New Category: Environment & Energy Simulations — Solar, Wind, Nuclear, Carbon Cycle

The Environment & Energy category launches today with 8 new interactive simulations. Each one is built around a real physical model used in the energy sector — not a cartoon approximation, but the actual equations that engineers and scientists use.

The 8 New Simulations

☀️ Solar Panel IV Curve Explore how temperature, irradiance, and shading affect photovoltaic efficiency. Visualise the maximum power point and fill factor in real time. Equivalent diode model · MPP tracking 🌬️ Wind Turbine Aerodynamics Visualise blade element theory and the Betz limit — the theoretical maximum fraction of wind kinetic energy a turbine can extract (59.3%). Blade element momentum theory ⚛️ Nuclear Fission Reactor Watch neutron multiplication in a fission chain reaction. Adjust enrichment, moderator density and control rod depth to find criticality. Monte Carlo neutron transport · k-eigenvalue 🌍 Global Carbon Cycle A systems-dynamics model of carbon flows between atmosphere, ocean, biosphere and lithosphere. Vary industrial emissions and observe equilibrium shifts. Box model ODEs · IPCC reservoir data 🌊 Tidal Energy Generator Simulate tidal stream flow through an underwater turbine array. See how turbine spacing and tip-speed ratio affect array power output. Actuator disc model · blockage correction 🌡️ Greenhouse Effect Interactive line-by-line radiative transfer: watch infrared photons absorbed and re-emitted by CO₂ and H₂O molecules in a simplified atmospheric column. Two-stream radiative transfer ☁️ Cloud Formation & Albedo Simulate adiabatic lifting, condensation nuclei, and droplet growth. Vary atmospheric humidity and particulate loading to observe cloud optical depth. Parcel theory · Köhler equation 🎈 Hot Air Balloon Thermodynamics Model the buoyancy, burn rate and heat loss of a hot air balloon. Find the minimum envelope temperature for lift-off at different altitudes. Ideal gas law · convective heat transfer

Featured: The Betz Limit

The wind turbine simulation is built around one of the most elegant results in applied physics: Betz's law. Albert Betz proved in 1919 that no wind turbine can capture more than 16/27 ≈ 59.3% of the kinetic energy in a wind stream. This is not a technological limitation — it is a fundamental consequence of fluid continuity.

Betz limit derivation (momentum theory)

C_P = P / (½ ρ A v³) ≤ 16/27 ≈ 0.593

where: ρ = air density, A = rotor swept area, v = free-stream velocity
Optimal axial induction factor: a = 1/3
Downstream velocity: v_wake = v(1 - 2a) = v/3

Modern turbines (Vestas V164, GE Haliade-X) reach C_P ≈ 0.48–0.50 — about 80% of the theoretical maximum. The gap is caused by blade tip vortices, viscous drag, and wake rotation. All these effects are included in our blade element momentum simulation.

Featured: Nuclear Criticality

The reactor simulation reproduces criticality using a simplified Monte Carlo neutron transport model. Each neutron is tracked individually: born from fission with a sampled energy, slowed by elastic collisions with the moderator, captured by U-238 resonances, or absorbed in U-235 to cause a new fission.

The effective multiplication factor k_eff determines reactor behaviour: k < 1 is sub-critical (reaction dies), k = 1 is critical (steady power), k > 1 is super-critical (exponential growth). Our moderator density slider shows how the light-water moderator, by thermalising neutrons, dramatically increases the fission cross-section of U-235.

All 8 simulations link directly to the Environment & Energy category page. Each includes a full mathematical description and educational context suitable for A-level / IB through to undergraduate engineering courses.