Rotational Kinematics & Kinetic Energy Matrix
Power: P = (2*π*N*T)/60 | Linear Velocity: v = ω * r | Flywheel Kinetic Energy: E_k = 0.5 * I * ω²
Triaxial Mechanics, Bending & Factor of Safety
Bending Stress: σ_b = M*y/I | Torsional Shear: τ = T*r/J | Factor of Safety: FoS = σ_yield / σ_max
Hydrodynamics, Head Loss & Pump Hydraulic Power
Reynolds: Re = ρVd/μ | Darcy Loss: h_f = f*(L/d)*(V²/2g) | Pump Power: P = ρ * g * Q * h_f
Thermodynamic Cycles & Composite Multi-Mode Heat Transfer
Carnot Efficiency: η = 1 - Tc/Th | Multi-Layer Wall Flux: q = ΔT / Σ(L/k)
Advanced Metal Weights & Structural Design Limits
Calculation Engine: Weight = Volume × Density | Buckling Guard: P_critical = (π² × E × I) / (K × L)²
🛡️ Column Buckling Safety Configuration
Industrial Profile Mass Matrix
Calculation Engine: Weight = Cross-Sectional Area (mm²) × Length (m) × Density (g/cm³) ÷ 1000
Advanced Fatigue Lifespan & Stress Concentration Modifiers
Modified Endurance Limit: S_e = k_a * k_b * k_c * S_e' | Nominal Stress Mod: σ_max = K_t * σ_nom
Euler Column Critical Buckling Elastic Stability Limits
Euler Formula: P_cr = (π² * E * I) / (K * L)² | Slenderness Ratio: λ = L_e / r_g
Compressible Gas Dynamics, Mach Number & Airfoil Drag Matrix
Aerodynamic Lift/Drag: F_d = 0.5 * C_d * ρ * A * v² | Mach Number: M = v / c
Vibro-Acoustics Sound Intensity, Power & Free-Field Pressure
Acoustic Intensity Level: L_I = 10 * log10(I / I_0) | SPL Free Field: SPL = L_w - 20log10(r) - 11