Sankey Diagrams: Visualizing the Flow of Energy
The Core Idea: Width Equals Quantity
Imagine you are watching a river. The main channel is wide, but it splits into several smaller streams. You can instantly tell which stream carries the most water just by looking at its width. A Sankey diagram works on exactly the same principle. It is a type of flow diagram where the arrows, or "branches," have a width that is directly proportional to the amount of whatever is flowing—be it energy, water, money, or even website visitors.
The most famous and foundational use of Sankey diagrams is in tracking energy. They help us answer critical questions: How much useful energy do we get from a power plant? Where does the rest of the energy go? The diagram makes the answers visually obvious. A thick arrow represents a large flow of energy, while a thin arrow represents a small one. This simple rule allows you to grasp complex data at a glance.
Building Blocks of a Sankey Diagram
To read or create a Sankey diagram, you need to understand its basic components. Every diagram is built from a few key parts that work together to tell a story about flow.
Nodes: These are the starting, ending, and branching points. Think of them as boxes or points that represent a stage in the process. For example, a node could be "Coal," "Power Plant," or "Home Appliance."
Flows: These are the arrows themselves. They connect the nodes and show the direction of the transfer. The most important feature is their width, which is scaled according to the flow rate or amount.
Labels: Each flow and node is typically labeled with a name and a value (e.g., "Electricity to Homes, 35 Joules"). This adds precise numerical information to the visual story.
A crucial scientific principle behind these diagrams, especially for energy, is the Law of Conservation of Energy[1]. This law states that energy cannot be created or destroyed, only transferred or transformed. In a perfect Sankey diagram, the total width of all arrows going into a node must equal the total width of all arrows leaving it. The "missing" energy that doesn't go to a useful output is often shown as "Waste Heat" or "Losses," reminding us that energy is conserved even when it's not useful.
A Simple Example: The Incandescent Light Bulb
Let's look at a classic example: an old-fashioned incandescent light bulb. When you turn it on, electrical energy flows in. What happens to it? A Sankey diagram makes this clear.
Imagine 100 Joules of electrical energy enters the bulb. The diagram would show a thick arrow labeled "Electrical Input (100 J)" going into the "Light Bulb" node. From this node, two main arrows emerge:
- A very thin arrow (about 5 J) pointing towards "Light Energy." This is the useful output we want.
- A very thick arrow (about 95 J) pointing towards "Waste Heat."
This visual immediately tells you that an incandescent bulb is highly inefficient. Most of the energy you pay for is wasted as heat, not light! We can calculate efficiency using a simple formula:
$Efficiency = (Useful Output Energy / Total Input Energy) * 100$
For the bulb: $Efficiency = (5 J / 100 J) * 100 = 5\%$
The diagram makes this low efficiency visually undeniable.
A More Complex System: A Car's Engine
Now, let's scale up to a more complicated system: a car engine. The energy flow here has more steps and more types of losses. A Sankey diagram for a typical gasoline-powered car might look like this:
A very thick arrow represents 100% of the energy from the gasoline entering the engine. This flow then splits into several branches:
- Useful Kinetic Energy: A moderately thick arrow (about 25%) that goes to actually moving the car.
- Heat Loss to Coolant and Exhaust: This is the thickest branch (about 70%), showing that most of the fuel's energy is wasted as heat.
- Friction Losses: A thinner arrow (about 5%) representing energy lost to overcoming friction in the engine's moving parts.
The "Useful Kinetic Energy" branch might then split further to show losses due to air resistance and tire rolling resistance before a final, small amount of energy is left for accelerating the car. This layered breakdown helps engineers identify the biggest areas for improvement, such as reducing heat loss or friction.
| Device/System | Total Input Energy | Useful Output Energy | Efficiency |
|---|---|---|---|
| Incandescent Bulb | 100 J | 5 J (Light) | 5% |
| LED Bulb | 100 J | 40 J (Light) | 40% |
| Gasoline Car Engine | 100 J | 25 J (Motion) | 25% |
| Electric Motor | 100 J | 90 J (Motion) | 90% |
Applying Sankey Diagrams to a National Energy Grid
One of the most powerful applications of Sankey diagrams is visualizing the energy flow of an entire country. These diagrams can show all the energy sources (like coal, natural gas, solar, and wind), how they are converted into usable forms (mainly electricity), and how that energy is finally consumed by different sectors (like residential, industrial, and transportation).
For instance, a national Sankey diagram might start with a wide bundle of arrows on the left representing total energy resources. You would see a thick arrow for "Petroleum," another for "Natural Gas," and thinner ones for "Renewables." These flows go to "Electricity Generation" or "Direct Use." The "Electricity Generation" node would have a huge "Rejected Energy" (waste heat) arrow leaving it, often larger than the "Electricity" arrow itself, showing the inefficiency of thermal power plants. The electricity arrow then fans out to the various sectors that use it. Analyzing such a diagram helps policymakers understand energy dependence, identify waste, and plan for a more sustainable future.
Creating Your Own Simple Sankey Diagram
You can create a basic Sankey diagram for any process. Let's map the energy flow for a person riding a bicycle.
- Define the Input: The input is chemical energy from food. Let's say this is 1000 Joules.
- Identify the Outputs:
- Useful Output: Kinetic energy that moves the bicycle forward.
- Energy Losses: Waste heat from your body, sound, and friction in the bicycle chain and tires.
- Estimate the Values: A human body is inefficient. Only about 25% of the food energy becomes useful kinetic energy. The rest (75%) is waste heat.
- Useful Kinetic Energy: 250 J
- Waste Heat: 750 J
- Draw the Diagram: Draw a thick arrow from "Food Energy (1000 J)" to a "Human Body" node. From this node, draw one arrow that is one-quarter the width of the input arrow and label it "Kinetic Energy (250 J)." Draw a second arrow that is three-quarters the width of the input and label it "Waste Heat (750 J)."
You have now created a Sankey diagram that clearly shows the inefficiency of human metabolism during exercise!
Common Mistakes and Important Questions
Q: Can the width of an arrow in a Sankey diagram change along its length?
No. The width of a single arrow must remain constant. It represents a specific, constant flow quantity. If the flow splits or is lost, you show this by creating new, thinner arrows, not by making the original arrow get narrower.
Q: Are Sankey diagrams only used for energy?
Not at all! While they are perfect for energy, their use is much broader. You can use them to show the flow of materials in a recycling plant, the flow of money in a budget, the flow of water in a city's supply network, or even the flow of people through a website. Any process involving the transfer of a measurable quantity can be visualized with a Sankey diagram.
Q: What is the most common error when first interpreting these diagrams?
The most common error is forgetting that the diagram must obey conservation laws. People sometimes overlook small loss arrows. Always check that the sum of all inputs equals the sum of all outputs for the entire system and at each major node. If it doesn't, the diagram is incorrect or incomplete.
Footnote
[1] Law of Conservation of Energy: A fundamental law of physics which states that the total energy in an isolated system remains constant; it is said to be conserved over time. Energy can neither be created nor destroyed; rather, it transforms from one form to another.