ashfordeOU Turboprop Cycle (propulsion/turboprop/turboprop-cycle)
Use when the task is turboprop cycle analysis: converting the shaft power of the gas generator into propeller thrust, static thrust, and equivalent shaft power, and sizing the propeller operating point.
Domain quick reference
- Propeller (Froude) efficiency: the propeller accelerates the air from the free-stream velocity vf to the slipstream velocity vj, and the ideal efficiency is eta_p = 2 / (1 + vj / vf). When vj = vf there is no acceleration and eta_p = 1; when vj = 2 * vf the efficiency falls to 2/3. Real propellers reach 0.80 to 0.88 at cruise.
- Thrust from shaft power: at flight speed the useful thrust power is T * V, so T = eta_p * P / V with P the shaft power delivered to the propeller in W, V in m/s, and T in N. A 1 MW shaft at 100 m/s with eta_p 0.8 gives 8000 N.
- Static thrust: at zero flight speed the whole shaft power goes into the induced velocity, and actuator-disk momentum theory gives T0 = (2 * rho * A * P^2)^(1/3), with disk area A = pi/4 * D^2. A 1 MW shaft on a 3 m propeller at sea level (rho 1.225) gives about 25.9 kN, well above the cruise thrust.
- Equivalent shaft power: the residual jet thrust of the turboprop exhaust adds thrust power Tj * V, credited at the propeller efficiency: ESP = P + Tj * V / eta_p. ESP compares the whole powerplant with a pure propeller drive.
- Advance ratio: J = V / (n * D) with n = rpm / 60 in rev/s and D the propeller diameter in m. J measures the distance travelled per revolution in diameters.
- Power and thrust coefficients: Cp = P / (rho * n^3 * D^5) and Ct = T / (rho * n^2 * D^4) are the dimensionless forms of the shaft power and thrust; propeller performance charts plot Cp and Ct against J.
- Specific fuel consumption on shaft power: SFC = mf / P in kg/(kW h), converting the fuel flow in kg/s to fuel per kilowatt-hour of shaft power.
- Overall efficiency: eta_o = eta_th * eta_p * eta_m, the thermal efficiency of the gas generator cycle times the propeller efficiency times the mechanical efficiency of the shaft and gearbox.
Workflow
- Establish the operating point: flight velocity V, shaft power P, fuel flow mf, air density rho, propeller diameter D and speed rpm.
- Estimate the slipstream velocity and compute the propeller efficiency with propeller_efficiency.
- Compute the cruise thrust with thrust_from_shaft_power and the static thrust with static_thrust; the stand thrust is the sizing load for the propeller and gearbox.
- Credit any residual jet thrust with equivalent_shaft_power to compare the powerplant against a pure propeller drive.
- Compute the advance ratio, power coefficient, and thrust coefficient with advance_ratio, power_coefficient, and thrust_coefficient to place the operating point on the propeller chart.
- Close the loop with specific_fuel_consumption and overall_efficiency for the powerplant assessment.
Pitfalls
- Using the slipstream velocity below the flight velocity: the propeller accelerates the air, so vj must be >= vf; a vj below vf is unphysical and would return an efficiency above 1.
- Confusing static and cruise thrust: the static thrust from the actuator-disk relation is far larger than the cruise thrust at speed, and it is the stand condition that loads the propeller and gearbox.
- Forgetting the disk area in static thrust: T0 scales with the cube root of the area, so doubling the diameter raises static thrust by the cube root of 4, about 1.59.
- Using rpm instead of rev/s in the coefficients: n = rpm / 60 everywhere, or the power and thrust coefficients come out wrong.
- Crediting the jet thrust without the propeller efficiency: the equivalent shaft power divides Tj * V by eta_p, because the jet thrust is worth more shaft power the worse the propeller is.
- Dropping the mechanical efficiency: eta_o multiplies the thermal and propeller efficiencies by the gearbox and shaft efficiency, typically 0.97 to 0.99.
- Sizing the propeller at cruise only: the advance ratio and coefficients must be checked at the climb and stand conditions, where J approaches zero and the coefficients peak.
Behavior contract (gate 3)
The turboprop cycle logic is exercised by the gate 3 contract test: scripts/test_turboprop_cycle.py against scripts/turboprop_cycle_logic.py (stdlib unittest, offline). Run: python3 scripts/test_turboprop_cycle.py
Compliance
- FAR-33 is cited as reference only for the engine certification context; the propeller and actuator-disk relations are common propulsion methodology, paraphrased here. No proprietary or copyrighted text is reproduced.
- compliance: STANDARDS-REF, gated: false.