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For Students · Sail / Hydrofoil

Sail / Hydrofoil for a rooftop solar array

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a rooftop solar array live below — adjust the inputs and watch it respond, right in your browser.

Airfoil Polar

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Airfoil Lift & DragLive

the wing's polar

Controls

Presets

Angle of attack (°)

Aspect ratio

Lift rises almost linearly with angle of attack — until the airflow separates and the wing stalls, losing lift sharply. Drag has a fixed part plus induced drag that grows with lift squared and shrinks with aspect ratio. The lift-to-drag ratio, peaking at a modest angle, is the single number that governs a wing's efficiency.

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Data Inspector

Lift coeff. CL0.53

Drag coeff. CD0.033

Lift/Drag16.0

Statusattached

Governing equation

C_{D} = C_{D 0} + \frac{C _{L}^{2}}{π A R e} = 0.020 + \frac{0.5 3 ^{2}}{π \cdot 8 \cdot 0.85} = 0.033

Reading this result: Pre-stall: lift rises almost linearly with angle of attack at 6°, well below the ~15° stall angle. Adding camber would lift the entire curve higher.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Buoyancy

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Buoyancy & ArchimedesLive

floating equilibrium by density

Controls

An object floats with exactly the fraction ρ_object/ρ_fluid submerged. Denser than the fluid? It sinks. This is Archimedes' principle, live.

Presets

Object density (kg/m³)

Fluid density (kg/m³)

Object size

▶ Run in Python

Data Inspector

Fraction submerged60%

Statefloats

ρ ratio0.60

Governing equation

\frac{V _{s u b}}{V} = \frac{ρ _{o bj}}{ρ _{f l u i d}} = \frac{600}{1000} = 0.60 F_{b} = ρ_{f l u i d} g V

Reading this result: Lighter than the fluid (ρ ratio 0.60), so it floats with exactly 60% submerged — the submerged fraction equals the density ratio, and object size never changes it.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

Is this good for students?: Yes — this version of "Sail / Hydrofoil for a rooftop solar array" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.