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Field RPG. Appendix 2

Mathematics.

Let sword is one dimension object. It contains some parts. Each parts is described by it weight mi and distance from center of the mass to zero point xi. Let zero point will be guard of the sword. In this case:

X = sum mixi/sum mi (1)

Lets suppose that sword consist from the blade, handle and counterbalance. We must find m and x for each part and then calculate result by formula (1).

  1. Trapezoidal blade. It has length l1, width near guard S11, width near edge S12 thickness h1 and density ro1. Weight of blade:

    m1 = (S11 + S12)l1 h1ro1/2

    Distance from center of mass:

    x1 = -l1(S11 + 2S12)/ 3(S11 + S12)

  2. Rectagular handle. It has lenght l2, width S2, thickness h2� density ro2. Weight of handle:

    m2 = S2l2h2 ro2,

    distance:

    x2 = l2/2.

  3. Spherical counterbalance. It has radius r3 and density ro3. Weight of counterbalance:

    m3 = 4/3Pi ro3 r33,

    distance will be equal to the length of handle. So:

    �3 = l2.

Mass of counterbalance for given sword dimensions and place of center of the mass is:

m3 = -(m1(x1 - X) + m2(x2 - X))/(x3 - X).

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