Odd math project


Apr 23, 2008
Chattanooga, TN
I have a math project in my pre-calculus class. I have to turn in a portfolio and one section is a one page max paper on mathmatics applications. The more unique the better the grade. I was wondering if anyone would be willing to help me understand how mathmatics and long range shooters go together. We are working on trig and I understand that is part of long range shots. ANY HELP IS WELCOME! Thanks, Travis
There have been whole volumes written on the subject of long-range shooting. It is part science, part art.

Accuracy is a matter of consistency. The long-range shooter accounts for and attempts to minimize or control as many of the variables as he can.

It's not just external ballistics. The ballistic arc the bullet follows is only half the story. There's internal ballistics and, in the case of snipers, terminal ballistics.

One must account for the caliber, weight, length, ballistic co-efficiency, muzzle velocity and energy of the projectile. The volume and dimensions of the case. The weight, volume, type and burn rate of the propellant. The type of primer. The shape of the chamber and chamber mouth. The length, weight and profile of the barrel. The type and twist of the rifling. Freebore? The type of crown. Bedding. Pressure or free-floating?

I will not address the optics here because that is an entire block of mathematics all it's own.

All of this before a single round has left the barrel.

The range, elevation, aspect of the target relative to the shooter must be considered. At longer ranges, the descending arc (arc of fall) of the projectile become important.

Elevation/barometric pressure, humidity and temperature all affect the density of the air and subsequently the rate at which the projectile loses energy due to friction. A given rifle, zeroed dead-on with a given load at sea level in North Carolina, at 72F, and 20% humidity may not even be on the paper the next day in Colorado, at 10F and 0% humidity.

Snipers must consider whether the projectile will have sufficient energy remaining to effect the target. The transonic range of the bullet becomes important because the projectile loses a great deal of energy due to transonic yaw as it decelerates back down below the speed of sound (which is also variable, not constant, by the way).

Elevation differences between the shooter and target will effect the ballistic arc of the projectile causing the shooter to hit high or low.

But so far we've only considered the math. But shooting does not take place in a perfect world. The difference between a simply, technically competent shooter and a great shooter is how well he deals with wind.

Wind speed? Full-value? Half-value? Zero value? Steady? Gusting?

The shooter must account for these and offset his point of aim sufficiently to the left or right so that the wind pushes the projectile onto the target, rather than off. Given sufficient range and wind speed, the shooter may find himself aiming off into empty air to the right or left of his target, trusting that his reading of the wind will allow him to hit the mark.

Oh, by the way, did I mention coriolis effect?

Did I mention the vertical component of wind?

Does your head hurt yet?

All of this is just off the top of my head but the purpose is to illustrate to you that the math involved in long-range shooting is more than just calculating a simple ballistic arc from point A to point B. That's the Disney version.

Good luck.
WOW! Thankyou for the input on that one!lol I understood that there was more than one varable in long range shots but that blew my mind. I have balistic chart here at the house and I do some reloading. Maybe I just need to stick to that aspect, although I was really wanting to use the arc of a bullet for most of my paper.