---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- # How to calculate the effective force on the mast of a racing sailbot # (from "Numerical Methods", Chapra & Canale, McGraw-Hill) # We use online software www.wolframalpha.com. See here # We assume that the mast remains vertical. # If we know that f = 298·z/(z+10/6)·exp(-2·z/10), we must convert to an equivalent # total force (F) and calculate its effective location above the deck (d) integrate 298*(z/(z+10/6)*exp(-2*z/10)) from z=0 to 10 735.349011776... F integrate z*(298*(z/(z+10/6)*exp(-2*z/10))) from z=0 to 10 3199.674733368... moment (integrate z*(298*(z/(z+10/6)*exp(-2*z/10))) from z=0 to 10)/(integrate 298*(z/(z+10/6)*exp(-2*z/10)) from z=0 to 10) (o: 735.349011776.../3199.674733368...) 4.351232791678856599... (m) d = moment/F # T: tension in the cable # H and V; unknown reactions on the mast transmitted by the deck atan(1/10) 0.09966865249116... theta 5.711° V = F*d; V (kg) 3199.674733368... # 3199.675 T = F*d/cos(theta); T 3199.674733368/cos(atan(1/10)) 3215.6333098... T = 3220 kg H = F-T*sin(theta); H 735.349011776-3215.6333098*sin(atan(1/10)) 415.38153844... H = 415 kg