The Boeing 787-8 Dreamliner has a maximum weight of 502,500...

The Boeing $787-8$ Dreamliner has a maximum weight of 502,500 lbf, a wingspan of $197 \mathrm{ft}$, a wing area of $3501 \mathrm{ft}^{2}$ and cruises at $567 \mathrm{mi} / \mathrm{h}$ at $35,000 \mathrm{ft}$ altitude. When cruising, its overall drag coefficient is about $0.027 .$ Estimate $(a)$ the aspect ratio (b) the lift coefficient, $(c)$ the cruise Mach number, and ( $d$ ) the engine thrust needed when cruising.

Key Concepts

Aerodynamic Drag

Aerodynamic drag is the aerodynamic force that opposes an aircraft's motion through the air. It is determined by factors like the drag coefficient, the reference area, the square of the velocity, and the air density. Minimizing drag is essential for improving fuel efficiency and overall performance, especially during cruise flight where balance between thrust and drag is maintained.

Aspect Ratio

Aspect ratio is a measure of the slenderness of a wing, defined as the ratio of the square of the wingspan to the wing area. It plays a critical role in determining the aerodynamic efficiency of an aircraft by influencing induced drag; higher aspect ratios typically lead to reduced induced drag, which is beneficial for cruise performance.

Lift Coefficient

The lift coefficient is a dimensionless number that characterizes the lift generated by a wing at a given angle of attack and flow conditions. It relates the lift force to the dynamic pressure and wing area, and it is crucial for analyzing flight performance and ensuring that the lift produced balances the aircraft’s weight in straight-and-level flight.

Mach Number

Mach number represents the ratio of an aircraft's speed to the speed of sound in the surrounding air. It is an important concept in aerodynamics because it helps in understanding the effects of compressibility on the airflow around the aircraft at high speeds, influencing stability, control, and aerodynamic heating.

Engine Thrust Requirement

Engine thrust is the force produced by an aircraft's engines to overcome drag and maintain flight, particularly in steady, level flight where thrust must equal the drag. Determining the engine thrust requirement involves calculating the drag force using parameters such as the drag coefficient, airspeed, air density, and reference area, ensuring that the engines provide sufficient thrust to sustain cruise conditions.

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