ballistics physics question

Discussion in 'General Gun Discussions' started by Eleanor416Rigby, May 6, 2017.

Thread Status:
Not open for further replies.
  1. BigFatKen

    BigFatKen Member

    Joined:
    Dec 5, 2005
    Messages:
    1,008
    Location:
    Walnut Hill, about 35 miles west of Auburn, AL
    I saw an Army video taken by a soldier of a buddy exiting their large sleeping bunker. A ping is heard as a rifle bullet hits his helmet and is further deflected. With the various sounds in the enclosed bunker, the rifle report is unheard. Might have been a 9x39.[​IMG]
     
  2. pintler

    pintler Member

    Joined:
    Jan 26, 2008
    Messages:
    519
    FWIW, here's an interesting video on the problems of estimating range using the crack-thump delay. For example, 5.56 and 7.62x39 timings are pretty different.

     
  3. Eleanor416Rigby

    Eleanor416Rigby Member

    Joined:
    Dec 19, 2012
    Messages:
    91
    Location:
    Central Texas
    Maybe you can't do it by hand, and I currently can't, but the people who program the ballistics calculators can.
    That's what makes it an interesting question and what requires calculus. Constant forces are relatively easy to figure, but constantly changing ones are tougher.
     
    .308 Norma likes this.
  4. Eleanor416Rigby

    Eleanor416Rigby Member

    Joined:
    Dec 19, 2012
    Messages:
    91
    Location:
    Central Texas
    Thanks to all for replying. In summary, yes, we can use ballistics calculators and get pretty close after a series of trial and error estimations. That's practical if inefficient. To find out how to figure that constantly-decreasing drag coefficient, I should go to my local physics professor. Clearly BC is critical. It's not a particularly practical question, and it's even less practical for high BC bullets that start out much above the speed of sound because the range involved is beyond usual shooting distances. For rifles in older calibers, pistols, and PC carbines it's within shooting distance. Thanks again to everybody who contributed to the discussion.
     
    .308 Norma likes this.
  5. Jim Watson

    Jim Watson Member

    Joined:
    Dec 24, 2002
    Messages:
    31,704
    Location:
    Florence, Alabama
    I would go for a graphical solution to avoid the trial and error.
    Plot the time of flight vs distance for the bullet and the sound wave vs distance on the same scale and see where the lines intersect.

    If you can get Phil Sharpe's 'Complete Guide to Handloading', it has a method for determining bullet velocity by ear. Weren't any consumer chronographs in 1951.
     
  6. Berger.Fan222

    Berger.Fan222 Member

    Joined:
    Oct 10, 2014
    Messages:
    548
    Location:
    TX
    I've written ballistic calculators and other code that numerically integrates differential equations. The reason it is done by computer rather than by hand is the large number of calculations involved. Most low drag rifle bullets will be in flight for several seconds for the sound to catch up. Typical time steps are less than a millisecond in these numerical integrations. The formula for each time step is fairly complicated and involves 10-50 individual calculations, depending on how it is organized. Do the math on the total number of calculations and you see pretty quickly why one uses a computer to do them rather than doing over 10,000 calculations by hand to obtain a single result.
     
  7. svtruth

    svtruth Member

    Joined:
    Mar 10, 2005
    Messages:
    1,701
    Location:
    Bradford, VT
    At its best, my calculus was not equal to the task, today I'm better able to do ten pull-ups than solve it, but the principle is pretty easy.
    The distance sound travels will be velocity times time. Since the velocity is constant, a graph of it would look like a rectangle with velocity up the y-axis and time across the x-axis, a nice little rectangle. In calculus terms, the integral.
    Now the bullet's distance will be the area under a curve with velocity up the y-axis and time along the x-axis. The shape of this area will be rather like the flight of the bullet itself, starting out horizontal and inflecting down at an ever steepening angle.
    The answer to your question is when these two areas are equal.
     
  8. stoky

    stoky Member

    Joined:
    Sep 19, 2005
    Messages:
    1,733
    Location:
    Wyomin!
    shhhhhhhhhhhhh
    don't tell the Palma boys
     
  9. lysanderxiii

    lysanderxiii Member

    Joined:
    Mar 21, 2015
    Messages:
    2,375
    Location:
    North Carolina
    Sorry, no.

    M118 is still above sonic at 1000 yards. And that's not a really fast bullet.
     
  10. Haxby

    Haxby Member

    Joined:
    Jan 15, 2011
    Messages:
    993
    Thanks to people who have written ballistic calculators, it is possible to look this stuff up.
    Under one specific set of conditions, a Sierra 30 caliber 150 grain HPBT started at 2600 fps will travel 1723 yards in the same time it will take sound to travel 1723 yards.
     
  11. denton

    denton Member

    Joined:
    Feb 22, 2011
    Messages:
    1,992
    Location:
    Free state of Utah
    Your answer brought a smile. You're absolutely correct of course. External ballistics involves some pretty snappy math. An exact, analytic answer to the original question would keep you busy for quite a while.
     
  12. hdwhit

    hdwhit Member

    Joined:
    Nov 16, 2015
    Messages:
    4,930
    Location:
    Salem, AR
    No.

    Each bullet will have a different response to air resistance (this is approximated by the Ballistic Coefficient but not exactly) so it's time to target is not linear. Thus, the equation would be a non-linear differential equation using terms whose coefficients have probably never been directly measured and could only be estimated or determined empirically.

    As posters like Berger.Fan222 and JimWatson have already posted, you can approximate this with ballistic computations, but a deterministic formula is would be unique to each bullet and muzzle velocity.
     
  13. jmar

    jmar Member

    Joined:
    Feb 27, 2016
    Messages:
    262
    What is the reasoning behind this question?
     
  14. RetiredUSNChief

    RetiredUSNChief Member

    Joined:
    Jul 9, 2012
    Messages:
    10,779
    Location:
    SC (Home), VA (Work)
    All this talk about ballistics calculators and computer crunching...I'd be interested in seeing someone actually crunch some numbers for some pistol rounds as they see fit, then compare the results using my methodology and assumptions.

    I'm curious to see how the results compare and whether they validate or refute my assumptions.
     
  15. Haxby

    Haxby Member

    Joined:
    Jan 15, 2011
    Messages:
    993
    Sierra 9mm 125 gr. 1325 fps, speed of sound 1125 fps.
    Bullet slows to 1125 fps at 64 yards. Sound catches bullet at 140 yards.
     
  16. RetiredUSNChief

    RetiredUSNChief Member

    Joined:
    Jul 9, 2012
    Messages:
    10,779
    Location:
    SC (Home), VA (Work)
    So...

    0.37 seconds?
     
Thread Status:
Not open for further replies.
  1. This site uses cookies to help personalise content, tailor your experience and to keep you logged in if you register.
    By continuing to use this site, you are consenting to our use of cookies.
    Dismiss Notice