How Do I Calculate the Pulley Ratio for a Complex Boat Pulley System?

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To calculate the pulley ratio for a complex boat pulley system, only the information in the provided drawing is necessary. The method involves breaking the pulley system into sections and summing the tensions to determine the ratio. The user calculated a ratio of 9T:1T and seeks confirmation of this result. It's essential to ensure that the sum of forces equals zero in both the X and Y directions and that the tension remains constant in each rope. Verifying these conditions will confirm the system's static equilibrium and the accuracy of the calculated ratio.
Darknes51986
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A guy at work gave me this drawing I have attached and asked me to find the pulley ratio. Do I need any other information such as rope lengths, pulley diameters, or load? I traded in my machine design book and don't remember exactly how to calculate the ratio. Is there anything else I can calculate involving the load that would be helpful if I knew the weight of the boat. Thanks for any info.
 

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  • pulley.JPG
    pulley.JPG
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Nope, you don't need anything other than what is in the picture.
 
So what I do is break up the pulley into sections and add up the tensions (T) right? With the tensions from each section I can get the ratio? Is this correct? I re-drew the drawing with my work on it. 9T:1T is my answer I just need someone to check that.
 

Attachments

  • pulley2.JPG
    pulley2.JPG
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Can anyone confirm my answer or is it off?
 
Check to verify the sum of the forces is equal to zero in both the X and Y directions. Also verify the tension in any given rope is constant. If both of these are good, then the system is in static equilibrium.
 

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