Vertical Axis Wind Turbine (VAWT) Dynamic Analysis Tool

Inputs:

Configurable

Environmental Parameters

True Wind, v (MPH)

Temp (°F)

Rel. Humidity (%)

Baro Press (inHg)

Turbine & Blade Geometry

Radius, r (m)

# blades (int)

Blade cord (m)

Blade span (m)

Blade thick (m)

Aerodynamic Data & Kinematics

Blade Lift Coeff vs. AOA

Blade Drag Coeff vs. AOA

Blade angle vs. α: Function of α (deg)

Analysis Upper Limit (h/v ratio)

Angular Velocity, ω (rad/s)

Outputs:

Live Computed

Collision Status:

No Collision Clearance: 0.5571 m (Safe)

Blade Collision Check

Ensures adjacent blades do not physically collide during complete 360° orbit.

Clearance = 2·r·sin(π/N) - c

Turbine swept area, S:

0.5056 m² 5.4423 ft²

Turbine Frontal Swept Area (S)

Frontal capture area normal to oncoming wind (+X), dynamically evaluated across 360°:

S = (Y_max - Y_min) · span

Solidity ratio, σ:

59.3354% 19.0986% (circumferential)

Solidity Ratio (σ)

Ratio of total blade planform area to rotor frontal swept area:

σ = (N · c · span) / S = (N · c) / (Y_max - Y_min) · 100%

Air Density, ρ:

1.1578 kg/m³ 0.0723 lb/ft³

Moist Air Density (ρ)

Thermodynamic air density (CIPM standard / Tetens vapor pressure formulation):

ρ = (p_dry / (Rd · T)) + (p_vapor / (Rv · T))

Power Avail in Wind:

405.3402 W 0.5436 HP

Power Available in Wind (PW)

Total kinetic power flux available in oncoming True Wind stream tube:

PW = (1/2) · ρ · S · |v|³

Starting angle, α for each blade:

0°, 90°, 180°, 270°

Starting Blade Angles

Equally spaced azimuth angles around platform perimeter:

α_i = α₀ + (i · 360° / N)

Headwind, h:

4 m/s 8.9478 MPH

Headwind Magnitude (|h|)

Wind velocity experienced by blade strictly due to turbine rotation:

|h| = r · ω

Headwind to True Wind ratio, h/v:

0.3579 Tip Speed Ratio

Headwind to True Wind Ratio (h/v)

Turbine Tip Speed Ratio (TSR, λ):

h/v = |h| / |v| = (r · ω) / |v|

Total Platform Torque, τ:

0 N·m Instant: 0 N·m

Total Platform Torque (τ)

Instantaneous torque and average torque integrated across full 360° at 5° steps:

τ(α) = Σ (F_tau,i · r) τ_avg = (1/72) · Σ τ(α_k)

Turbine Power, P:

0 W 0 HP

Turbine Mechanical Power (P)

Mechanical shaft power output of turbine:

P = τ_avg · ω

CoP:

0 Efficiency: 0%

Coefficient of Power (CoP)

Overall aerodynamic power conversion efficiency:

CoP = P_turbine / PW = (τ_avg · ω) / PW

Torque Ripple for each blade:

0 N·m Ripple: 0%

Single Blade Torque Ripple

Peak-to-peak torque variation produced by a single blade across 360°:

Δτ_blade = τ_max - τ_min Ripple % = (Δτ_blade / τ_blade,avg) · 100%

Torque Ripple for total Turbine:

0 N·m Ripple: 0%

Total Turbine Torque Ripple

Fluctuation in combined multi-blade shaft torque across 360°:

Δτ_total = τ_total,max - τ_total,min Ripple % = (Δτ_total / τ_avg) · 100%

Image Key & Control:

True Wind:

Apparent Wind:

Headwind:

Lift:

Drag:

Resultant:

Torque force:

Arrow Scale:

Blade Forces:

Kinematics & Position

Azimuth α:

0°

Blade Azimuth Angle (α)

Angular position of the selected blade on the rotor platform orbit:

α = (α_platform + b · (360° / N)) mod 360°

Position (x, y):

(0.5, 0) m

Blade Position (x, y)

Cartesian coordinates of the blade pivot on the platform circle:

x = r · cos(α) y = r · sin(α)

Radial r̂:

(1, 0)

Radial Unit Vector (r̂)

Unit vector directed outward from the central hub to the blade pivot:

r̂ = (cos(α), sin(α))

Tangential t̂:

(0, 1)

Tangential Unit Vector (t̂)

Unit vector tangent to the orbit in the direction of CCW rotation:

t̂ = (-sin(α), cos(α))

Wind Velocities

True Wind v:

8.9408 m/s (8.9408, 0) m/s

True Wind Velocity (v)

Free-stream true wind velocity vector parallel to +X direction:

v = (|v|, 0)

Headwind h:

4 m/s (0, -4) m/s

Headwind Velocity (h)

Relative wind induced by blade rotation through air, directed opposite to travel (-t̂):

h = -|h|·t̂ = (|h|·sin(α), -|h|·cos(α)) |h| = r · ω

Apparent v_A:

9.7947 m/s ∠ 335.89°

Apparent Wind Velocity (v_A)

Vector sum of true wind and headwind at the blade:

v_A = v + h |v_A| = √(v_{A,x}² + v_{A,y}²)

Blade Orientation & Airfoil

Pitch θ_blade:

90°

Blade Pitch Angle (θ_blade)

Blade orientation angle relative to the radial line r̂:

θ_blade = f(α) [evaluated formula]

Chord θ_c, ĉ:

90° ĉ: (0, 1)

Chord Global Angle & Unit Vector (θ_chord, ĉ)

Orientation of the airfoil chord line in the global coordinate frame:

θ_chord = (α + θ_blade) mod 360° ĉ = (cos(θ_chord), sin(θ_chord))

Angle of Attack AAOA:

10.62°

Apparent Angle of Attack (AAOA)

Angle between blade chord (pointing to LE) and oncoming relative wind:

AAOA = (θ_chord - θ_incoming) mod 360° θ_incoming = (∠v_A + 180°) mod 360°

Coeffs C_l, C_d:

C_l: 0, C_d: 0.05

Airfoil Polar Coefficients (C_l, C_d)

Section lift and drag coefficients interpolated from 360° lookup table:

C_l = Polar(AAOA) C_d = Polar(AAOA)

Area B, Pressure q:

58.7612 Pa B = 0.075 m²

Blade Area & Dynamic Pressure

Projected planform area B and flow stagnation pressure q:

B = c · H q = 0.5 · ρ · |v_A|²

Forces & Torque

Lift Force L:

0 N (0, 0) N

Aerodynamic Lift Force (L)

Force acting strictly perpendicular (90° CW) to apparent wind v_A for positive C_l:

L = C_l · q · B · n̂_lift n̂_lift = (v̂_{A,y}, -v̂_{A,x})

Drag Force D:

0.2204 N (0.2012, -0.09) N

Aerodynamic Drag Force (D)

Force acting strictly parallel to apparent wind direction v_A:

D = C_d · q · B · v̂_A |D| = C_d · q · B

Resultant R:

0.2204 N (0.2012, -0.09) N

Resultant Aerodynamic Force (R)

Vector sum of lift and drag forces acting on the blade:

R = L + D = (L_x + D_x, L_y + D_y) |R| = √(R_x² + R_y²)

Torque Force F_τ:

-0.09 N (0, -0.09) N

Tangential Torque Force (F_τ)

Component of Resultant force tangent to orbit driving rotation (t̂):

F_τ = R · t̂ = R_x · t_x + R_y · t_y F_τ_vec = F_τ · t̂

Blade Torque τ:

-0.045 N·m

Blade Instantaneous Torque (τ)

Shaft mechanical torque produced by this blade:

τ = F_τ · r

Top-Down Coordinate View (CCW Rotation) True Wind: Left → Right (+X)

CoP vs. Headwind to True Wind ratio (h/v)

Torque vs. Platform Angle α (Torque Ripple)

0° - 360° (5° steps)

Airfoil Aerodynamics: Cl & Cd vs. Angle of Attack (0° to 360°)

Referenced from airfoil_data.js

CoP vs. Headwind to True Wind ratio (h/v)

Torque vs. Platform Angle α (Torque Ripple)

Airfoil Aerodynamics: Cl & Cd vs. Angle of Attack (0° to 360°)

Airfoil Lookup Table (airfoil_data.js)