Sankey Diagram Physics: Visualising Energy Flows and the Physics Behind Them

In teaching, designing, and analysing physical systems, the Sankey diagram offers a powerful visual language. This article explores sankey diagram physics in depth, explaining how these diagrams capture conservation laws, energy quality, and real-world losses. By combining clarity with rigour, sankey diagram physics becomes a practical tool for engineers, scientists, and students alike, helping to diagnose inefficiencies, compare options, and communicate complex flows with elegance.

The essence of sankey diagram physics: a quick primer

At its core, a Sankey diagram (capitalised as Sankey Diagram when used as a formal term) represents flows where the width of each arrow is proportional to the amount of material or energy moving along that path. The visual weight encodes magnitude, while the geometry reflects connectivity. In physics terms, a Sankey diagram is a map of conserved quantities through a system boundary: inputs enter, outputs leave, and losses siphon away through various channels. This mirrors fundamental principles such as the conservation of energy and mass, along with the irreversibilities that create real-world dissipation.

Physics principles embodied by Sankey Diagrams

Conservation laws as the backbone

One of the most important elements of sankey diagram physics is the strict accounting of what enters and leaves a system. In a closed or open system, the total inflow must equal the total outflow plus any accumulation. For energy, this is the first law of thermodynamics: energy cannot be created or destroyed, only transformed. Sankey diagrams visualise these transformations: input energy is diverted into useful work, heat, sound, or stored in reserves. The widths adjust to the quantity of energy, while the flow directions reflect transformation pathways.

Energy quality and irreversibility

Sankey diagram physics also invites attention to energy quality. Not all energy flows maintain their usefulness. In many systems, high-quality energy (like mechanical work or electricity) is degraded to lower-quality forms (heat at ambient temperature, wasted heat, or frictional losses). In the diagram, these degradations are shown as broader paths for losses, emphasising how much energy is irreversibly dispersed. This is not just bookkeeping; it is a visual representation of thermodynamic irreversibility and entropy production within the process.

Mass balance and continuity

Where material flows are relevant, such as fluid networks or chemical processes, the sankey diagram philosophy mirrors mass conservation. The sum of inflows to a node must equal the sum of outflows, accounting for accumulation if the diagram captures a dynamic moment in time. This aligns with the continuity equation in fluid dynamics, which ensures that what goes in must, subject to accumulation, come out. The diagram therefore becomes a compact summary of the mass or energy balance of a system.

Analogies with circuit theory

There is a fruitful analogy between sankey diagram physics and electrical circuits. Flows in a Sankey diagram can be interpreted as currents, while the widths correspond to magnitudes akin to electrical power or charge flow. Just as Kirchhoff’s laws govern currents and voltages in circuits, Sankey diagrams enforce a form of “Kirchhoff-like” accounting for energy through nodes. This makes Sankey diagrams particularly useful in teaching energy systems in electrical engineering and physics departments, where students can link circuit intuition with energy accounting.

When to use sankey diagram physics in practice

Engineering design and optimisation

Engineers use sankey diagram physics to compare design options, identify bottlenecks, and quantify potential gains. Whether evaluating a power plant, a manufacturing line, or a renewable energy system, Sankey diagrams reveal where the largest losses occur and how redesigns might redirect flows to improve overall efficiency. The visual emphasis on major paths helps decision-makers grasp trade-offs quickly, without getting lost in numerical minutiae.

Energy budgets in buildings and environments

In building physics and environmental sciences, Sankey diagrams illustrate how energy is produced, consumed, and lost. They help quantify heating and cooling demand, lighting and appliance use, and renewable generation. By presenting a clear energy budget, they support strategies for reducing peak loads, improving insulation, and shifting usage patterns to match available resources.

Education and outreach

For students and the general public, sankey diagram physics offers an intuitive entry point to topics such as thermodynamics, energy systems, and sustainability. A well-designed diagram can convey complex ideas at a glance—where energy goes, how much is wasted, and why efficiency matters—without requiring advanced mathematics.

Constructing a robust sankey diagram: a practical guide

Defining the system boundary

A precise system boundary is essential. In sankey diagram physics, the boundary defines what is considered input, what is treated as output, and where losses are allocated. A poorly chosen boundary can obscure critical pathways or inflate the apparent efficiency. Always document the scope: what is included, what is excluded, and why.

Identifying flows and units

List every significant input, output, and loss. Choose consistent units and ensure that the units are meaningful across the diagram. For energy diagrams, common units are joules or kilowatt-hours; for material flows, kilograms or tonnes. Consistency ensures that the widths of arrows add up to the total input and equal total outputs plus losses.

Determining the scale and visual balance

The width of each arrow should be proportional to the magnitude it represents. The scaling factor must be chosen so that the most important flows are visually prominent, while minor channels remain legible. A readable diagram often uses a limited set of thickness tiers and a clear colour scheme to distinguish between categories of flow, such as useful energy versus losses.

Colour, legend, and readability

Use colour to differentiate classes of flow (e.g., electrical, thermal, mechanical) and to highlight successful pathways or critical losses. A concise legend is essential, especially in complex diagrams with many branches. For public-facing materials, simplicity and clarity trump exhaustive detail.

Dynamic vs static diagrams

Static Sankey diagrams capture a snapshot of a system at a given moment. If the system varies with time, dynamic Sankey diagrams or stacked diagrams can illustrate how flows evolve, revealing trends and transient behaviours. In physics teaching, dynamic diagrams can demonstrate how energy transitions occur during startup, load changes, or failure events.

Common forms of sankey diagrams in physics contexts

Energy budgets for power generation and use

From wind turbines and solar farms to coal-fired plants, sinkable energy enters as fuel or resource, and useful output travels onward as electrical energy or mechanical work. Loss channels such as heat exhaust, friction, radiation, and parasitic consumption become evident in sankey diagram physics. The resulting visual helps engineers target the largest inefficiencies and prioritise improvements.

Thermodynamic cycles and heat engines

In a heat engine, a Sankey diagram shows the input heat from a high-temperature reservoir, the useful work produced, and the heat rejected to a low-temperature reservoir. It highlights the parasitic and irreversibility losses that limit efficiency. This is a concrete application of energy conservation and the second law of thermodynamics, presented in a format that is immediately interpretable.

Electrical grids and energy storage architectures

Electrical systems, with their complex flows of power, can be mapped in Sankey diagram physics to illustrate generation, transmission, distribution, storage, and consumption. Storage losses, conversion inefficiencies in power electronics, and standby consumption appear as distinct pathways, enabling a visual audit of grid performance and resilience.

Environmental energy budgets and climate science

In climate studies, Sankey diagrams summarise energy budgets for the Earth or for regional ecosystems. The approach helps communicate how solar radiation is absorbed, reflected, stored, or converted into heat, wind, and rainfall processes. By visualising these large-scale flows, researchers and policymakers can discuss where interventions might improve energy efficiency or reduce waste heat at the system level.

Advanced topics in sankey diagram physics

Multi-commodity and cross-domain flows

Some systems involve multiple simultaneous commodities—such as energy, water, and materials—whose flows interdepend. Multi-commodity Sankey diagrams extend the standard model by representing several kinds of flow on parallel tracks, while ensuring conservation across the network. This is particularly useful in industrial ecology and integrated resource planning, where energy, water, and material cycles intersect.

Uncertainty and sensitivity in diagrammatic representations

Real-world data carry uncertainty. In sankey diagram physics, uncertainty can be represented by shading, error bands, or multiple diagram variants reflecting optimistic, baseline, and pessimistic scenarios. This helps stakeholders understand how changes in input assumptions ripple through the diagram, reinforcing a physics-informed approach to decision-making.

Dynamic Sankey diagrams and time-resolved physics

For systems that evolve rapidly, time-resolved diagrams show how flows change, allowing the viewer to trace the evolution of energy pathways during transients. This is especially valuable in automotive engineering, aerospace, and process control, where instantaneous and cumulative effects matter for safety and performance.

Common misconceptions and how sankey diagram physics counteracts them

“All diagrams look the same”

While many diagrams share a visual language, sankey diagram physics emphasises the underlying physics: the interpretation depends on units, boundaries, and the meaning of each arrow. A diagram with thick light-blue arrows for electricity and thick orange arrows for heat communicates different physics than a diagram that uses a single colour for all flows.

“A bigger diagram means greater efficiency”

Size does not equate to efficiency. A diagram can be visually crowded yet reveal a highly efficient system if most input energy flows to useful work with minimal losses. Conversely, a simple diagram may expose major losses that dominate the energy budget. The physics lies in the proportion of useful pathways relative to total input, not in the diagram’s scale alone.

“All losses are equally important”

In sankey diagram physics, prioritising losses requires quantitative assessment. The largest loss channel may dominate the system’s performance, but small, persistent losses can accumulate over time or across many units. A rigorous diagram highlights both the magnitude and the impact of each loss channel, guiding effective mitigation strategies.

Case study: a wind-to-grid Sankey Diagram – a practical example

System overview

Consider a simplified wind energy installation feeding electricity into a regional grid. Wind kinetic energy is converted by a turbine rotor into mechanical power, which the generator then converts into electrical energy. Losses occur in aerodynamic efficiency, gearbox and generator losses, converter losses, and grid integration losses. The Sankey diagram for this system captures inputs, useful outputs, and various loss channels, clarifying where improvements would most improve overall delivered energy.

Key flows and interpretation

The wind input appears as a wide arrow entering the system. A substantial portion becomes useful electrical energy, but significant fractions are diverted to kinetic energy losses, mechanical friction, and heat. The generator and power electronics contribute additional losses, while a portion of energy may be stored or exported. The diagram makes the relative scale of these paths immediately apparent, guiding engineers to focus on blade aerodynamics, bearing design, and converter efficiency for maximum gain.

From diagram to decision-making

By comparing Sankey diagrams for different turbine designs or operating strategies, a team can rapidly assess which configuration yields the highest delivered energy with acceptable reliability. This is the strength of sankey diagram physics in practice: it translates complex thermodynamic and electromechanical interactions into a single, interpretable picture that supports evidence-based decisions.

Software options and accessibility

There are several tools useful for creating Sankey diagrams in physics contexts. Spreadsheet-based solutions with add-ins offer quick, approachable options for educators and researchers. Dedicated diagram software provides advanced features such as multi-layer layouts, dynamic data linking, and interactive capabilities. In academic settings, open-source libraries and web-based tools enable reproducible diagrams that can be shared with colleagues and students alike.

Data preparation and validation

Accurate sankey diagram physics rests on clean data. Prepare a data table that lists each flow, its source, destination, and magnitude with consistent units. Validate that the sum of all inputs equals the sum of all outputs plus losses for the chosen time frame. When presenting to non-technical audiences, consider simplifying the dataset to the most impactful flows to maintain clarity without sacrificing truthfulness.

Best practices for legibility and interpretation

Angles, curvature, and layout influence readability. Avoid overly complex diagrams with too many branches in a single row. Use a logical flow direction, typically left-to-right or top-to-bottom, and reserve distinct colours for related categories. A well-crafted sankey diagram in physics communicates both the quantitative truth and the qualitative story of the system.

Overinterpretation risks

Like any visual tool, Sankey diagrams can mislead if misused. It is essential to accompany diagrams with quantitative context, such as the data source, measurement uncertainty, and the assumptions behind boundary definitions. Transparently presenting these factors ensures that sankey diagram physics supports robust conclusions rather than cursory impressions.

Complexity vs accessibility

There is a trade-off between detail and comprehension. In physics education and public communications, a layered approach—starting with a simple diagram and progressively adding detail—helps audiences build intuition without becoming overwhelmed. The goal is to illuminate physics, not to obscure it behind excessive complexity.

Pedagogical strategies

Use Sankey diagrams as a bridge between qualitative descriptions and quantitative analysis. Begin with a clear qualitative narrative of a system, then introduce a Sankey diagram to quantify the story. Encourage students to modify inputs and observe how the diagram responds, reinforcing the link between energy flows, conservation laws, and real-world performance.

Public demonstrations and outreach

Public-facing diagrams should emphasise clarity and relevance. A well-designed sankey diagram can answer questions such as: Where does energy go in a household, or how does a national energy mix perform across seasons? Pair diagrams with simple captions and a short explanation of the physics involved, and you’ll enable non-specialists to grasp essential concepts without sacrificing scientific integrity.

Interdisciplinary applications

As systems become more complex and interconnected, sankey diagram physics will extend beyond energy to information, material cycles, and environmental footprints. The cross-pollination of disciplines—from climate science to bioengineering—will broaden the use of these diagrams, while maintaining a principled grounding in conservation laws and thermodynamics.

Real-time, data-driven diagrams

The rise of sensor networks and smart instruments makes real-time Sankey diagrams increasingly feasible. Dynamic, live diagrams could monitor a facility, show current efficiency, and alert operators when losses exceed thresholds. This convergence of physics, data science, and visual analytics represents an exciting frontier for sankey diagram physics.

Sankey diagrams offer more than a visually pleasing representation; they embody core physical principles in a form that is accessible, shareable, and actionable. By focusing on energy conservation, quality differences, and loss pathways, sankey diagram physics provides a rigorous yet intuitive framework for analysing complex systems. Whether used for engineering optimisation, environmental budgeting, or education, these diagrams illuminate how energy and matter move through the world, helping us design better, more efficient, and more sustainable technologies.

What exactly is a Sankey Diagram in physics?

A Sankey Diagram is a flow diagram where the width of the arrows is proportional to the magnitude of the flow. In physics, it is used to visualise energy or mass transfers within a system, emphasising conservation, transformations, and losses. The diagram helps communicate how a system processes inputs into outputs and where inefficiencies occur.

How can I create a Sankey diagram for my physics project?

Start by defining the system boundary, listing all inputs, outputs, and losses. Choose consistent units, decide on a scale, and assign colours to different flow categories. Use software tools that support Sankey diagrams, input your data, and adjust the layout for readability. Inspect the diagram critically to ensure it accurately represents conservation and transformation paths.

Why are Sankey diagrams useful in teaching thermodynamics?

Thermodynamics concerns energy transfer, work, heat, and irreversibility. Sankey diagrams provide a concrete, visual means to track how energy is converted and dissipated, making abstract concepts tangible. Students can compare theoretical maximum efficiencies with practical realities, improving understanding and retention.