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How to calculate the trajectory of a mortar round.

  1. Feb 19, 2009 #1
    Hi, I didn't post this question in the Homework section as it is not home work and does not seem to fit with the template.

    I was wondering if someone could help me out with trying to calculate certain unknowns when computing the trajectory of a mortar round.

    I think the solution to the problem involves some sort of re-arrangement of the kinematic equations required to solve trajectory problems where you are provided with an initial velocity and an angle.

    I figure that when trying to hit a target with a mortar. You already know the distance the projectile is required to travel and you also know the force applied to the projectile to cause it to travel. I need to compute the angle that is required in order to make the round land in the right place.

    I have attempted to work backwards from examples which provide you with an angle and a force and require you to compute the landing point and max height etc, but I have found that I can not find the Time variable required??

    Can someone help me out, maybe I am not using the correct equation for this.

    Any help would be appreciated, thanks.
  2. jcsd
  3. Feb 19, 2009 #2


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    Science Advisor

    Quick question before you can go any further: Are you taking air resistance into account or not?

    If not, it is a relatively simple problem. If so, it gets a bit stickier.
  4. Feb 20, 2009 #3
    If I recall me readings correctly, this problem was one of the first solved with electronic computers.

    I believe they took into account:
    - Distance.
    - Elevation change.
    - Air density, in account of air resistance.
    - Side wind speed.

    Frankly, this shouldn't be too difficult using either MS Excel or Mathcad.
  5. Feb 20, 2009 #4
    How about Coriolis effect,
    air density as a function of humidity, temperature, and altitude,
    g as a function of altitude,
    the phase of the moon...
  6. Feb 20, 2009 #5


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    Homework Helper

    The computers were used to fill in tables of data where actual motars were fired and the shell impact positions were measured over a range of conditions to generate the coefficients for the differential equations that the computer would then numerically integrate. Previously, analog computers were used to do this. ENIAC wasn't completed until after WW2 had ended so it missed it's original goal.

    ENIAC was designed and built to calculate artillery firing tables:

    a skilled person with a desk calculator could compute a 60- second trajectory in about 20 hours. The analog differential analyzer produced the same result in 15 minutes. ENIAC required 30 seconds--just half the time of the projectile's flight.:

    Differential analyser:
    Last edited: Feb 20, 2009
  7. Feb 20, 2009 #6
    Hi guys, thanks for all your replies. I am a computer science major, so I know all about ENIAC :).

    No I don't need to take into account the wind resistance or any other variables. I am writing a First Person Shooter video game so all those variables can be neglected

    It turns out the following wikipedia page has the answers:

    This is the formula that I needed. Looking at it I can kind of see how it was derived.

    theta = 1/2 arcsin ( gd / v^2 )

    Thanks for your help anyway.
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