Where the Rest of the Energy Goes — Reading a Sankey
An electric winch is fed a steady 2500 W, whatever you do to it. One slider sets its efficiency, and the Sankey diagram beside it redraws live: one arrow in, two arrows out, every width in true proportion to the energy it carries. Squeeze the useful branch and the rest has nowhere to go but out of the motor casing as heat — and the same 250 kg load takes longer to reach the top on the same electricity.
Como usar esta simulação
- Efficiency of the winch — the single slider, 20% to 95%, with 70% and 85% marked on the track, two efficiencies worth comparing.
- Drag anywhere on the scene to walk round the winch and read the Sankey square on.
O que observar
- Useful + wasted always adds back to 2500 W. That is the whole trick to reading a Sankey.
- The useful energy is stuck at 14.7 kJ — mgh for 250 kg through 6.0 m — no matter where you put the slider. What a poor efficiency changes is the electricity you had to buy to get it.
- Halve the efficiency and the lift takes twice as long on twice the electricity, for exactly the same result at the top.
- The motor casing glows redder and the heat haze above it thickens as the waste branch widens: the wasted energy is not lost, it is in the room.
A física por trás
Efficiency is the fraction of the input that leaves as useful output, η = useful output energy ÷ total input energy. It is a pure number with no unit, quoted as a decimal or a percentage, and no real device ever reaches 1. The rule that makes a Sankey diagram useful is conservation: the input equals the sum of everything leaving, so a missing output can always be found by subtracting the known ones from the total. Here the cable force is mg = 2450 N, so the useful power sets the speed, v = P_useful / 2450. At 73.5% the winch turns 2500 W into 1837.5 W of lifting, the load rises at 0.75 m/s, the 6.0 m lift takes 8.0 s, and 20.0 kJ of electricity has bought 14.7 kJ of lifting with 5.3 kJ dissipated — mostly as thermal energy in the windings.