How to Calculate the Mechanical Advantage of Hauling Systems

1. How to Calculate the Mechanical Advantage of Hauling Systems By Tim Fox & Mick Holton

2. There are three types of hauling systems… • Simple • Compound • Complex

3. Simple Hauling Systems A simple hauling system is when all moving pulleys are attached to the load.

4. Compound Hauling Systems A compound hauling system is a simple hauling system that is pulling on the end of another simple hauling system.

5. Complex Hauling Systems A complex hauling system is created when you have a moving pulley that is travelling in the opposite direction to the load.

6. There are two methods that can be used to calculate mechanical advantage. • “Counting the Lines” & • “Adding the Tensions”

7. Counting the Lines Method Simple Hauling Systems To calculate the mechanical advantage of a simple hauling system all you have to do is: Starting at the hauling line, count the number lines that are attached directly to the load or attached to the pulley that is attached to the load.This will tell you the mechanical advantage of the system.

8. Here is a simple hauling system example Cover the top half of the hauling system and count the number of lines attached to the load pulley. 2 1 In the example there are two lines therefore the mechanical advantage is 2:1

9. This simple hauling system is different In this example the hauling line goes through a pulley at the anchor end of the system. 2 1 If you cover the top section of the hauling system you can see that only two lines are attached directly to the load pulley. The mechanical advantage of this system is still 2:1

10. Compound or Multiplying Systems The system below the red line is a 2:1, count the lines to check for yourself We can use the “Counting the Lines” method to calculate the mechanical advantage of compound systems. Draw a line at the point of attachment of the prussic loop. The M.A. of these two systems is then calculated as follows: The system above the red line is a 3:1 3:1 x 2:1 = 6:1

11. Adding the Tensions Method In simple terms if there is a 100kg load on one side of a pulley… 200kg 100kg 100kg … there must be a 100kg load on the other side of the pulley… … and there must be a 200kg load on the end of the pulley. This principle applies to pulleys that move with the load and fixed pulleys. 100kg 100kg 200kg

12. 1 1 Adding the Tensions Method on a simple hauling system Lets look at the amount of tension on each part of the hauling system. If we apply one unit of tension to the hauling line… …there will be one unit of tension on all three lines… 1 … There are three lines attached to the load pulley, therefore there are three units of tension on the load… 3 The mechanical advantage is 3:1

13. 1 1 Adding the Tensions Method 2 This method also makes it easy for you to calculate the load being applied to anchor systems 1 Because there are two lines attached to the anchor pulley there are two units of tension on the anchor 3

14. Adding the Tensions Method on a compound hauling system Using the “Adding the Tensions” method to calculate the mechanical advantage of a compound system you look at the amount of tension you are applying to the hauling line… … BUT YOU STOP WHEN YOU REACH A PRUSSIC KNOT…

15. Adding the Tensions Method If we apply one unit of tension to the hauling line… 1 1 …there is one unit of tension here… 1 …and one unit of tension here… This rule continues until we reach the prussic knot

16. Adding the Tensions Method There is one unit of tension on either side of the pulley attached to the prussic loop, therefore there must be two units of tension on the prussic loop 1 1 1 2 There is one unit of tension here and two units of tension on the prussic loop therefore there are three units of tension just below the prussic loop. 3

17. Adding the Tensions Method 1 1 There are three units of tension on this side of the pulley… 1 2 3 3 …therefore there must be three units of tension on the other side.

18. Adding the Tensions Method 1 We now “Add the Tensions” being applied to the load pulley. 1 1 2 3 + 3 = 6 3 3 We started by applying a force of 1 to the hauling line and ended up with a force of 6 at the load pulley, therefore the mechanical advantage is 6:1. 6

19. Adding the Tensions Method on a complex hauling system You cannot use the “Counting the Lines” method to calculate the M.A. of a complex system, but its easy using the “Adding the Tensions” method… 2 Step 1. Begin with the single tension on the haul line then 1 unit of tension on each fall of rope until the prussic knot is reached. 1 1 1 2 Step 2. Work out the tensions at both of the prussic loops. 1 + 1 = 2

20. Adding the Tensions Method Step 3. Calculate the tension above the first prussic knot by adding 2 + 1 = 3. If there is 3 on one side of the pulley there must be 3 on the other side. 3 2 3 1 1 1 5 Step 4. Calculate the tension below the second prussic knot by adding 3 + 2 = 5. If there is 5 on one side of the pulley there must be 5 on the other side. 2 5

21. Adding the Tensions Method 3 2 Step 5. We now “add the tensions” being applied to the load pulley. 5 + 5 = 10. 3 1 1 1 5 2 5 The mechanical advantage is 10:1 10

22. Adding the Tensions Method Have a go at this example… Because all three units are attached to the pulley you add them all together and the answer is 3 The Mechanical Advantage is 3:1 1 1 1 3

23. Adding the Tensions Method Here is an example with a double pulley at the load… 1 1 1 We didn’t have any prussic knots so each fall of rope throughout the whole system has a single unit of tension. All four units are attached to the pulley so we simply add them all together and the answer is 4 The Mechanical Advantage is 4:1 1 4

24. The Difference Between Advantage & Disadvantage A hauling system is reeved to disadvantage when the hauling line is going through a pulley that does not add to the mechanical advantage of the system, it only adds friction. A 2:1 reeved to advantage A 2:1 reeved to disadvantage This is usually the last pulley in the system and is referred to as a redirection pulley.

25. The term disadvantage only means there is extra friction in the system to achieve the mechanical advantage of the system you have built. Don’t be put off using redirectional pulleys; the term reeved to “disadvantage” is a technical term only. You can use redirectional pulleys whenever they will make the job of the hauling party easier. There can be advantages to reeving a system to disadvantage.

26. The End