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#   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