A turbofan engine installed under an aircraft wing produces an uninstalled gross thrust $F_g = 120\text{ kN}$ at a ram drag $F_{\text{ram}} = 30\text{ kN}$. The nacelle external cowl experience an inlet spillage drag $D_{\text{spill}} = 3.0\text{ kN}$ and an afterbody boattail pressure drag $D_{\text{boat}} = 2.0\text{ kN}$. The net installed propulsive thrust $F_{\text{inst}}$ delivered to the airframe (in $\text{kN}$) is:

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### 1. Strategy & Theoretical Principles 1. Net uninstalled engine thrust is: $$F_{\text{net}} = F_g - F_{\text{ram}}$$ 2. Net installed thrust accounts for aerodynamic nacelle drag penalties: $$F_{\text{inst}} = F_{\text{net}} - \sum D_{\text{nacelle}} = (F_g - F_{\text{ram}}) - (D_{\text{spill}} + D_{\text{boat}})$$ ### 2. Analytical Formulation & Calculation Given: - Gross thrust $F_g = 120\text{ kN}$ - Ram drag $F_{\text{ram}} = 30\text{ kN}$ - Spillage drag $D_{\text{spill}} = 3.0\text{ kN}$ - Boattail drag $D_{\text{boat}} = 2.0\text{ kN}$ 1. Uninstalled net thrust: $$F_{\text{net}} = 120 - 30 = 90\text{ kN}$$ 2. Installed net thrust: $$F_{\text{inst}} = 90 - (3.0 + 2.0) = 90 - 5.0 = 85.0\text{ kN}$$ ### 3. Distractor Forensics - Candidate reporting uninstalled net thrust gets $90\text{ kN}$. ### 4. Exam Trap & Standard Reference - **Trap Alert:** Installed thrust always deducts nacelle aerodynamic losses (spillage, boattail drag). - **Standard Reference:** Mattingly, J.D., *Elements of Propulsion*, Chapter 1.

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