Flywheel Energy Calculator

# Flywheel Sizing & Usable Energy Calculation
import math

def calculate_flywheel(R_o_mm, thickness_mm, density_kg_m3, n_max_rpm, n_min_rpm, geometry="solid"):
    R_o_m = R_o_mm / 1000.0
    b_m = thickness_mm / 1000.0
    
    # Mass and Inertia (Solid disk example)
    volume = math.pi * (R_o_m**2) * b_m
    mass = density_kg_m3 * volume
    I = 0.5 * mass * (R_o_m**2) # kg.m^2
    
    # Angular Speeds
    omega1 = 2 * math.pi * n_max_rpm / 60.0
    omega2 = 2 * math.pi * n_min_rpm / 60.0
    omega_mean = (omega1 + omega2) / 2.0
    
    # Energy Capacity
    E_max = 0.5 * I * (omega1**2)
    E_min = 0.5 * I * (omega2**2)
    delta_E = E_max - E_min # Joules
    
    Cs = (omega1 - omega2) / omega_mean
    v_tip = omega1 * R_o_m # m/s
    hoop_stress_MPa = (density_kg_m3 * (v_tip**2)) / 1e6
    
    return {
        "mass_kg": mass,
        "inertia_kg_m2": I,
        "usable_energy_J": delta_E,
        "usable_energy_Wh": delta_E / 3600.0,
        "fluctuation_Cs": Cs,
        "tip_velocity_m_s": v_tip,
        "hoop_stress_MPa": hoop_stress_MPa
    }

# Inputs
res = calculate_flywheel(
    R_o_mm=400,
    thickness_mm=80,
    density_kg_m3=7850,
    n_max_rpm=300,
    n_min_rpm=270
)
print(f"Moment of Inertia: {res['inertia_kg_m2']:.2f} kg·m²")
print(f"Usable Energy (ΔE): {res['usable_energy_J']:.1f} J ({res['usable_energy_Wh']:.3f} Wh)")
print(f"Fluctuation (Cs): {res['fluctuation_Cs']:.3f}")
print(f"Tip Speed: {res['tip_velocity_m_s']:.2f} m/s | Hoop Stress: {res['hoop_stress_MPa']:.2f} MPa")

% Flywheel Kinetic Energy Script
Ro = 400 / 1000;
b = 80 / 1000;
rho = 7850;
N1 = 300;
N2 = 270;

mass = rho * pi * Ro^2 * b;
I = 0.5 * mass * Ro^2;

w1 = 2 * pi * N1 / 60;
w2 = 2 * pi * N2 / 60;

delta_E = 0.5 * I * (w1^2 - w2^2);
v_tip = w1 * Ro;

fprintf('Inertia: %.2f kg.m^2\n', I);
fprintf('Usable Energy: %.1f Joules\n', delta_E);
fprintf('Tip Speed: %.2f m/s\n', v_tip);