Energy efficiency calculations and improvements

Principles of energy • Conservation and dissipation of energy

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What is the effect of operating speed on frictional losses?

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Higher operating speeds typically increase frictional and aerodynamic losses, which raises unwanted dissipation and lowers efficiency.

Key concepts

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Definition and equations for efficiency

Efficiency expresses the useful fraction of energy input, calculated by efficiency = useful output energy transfer / total input energy transfer. The same ratio applies to power: efficiency = useful power output / total power input. The result is dimensionless and often converted to a percentage by multiplying by 100. Correct units must match in numerator and denominator to obtain a valid ratio, for example both energies in joules or both powers in watts .

Interpreting efficiency values and limiting factors

An efficiency of 1 (or 100%) indicates all input energy becomes useful output; real systems never reach 100% because some energy always dissipates to less useful stores such as thermal energy, sound or vibrations. Limiting factors include friction, electrical resistance, air resistance, heat losses through conduction and imperfect energy conversion processes. Device geometry, material properties and operating speed influence the amount of dissipation .

Calculations from energy and from power

Energy-based calculations use energy transfers (in joules): efficiency = useful energy output / total energy input. Power-based calculations use rates of transfer (in watts): efficiency = useful power output / total power input. Both methods yield the same dimensionless efficiency when applied consistently. Examples include comparing electrical energy supplied to a motor with gravitational potential energy gained by a lifted mass, or comparing electrical input power to useful mechanical output power during steady operation fileciteturn0file9.

Ways to increase efficiency

Efficiency increases when energy losses to unwanted stores are reduced. Common measures include reducing friction with bearings or lubrication, streamlining to reduce air resistance, insulating components to reduce heat loss, improving electrical connections to reduce resistive heating, and selecting materials with lower thermal conductivity where heat retention is required. Machines can improve useful output by changing the path or magnitude of forces so that less work is wasted against resistive forces fileciteturn0file7.

Practical constraints and trade-offs

Measures that raise efficiency often introduce trade-offs: thicker insulation reduces heat loss but increases cost and weight; streamlining reduces drag but can complicate manufacturing; adding bearings or lubrication reduces friction but requires maintenance. Real-world optimisation balances increased useful output, cost, safety and durability. Efficiency improvements must consider the whole system, because reducing one loss can shift dissipation elsewhere or change operating conditions .

Key notes

Important points to keep in mind

Always use the same units for useful output and total input before forming the efficiency ratio.

Express efficiency as a decimal between 0 and 1 or as a percentage by multiplying by 100.

Identify the useful output clearly (electrical, mechanical, thermal) before calculating efficiency.

Reduce dissipation by lowering friction, improving lubrication and using bearings.

Minimise heat loss with insulation and minimise air resistance with streamlining.

Consider whole-system effects and trade-offs when proposing changes to increase efficiency.

In power calculations use steady-state power input and useful power output for accurate efficiency values.

Practical measurements often include electrical input energy (joulemeter or V × I × t) and mechanical output (mgh for lifts).