Expression 11: "y" Subscript, 2 , Baseline tilde left parenthesis, "x" Subscript, 2 , Baseline minus 1 , right parenthesis Superscript, "c" , Baseliney2~x2−1c
11
Expression 12: "f" left parenthesis, "x" , right parenthesis equals StartFraction, Start integral from 0 to "x" , end integral, left parenthesis, "t" minus StartNestedFraction, "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline NestedOver "r" Subscript, "o" "f" , Baseline , EndNestedFraction , right parenthesis squared "d" "t" Over left parenthesis, "x" plus "r" Subscript, "e" "l" "o" "a" "d" "T" "i" "m" "e" , Baseline , right parenthesis , EndFractionfx=∫x0t−magSizerof2dtx+reloadTime
12
Once you hit ~73-71% capacity, reload for maximum dps (assuming 3 second reload such as Mag Blaster DX. Reload later if slower reload, reload earlier if faster reload). Probably better to go slightly over. Obviously draining out entirely is best for energy efficiency. Source for rough mag blaster damage stats: https://www.youtube.com/watch?v=sNNkuWwzHN4
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Magazine size also has an effect on optimal reload, but much lower effect. larger magazine size needs to reload earlier
14
Expression 15: left parenthesis, "x" minus StartFraction, "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline Over "r" Subscript, "o" "f" , Baseline , EndFraction , right parenthesis squaredx−magSizerof2
15
Expression 16: "f" prime left parenthesis, "d" plus StartFraction, "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline Over 2 "r" Subscript, "o" "f" , Baseline , EndFraction , right parenthesis tilde 0 left brace, StartAbsoluteValue, "d" , EndAbsoluteValue less than or equal to StartFraction, "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline Over 2 "r" Subscript, "o" "f" , Baseline , EndFraction , right bracef′d+magSize2rof~0d≤magSize2rof
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Expression 17: "d" plus StartFraction, "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline Over 2 "r" Subscript, "o" "f" , Baseline , EndFractiond+magSize2rof
equals=
6.8 5 3 4 8 7 2 4 26.853487242
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Expression 18: "o" Subscript, "p" "t" "i" "m" "a" "l" "R" "e" "l" "o" "a" "d" "P" "o" "i" "n" "t" , Baseline equals "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline minus "r" Subscript, "o" "f" , Baseline times left parenthesis, "d" plus StartFraction, "m" Subscript, "a" "g" "S" "i" "z" "e" , Baseline Over 2 "r" Subscript, "o" "f" , Baseline , EndFraction , right parenthesisoptimalReloadPoint=magSize−rof·d+magSize2rof
equals=
1060.7 9 0 7 6 5 4 81060.79076548
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I just realized that this technically isn't 100% accurate, but summations are laggy as fuck and a pain in the ass to work with, and this is close enough anyway.
