Aerospace Recovery Systems, Rocketry & Fluid Drag Mechanics
Parachute Terminal Velocity, Canopy Diameter & Impact KE
Calculate Steady-State Canopy Drag Force m*g, Terminal Descent Rate Vt = SQRT((2*m*g)/(rho*Cd*S)), Equivalent Circular Canopy Diameter SQRT(4*S/PI()), and Touchdown Impact Kinetic Energy.
Size recovery canopies for safe touchdown kinetic energy across thin high-altitude dropzones!
Sounding-rocket, UAV, and planetary-probe recovery engineers size parachute canopies by equating downward payload weight m*g against aerodynamic bluff-body drag 0.5 * rho * V_t^2 * C_d * S, giving Terminal Descent Velocity V_t = SQRT((2 * m * g) / (rho * C_d * S)) and Equivalent Flat-Circular Canopy Diameter D = SQRT((4 * S) / PI())! Watch the high-altitude touchdown kinetic-energy trap: because Landing Impact Kinetic Energy KE = 0.5 * m * V_t^2 simplifies algebraically to (m^2 * g) / (rho * C_d * S), landing at a high-elevation plateau where air density rho is halved increases descent speed by +41.4% (SQRT(2))—and DOUBLES structural impact kinetic energy at touchdown!
Verify on a 120 kg UAV Recovery System—Total_Suspended_Mass m = 120 kg (B2), Dropzone_Air_Density rho = 1.20 kg/m^3 (B3), Toroidal_Canopy_Drag_Coeff C_d = 1.60 (B4), and Canopy_Reference_Area S = 25.0 m^2 (B5, with g = 9.81 m/s^2): Steady-State Canopy Drag Tension equals 120 * 9.81 = 1,177.20 N (E2); Terminal Descent Velocity is SQRT((2 * 1,177.20) / (1.20 * 1.60 * 25)) = SQRT(49.05) = 7.00 m/s (E3); Equivalent Circular Diameter is SQRT(100 / PI()) = 5.64 m (E4); and Touchdown Impact Kinetic Energy is (120 * 1,177.20) / 48 = 2,943.00 J (E5)!
| Recovery Parachute Metric (m=120 kg, rho=1.20 kg/m^3, Cd=1.60, S=25 m^2) | Formula | Verified Output |
|---|---|---|
| Steady Canopy Drag Tension (N) | Total_Mass_kg * 9.81 | 1,177.20 N |
| Terminal Descent Velocity (m/s) | SQRT((2 * m * 9.81) / (rho * Cd * S)) | 7.00 m/s (9.90 m/s @ rho=0.60) |
| Circular Canopy Diameter (m) | SQRT((4 * Canopy_Area_m2) / PI()) | 5.64 m |
| Touchdown Kinetic Energy (J) | (m^2 * 9.81) / (rho * Cd * S) | 2,943.00 J (5,886.00 J @ rho=0.60) |
Parachute Terminal Velocity & Touchdown Kinetic Energy Formula
Validate strictly positive Payload_Mass, Air_Density, Drag_Coefficient C_d, and Canopy_Area S!
=LET(ms_k, B2, rh_a, B3, cd_p, B4, ar_s, B5, IF(OR(ms_k <= 0, rh_a <= 0, cd_p <= 0, ar_s <= 0), "Invalid Recovery Canopy Input", ROUND(((ms_k ^ 2) * 9.81) / (rh_a * cd_p * ar_s), 2)))High-Altitude Half-Density Dropzone Check (Set Air Density = 0.60 kg/m^3)
Halve Dropzone_Air_Density B3 to 0.60 kg/m^3: Terminal Descent Rate E3 increases to 9.90 m/s and Touchdown Impact Kinetic Energy E5 doubles cleanly from 2,943.00 J to 5,886.00 J!
=IF(ISTEXT(E2), E2, ROUND(SQRT((2 * B2 * 9.81) / (B3 * B4 * B5)), 2))Try the example
Use the original values or change them to test your understanding.