Ridge Turbine and Night Battery

What is modelled

Wind turns a rotor that has inertia, the rotor feeds a battery, and a cottage draws a constant load. The page integrates the rotor speed and the battery energy in half-second steps while the clock runs 600 times faster than real time, so a night of twelve hours takes about a minute and a quarter.

Equations

• Turbine power P = ½ ρ A Cd v³ η, so doubling the wind gives eight times the power.
• Rotor lag dω/dt = (ωtarget − ω) / τ with τ = 1.4 s + m / 1000 kg·s and ωtarget = 0.9 v / 3.5.
• Battery E(t + Δt) = clamp(E + (Pgen − Pload − Pbrake) Δt / 3600, 0, Emax) in watt hours.
• Break-even wind v* = (2 Pload / ((1 − fbrake) ρ A Cd η))1/3.

Checks run in the page

• The formula against the cubic law and the factor of eight for doubled wind.
• Rotor speed after one time constant against 1 − 1/e of the target.
• Stepped battery energy in steady wind against the analytic straight line.
• Bisection for the break-even wind against the closed form.

Honest simplifications

The effective drag coefficient C_d is an illustrative lumped number, not a validated power coefficient; there is no cut-in, rated power or yaw, the air density is constant, the gusts are two fixed sine waves and the battery is ideal with no losses or ageing.

• Press Storm watch and see the battery fill and the surplus get braked away.
• Press Calm night, drained and read the autonomy in hours before a blackout.
• Raise the rotor mass and watch the rotor speed lag the gusts.