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Math Formulas in Shooting Guns; Sniper Mil Dot Range Estimation Formula, Momentum & More

In this blog, Shooting Range Industries will address the basics of math encountered in shooting sports. Most shooters in the US are more familiar with the Imperial system of measurement we inherited from the British, for better or worse. We use inches, feet and yards for length and pounds for weight. However, it seems that the military is using more metric units all the time. The klick is a kilometer and snipers are using more metrics in hitting the target. There are a few things to keep in mind:

Symbols in Shooting Formulas

Not everything in Microsoft Word translates to HTML or the other page markup languages used on the internet, leaving us two choices. We can use traditional computer symbols or turn the equations into illustrations and import them into our blogs. It is just easier to use the older more traditional symbols like * for multiplication, / for division and fractions which are divisions in disguise. The up carrot ^ is used for powers. Like a squared is a^2, raised to the 4th power it is a^4. This is all a hold over from the days of DOS and CPM operating systems. Square root of a number is a^1/2, cube root would be a^1/3. So, using the above kinetic energy is: KE = 1/2 mass * velocity^2. Expansion ratio is the cartridge volume compared to cartridge + the bore volume or ER = Cv:Cv+Bv.

Sniper Mil Dot Range Estimation Formula

The mil is used in mil dot scopes to estimate the range. The mil has the unique ratio of 1:1000. In other words one mil equals 1 yard at a 1000 yard, or 1 meter at 1000 meters or 1 foot at a 1000 feet. If you know the size of a target, like an adult male is about 24 inches across the chest you can us the mil dots to estimate the range. Range = size of target/mils. If a human torso is about 600mm wide or 24 inches wide and measures 2 mils wide the range is 600/2 = 300 meters. Why metric, mm is a unit 1/1000th of a meter or the magic ratio of 1:1000. You can estimate range computation in your head if you must. But in imperial units it is 24000inchs/2 = 12,000 inches/36 is about 333.33 yards. Much easier in metric, but only a handful of us use mil dot scopes. Or you can use the conversion of range = (target inches/mils)*27.78 for yard or 25.4 for meters.

Momentum & Kinetic Energy Relation Formula

When calculating kinetic energy or momentum there some conversions you need. First you need to convert grains weight to mass. This is done by: m = grain/7000*32.17. There is 7000 grain per pound, so you’re converting the weight to pounds. But weight is a force and you need mass. The acceleration due to gravity is about 32.17 feet per second per second or ft/sec^2. Now you have mass. Weight is mass in a gravitational field. Earth’s gravitation field is about uniform at any place you would be doing any shooting. So g=32.17 ft/sec^2. You can multiply it by the velocity to get momentum or times the velocity squared if you’re going for energy. Since KE = 1/2 * m*v^2 you can just take grains * velocity^2 then divide by 450,400 for KE = g*v^2/450,400 and you have energy in foot-pounds. For momentum it is p = m*v = grains*velocity/225,200 and you have the momentum in pounds-feet. Of course, grains is the bullet weight.

There will be more later, but this blog is to let you know why we need to present math formulas the way we do. Apparently subscripts and superscript don’t port well from Word to the internet markup languages. Not much new but we now have a foundation hopefully of understanding.