Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?

Correct result:

l =  313.4 m

Solution:

a=10 D1=50 D2=200 x=350 n=(D2−D1)/a=(200−50)/10=15 o=π⋅ D x1=D1=50 d=2⋅ a=2⋅ 10=20 x2=x1+(n−1)⋅ d=50+(15−1)⋅ 20=330 s=(x1+x2)/2⋅ n=(50+330)/2⋅ 15=2850 l1=π⋅ s=3.1416⋅ 2850≐8953.5391 l2=l1/1000=8953.5391/1000≐8.9535 m=x/a=350/10=35 l=m⋅ l2=35⋅ 8.9535=313.4 m

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