How to calculate the trajectory of a mortar round.

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    Trajectory
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Discussion Overview

The discussion revolves around calculating the trajectory of a mortar round, focusing on the necessary parameters and equations involved in determining the launch angle required to hit a target. The scope includes theoretical considerations and practical applications, particularly in the context of video game development.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks assistance in calculating the angle needed for a mortar round to hit a target, given initial velocity and distance.
  • Another participant questions whether air resistance is being considered, indicating that it complicates the problem.
  • Several participants reference historical methods of solving similar problems using early computers, mentioning factors like distance, elevation change, air density, and wind speed.
  • One participant suggests that additional factors such as the Coriolis effect and variations in gravitational acceleration could also be relevant.
  • A later reply indicates that the original poster does not need to consider air resistance for their application in a video game, suggesting a simplified approach.
  • The original poster cites a formula found on Wikipedia for calculating the angle of projectile launch.

Areas of Agreement / Disagreement

Participants express a range of views on the factors to consider in trajectory calculations, with some advocating for a comprehensive approach that includes various environmental factors, while the original poster indicates a preference for a simplified model without those considerations. No consensus is reached on the necessity of including air resistance or other complexities.

Contextual Notes

Participants mention various historical and technical aspects of trajectory calculations, including the limitations of early computing methods and the specific conditions under which those calculations were made. The discussion reflects differing assumptions about the relevance of certain variables based on the context of the problem.

Who May Find This Useful

This discussion may be useful for individuals interested in projectile motion, particularly in applied contexts such as video game design, as well as those exploring the historical development of computational methods in physics.

mcvwi623
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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.
 
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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.
 
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.
 
skeleton said:
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.

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...
 
skeleton said:
If I recall my 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.
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:
http://en.wikipedia.org/wiki/ENIAC

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.:
http://ftp.arl.mil/~mike/comphist/eniac-story.html

Differential analyser:
http://en.wikipedia.org/wiki/Differential_analyser
 
Last edited:
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:
http://en.wikipedia.org/wiki/Trajectory_of_a_projectile

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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