A turbojet aircraft cruises at a constant altitude and constant true airspeed $V = 240\text{ m/s}$ with an aerodynamic lift-to-drag ratio $L/D = 16.0$. The engine thrust-specific fuel consumption is $TSFC = 2.0 \times 10^{-4}\text{ N}/(\text{N}\cdot\text{s})$. If the gross takeoff weight is $W_0 = 100,000\text{ N}$ and the fuel consumed is $20,000\text{ N}$ ($W_1 = 80,000\text{ N}$), what is the Breguet cruise range (in km) to the nearest integer?

Answer Key:

4284

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Governing Concept:** For jet-propelled aircraft where fuel burn is proportional to thrust ($dW/dt = -c_t T = -c_t W / (L/D)$), integrating over cruising flight yields the Breguet Jet Range equation. 2. **Stage 2: Mathematical Formulation:** * $R = \frac{V}{c_t} \left(\frac{L}{D}\right) \ln\left(\frac{W_0}{W_1}\right)$. 3. **Stage 3: Parameter Substitution:** * $V = 240\text{ m/s}$, $c_t = 2.0 \times 10^{-4}\text{ s}^{-1}$, $L/D = 16.0$. * Velocity-to-consumption ratio: $\frac{V}{c_t} = \frac{240}{2.0 \times 10^{-4}} = 1.20 \times 10^6\text{ m}$. * Weight ratio: $W_0 / W_1 = 100,000 / 80,000 = 1.25$. * Natural log: $\ln(1.25) \approx 0.22314355$. 4. **Stage 4: Numerical Calculation:** * $R = (1.20 \times 10^6) \times 16.0 \times 0.22314355 = 4,284,356\text{ m} = 4284.36\text{ km}$. * To the nearest integer: $4284\text{ km}$. 5. **Stage 5: Official Reference:** John D. Anderson Jr., *Introduction to Flight*, Chapter 6; Bandu N. Pamadi, *Performance, Stability, Dynamics, and Control of Airplanes*, Chapter 2.

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