# Compound Machines Efficiency

on . Posted in Dimensionless Numbers

Compound machines efficiency, abbreviated as $$n_{comp}$$, a dimensionless number, are mechanical systems that consist of two or more simple machines working together to perform a specific task.  Simple machines are basic mechanical devices that amplify or change the direction of force, making tasks easier to accomplish.  Compound machines combine the effects of these simple machines to achieve more complex tasks.

The efficiency of a compound machine refers to the ratio of the useful output work done by the machine to the input work supplied to the machine.  In other words, it measures how effectively the compound machine converts the input energy into useful output energy.  It's important to note that no machine can be 100% efficient due to factors such as friction, mechanical losses, and other inefficiencies inherent in the system.  Some energy will always be lost in the form of heat or other non-useful forms.

When dealing with compound machines, the efficiency calculation takes into account the combined effects of the individual simple machines within the compound system.  The efficiency of each individual simple machine can also be a factor in the overall efficiency of the compound machine.

Calculating the efficiency of a compound machine is essential for engineers and designers to evaluate the performance of the system and make improvements to increase efficiency where possible.  It's also useful for comparing different machine designs and selecting the most suitable one for a particular application.

## Compound machines efficiency formula

$$\large{ n_{comp} = n_1 \; n_2 ... }$$
Symbol English Metric
$$\large{ n_{comp} }$$ = compound machines efficiency $$\large{dimensionless}$$
$$\large{ n_1 }$$ = efficiency of the first machine $$\large{dimensionless}$$
$$\large{ n_2 }$$ = efficiency of the second machine $$\large{dimensionless}$$

## efficiency of a Compound machine formula

$$\large{ n = \frac{ W_o }{ W_i } }$$
Symbol English Metric
$$\large{ n }$$ = efficiency of a compound machines $$\large{dimensionless}$$
$$\large{ W_o }$$ = useful output work $$\large{lbf-ft}$$ $$\large{J}$$
$$\large{ W_i }$$ = input work $$\large{lbf-ft}$$ $$\large{J}$$