Math question re bullet drop

[M-61]

Need some help with this question. I would like to know a bullets drop at a specific range.
e.g. 7.62 NATO cartridge. What drop is there from 450 yards to 451 yards. In that ONE yard measuring from 450yds and ending at 451yds is there a way to figure that drop? I know it is going to drop but I am lost in trying to figure this out.

 

[MrMajestic]

Muzzle velocity and bullet ballistic coefficient?

 

[hogpatrol]

Need some help with this question. I would like to know a bullets drop at a specific range.
e.g. 7.62 NATO cartridge. What drop is there from 450 yards to 451 yards. In that ONE yard measuring from 450yds and ending at 451yds is there a way to figure that drop? I know it is going to drop but I am lost in trying to figure this out.

Applied Ballistics can output the trajectory chart in increments of 1 yard or 1 meter. Don't know about other programs or apps.

 

[M-61]

Muzzle velocity and bullet ballistic coefficient?

Well....it is not fixed...I am not working towards a particular cartridge and gave the 7.62 as an example. But say then a 7.62 military ball round.
Can you work with that to give me a number? The question is the result of a discussion and I can't do it.

 

[M-61]

Applied Ballistics can output the trajectory chart in increments of 1 yard or 1 meter. Don't know about other programs or apps.

Thanks....so this is not something one can sit down with a pencil and paper and figure out?

 

[hogpatrol]

Thanks....so this is not something one can sit down with a pencil and paper and figure out?

It's all math and there is a formula but why? What about a headwind, crosswind, station pressure, elevation, etc.? To me, sitting down with a calculator and/or a pencil and trying to figure out ANY drop is an exercise in futility.

 

[mr45man]

Thanks....so this is not something one can sit down with a pencil and paper and figure out?

Stephen Hawking could, the rest of us not so much.
I am sure there is a formula to do what you are after though.

 

[Toby Bradshaw]

Well....it is not fixed...I am not working towards a particular cartridge and gave the 7.62 as an example. But say then a 7.62 military ball round.
Can you work with that to give me a number? The question is the result of a discussion and I can't do it.

Google "Pejsa ballistics," download the spreadsheet, and put the desired range in the "special range" cell. For example, if you put 451 yards in the "special range" cell, you'll see that the drop from 450 to 451 is in the neighborhood of a quarter inch, depending on the usual parameters (muzzle velocity, BC, barometer, temperature, etc.)

 

[expiper]

http://www.jbmballistics.com/cgi-bin/jbmtraj-5.1.cgi

 

[watercam]

+1 for JBM - use Simplified Trajectory and fill in the blanks. It has to do with bullet caliber, weight, Ballistic coefficient, velocity, atmospheric conditions. If you know basic physics you know that drop is 32ft./sec./sec.. You need time of flight but to get down to 1 yd. increment at that range is more decimal points!

 

[Alexander-M]

For that short of a distance, the BC would be insignificant. Simply use the formula to determine an object in free fall, as follows:
Distance an object falls in a time period = (1/2) x g x Time-squared, where g= acceleration due to gravity, or 32.2 f/s/s

In this case, lets say that the speed of the bullet at 450 yards is 1500 fps, or 500 yards per second. This means that it will take (1/500 =) 0.002 seconds to travel one yard. That is the time we will use in the formula.

(1/2) x 32.2 x (0.002)(0.002) = 0.5 x 32.2 x .000004 = 0.000064 feet drop in one yard
Note that the units work out: 32.2 f/s/s with .002s x .002s cancels the seconds, leaving just feet for the answer.

Alex

PS. Open to and welcome any corrections.

 

[T.Rhodes]

Assuming the bullet is traveling horizontal and perfectly flat, then gravity will be pulling it down at a constant rate of 32ft/sec2(squared). You need to know the amount of time it takes for the bullet to cross the one yard distance from 450 to 451. That's where you would need to know M-velocity and ballistic calculator to determine the speed remaining at the 450 yard mark.

Afraid that's not much help answering your question, but there needs to be a little more info to start developing an answer, IMO.

P.S. I think Alex and posted at about the same time...I like his response better.

 

[Ggmac]

What if you knew the velocity , bullet weight , BC at the range you desire , use an appropriate load ( reduced ) to duplicate the velocity at 100 and set up a chrono , or better yet duplicate the velocity at 450 and shoot it at 10 and 11 yds with 2 chronos . That would be easier for me since my math skills aren't what they use to be !

 

[DRNewcomb]

Everyone's over-thinking the problem. Just take the drop between 450 yards and 500 and divide by 50. Close enough for engineers.

 

[M-61]

Thanks to all for the replies.
Where this originated from was a 'show' on TV (AHC?) It was a show dissecting "Saving Private Ryan". Many aspects of it relating Hollywood vs reality.
The sniper shot in the village was looked at. Now I may have some of this wrong...it was on late. In the French village the American sniper shoots a German sniper going though the Germans snipers scope (ala Carlos Hathcock). The show says the distance was said to be 450yds in the movie.
They (the dissectors) try to duplicate the shot. They are unsuccessful and the reason is given the drop of the bullet would not allow it to exit the ocular end due to bullet drop. They point out that bullet entering the top of the objective lens was on such a severe angle it could only exit the bottom of the scope in front of the eyepiece. It just seemed like a hell of a drop to me. Granted it's WWII, the Germans scope tube probably was 1" in diameter, and I guess the objective lens was maybe 40mm tops. The scope body maybe one foot long. The American would have been shooting a 30-06. I missed what the show was shooting to try, unsuccessfully, to reproduce the shot. It surely was a modern high end version of a rifle a sniper would use.
They did NOT mention what the objective lens did to the bullets trajectory as the bullet smashed though it. Carlos did make a similar shot but not at that range. (still impressive to say the least).
Maybe someone else saw the show and will correct what I screwed up, like I said it was on late and the beer was finished.

 

[T.Rhodes]

DRNewcome, I like the simplicity of your idea...BUT the drop is not a linear function (probably dang close though at the distance in this question). And if picking all the nits in this, would go with Alex's input to solve this.

 

[T.Rhodes]

M-61 - I believe that Myth Busters did a recreation of that shot. I thought they proved it could be done...maybe I'm wrong on that.

Talking about angle of drop, in the video by Todd Hodnett, Art of the Precision Rifle, he sets up shot at 853 meters (little over 1/2 mile) and compares line of sight to trajectory. Turns out there is about 1-2 degree difference.

 

[Ggmac]

Myth busters did it ! And it wasn't possible . Though they tried again using the more appropriate # of lenses in the MOSIN PU scope and it did penetrate but not lethal . The first scopes were basic 4x modern scopes which have many more lenses , they also were not using armor piercing ammo .

 

[M-61]

I have ONE problem with Mythbusters. They did a segment on how hitting two hammer faces together is perfectly safe. After that, they sort of lost their credibility with me. ( I don't think they care)

This show I saw was not mythbusters, I think it was what I get which is called AHC. American Heroes Channel, however maybe the Smithsonian Channel. Can't find it on a search. Just wanted to make sure I got that yardage correct.

I guess one could take a piece of 1½ inch x one foot PVC put a piece of tape on the front, set it 450 yards away and have at it with anything. I have a better chance at that opposed to trying the math!

 

[rminut]

Everyone's over-thinking the problem. Just take the drop between 450 yards and 500 and divide by 50. Close enough for engineers.

not quite, not even for undergraduate engineering degrees, and you should be grateful for that the next time you fly in a plane or drive over a tall bridge. but that type of averaging is close enough to get you a phd in astro physics.