Mechanical advantage

Working with sheaves? This page can help you understand mechanical advantage, including how to calculate the hook block and the load in the lead line to the winch.

Mechanical Advantage

Large capacity cranes have several parts of rope to the main hoist, making the main hook move slowly. Reducing the number of parts gives a faster hook speed. However, it's important to make sure that the falls are not reduced from only one side of the boom head sheaves and the main hoist block. The wire rope must be evenly distributed across the sheaves to ensure safe operation of the hook block.

Mechanical advantage - using parts of line to achieve more with the same effort.

A wire rope reeved through sheaves to create a mechanical advantage was historically known as a 'purchase'.

Self-lubricating sheaves are recommended. If reservoirs are used they should be filled regularly.

How to work out the load in a single part of a purchase (mechanical advantage)

Friction

The greatest load on any rope in a purchase is the load in the lead rope to the winch. This is because of the friction between the rope in the groove of the sheave and the sheave pin.

Friction is between around 3% and 5% per sheave. (I.e. up to one twentieth of the rope load that would occur if there was no friction).

Effects that are usually not included when dealing with reeving wire rope are:

• friction
• acceleration
• deceleration.

This is unless a number of falls are used or the rope velocity is high.

Calculating the hook block load capacity

When a load is at rest suspended from the lower block, the hook block load (the load in each part of the rope purchase) is found as follows:

Hook block load = total load on lower block divided by the number of parts of rope supporting load.

Note: The total load on the lower block includes the load to be lifted plus associated rigging equipment including:

• packings
• slings
• shackles
• blocks.

Here's an example including frictional effects:

Total load on the lower block = 10t including gear

Number of parts of rope = 5 supporting the moving block Becket load (BL). So:

10t ÷ 5 = 2t

But as lifting starts, friction causes the load in the rope falls to increase by up to 5% for each sheave the rope passes over, including lead sheaves (if any).

Calculating the load in the lead to the winch

Here's how to calculate the load in the lead to the winch (given 5% friction):

Load in lead to winch (LL) = HB divide (HB x number of sheaves x 0.05)

= HB + (HB x number of sheaves x 5 divide 100)

Here's how to calculate the maximum load that can be lifted for a given load in the lead:

Load = LL x no. of parts supporting load 1 + (number of sheaves x friction)

Example 1:

Number of sheave in purchase = 5 (3 top block + 2 bottom block)

Number of parts of rope = 5 supporting lower block

Number of lead blocks = 2 (7 sheaves in total)

Total load on lower block = 10t

Hook block load = 10 divided 2 = 2t

Load in lead rope to winch = 2 + (2 x 7 + 20)

= 2.7t

Example 2:

Calculate maximum load for the above arrangement using a winch with a 2.7t line pull

Load = 2.7 x 5
1 + (7 x 0.05)
13.5
1.35
= 10t

The calculations above do not allow for:

• sudden impact (shock loading)
• acceleration
• deceleration which can cause very high loads in the rope.