## Solving the point mass model of a dartâ€™s trajectory, part two

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.

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