Mechanical Advantages: Counting Tensions and Estimating System Efficiency Part 1

all right this is part one of two mechanical advantages counting tensions and estimating system efficiencies this is going to be a quick talk about counting tensions in a mechanical advantage system or an MA for some this technique is used when first learning mechanical advantage system so they can see how the weight and percentages are distributed throughout the system for others used for determining the mechanical advantage of more complicated radio systems like Spanish burdens and for others you just use as a quick means to determine what kind of force is being placed on the anchor depending on what you're setting up and if what the change of directions actually do but we first have to grasp this concept of counting tensions before we can move on to counting or estimating system efficiencies this is just going to be a quick review this is kind of presuming that you know a little bit about mechanical advantages so this is kind of bring things into the forefront here before we start talking about some of the procedures so from left to right we're going to go through this this graph is going to show the behavior and dynamics of various mechanical data systems this shows the course requirements and distance a pool required to move a load one foot so on the bottom here you can kind of see how we have the one slip marker for each one of these systems and we have a 1 2 1 a 2 2 1 a 3 2 1 z drag and then obviously we have a 5 to 1 complex so we're looking at a simple one-to-one you'll see that some people will count mechanical advantages of simple system so it's pretty easy to do you just can kind of count how many lines are supporting your load remember at the top here and we pull our rope out where that end of the rope connects to will help us determine a simple 1 rope system mechanical advantages so if the Rope starts at the loop right we're going to have an odd system which we see right here are 1 2 1 we also see that on our 3 1 5 2 1 if the Rope actually starts at the Anchor Denner mechanical advantage is going to end up being even so let's walk our way through this real quick so I'm not far left here we have a wonder 1 system so we have the load the Rope starts at the load comes up through a progressive capture and then it's pulled down so the direction of force is going to be down in a 1 to 1 we're not really getting a mechanical advantage will actually learn that we get less than 1 to 1 when we're looking at efficiencies because of the friction in the pulley but for our purposes right now all we have to do to move this load 1 foot is pull one foot here so if this load is 200 pounds we're going to have to theoretically put 200 pounds of force on this to move it so the force that we're hauling as a hauler is going to be equal to what that load is when we're talking theoretical little systems and to be able to move it 1 foot we only have to pull one foot we look at a two-to-one system theoretically this is going to cut the weight of the load in half although now we have to pull two feet to be able to move that load one foot so just like anything in physics what you have to increase the distance of we're talking levers right the longer that lever the bigger the MA is going to bit get as long as we're pulling on the end of the lever so in this case in rope we're going to have to pull greater distances to be able to get that mechanical advantage so for us we're going to have to pull 2 feet to move this load one foot but theoretically it's going to cut our weight in half so with a 200 pound load we're roughly going to have to be pulling 100 pounds the other 100 pounds is going to be on this anchor when we're looking at our 3 2 1 right we can see if there's three ropes that are supporting our load down here this actually kind of creates our new load here whenever we put a drag system in there so from here we got one line two lines three lines so we know it's a three to one and we'll be counting the Simpsons here in a little bit but on the three to one we know that we're going to have to pull three feet to move that load one foot and the advantage of that is we're theoretically cutting that loads weight down by one third so what we're pulling is one third and then the other two-thirds is going to be on the anchor here now this is a five to one so this is one of the reasons that a lot of people get into counting tensions because once we get into complex mechanical advantages we can't count the lines any longer so what we have here is a five to one and we'll talk about how to count tensions to get that but on a five to one we're going to have to pull five feet of rope to move that load one foot the good part about that is the theoretical force that we're going to have to apply is basically one-fifth of what that load is right quick overview got to go over this this presentation assumes that the reader has basic understanding of mechanical advantage rope systems will be counting tensions within a mechanical advantage system to determine the theoretical mechanical advantage theoretical mechanical advantage assumes that we live in a church in this world which we all know is not correct so friction acquired within a pulley and or oppressor is ignored when we're counting tensions there are sometimes easy ways to find MMA at a simple or compound halt system you may count the line supporting the load of a simple system or breakdown a compound mechanical advantage into its individual simple mas and then multiply them together and we'll see those here in a couple slides the problem arises when we look at a traditional complex Hall system and some of the spanish burton variants concepts so remember we're always going to start counting tension from the whole line which is where your hands are going to grab that rope to start pulling and we're going to work our way back through the system and end at the road the number that we hit on at the load is what that mechanical advantage is going to be it's just a ratio between what our input is and our output so when we write that 5 to 1 the 1 is going to be our input the 5 is what the output resulting output is going to be we'll always start with 1 tension on the whole line once we know the mechanical advantage 3 1 5 2 1 6 1 we can then input estimated weight values that's desired so like we've mentioned before if we know that it's a two-to-one that we're hauling on and we know our load is approximately 200 pounds we can then divide that 200 by 2 and realize that we're going to be pulling on our whole line approximately 100 pounds all press X except at the PCB the progressive capture device are going to be a point to add numbers so we stop at all rope graphs to see if we need to perform any addition within our system and hopefully this clears clarifies once we start getting this thing going all right toys are a wholesome force multiplier so the pulley wheels here that are moving pulleys would add to the mechanical advantage and that a stationary or standing pulley which is usually at an anchor doesn't do anything to our ma which is correct but no matter regardless of where that pulley is a is always going to magnify force and we're going to see that in when we count tensions and then we count efficiencies so it's kind of a quick cheat we can always look at whatever pool you have majority of all pulleys have this something talking about what it's rated at on the front so whether this is 30 kilo Newtons and the point that we have here or it's thirty six kilonewtons or forty kilo Newtons whatever that number is you're always going to see it with half that number in and half that number out so we're talking about thirty kilo means here so fifteen goes into this pulley then fifteen has got to come out and what we're going to have is thirty in this case right here at the apex of it so in our cases we'll be counting tension so we'll have one tension coming in will always have one tension coming out and then we're going to have two tensions up here so we just simply add these two numbers which in our case is accounting tension will be one on one but as we get into larger numbers we may have a three goes in three comes out and then we're going to have six at the top so these numbers will get added together to see what this number is it's going to be sitting on your pressing or potentially your anchor so remember Newton's third law when we're doing this DMA is the final number is going to be at the note the load and don't ignore the anchor number and we'll see in some cases the tensions that are on the anchor or greater than the tensions were actually hauling all right so this get started as my counting tension so like we said before bro is going to start on the whole line and we're always going to start with the one so remember as we work our way from the hall line all the way back to the load we're going to start this on the left and work our way through so if a one starts off with our ha grow is going to do one tension is coming in so as that goes up to our first pulley which is our progressive capture if one comes in one has to come out and that's going to leave us two up here at the apex so just like we talked about before with the fifteen and fifteen equals thirty so we're using one tension now so we're using tension so if one comes in one has to come out and two is left here at the apex of that one comes down one comes down and one terminates at the load so we know we have a wonder one so now we're going to move on to another one so like I said before we're always starting at the hollow line we're starting to green one so we start hauling with one tension that's one comes in we know that one has to I'm out and at the apex we add those numbers together we know we have a tube and we know we have a teat one mechanical advantage but that one continues up and so one tension is here so when we think about a two to one and we cut that weight in half the anchor has one tension we have that other tension so no matter what that load is if it's a hundred pounds we got 1550 it's 200 pounds we got 100 100 so one comes in one comes out two is left with the load we always count the number that is terminate to the load so we know it's a two to one now this is basically it looks very similar to this next one except we come back up to anchor and do a change of direction so this is actually going to be a two to one with the change of direction this adds a little bit of confusion on people when they're first learner mechanical advantages because it's like oh well we just added this or is it a three to one is it what is it so you'll see it's actually the same thing so as we start off with a one because this is our whole line if one comes in one has to come out and we have to add our anchor we continue on one comes down one comes out one comes in one has to come out and we have to at our load which means it's a two to one and then this one comes up here and turn and terminates so because we put a change of direction in and we're pulling against our anchor although we have a two to one down here we actually have three tensions up here at our anchor so if we wanted to think what that really means let's say our load was 200 pounds so we know that we're inputting 100 pounds here so if we input a hundred pounds we know that we have to have 100 pounds coming out and that means we have 200 pounds right here so 100 comes down 100 comes down 100 goes in 100 has to come out which means we have 200 down here which is accurate and then that other 100 comes up here so when we add those together we actually have 300 pounds of force on our anchor yet we're hauling 200 pounds and it's because of that last change of direction or redirect that is adding that extra weight to our anchor all right getting into some more complicated systems so we're going to start here at our Hall line we're pulling with the anchor and you'll see when we pull with the anchor that our anchor weight is typically not going to be exceeding what our weight is down here so with a wonder with the starting off with one tension we have one that comes down so we work our way one comes in one has to come out and now we have to that too that's at that apex of that pulley is actually going to sit on that rope graph so whether that's a key block or whether that's a press like a two is just going to sit there and if you remember when we're talking about our overview any time we see a rope grab that's going to kind of equal a plus sign or an addition sign in our head so one comes in one comes out two is on depressive one comes up one comes up one goes in one has to come out two is sitting on the Anchor Point one comes down and as one comes down we meet the rope grab which is a plus sign so 1 plus 2 is going to be 3 so we have 3 tensions from this point of the rope so if one tension in here we have two tensions here when these meet we have three tensions to go to or low telling us that we have a three to one and this is a ZJ configuration so continuing with that we basically put the change of direction and over here so let's figure this one out once starts so one comes in one comes out we have to add our anchor the 1 continues down if one comes in one comes out and we have two sitting on our prusik as one comes in one comes out and we have another two tensions on our anchor that one continues down one continues down it meets our rope graph which has two sitting on it so one plus two is three so we still have a three two one it just has a change of direction but where we can see here is because we're pulling against the anchor we actually have an extra tension on our anchor so we're putting more force on our anchor than what we actually have on our load the last one here is going to be a Spanish burden so this is one of the complex variants that we are talking about before you're going to see this sometimes and some mountaineering configurations you can use a court of light you can use a sling different things to put in as this rope so the red rope the red color signifies another rope and the yellow is our main line so once again we're going to start here on our tensions just so you know right here this signifies that our whole rope length is run out and this is the terminal part of the rope so there's not enough that we can build a ma system off of so we add the second portion on start with a 1 on our whole line so if one comes in one has to come out and we're left with two on this project and this one is actually terminates here so this could be nothing but a figure eight knot or a clove hitch or anything like this so one comes in one comes out and one terminates here so we just have one sitting on that to go back up to our to which is being pulled so to comes in to comes out that leaves us for a Paragon occur but to continues down it meets with that prusik which has one on it which gives us a three to one Spanish Burton okay moving on the first one we're going to hit is on the left so we broke out these two pulleys typically what you're going to find in a five to one simple mechanical advantages this is going to be a double pulley so we kind of broke it out so we can count on it a little bit easier so each one of these is one separate sieve that's in a double pulley so once again Hall line we know that we are pulling with our anchors so we know that that force on our anchor isn't going to be magnified like it is when we're pulling against it so we start with one tension one tension comes in one tension comes out and two is left on one of these sheets as one comes up one comes out and the first two is left on our anchor point one comes in our second chief of our double pulley one comes out and we're left with another two which equals four so four is sitting on that prusik or a rope grab of your choice there one comes in one comes out two is left so that means we have a four total on our anchor that one continues down meets up with our rope grab that is one plus four which means we have five tensions so that is a five to one simple mechanical advantage and like we said before that's a double pulley now we're going to look at another five to one this is a five to one complex which we use quite a bit once again we are pulling against the anchor so we know what to expect a higher number up here so when we start there we start with one one comes in one comes out two is left here so two is sitting on that prusik right now one comes down one comes out two sitting on this pressing one comes up meets the two that's sitting on that press 'ok and we have three in this segment of our rope so three is going to come in three has got to come out which leaves six so three plus three is going to be 6 so we have 6 here on our anchor that 3 continues down the line meets up with the 2 that is on our rope graph so 3 plus 2 is 5 and we have a 5 to 1 complex ma now we're going to go to a 5 to 1 crevasse and people call it a 5 to 1 Spanish Burton by utilizing second line five to one crevasse is what it typically goes by not too uncommon and a lot of mountaineering techniques especially when you're just using that mechanical advantage to help a climber get through a crux or something like that so we start with our one on our haul line so here's our haul line so one comes in one has to come out and we are left with two the sitting into the force here so while we're pulling that that two comes in and two comes out so that two terminates up here and we are left with four sitting right here that is because 1 + 1 equal to - coming in - coming out equals 4 so 4 is sitting there on that press 'ok now when we go back to our original system here that one that came out one goes in one comes out we have two there which is going to leave us with four at the anchor one in one out one comes down one comes down and meet with the press 'ok that has four tensions on it 4 plus 1 is going to be 5 so that is a 5 to 1 crevasse alright getting even more awkward we have a 7 to 1 Spanish burden here looks pretty complicated when you look at it basically what we have here is 2 terminating points so we have a if you can imagine we have potentially a clove hitch the ghosts are here or we technically say we have a short piece of 1/4 let that locks off so this is tied off and this is tied off and this is tied off and this goes through as our haul line this is one large piece of rope that terminates right here so we set this up start it with one because this is our haul line so one's going to come in one is going to come out and we have two sitting right here that one continues down and terminates right here so now we have that - that - comes in and 2 comes out so note that we don't have pulleys here but we have carabiners which also are going to magnify that force so we treat them just like their pulleys so 2 comes in 2 comes out and now we have 4 sitting there to put students forward that's going to be sitting on that pressing that 2 comes down and it term because these are acting independently of each other one plus two is equal three so three is going to be sitting on a rope grab come back up to where four was if four comes in four has to come out and we have a total of eight on our anchor that four is going to be coming on down that four meets with the three and we have seven so that's a seven to one spanish burton configuration and we have eight tensions on our anchor oddly enough because we're pulling against it when we come over here you're going to see this is a compound so if we break it down we can see that this looks just like a three to one and we're usually pulling so forget that these two pulleys are here that's a three to one but if we look at it we actually have another three to one pulling on top of a three to one so we can break this into two systems we know if we have two a simple mechanical advantage is working together and like that that's a compound so we have a three to one point on the three to one so we know it's a nine to one but to double check our work we're going to start at the whole line and we're going to see that we have one tension coming in here so one tension comes in one tension has to come out and we have to sitting right here in the prusik as one comes in one comes out we have two on this anchor spot one continues down meets up with the two and we have three at this portion right here so if three comes in three has to come out and we have a total of six sitting here on this press ik so three and three is going to be six as that three comes out three comes in three comes out we have a six on our anchor so when we have these two together we have eight tensions there that three continues down and that three meets with our six and gives us a nine to one compound so we've talked about simple mechanical advantages we've talked about complex mechanical advantages and that's our compound mechanical advantages where they're compounding each other by putting an MA on top of an MA lastly we're just going to talk about piggybacking so this is pretty common tear this is a four to one five to one system that's the Phantom Paul kit you can see an Aztec version of that with a little bit bigger diameter that you'll see some teams using and in the end what happens is we have one main line that is here and terminates right here and then we just take our separate system that's already pre-configured into a mechanical advantage and we attach that on to our main line so no matter what we recognize that this is just a one-to-one so this isn't adding any kind of a mechanical advantage to us whatsoever so when we add our in this case three to one mechanical advantage on two that will go through but realize you can put a four to one five to one you see a lot of different systems for confined space or for simple mountain whole kits so start with our hollow line that's one one tension comes in one tension comes out that two is sitting on that prusik one comes in one comes out we have two on our anchor right here is that one comes down it meets with the two and then we have three so because this adds nothing to it this is not a mechanical mechanical advantage this is simply pulling on a mainline we just simply have a three to one if this was a four to one coming down we're just going to have a four to one or a five to one depending on what you have we just have to remember as we're pulling that we're going to get slack in this whole area whatever is beyond where rope grab is we're going to get slack so before we can actually reset our piggyback system we have to take the slack out of this by pulling that through having a capture into a progressive capture here and then this will be holding our load where we can actually reset this for efficiency so that is the end of counting tensions part one what we're going to do is build on that for our second podcast or video cast and show how we can use that same technique of moving our way through our system but this time we're going to actually be looking at what the actual efficiencies are of various pulleys and various devices that we may be use in our system thanks

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Length: 21min 30sec (1290 seconds)

Published: Tue Apr 04 2017