# Compressed Air System Efficiency

When I run engines on compressed air I often wonder about the efficiency. A large electric motor driving a piston compressor that is in turn supplying a small engine that is sometimes barely able to overcome friction, sometimes quite powerful. So what is the end to end efficiency?

So, I googled “Compressed Air System Efficiency” and found an interesting paper on the subject. We see from Wulfinghoff that the efficiency is around 12.5% for air tools.

Compressed air is an inefficient power source. It takes about 8kW of compressor input power to provide 1kW of power at an air tool.

Wulfinghoff Energy Services Inc.

#### Block Diagram

When looking at energy transmission of any kind it is good to look at the block diagram. Here is my first attempt:

From a mechanical input to an air compressor and then to an air motor and out to a mechanical output. For the mechanical input and output I’m thinking of a rotating shaft at a given rpm and torque, hence power input/output.

#### Air Compressor

For a piston compressor with up to three stages of compression the mechanical power required to drive it can be calculated using the following formula:

HP = (144 N P1 V k / 33000 (k-1)) ((P2 / P1)(k-1)/Nk – 1)

where:

• HP = horsepower
• N = number of compression stages
• k = 1.41 = adiabatic expansion coefficient
• P1 = absolute initial atmospheric pressure [psi]
• P2 = absolute final pressure after compression [psi]
• V = volume of air at atmospheric pressure [cfm]

#### Air Motors

If we then look at air motors that are commercially available we can see from the specification the output torque and speed for a given input air pressure and volume flow rate.

We can then simply calculate the input power to an air compressor that matches the air motor input requirements.

The overall efficiencies of the compressor and air motor system ranges between 12.4 and 34.3% depending on type of motor. However this is a simple approximation for the compressor and there will be other losses in the pipes and valves that need to be accounted for.

This gives us a good idea for the overall system efficiency, but it misses the energy storage part. This is very simple, but still useful to go back to the simple block diagram:

The major difference that I see in adding the compressed air storage block is that we now have a cooling of the gas after it has been compressed. This will be a significant pathway for energy out of the system. Simply we can look at the equation PV/T = constant. Heating the air in the compressor and then cooling it in the air storage tank means it will drop in pressure. This is a significant issue and in large Compressed Air Energy Storage systems they have a dedicated heat recovery system.

#### Conclusion

Piston displacement air motors can be significantly more efficient off the shelf than vane motors.

An efficiency of around 12.5% is not a bad first general approximation for the overall system efficiency.

An efficiency of 34% is achievable for a compressed air system, but for simple model engines this is likely to be less than this and I would suggest 12.5% as a starting number is reasonable and aligns with the first reference that I found.

#### References

1. “Compressed Air System Efficiency”, Wulfinghoff Energy Services, Inc.
2. Huco Air Motors – small metal and plastic air motors