For a high-bypass turbofan engine operating at a fixed subsonic cruise flight Mach number and fixed core turbine entry temperature (TET), increasing the bypass ratio (BPR) produces which of the following operational effects?

(A) Increases overall propulsive efficiency ($\eta_p$)

(B) Decreases Thrust Specific Fuel Consumption (TSFC)

(C) Decreases average jet exhaust exit velocity relative to ambient air

(D) Increases the specific thrust (thrust per unit total airflow)

Answer Key:

A, B, C

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Propulsive Efficiency:** $\eta_p = \frac{2}{1 + (V_j / V_\infty)}$. As BPR increases, the cold fan stream dilutes the core jet, reducing mixed jet velocity $V_j$. As $V_j \to V_\infty$, $\eta_p \to 100\%$ (Statement A and C are TRUE). 2. **Stage 2: Fuel Consumption:** TSFC is inversely proportional to overall efficiency ($\eta_o = \eta_{th} \times \eta_p$). Since $\eta_p$ rises, TSFC drops (Statement B is TRUE). 3. **Stage 3: Specific Thrust:** Specific thrust $F / \dot{m}_{total} \approx (V_j - V_\infty)$. As $V_j$ decreases, specific thrust decreases, requiring larger nacelle diameters (Statement D is FALSE). 4. **Stage 4: Official Reference:** Jack D. Mattingly, *Elements of Propulsion*, Chapter 6.

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