The 3D scene
Pick a source and the matching machine appears next to the cabin: a tilted solar array (P = G A eta), a wind rotor whose speed follows the wind (P = eta 1/2 rho A u^3), a water wheel under a flume (P = rho g Q H eta) or a pedal generator (P = eta Ph - losses). The sun and sky follow the clock of the 24-hour window, glowing dots show energy flowing source to battery to cabin, the gauge beside the battery cabinet shows stored energy, and the lamp and window go dark when the load cannot be met.
All numbers come from the same lab.js solver as the 2D companion, so both pages agree. Drag to orbit, scroll or pinch to zoom.
The science
Every case-study file computes P for one source and integrates E = Pt. The lab keeps those exact power laws and adds what makes them useful: availability over a day, a battery with a finite capacity and charge-path efficiency, and a load that must be met.
Equations as delivered in the case-study files
P(t)=ηAG sin(πt/T) [W]; E(t)=ηAG T(1−cos(πt/T))/π [J].
P=G A η [W]; dE/dt=P [J/s]; E(t)=E₀+Pt [J].
P=η(ρ A u³/2) [W]; dE/dt=P [J/s]; E(t)=Pt [J].
Pnet = ηPₕ − Pₗ [W]; dE/dt=Pnet [J/s]; E(t)=E₀+Pnet t [J].
P=ρ g Q H η [W] with ρ=1000 kg/m³; dE/dt=P [J/s]; E(t)=E₀+Pt [J].
What this lab adds
dE_batt/dt = ηc·P(t) − P_load, clamped to 0 ≤ E ≤ E_cap [W]
Solar day profile: P(t) = P_peak sin(π (t − 6 h)/12 h) for 06:00–18:00, so ∫P dt = P_peak·24/π [Wh]
Betz limit for a wind turbine: η ≤ 16/27 ≈ 0.593
Assumptions in the delivered files
- Ideal time-compressed half-sine illumination during scenario duration T, fixed area and efficiency.
- Constant irradiance, uniform illumination and constant conversion efficiency; shadows, heating and inverters omitted.
- Steady uniform wind at the rotor, fixed effective extraction fraction below Betz limit; no gust turbulence, cut-in/out or generator dynamics.
Honest simplifications of this lab
- Weather is not random: a steady, daylight half-sine or 09:00–17:00 availability profile is assumed, not measured data.
- The battery has no self-discharge, depth-of-discharge limit or ageing; the charge path has one efficiency number.
- The solar efficiency does not vary with temperature; the hydro head and wind speed are constant.
- Battery size and load are expressed relative to the mean source power so one scale works for every preset; they are lab choices, not values from the files.
Independent check The page recomputes the 24 h energy with closed forms (P_peak·24/π, the battery balance, the unmet-load formula); the test file repeats this with an independent minute-by-minute integrator and exact power laws.
Educational model. The 3D scene is a visual aid; rotor, wheel and pedal speeds are illustrative and not scaled to the computed power. Numbers, plots and checks are those of the 2D companion.