Aerospace Propulsion, Gas Turbines & Flight Thermodynamics
Turbofan TSFC, Propulsive Efficiency & Overall Efficiency Formula
Calculate High-Bypass Turbofan Froude Propulsive Efficiency 2 / (1 + Vj / V0), Hourly Fuel Burn from Thrust-Specific Fuel Consumption (TSFC), Propulsive Thrust Power F*V0, and Overall Aircraft Thermodynamic Efficiency.
See why high-bypass turbofans move massive air slowly to maximize Froude efficiency!
Why did commercial airliners evolve from roaring, narrow pure-turbojets to wide-diameter high-bypass geared turbofans? Froude’s Ideal Propulsive Efficiency eta_p = 2 / (1 + V_j / V_0) proves that accelerating a small mass of exhaust to a huge jet velocity V_j wastes kinetic energy in the wake, whereas accelerating a massive bypass fan stream only slightly faster than aircraft cruise speed V_0 pushes eta_p above 80%! Meanwhile, Thrust-Specific Fuel Consumption TSFC (in g / (kN*s), or mg / (N*s)) determines fuel mass flow m_dot_f = (Thrust_kN * TSFC) / 1000 kg/s (or * 3.6 for kg/hr), letting propulsion engineers verify Overall Efficiency eta_overall = eta_thermal * eta_p = Thrust_Power_MW / (m_dot_f * Fuel_LHV_MJ_kg)!
Verify on a Widebody High-Bypass Turbofan at Mach 0.84 Cruise—Cruise_Speed V0 = 250 m/s (B2), Effective_Exhaust_Velocity Vj = 350 m/s (B3), Net_Cruise_Thrust F = 60 kN (B4), Engine_TSFC = 16.0 g/(kN*s) (B5), and Jet-A_Lower_Heating_Value LHV = 43.2 MJ/kg (B6): Froude Propulsive Efficiency is 2 / (1 + 350 / 250) = 0.8333 (83.33% in E2); Hourly Fuel Burn is 60 * 16 * 3.6 = 3,456.00 kg/hr (0.96 kg/s in E3); Propulsive Thrust Power is (60 * 250) / 1000 = 15.00 MW (E4); and Overall Thermodynamic Efficiency is 15.00 / (0.96 * 43.2) = 0.3617 (36.17% in E5—implying a 43.4% Brayton core thermal efficiency)!
| Turbofan Cruise Metric (V0=250 m/s, Vj=350 m/s, F=60 kN, TSFC=16 g/kNs) | Formula | Verified Output |
|---|---|---|
| Froude Propulsive Efficiency | 2 / (1 + V_jet / V_cruise) | 0.8333 (0.5000 @ Vj=750 m/s) |
| Hourly Fuel Mass Flow (kg/hr) | Thrust_kN * TSFC_g_kNs * 3.6 | 3,456.00 kg/hr (0.96 kg/s) |
| Propulsive Thrust Power (MW) | (Thrust_kN * V_cruise_ms) / 1000 | 15.00 MW |
| Overall Propulsion Efficiency | Thrust_Power_MW / (m_dot_f * LHV) | 0.3617 (36.17% Cruise Efficiency) |
Turbofan Overall Thermodynamic Efficiency Formula
Validate V_0 > 0, V_j >= V_0 (positive net momentum thrust requires exhaust velocity at least flight speed!), Thrust > 0, TSFC > 0, and LHV > 0!
=LET(v_cr, B2, v_jt, B3, f_kn, B4, ts_f, B5, q_hv, B6, IF(OR(v_cr <= 0, v_jt < v_cr, f_kn <= 0, ts_f <= 0, q_hv <= 0), "Invalid Turbofan Parameter", LET(md_f, (f_kn * ts_f) / 1000, p_th, (f_kn * v_cr) / 1000, ROUND(p_th / (md_f * q_hv), 4))))Low-Bypass Turbojet Exhaust Comparison (Set Jet Exhaust Vj = 750 m/s)
Raise Exhaust_Velocity B3 to 750 m/s (3x cruise speed, typical of an older low-bypass military turbojet): Froude Propulsive Efficiency E2 plunges from 83.33% down to 2 / (1 + 3) = 0.5000 (50.00%)!
=IF(OR(B2 <= 0, B3 < B2, B4 <= 0, B5 <= 0, B6 <= 0), "Invalid Turbofan Parameter", ROUND(2 / (1 + B3 / B2), 4))Try the example
Use the original values or change them to test your understanding.