{"id":1061,"date":"2024-05-20T10:50:14","date_gmt":"2024-05-20T14:50:14","guid":{"rendered":"https:\/\/www.sailons.com\/northerncomfort\/?p=1061"},"modified":"2024-05-20T11:30:45","modified_gmt":"2024-05-20T15:30:45","slug":"using-math-to-lift-a-dinghy","status":"publish","type":"post","link":"https:\/\/www.sailons.com\/northerncomfort\/2024\/05\/20\/using-math-to-lift-a-dinghy\/","title":{"rendered":"Using math to lift a Dinghy"},"content":{"rendered":"\n
\"Dinghy<\/figure>\n\n\n\n

Understanding Lever Mechanics: Lifting a 100-Pound Object at Different Angles<\/h3>\n\n\n\n

When lifting heavy objects, leveraging simple machines like levers can make the task significantly easier. Here is some math to show how this simple lever can be used to ease off the weight of the dinghy. I find this little ‘how does math help’ thinking interesting to work through.<\/p>\n\n\n\n

The Scenario<\/h4>\n\n\n\n

Imagine you have a 100-pound dinghy attached to one end of a bar (acting as a lever), with the other end fixed at a pivot point on the transom. You use a rope to pull the dinghy upwards. As you pull, the bar lifts the dinghy, creating different angles relative to the horizontal ground. What forces are at play when the bar is at 30 degrees, 45 degrees, and 60 degrees above the horizontal?<\/p>\n\n\n\n

Lever Mechanics and Angles<\/h4>\n\n\n\n

When the bar is at an angle \u03b8<\/em>, the weight W<\/em> of the dinghy can be resolved into two components:<\/p>\n\n\n\n

    \n
  1. A component parallel to the bar<\/li>\n\n\n\n
  2. A component perpendicular to the bar (which is effectively supported by the bar)<\/li>\n<\/ol>\n\n\n\n

    The component of the weight perpendicular to the bar is given by W<\/em>cos(\u03b8<\/em>). This is the component of the dinghy’s weight that is transferred to the bar.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    What Does This Mean?<\/h4>\n\n\n\n

    The calculations show that as the angle of the bar increases, the vertical component of the weight also increases. This means that lifting the dinghy becomes progressively easier as the bar gets closer to the vertical position as more of the weight transfers to the vertical.<\/p>\n\n\n\n

    When the bar is at 30 degrees, the effective weight you need to lift is 86.6 pounds, making it the hardest angle. At 45 degrees, the bar is taking up 70 pounds requiring you need to lift 30 pounds (100 – 70 = 30), and at 60 degrees, that bar has 50 pounds.<\/p>\n\n\n\n

    Understanding these mechanics can help you plan more efficiently when lifting heavy objects using levers. For example, keeping the lever closer to horizontal makes lifting harder, while raising the angle decreases the required lifting force.<\/p>\n\n\n\n

    How does this affect the dinghy lift?<\/h4>\n\n\n\n

    The dinghy becomes progressively easier to haul out of the water as the lever (bar) slowly lifts up. at about 60 degrees, half the weight is on the bar and half the weight is on the ropes (arch) so this simple lift principal will greatly reduce the strain on the arch and lifing mechanics.<\/p>\n\n\n\n

    Interestingly, you do need to overcome the angle and the transfer of the weight of the dinghy to get it above 0 (horizontal) which is why placing the pulleys overhead greatly reduce the effort. It is about double the weight to get the dinghy off the water, 60 pounds becomes 120 pounds dry weight.<\/p>\n\n\n\n

    \"\"<\/figure>\n\n\n\n

    Using the pulleys, with 4 passes reduces this weight to 50 pounds ( its actually a simple weight (W) divided by the mechanical advantage (4 pulleys) so 200\/4 = 50 lbs. So I installed 2 pulley systems to further half the weight so 200 lbs becomes 200\/8 = 25 lbs.<\/p>\n\n\n\n

    Overall the dinghy lift is working quite well, and I am glad that half the weight is on the transom as when the seas get bouncy, there is added strain on the tie downs as the weight increases with each bounce. The block and tackle is rated at 2000 lbs and the arch stainless steel breaks at 3500 lbs per inch bringing a total of minimum 4000 lbs required to break the pulleys and rope. I think we will be ok.<\/p>\n","protected":false},"excerpt":{"rendered":"

    Understanding Lever Mechanics: Lifting a 100-Pound Object at Different Angles When lifting heavy objects, leveraging simple machines like levers can make the task significantly easier. Here is some math to show how this simple lever can be used to ease...<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[],"class_list":["post-1061","post","type-post","status-publish","format-standard","hentry","category-blog"],"yoast_head":"\nUsing math to lift a Dinghy<\/title>\n<meta name=\"description\" content=\"a simple machine (lever) to lft the dinghy, is it enough, why does it help? 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