Category
Aerospace Engineering
Aerospace engineering formulas and calculators for aerodynamics, propulsion, and flight mechanics in aircraft and spacecraft design. Includes lift, drag, thrust, and orbital trajectory equations.
91Formulas
2Subcategories
Updated Oct 2026
Aerodynamics
Service Ceiling Criterion
R/C_service = 0.508 m/s (100 ft/min)
Aerodynamics
Absolute Ceiling Relation (Zero Rate of Climb)
R/C = 0 at Absolute Ceiling
Propulsion
Propeller Aircraft Range (Simplified)
R = (η_p/c_p) * (C_L/C_D) * ln(W_i/W_f)
Propulsion
Propeller Aircraft Endurance (Simplified)
E = (η_p / c_p) * (C_L^1.5/C_D) * sqrt(2*ρ*S) * (W_i^-0.5 - W_f^-0.5) / (-0.5)
Propulsion
Hohmann Transfer Total Delta-V
Δv_total = Δv1 + Δv2
Propulsion
Orbital Plane Change Delta-V
Δv = 2 * v * sin(Δi/2)
Aerodynamics
Stagnation Point Convective Heating Rate (Simplified)
q̇ = k * sqrt(ρ/R_n) * V^3
Propulsion
Choked (Sonic) Mass Flow Rate
mdot = (p_c * A_t / sqrt(T_c)) * sqrt(γ/R) * (2/(γ+1))^((γ+1)/(2*(γ-1)))
Propulsion
Ideal Rocket Nozzle Exit Velocity
V_e = sqrt((2*γ/(γ-1)) * R * T_c * (1 - (p_e/p_c)^((γ-1)/γ)))
Propulsion
Overall Propulsion Efficiency
η_o = η_th * η_p
Propulsion
Brayton Cycle Thermal Efficiency
η_th = 1 - 1/(r_p^((γ-1)/γ))
Propulsion
Propulsive Efficiency
η_p = 2*V_0 / (V_e + V_0)
Propulsion
Ramjet Thrust Equation (Simplified)
F = mdot * (V_e - V_0)
Propulsion
Turbojet Thrust Equation
F = mdot * (V_e - V_0) + A_e * (p_e - p_0)
Propulsion
Thrust Specific Fuel Consumption (TSFC)
TSFC = mdot_f / T
Propulsion
Fuel Flow Rate
mdot_f = TSFC * T
Propulsion
Specific Range
SR = V / (c * T)
Aerodynamics
Bank Angle for Coordinated Turn
φ = arctan(V^2 / (g * R))
Aerodynamics
Load Factor in Coordinated Turn
n = 1 / cos(φ)
Aerodynamics
Aircraft Roll Moment of Inertia (Simplified Wing Model)
I_xx ≈ (m_wing * b^2) / 12
Aerodynamics
Gyroscopic Precession Rate
Ω_p = M / (I * ω_s)
Aerodynamics
Centrifugal Force on Rotor Blade Element
F_c = m * Ω^2 * r
Aerodynamics
Rotor Solidity Ratio
σ = (N_b * c) / (π * R)
Propulsion
Momentum Theory Induced Velocity (Hover)
v_i = sqrt(T / (2 * ρ * A))
Propulsion
Figure of Merit (Rotor Hover Efficiency)
FM = P_ideal / P_actual
Propulsion
Helicopter Disk Loading
DL = W / A
Aerodynamics
Helicopter Rotor Blade Tip Speed
V_tip = Ω * R
Propulsion
Propeller Power Coefficient
C_P = P / (ρ * n^3 * D^5)
Propulsion
Propeller Thrust Coefficient
C_T = T / (ρ * n^2 * D^4)
Propulsion
Propeller Advance Ratio
J = V / (n * D)
Propulsion
Propeller Efficiency
η_p = T * V / P_shaft
Propulsion
Power Available (Propeller-Driven Aircraft)
P_avail = η_p * P_shaft
Propulsion
Power Required for Level Flight
P_req = D * V = (C_D * q * S) * V
Aerodynamics
Landing Ground Roll Distance (Simplified)
s_L ≈ 1.69 * W^2 / (g * ρ * S * C_Lmax * D_avg)
Aerodynamics
Takeoff Ground Roll Distance (Simplified)
s_TO ≈ 1.44 * W^2 / (g * ρ * S * C_Lmax * T)
Aerodynamics
Fuel Weight Fraction
W_f/W_0 = 1.06 * (1 - W_x/W_0)
Aerodynamics
Empty Weight Fraction
W_e/W_0 = W_empty / W_0
Aerodynamics
Torsional Divergence Speed (Simplified)
V_d = sqrt(K_θ / (q_coeff * e * c * C_Lα * S))
Aerodynamics
Wing Root Bending Moment (Elliptical Load, Simplified)
M_root ≈ (4/(3π)) * L * (b/2)
Aerodynamics
Simplified Flutter Speed Estimate
V_f ≈ ω_θ * b * sqrt((I_α/(ρ*b^4)) * (something))
Aerodynamics
V-n Diagram Positive Limit Load Factor
n_max = 2.1 + 24000/(W + 10000)
Aerodynamics
Dutch Roll Natural Frequency (Approx.)
ω_d ≈ sqrt((N_β * q̄ * S * b) / I_z)
Aerodynamics
Phugoid Mode Period (Approx.)
T_ph ≈ 2π * sqrt(2) * V / g
Aerodynamics
Short Period Natural Frequency (Approx.)
ω_sp ≈ sqrt((-M_α * q̄ * S * c̄) / I_y)
Aerodynamics
Pitching Moment Coefficient
C_m = M / (q * S * c̄)
Aerodynamics
Static Margin
SM = (x_np - x_cg) / c̄
Aerodynamics
Neutral Point Location
x_np = (C_L,α,wb * x_ac,wb + C_L,α,t * η * (S_t/S) * x_ac,t) / (C_L,α,wb + C_L,α,t * η * (S_t/S))
Aerodynamics
Center of Pressure Location
x_cp = x_ac - (C_m,ac / C_L)
Aerodynamics
Kutta-Joukowski Theorem
L' = ρ * V * Γ
Aerodynamics
Blasius Laminar Boundary Layer Thickness
δ = 5.0 * x / sqrt(Re_x)
Aerodynamics
Turbulent Flat Plate Skin Friction Coefficient
C_f = 0.074 / Re_x^(1/5)
Aerodynamics
Laminar Flat Plate Skin Friction Coefficient
C_f = 1.328 / sqrt(Re_x)
Aerodynamics
Sutherland's Law (Viscosity)
μ = μ0 * (T/T0)^(3/2) * (T0+S)/(T+S)
Aerodynamics
Stagnation Pressure
p0 = p * (1 + ((γ-1)/2) * M^2)^(γ/(γ-1))
Aerodynamics
Stagnation Temperature
T0 = T * (1 + ((γ-1)/2) * M^2)
Aerodynamics
Speed of Sound (Ideal Gas)
a = sqrt(γ * R * T)
Propulsion
Area-Mach Number Relation (Isentropic Nozzle)
(A/A*)^2 = (1/M^2) * ((2/(γ+1))*(1+((γ-1)/2)*M^2))^((γ+1)/(γ-1))
Aerodynamics
Critical Mach Number Relation
C_p,cr = (2/(γ*M_cr^2)) * (((1+((γ-1)/2)*M_cr^2)/(1+(γ-1)/2))^(γ/(γ-1)) - 1)
Aerodynamics
Prandtl-Glauert Compressibility Correction
C_p = C_p0 / sqrt(1 - M^2)
Aerodynamics
Normal Shock Downstream Mach Number
M2^2 = (1 + ((γ-1)/2)*M1^2) / (γ*M1^2 - (γ-1)/2)
Aerodynamics
Normal Shock Pressure Ratio
p2/p1 = 1 + (2γ/(γ+1)) * (M1^2 - 1)
Aerodynamics
Isentropic Density Ratio
ρ0/ρ = (1 + ((γ-1)/2) * M^2)^(1/(γ-1))
Aerodynamics
Isentropic Pressure Ratio
p0/p = (1 + ((γ-1)/2) * M^2)^(γ/(γ-1))
Aerodynamics
Isentropic Temperature Ratio
T0/T = 1 + ((γ-1)/2) * M^2
Propulsion
Total Impulse
I_t = ∫ F dt ≈ F_avg * t_b
Propulsion
Characteristic Velocity
c* = p_c * A_t / mdot
Propulsion
Nozzle Thrust Coefficient
C_F = F / (p_c * A_t)
Propulsion
Effective Exhaust Velocity
v_e = Isp * g0
Propulsion
Rocket Mass Ratio
MR = m0 / mf
Propulsion
Hohmann Transfer First Burn Delta-V
Δv1 = sqrt(μ/r1) * (sqrt(2*r2/(r1+r2)) - 1)
Propulsion
Tsiolkovsky Rocket Equation
Δv = v_e * ln(m0 / mf)
Propulsion
Thrust-to-Weight Ratio
T/W = Thrust / Weight
Propulsion
Breguet Endurance Equation (Jet)
E = (1/c) * (L/D) * ln(W_i / W_f)
Propulsion
Breguet Range Equation (Jet)
R = (V / c) * (L/D) * ln(W_i / W_f)
Aerodynamics
Glide Ratio
Glide Ratio = L/D = Horizontal Distance / Altitude Lost
Propulsion
Rate of Climb
R/C = (T - D) * V / W
Aerodynamics
Radius of Turn (Coordinated)
R = V^2 / (g * tan(φ))
Aerodynamics
Stall Speed
V_stall = sqrt(2*W / (ρ * S * C_Lmax))
Aerodynamics
Lift-to-Drag Ratio
L/D = C_L / C_D
Aerodynamics
Wing Loading
W/S = Weight / S
Aerodynamics
Oswald Efficiency Factor Relation
e = C_L^2 / (π * AR * C_Di)
Aerodynamics
Induced Drag Coefficient
C_Di = C_L^2 / (π * e * AR)
Aerodynamics
Wing Aspect Ratio
AR = b^2 / S
Aerodynamics
Coefficient of Drag
C_D = D / (q * S)
Aerodynamics
Coefficient of Lift
C_L = L / (q * S)
Aerodynamics
Dynamic Pressure
q = 1/2 * ρ * V^2
Aerodynamics
Mach Number
M = V / a
Propulsion
Specific Impulse
I_sp = F / (ṁ·g₀)
Propulsion
Rocket Thrust Equation
F = ṁv_e + (p_e − p_0)A_e
Aerodynamics
Drag Equation
D = ½ρv²C_D·A
Aerodynamics
Lift Equation
L = ½ρv²C_L·A