btrettel's Nerf blog

random thoughts about the ballistics of foam darts

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Solving the point mass model of a dart’s trajectory, part two

Posted by btrettel on June 12, 2011

I wrote a technical paper about solving these equations and made some conclusions for design. I have fully solved the flat-fire case given that the x velocity stays above a certain number (and it generally will).

(Original link broken: My newer notes contain that paper and more.)

The take-home message is pretty simple: Keep kinetic energy constant. If you reduce the drag coefficient multiplied by the cross-sectional area, you’ll increase range. If you reduce the muzzle velocity divided by the dart mass, you’ll increase range.

The latter conclusion is not too surprising to me as I already knew dart mass had an effect like that, but to quantify the effect is very nice.

I’d happily accept corrections, comments, questions, suggestions, and whatever else.

This entry was posted on June 12, 2011 at 8:13 pm and is filed under Exterior ballistics, Math. You can follow any responses to this entry through the RSS 2.0 feed. Responses are currently closed, but you can trackback from your own site.

2 Responses to “Solving the point mass model of a dart’s trajectory, part two”

  1. Hi said

    June 13, 2013 at 8:21 am

    Technical paper link not working, just so you know.

  2. btrettel said

    June 13, 2013 at 9:53 am

    I deleted that paper because my new notes contain all that paper did and more. I’ve added a link above. Thanks for the notification.

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