Approximate "Range" Calculations

J

johnwilliamson062

Moderator
This is a little bit of a lazy post, but I was hoping someone with a little more knowledge/expertise would be interested and some other people might enjoy the discussion. I looked a bit online and found the more complicated physics equations, but none that fit my need.

There are four common "range" terms I am aware of:

*Edit:I removed the first three to discuss another day. The max dangerous range is enough to tackle in one thread.

Dangerous Range:
The range at which a projectile fired at the optimum angle will travel.

The dangerous range is what I am currently most concerned about.

I was wondering if there are some basic approximate equations for these ranges. Equations someone who graduated high school with decent math grades could plug a few numbers into and then calculate with a basic five function calculator.

Without going into it I think the only input necessary should be FPS at barrel. I would prefer not to complicate it with variable inputs like air resistance coefficients specific to each bullet. End users will not be able to calculated this number anyways. I estimate the difference will not be significant for most shooters purpose with the exception of something like a slug, so maybe a separate slug equation. I think it might be best to use a generic value for a common bullet when formulating the equation and then just go with it.

I don't have time to deal with right now, but will likely revisit it later tonight or maybe tomorrow(at least the dangerous range equation). Any work, hints, comments, positive criticisms, hints, etc. would be greatly appreciated. There was a time when I could probably pound out the equation I wanted in a few minutes, but I will have to review quite a bit to get there now. Don't want to get started in the wrong direction.
 
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Never heard the words point blank range used in a quantitative sense.

Maximum effective range (point target) was used to denote the distance at which you could reasonably expect to hit a point target (usually a person) and do him damage. I don't think you calculate this. I think it's done by experiment.

Maximum effective range (area target) is the same as above, but you are firing at a grouping of point targets - usually a squad or so - and can reasonably expect to scare (suppress) the heck out of them. Again, I don't think you calculate the distance.

Dangerous range. Never heard of it. I understand what you mean, what is the maximum distance the bullet will travel if fired at the optimal elevation. I am more familiar with the conscept of Surface Danger Zone which is the distance and angle into which you might expect bullets shot on a range to go (and you want people to stay out of) by any likely means. I don't know if there are formulas, but there are charts that show this for various caliber cartridges that are used in locating and designing ranges.
 
Quick Google search led me to this. Not sure if it's exactly what you're looking for, but just uses some 11th grade algebra to determine a bunch of different things (including maximum distance) as long as you know the angle you fired, and the initial velocity. Unfortunately, it doesn't factor in wind resistance, but using these, you will at least know that your dangerous range is within the distance you calculate, and no further.

http://www.ehow.com/how_5185428_calculate-bullet-trajectory.html
 
There is a lot more to the problem then can be answered here with reason.

I'll try to take them one at a time:

Max Point Blank Range would be the distance one can shoot a given round so as at any time in the bullet path, its no higher or lower then a given target.

Lets say we are hunting deer. The vital area of the average deer is 10-11. So what one wants to do is sight his rifle in at a range that the path of the bullet will be no higher then 5.5 inches high nor 5.5 inches low.

That changes with the target. An elk for example has a vital are of 15 inches so you can sight the rifle so as not to be any higher then 7,5 or any lower then 7.5 inches.

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Dangerous range is a bit simpler. The army has determined that it takes 60 ft lbs of energy to produce a disabling wound.

Simply figure the range a given bullet weight at a certain velocity can still produce 60 ft lbs of energy.

This is not to say that is a reasonable range one can hunt. The army has different criteria then hunters.

One should determine the optimum game weight.

In his book, "Big Game Rifles and Cartridges" Edward Motunas came up with a formula to identify lethality. You can find Montunas theory explained by Bryan Litz (Ballistician for Berger Bullets) in his book 'Applied Ballistics for Long Range Shooting. I'm not going to explain it here.

I found it to be reasonable to give one a better chance of taking game with less chance of wounding and loosing a critter do to being under gunned.

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As to dangerous range - area. This is something I'm more familiar with. Its something I taught in Machine Gun schools. Lets assume you have a maneuver element that is trying to close with the enemy. You have a cover unit used to protect that moving unit as it moves to contact the enemy.

You don't really care about pin point accuracy, you are trying to pin down a group of enemy soldiers so as the friendlies can get close.

It takes a bit of math but its really simple, What you want is to fire over the friendlies yet have the rounds fall on the enemy position. You need to figure the safe zone where the arc of the bullet reaches a point over the head of the friendlies and a point where the arc comes down on the enemy.

That would be a safe zone, two points where you can start shooting and the second where you have to stop. This can be done with machine guns or rifles.

Again I wont give the formula's here unless someone really wants it, it would just muddy the waters.

The max. effective range would be a bit different. You have to take into account the accuracy of the round/rifle, the ability of the shooter to judge range, and the ability of the shooter to judge wind. Throwing the three in the pot, you come up with an average range one can hit a target with a reasonable percentage of success. There is no flat answer to this without knowing the rifle/ammo, and shooters ability to judge range and wind.

For example the range part percentage could be increased with a laser range finder on a reflective target. Wind percentage can be increased with a good wind meter. The rifle/ammo percentage can be increased with the experience of the shooter, the careful putting together the rifle/sights, and the careful construction of ammo.

As you can see there are a lot of variables.

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I was always taught that about 5 miles was possible with the right angle of elevation with most modern centerfires About 2 miles for rimfires. Figuring the exact range would be almost impossible to calculate because of varying conditions that could be hard to figure. At 5 miles altitude, temperature, wind speed and direction, humidity, etc could make a huge.
 
The formula I was thinking of most was the max dangerous range. THe reason I became interested is i have once again run across someone who absolutely fails to understand shooting at a piece of paper 5 feet high in a flat field is unsafe even if there is no house within 1000 yards.

If we use 60 ft lbs that makes it a bit complicated. For something like a 300 grain bullet I am guessing it is still dangerous where it comes down, but a 42 grain 22-250 likely is not. FOr my purpose I don't think this is neccessary. We can assume wherever it comes down bad things may happen.

I have heard something along the line of the 5 mile rule, but I would rather give something a little closely related to the situation. For one thing, I doubt 9mm can go 5 miles.

I will remove the other items as they are obviously more complicated and variable than the max dangerous range.
 
Most Ballistic programs only go to 5000 yards.

Taking a 9mm, 125 gr bullet at 1100 fps it drops to 60 ft lbs of energy between 1400-1500 yards or .8 of a mile.

In figuring the safety of ranges Army Ordnance lst 5500 yards (3.12 miles) as the extreme range of a 30 cal bullet with a BC of .56 @ 2600 FPS MV.

If I modified my BC program right that would be about 60 ft lbs.

Normal small arms ammo reach their max range with the barrel is elevated between 29 and 35 degrees. Anything more would cause the bullet to fall short, as in mortors.

Of course we arn't going to hit anything at that range, but it does show the down range danger of a given bullet. Hense, the "Be sure of your back ground" firearm safety rule.

Except for range safety, this is kind of useless information since I doubt we get into WWI type warfare where we are lobbing rounds at trenchs several thousand yards away. Even then I think the max was limited to about 2500 yards.
 
The Army surface danger zone extends for a certain distance from the firing position as well as out to the sides. There is an additional area out beyond this distance, but the distance itself is:

.22 LR 1400m
9 mm 1800 m
.45 ACP 1690 m
5.56 ball (55 g) 3100 m
5.56 ball (62 g) 3437 m
7,62 ball 4100 m
.50 ball 6500 m

You can find all of this stuff and exactly what it means in DA PAM 385-63 which you can pull of the net at http://www.campbell.army.mil/campbell/Safety/Documents/DA PAM 385-63.pdf.

These numbers come from Table B-1 which is around p175.
 
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