---------- ---------- ---------- ---------- ---------- ---------- ---------- ---------- # How to calculate the effective force on the mast of a racing sailbot # (from "Numerical Methods", Chapra & Canale, McGraw-Hill) [ continuation from 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) f = function(z) 298*(z/(z+10/6)*exp(-2*z/10)) F = integral(f,0,10); F # 735.349 g = function(z) z*f(z); M = integral(g,0,10) # moment # 3199.675 d = M/F; d # 4.351233 (m) # T: tension in the cable # H and V; unknown reactions on the mast transmitted by the deck theta = atan(1/10) V = F*d; V (kg) # 3199.675 T = F*d/cos(theta); T # 3215.633 (kg) 3220 kg H = F-T*sin(theta); H # 415.3815 (kg) 415 kg