physics 101, -or- muzzle velocity and maximum range

[spacemanspiff]

so i'm taxing the ol noodle over the weekend, mulling over some article i read recently but cant find again. i seem to recall a table of bullet velocity of a 30 cal (cant quite remember if its 30.06, .308, or whatnot).
the table showed the muzzle velocity being about 2900 fps, and at 500 yards that velocity dropped to 1000 fps (may have been 800 yards though).

so my question is this: with the velocity dropping, whats the average time it would take for a projectile to reach a target at 500 yards? 800? 1000?
how about this? lets use a .243 for the caliber, that has a flatter trajectory iirc, should make answering this question easier. also, the setting in question is a windless day, 60 degrees, sea level elevation.
if you have data for other scenarios i'd be interested in that as well.

 

[BillL223]

Running your problem on Sierra Infinity Ballastic software, loading a 70 gr .243 @ 3100 muzzel velocity (I don't know if this is realistic for a .243), I get a time of flight of .69 sec for 500 yds, 1.41 sec for 800 , and 2.02 for 1000 yds.

 

[Sunray]

That'd be done with the Distance-Time-Velocity equations they made us learn in grade school Arithmetic. I can never remember what you did with what though.

 

[Bill Hook]

DTV isn't constant, so I doubt grade school arithmetic would answer the question.

 

[spacemanspiff]

even if it did, i was homeschooled. my mamma taught me evrything there is to know bout numbers and riting. didnt need to learn no readin though. thats for those fancy types who live on yonder.

 

[uglygun]

Download Balistic 4.13 on the following link, (the Bal4.13zip), it's pretty easy to use.

If you know the balistic properties of the bullet you can enter those, usually the "G1" drag function is used for modern bullets which is what most balistic software programs assume or ask for. Enter the BC, enter the muzzle velocity, and it can output properties out to 1k yards in various increments you call out.

Will ask for atmospheric conditions as well if you want to get that technical. http://www.snipercountry.com/ballistics/index.html

 

[FireInTheHole]

Its a function of Time, Initial Speed (muzzle velocity), Distance to Target, Barometric Pressure and Wind Resistance. (ballistic coefficient) There are a couple more variables that can be tossed in, but in most cases they difference would likely be negligible.

Each bullet has a different BC so for all but the most perfectly made match round there will be error in any calculation.

EDIT: This might be a differential equation. Any more math types out there care to provide some input? I'm not taking physics until spring.....

 

[P95Carry]

Despite my engineering training .. my ''pencil & paper'' math is diabolically rusty!!

This situation tho is essentially an exponential decay ... due to the factors of gravity and drag mainly ...... energy is lost. I would have to look up a few things on the calculus but this is a dv/dt ... analysis I think ...... tho whether this remains first order only I cannot be sure.

That's how damn rusty you get with age, and excessive use of ''do it for you'' software etc.

As has been mentioned already .. if the bullet BC, weight and MV is known and enviro conditions, then there seem to be several software progs out there that make it all real easy.

 

[uglygun]

Yes, for the most part it's something that needs calc. level math if a person wants to be as precise as possible.


The balistic coeffecient is a variable that changes depending on other variables, a 168grn Sierra Match King at 2700fps will have a different coeffecient for air restistance/friction than if that same bullet is moving at 2800fps. For the most part, balistic coeffecients are an average value calculated for the bullet's flight over a given distance with known velocities. For this reason, Sierra often gives 3 different BC values for their bullets, usually broken up into 2 different super sonic flight ranges and a subsonic flight range as well and they are used based upon the muzzle velocity a certain chambering can be expected to deliver.


Variables that change the BC of a bullet even with a constant velocity are barometric pressures which varry depending on altitude, humidity, and temperature.


It can get pretty complicated but there are some equations out there that simplify it just a tad, still pretty complex even then. To work out the balistics of a bullet/cartridge without the equations, that would take somebody who's got quite a head on their shoulders to weigh in all the variables. Up through Calc II math and I still don't feel I have enough math to be fully comfortable working with the stuff simply because it is not single variable calc but rather multivariable. It is just easier to use a balistic software program while understanding some of the more simple variables.

 

[Bill Hook]

I took and promptly forgot Calculus. I only know enough to say that it would require some to solve for variation.

 

[JohnBT]

I had a year of The Calculus in high school and two more in college.

The dog ate my homework.

John

 

[E=MC^2]

I always use this online service to do my ballistic calculating. It also has TOF(time of flight) data.

Ballistic Calculator

 

[P95Carry]

E=MC^2 - got an error 404 from your link .. can you check it out ... be interested to go look.

The URL you gave goes to no filename just a folder called ''calc'' so unless there was an ''index.htm'' .. there won't be any page come up without a filename.

 

[twoblink]

You can take a derivative to calculate the smooth reduction in speed due to drag, if you know the drag go efficient.

you can then plot (as gravity is constant) the parabolic curve.

Take the distance, and plug it back, and you get instantanous time..

Or use a spreadsheet

 

[ShaiVong]

I'm taking applied Calculus ATM, and I feel confidant I could solve the equation... If I knew what it was

 

[CaesarI]

No Calc needed. Time to flight *and* drop are products of *average* velocity, which can be calculated pretty easily if you know the range you wanna calculate.

"Thou needest not yonder Calculus if Ye know how to take the average."

-Morgan

 

[E=MC^2]

E=MC^2 - got an error 404 from your link .. can you check it out ... be interested to go look.

Here's the address I'm using. Hope you can get it to work.


http://www.handloads.com/calc/

 

[P95Carry]

Thx buddy .. well, same URL by look of it so ... maybe there was just a brief server downtime previously .. it's come up fine now.

Many thx!