Velocity Ratio – definition, formula, and values

The Velocity Ratio of a machine and the Velocity Ratio Formula are the topics of this physics article. Also, we will see how the value of the Velocity Ratio varies in the case of speed multiplier machines and Force multiplier machines.

Velocity Ratio | Definition of Velocity Ratio

The velocity ratio of a machine is defined as the ratio of the velocity of the effort to the velocity of the load. In other words, it is the ratio of the displacement of the effort to the displacement of the load. For an ideal machine, the velocity ratio value equals the mechanical advantage of the machine.

Velocity Ratio is a term related to a machine that gives an idea of whether the machine will make a speed gain, or it will make a force multiplication, or the machine will just have a direction change of the effort.

Velocity Ratio lets us know if the displacement of load is equal to or more or less than the displacement of effort.

Velocity Ratio Formula

The velocity Ratio Formula is represented by 2 equations listed below.
1) Velocity Ratio = velocity of the effort / the velocity of the load = VE  / VL …… (1)
2) Velocity Ratio = displacement of the effort / displacement of the load = dE  / dL …….. (2)

Deriving the Velocity Ratio formula as displacement ratio

We will start with the equation of the Velocity Ratio as the ratio of 2 velocities, as per its definition.
Velocity Ratio = velocity of the effort / velocity of the load = VE  / VL

Now, if the effort makes a displacement dE in time t, then the velocity of effort VE = dE/t
similarly, if the load makes a displacement dL in time t, then the velocity of load VL = dL/t

Hence, Velocity Ratio = VE  / VL = (dE/t) / (dL/t) =dE  / dL

This is how we can prove that the Velocity Ratio is represented by another displacement ratio formula which is like this:
Velocity Ratio = dE  / dL = ratio of the displacement of the effort to the displacement of the load.

Velocity Ratio value

Let’s see how the Velocity Ratio value differs in cases of Speed multiplier machines and Force Multiplier machines.

The Velocity Ratio value of Speed multiplier machines | Speed Gain in machines

When the Velocity Ratio < 1, then the machines act as Speed Multipliers. In other words, the velocity ratio of the speed multiplier machines is less than one.

When the Velocity Ratio value of a machine is less than 1 then we can say that machine provides a speed gain. From equation 1 above you can say that in this case, the velocity of the load is more than the velocity of the effort.

And as per equation 2 above you can also say that the displacement of load > displacement of effort. This refers to speed gain. Think about the pair of blades of scissors as an example.

When Velocity Ratio<1 for ideal machines, then MA is also <1. So these machines are not ‘force multipliers’. As these machines provide speed gain as said above, these are also known as speed multipliers.

Examples: All levers of class 3 ( Tong, spade used for lifting a load), Scissors with long blades (it’s a class I lever with load arm longer than its effort arm)

The Velocity Ratio value of Force Multiplier machines | Force multiplication in machines

When the Velocity Ratio > 1, then the machines act as Force Multipliers. In other words, the velocity ratio of the force multiplier machines is more than one.

When the Velocity Ratio value of a machine is more than 1 then we can say that machine provides a force multiplication. From equation 1 above you can say that in this case, the velocity of the effort is more than the velocity of the load.

And as per equation 2 above you can also say that the displacement of effort > displacement of the load.

For an ideal machine with the Velocity Ratio > 1, we can say the mechanical advantage (MA) of it is also more than 1. Obviously, it indicates a force multiplication. (as the load is greater than effort when MA >1). These machines whose MA > 1 are called force multipliers.

Examples: all levers of class 2 (ex. nutcracker, wheelbarrow, bar to lift load), some class 1 levers (crowbar, pliers)

Related readings:

Types of levers

MA of levers


Velocity Ratio – definition, formula, and values
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