Tidal Kite Power: Crosswind Plane & Power Curve (2D)

Tidal Stream

Current speed 1.4 m/s

Kite speed ratio k 6.0×

Kite & Turbine

Rotor diameter 1.5 m

Figure-8 amplitude 14 m

Live Output

Effective flow speed

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Instant power

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Loop period · sustained annual energy @ this power

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Power Curve (P ∝ v³) & Time Strip

P vs v_eff—

How it works

This is the 2D companion to the 3D tidal-kite flight sim: instead of a rendered 3D scene, this diagram draws the actual crosswind plane — the flat plane, perpendicular to the ambient current, in which the kite's figure-8 loop physically happens (the same plane Loyd's crosswind kite-power theory is diagrammed in). The kite position is computed directly as a 2D lemniscate parametric curve, not projected from a 3D scene:

x(θ) = A · sin(θ)
y(θ) = A · 0.275 · sin(2θ)
v_eff ≈ k · v_current
P = ½ · ρ_seawater · A_rotor · Cp · v_eff³
A_rotor = π (D/2)²,  ρ ≈ 1025 kg/m³,  Cp ≈ 0.42

The angular rate θ̇ = 2π / period is set from the same lap-period formula as the 3D sim (lap length ≈ 5.2·A over the kite's own flight speed), so the loop you see traces at the physically correct rate for the current settings. The right-hand chart plots the full cube-law power curve P(v) as a static curve with a live marker at the current operating point, plus a rolling strip chart of effective flow speed and power over the last several seconds — a genuinely distinct 2D-native way to see the same physics that the 3D flight visualizes as a flying kite.

Current speed — the real, ambient tidal stream velocity at the site.
Kite speed ratio k — how many times faster the kite's figure-8 flight moves through the water than the current itself.
Rotor diameter — swept size of the small turbine mounted on the kite; only changes the power curve's vertical scale.
Figure-8 amplitude — physical size of the flight loop drawn in the crosswind plane; a larger loop at the same k takes proportionally longer per lap.

Kite + turbine Tidal current flow Tether & anchor