Triangle or Square?

What is the optimum shape for a thinsat?

Triangle

Square

Tri.png

Quad.png

Area

A = \sqrt{3} C^2 / 4

A = Q^2

Side

C = 2 \sqrt{A / \sqrt{3} }

Q = \sqrt{A}

Height

B = (\sqrt{3}/2) C = \sqrt{\sqrt{3}A}

Ratio

C = ( 2 /\sqrt[4]{3} ) Q ~ \approx ~ 1.51967 ~ Q

Q = ( \sqrt[4]{3}/2 ) C ~ \approx ~ 0.65804 ~ C

Rotational
Center

Average
Force F/2

TriA.png

TriB.png

QuadA.png

QuadB.png

Moment of
Inertia I

Torque T

Angular
acceleration
\dot \omega