to convert feet per sec-
ond (f.p.s.) to miles per hour (mph) is to divide the f.p.s. by 3 and multiply the answer by 2. The result will be within 3%. Need the answer dead on? Multiply the f.p.s. by 0.6818 to obtain mph or by 0.0114 for miles per minute (m.p.m.). Example: 900 f.p.s. divided by 3 = 300 times 2 = 600 mph. Example: 900 f.p.s. times 0.6818 = 613.6 mph. Example: 900 f.p.s. times .0114 = 10.26 m.p.m. For readers who prefer a chart:
f.p.s. mph f.p.s. mph 800 545 900 614 1,000 682 1,100 750 1,200 818 1,300 886 1,400 955 1,500 1023 1,600 1091 1,700 1159 1,800 1227 1,900 1295
2000 1364 2100 1432 2200 1500 2400 1636 2600 1773 2800 1909 3000 2045 3200 2182 3400 2318 3600 2454 3800 2591 4000 2727
The use of computers has changed the symbols used in formulas. An aster-
isk ( * ) is used instead of an ( x ) to indi- cate multiplication. Today a slash mark ( / ) indicates division. The number to the left is the numerator (top number) and to the right is the denominator (bottom number). At first, this may look strange. Just remember that when you
see an *, it means to multiply the same as if the symbol had been x. This method is used in many books, partly to avoid
confusion between the multiplication sign and an x used for an unknown. While we are discussing fractions,
an inverse proportion or to vary inverse- ly are just fancy words that mean as one quantity increases, the other decreases. As one goes up, the other goes down or the other way around. In some formulas we see the Greek
sigma (σ). If you are not familiar with it, don’t be concerned. Swiss mathemati- cian Leonard Euler established sigma as the symbol for the sum of a finite number. Sum is the key word as it is used to indicate the process of adding. When working on problems involving average or central tendency, it is used for cumulation (successive additions). Frequently the numbers involved
are long with a lot of zeros. Many cal- culators cannot accept over 8 digits and that is not enough for some of these problems. (Or the national debt, but this is not the place to discuss politics.) There is a method to handle extra
long numbers called scientific notation. The huge number is expressed as a man- tissa or base number times 10 and raised to an exponent or power. Confused? It means to take the base number times 10 and raise to a power by multiplying it by itself the amount of times the power indicates. The decimal point is placed the number of spaces as the exponent. + or - can be used for positive or negative numbers. Positive shifts the decimal to the right and negative to the left. Example: (Mantissa * 10 power.)
3.8895 * 108 = 388,950,000. The decimal is moved 8 places
to the right (positive) adding zeros as required.
000 000 000 37982 The decimal is moved 16 places
to the left (negative) adding zeros as required. Most modern scientific calculators
have keys for scientific notation. Check your manual or instruction book. The following are two formulas using scientific notation. Energy = 1 / 2 mv2 / 4.51 (105
= (bullet weight) v2 v / 2.25 (105 )
momentum = mV = (bullet weight) )
Don’t let that scare you. First, it is
not as hard as it looks and second, both of those formulas have much easier ver- sions. And to repeat what has already
www.varminthunter.org Page 85 Example: 3.7982 * 10-16 = .000 000
been said, even if you cannot add 2 plus 2 and get 4, most ballistic science can be understood without the math, but it must be included in most articles and books for the readers who want it. Sort of like pickles on a sandwich. Most places give them to you, but if you don’t want them, you may skip them. Formulas may be expressed in dif-
ferent ways. If the proper numbers are put into the formula and it is worked correctly, then the answer will be what is requested. But there may be different ways of expressing the same thing. For- mulas can use different information or equations can be combined. Therefore, we could arrive at the same place by a different road. For example, we can say the sine of angle x is y. We can also say y = sine x. Both look and sound different but they say the same thing. Many young students and adults
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