IB Physics SLTopic A.3 — Work, Energy & PowerPaper 1 & 2Energy Flow (Sankey) Diagrams~7 min read
Energy Flow (Sankey) Diagrams
An energy flow diagram — usually called a Sankey diagram — turns conservation of energy into a picture. Instead of writing out “total in = useful out + wasted,” you draw it, with the width of every arrow standing in for an amount of energy.
📘 What you need to know
A Sankey diagram is a to-scale picture of an energy transfer — arrow width represents the size of the energy flow
The branch continuing in the original direction shows the useful energy output
Any branch that splits off, usually drawn downward, shows wasted energy
Because energy is conserved, the input arrow’s width always equals the combined width of every branch leaving it
Comparing two devices’ diagrams side by side instantly shows which one wastes less energy
Why Bother Drawing Energy as Arrows?
Numbers on their own can be hard to compare at a glance. A Sankey diagram fixes that by making the size of the arrow do the talking — a wide branch carries a lot of energy, a thin one carries very little. You can read off roughly how efficient a device is just by eyeballing how much of the diagram bends away from the main flow.
The Three Rules
Arrow width is proportional to energy — double the energy, double the width
The arrow pointing onward in the same direction as the input is the useful output
Arrows that branch off (typically drawn heading down) represent energy wasted to the surroundings
Same energy input, very different diagrams — the LED bulb’s slim wasted-heat arrow shows it converts far more of its input into useful light
Comparing Devices With Energy Flow Diagrams
Two devices can take in exactly the same amount of energy and still look completely different on a Sankey diagram. The device with the narrower wasted-energy branch is the more efficient one, since a bigger share of its input arrow survives all the way to the useful-output branch.
This is exactly why an LED bulb and an old-style filament bulb look so different when drawn this way: both might take in the same 60 J, but the LED sends most of that straight through as light, while the filament bulb loses the majority of it as heat before it ever becomes light.
The rule behind every diagram
Total energy in = Useful energy out + Wasted energy
Drawing Your Own Energy Flow Diagram
🧭 Recipe: Building a Sankey Diagram From Scratch
Plan the widths first — work out how wide the input arrow, useful-output arrow, and wasted-energy arrow each need to be before you draw anything
Draw the input — start with the left-hand edge of the main arrow and the line running along its top
Add the useful arrow — continue the flow in the same direction, at its correct (usually reduced) width
Mark the wasted branch — carefully place the start and end points for the wasted-energy arrow so the gap between them matches its width
Join it up — connect the markings to complete the wasted-energy arrow, usually angled or bent downward
Quick recap: Arrow width = amount of energy. Straight-through arrow = useful. Branching arrow = wasted. The input arrow’s width always equals the combined width of everything leaving it.
WE 1
A winch motor is used to lift a crate. Its energy flow diagram shows 640 J of input energy, with an arrow labelled “energy transferred to the crate” carrying 410 J. Determine the wasted energy.
Step 1 — State conservation of energy
Total energy in = Useful energy out + Wasted energy
Step 2 — Rearrange for wasted energy
Wasted energy = Total energy in − Useful energy out
Step 3 — Substitute the diagram’s valuesWasted energy = 640 − 410= 230 J
WE 2
An electric scooter’s motor draws 150 W. Its power flow diagram shows a useful output of 60 W, gearbox friction losses of 40 W, and motor-heating losses of 35 W, with a fourth, unlabelled branch for the remaining losses. Determine the size of that remaining branch.
Step 1 — State conservation of energy for power
Total power in = Useful power out + Friction losses + Heating losses + Remaining losses
Step 2 — Rearrange for the remaining losses
Remaining losses = Total power in − (Useful power out + Friction losses + Heating losses)
Step 3 — SubstituteRemaining losses = 150 − (60 + 40 + 35)= 15 W
💡 Top tips
Plan the widths of every arrow before you start drawing — it’s much harder to fix proportions after the fact
Use the input arrow’s width as your reference scale, then work out every other arrow as a fraction of it
When comparing two devices, look at the wasted branch first — it tells you the efficiency story faster than the useful branch does
Double-check your arrows sum correctly: useful + wasted should always rebuild the total input
⚠ Common mistakes
Drawing arrows freehand without checking their widths are actually proportional to the energy values
Forgetting that a diagram can have more than one wasted-energy branch — not every device has just one loss pathway
Mixing up energy diagrams (measured in joules) with power diagrams (measured in watts) — the arithmetic is identical, but the units aren’t interchangeable
Assuming the useful arrow is always drawn on top — check the labels rather than the position
Up next: Work Done — where we turn today’s energy language into the W = Fs equation you’ll use in almost every calculation from here on.
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