Mechanical Advantage 4. T Method and Complex Systems

in this video we're going to look at the t method a technique for calculating the ideal or theoretical mechanical advantage of any system this is a valuable technique for any aspiring roping technician to have in their toolbox and while initially it takes some focus and sketching with a pen and paper to pick up with practice you'll be able to apply it quickly and efficiently in the field at first applying the t method will involve labeling every point where a rope interacts with a system component with the tension on the rope or component at that point in the system with practice you'll be able to take some shortcuts to focus on the key areas of the system that you have an interest in we call the tension that we apply to the system t and we label the tension at every other point in the system as some multiple of t it may be 2t 3t 0.8 t or so on the easiest way to understand the t method is to walk through it with a simple example but before we do that there are two simple rules that will apply over and over when using the t method the first rule is how we treat pulleys here we have a rope entering and leaving a pulley if we say that the tension on the rope entering the pulley is one t and if we're looking for ideal mechanical advantage not considering the efficiency of the pulley we also say that the tension on the rope exiting the pulley is t the tension on our carabiner attached to the pulley we identify by adding together the tensions on each of the ropes coming out of the pulley in this case 1t plus 1t gives us 2t at the carabiner if we're looking for theoretical mechanical advantage we need to take the pulley efficiency into account if we say the efficiency of this pulley is 90 and again the input tension is 1t our output tension is going to be 90 percent or 0.9 of the input tension 0.9 times 1 is 0.9 so the tension on the rope leaving the pulley is 0.90 again to find the tension on the carabiner above the pulley we add our two rope tensions together one t plus 0.9 t is 1.9 t at this point the second rule is how we treat rope grabs ascenders process and so on rope grabs allow us to add tension to a rope so if we say this length of rope and we're going to ignore the pulley for this part if we say that this length of rope has a tension on it of one t and i'm going to attach a rope grab the rope grab has a tension of 2t on it to find the tension at the rope in front of the rope grab we simply add the two tensions together so we have one tee pulling on the rope below the rope grab and we have two t applied to the rope grab itself giving us three t on the rope above the rope grab next we're going to apply the t method to a simple three to one and a compound six to one to find their ideal mechanical advantages finally we'll introduce a complex mechanical advantage system and use the t method to find its ideal and theoretical mechanical advantage here's a system that should be familiar to us all we'll start by labeling the whole strand with the tension we apply t for now we'll focus on ideal mechanical advantage ignoring friction in pulleys this means we can come down from our input tension to the first pulley we made and label both the input and output rope tension as t now we have the tension of the rope on both sides of our pulley we can label the other side of our pulley t plus t is 2t now we'll follow the rope until it meets the next pulley again we can label the input and output rope tension as t and again we have t plus t or 2t on the other side of the pulley following the rope to the figure of eight attached to the load the rope still has a tension t now we've labeled all the components in our system we can add them up to find the forces on our load at the load we have two t from the pulley and t from the knot giving us a total of three t that means we input a force of t and the load experiences a force of three t confirming that this is a three to one before we're done we can incendity check our results if we draw an imaginary line down the center of our system and add the tensions leaving the system on both sides ignoring the total of the load because that would be double counting they should be equal on the left we have two t from the pulley and t from the figure of eight for a total of three t on the left on the right we have two t at the pulley and t on the whole line also giving us a total of three t it's not impossible for this check to turn out okay but for our analysis to still be wrong but it's an easy thing we can do to check our analysis and it makes it pretty unlikely we've made an error now we have a compound system that we saw in a previous video and we'll again use the t method to find its ideal mechanical advantage if you think you've got the hang of this you might want to pause the video here work it out yourself and then come back to the video to compare your results once again we start by labeling our input force t following the rope down to the first pulley we can label the rope entering and leaving the pulley t this gives us the tension of the rope on both sides of the pulley so we can find the tension on the rope grab t plus t is two t at the right grab returning to the rope with tension t leaving the pulley we follow it to where the rope enters the next pulley and again we have t entering and leaving the pulley with the rope tension of both sides of the pulley we can add those to find the tension on the anchor side of the pulley again t plus t is 2t following the rope from the pulley to where it enters the rope grab the rope has tension t before the rope grab the rope grab adds tension to the rope so tension t on the rope plus two t on the rope grab gives us three t on the rope in front of the rope grab which is also the tension entering the pulley at the load this means the tension leaving the pulley is also 3t and with the tension on both sides of the rope we can add 3t and 3t to c6t at the load finally following the rope to the figure of 8 we also have 3t at that point doing a quick sanity check we draw a line down the middle of our system and at the tensions leaving the system on each side on the left this is the tension on the load 6t on the right the tensions leaving the system are these ones t plus 2t plus 3t gives us 6t on the right which matches the tension on the left here we have a complex system i encourage you to pause the video at this point and apply the t method yourself to find the ideal mechanical advantage of this system once you're done you can compare your results to mine and then we'll finish by taking pulley efficiency into account and finding the theoretical advantage of this system starting with ideal advantage we start as always by labeling our input tension t coming down to our first pulley we have tension t on the rope entering and leaving the pulley with the tension on both sides of the pulley the tension on the rope grab is t plus t or two t following the rope to the pulley at our load we again have t on both sides of the pulley giving 2t on the load end of the pulley following the rope up we have t where it enters the rope grab plus 2t on the rope grab gives us 3t in front of the rope grab and entering the pulley at our anchor this means we also have three t on the other side of the pulley adding those together gives us six t at the anchor following the rope which has three t leaving the pulley to the figure of eight we have three t at the figure of eight adding together the tensions at our load two t plus three t gives us five t or a five to one ideal mechanical advantage once again we'll check our results by drawing a line down the middle of the system the tensions leaving our system on the left are the whole line pulley and figure of eight for a total of six t on the right the tension only leaves our system at the anchor which we've already said is six t with six t on both sides of the system we can be reasonably confident our calculations are correct finally we'll take the same system and find its theoretical mechanical advantage all the pulleys in our diagram are rock exotica omnis which we know have an efficiency of about 90 so we'll use that as our pulley efficiency in our calculations once again we start by applying tension t to the whole line coming down to the first pulley we have t entering the pulley but only 90 percent of t leaving the pulley 90 or 0.9 times t is 0.9 t so that's the tension leaving the pulley the tension on the rope grab then is t plus 0.9 t or 1.9 t following our nine t down to the pulley at the load we have point nine t entering the pulley which means we have ninety percent of point nine t leaving the pulley that's zero point eight one t now we can find the tension on the load end of the pulley 0.90 plus 0.81 t is 1.712 following our 0.81t along the rope we have 0.81 t at the rope below the rope grab adding the 1.9 t on the rope grab gives us 2.71 t above the rope grab where the rope enters the pulley at our anchor the rope leaving the pulley has 90 percent of 2.71 t which is 2.439 t having the rope tensions on both sides of the pulley the tension the pulley applies to the anchor is 2.71 t plus 2.439 t or 5.149 following the rope to the figure of 8 we also have 2.439 t at the figure of 8. looking at the tensions attached to our load we have 1.71 t at the pulley and 2.439 t at the knot giving us a total of 4.149 t or a 4.149 to 1 mechanical advantage theoretically checking our calculations by drawing a line down the middle of our system on the left the tensions leaving our system of the whole line and the pulley and figure of eight attached to our load adding these together gives a total of 5.149 t on the right tension only leaves our system at the anchor which we've already calculated as 5.1492 with the tensions on the left and right sides of our system being equal we can be reasonably confident our calculations are correct

Channel: Chris Bennetts-Cash

Views: 2,381

Rating: 5 out of 5

Keywords: Vertical Rescue, Haul System, Mechanical Advantage, MA, Roping, Rigging

Id: ON7NNDeUjW0

Length: 11min 0sec (660 seconds)

Published: Thu Jul 09 2020