Let's solve this step-by-step: --- **Step 1: Find the Power Required** At minimum power, the power required (\(P_{req}\)) for flight can be calculated using the following relationship: \[ P_{req} = \frac{W^{3/2}}{\sqrt{2 \rho S}} \cdot \frac{C_{D_0}^{1/2}}{C_L^{3/2}} \] But since we don't have air density (\(\rho\)) or \(C_{D_0}\), let's use a simplified approach. The **fuel consumption rate** is given: - **Engine burns:** 0.5 lb fuel/hp/hr - **Propeller efficiency (\(\eta\))**: 0.83 The **power delivered to the propeller** (\(P_{prop}\)) is related to the shaft power (\(P_{shaft}\)) by: \[ P_{prop} = \eta \cdot P_{shaft} \] But we need to find the **fuel consumption rate per hour** in terms of actual fuel burned. Let \(x\) be the fuel burned per hour (lb/hr). We know: \[ x = 0.5 \times P_{shaft} \implies P_{shaft} = \frac{x}{0.5} \] --- #### **Step 1 Explanation** We have set up the relationship between power required, propeller efficiency, and fuel consumption. To proceed, we need the total available fuel and the rate of fuel burn per hour. --- **Step 2: Find the Endurance (Flight Time)** - **Total fuel available:** 2000 lb - **Fuel consumption rate (x):** To find this, we need \(P_{shaft}\). - **Endurance (Time) =** \(\frac{\text{Total fuel}}{\text{Fuel burn rate per hour}}\) But we need the actual shaft power required. For minimum power required, we use: \[ \text{Minimum Power Required:} \quad P_{req} = \frac{D \cdot V}{\eta} \] But let's use the fuel consumption directly: \[ \text{Fuel burn rate} = 0.5 \times P_{shaft} \ (\text{lb/hr}) \] The minimum power required for endurance is when \(\frac{C_L^{3/2}}{C_D}\) is maximum. Given \(C_L = 0.715\), \(C_D = 0.060\). But since we don't have airspeed or density, let's use **fuel and burn rate**: \[ \text{Endurance} = \frac{\text{Total fuel}}{\text{Fuel burn rate per hour}} \] If more information (like power needed) is provided, we could calculate more precisely, but with the given data: - **Total fuel:** 2000 lb - **Fuel burn rate:** \(0.5 \times P_{shaft}\) But we need **power required**. If we assume the airplane is flying at the minimum power required and all fuel is used for the engine at the given rate: - Fuel burn rate per hour (\(x\)) = 0.5 × \(P_{shaft}\) - Endurance = 2000 lb / (\(0.5 × P_{shaft}\)) hours If more data (like power required) is provided, plug in that value. --- #### **Step 2 Explanation** The airplane can fly for as long as there is fuel, at the rate given by the engine's fuel consumption. The endurance is the total fuel divided by the hourly burn rate. --- ### **Final Answer** \[ \boxed{ \text{Endurance (hours)} = \frac{2000}{0.5 \times P_{shaft}} } \] Where \(P_{shaft}\) is the shaft power required (in hp) at minimum power condition. If more details about drag, airspeed, or power required are provided, you can compute a numerical answer. For now, this is the general solution with the data given.