To determine the condition at which a typical propeller aircraft achieves maximum (specific) range, it's important to consider the relationship between power, fuel consumption, aerodynamic drag, and lift.
The specific range of an aircraft is defined as the distance traveled per unit of fuel consumed. Mathematically, it can be expressed as:
\[ \text{Specific Range} = \frac{V}{F} \]
Where \( V \) is the airspeed and \( F \) is the fuel consumption. Given the relationship of fuel consumption to power, we have:
\[ F = c_P P_{br} \]
And since we can relate power required to drag as:
\[ P_{br} = \frac{D \cdot V}{\eta} \]
Where \( D \) is the drag force and \( \eta \) is the efficiency, we can substitute this into our specific range equation. The drag \( D \) can be calculated from the lift-drag polar you provided:
\[ D = \frac{1}{2} \rho V^2 C_D \]
Combining these relationships ultimately connects the specific range to the power required (which includes drag), as the dynamic balance between lift, drag, and thrust efficiently translates into fuel consumption.
For maximum range, we need to minimize the fuel consumption per distance per unit of power, effectively translating to a strategy to decrease drag while maximizing your lift-to-drag ratio (L/D). The maximum (specific) range condition is typically achieved at the minimum power required.
Therefore, the correct answer among the options you provided is:
C) Minimum power required (P_r,min).
This is because when the power required is minimized, the specific fuel consumption is also effectively minimized relative to the distance traveled, maximizing the range for a given amount of fuel consumed.