A long-range jet liner flies (almost exactly) level at constant speed, subject to the forces of drag fD=(1/2)CDrhoSv^2, thrust Ft, and weight Mg. Given the plane's wing area, lift and drag coefficients, speed and takeoff mass, calculate the engine power required for level flight during the cruise phase of its long nonstop flight, as a function of distance traveled. Numerical evaluation of all coefficient in your result will be required.

To calculate the engine power required for level flight during the cruise phase of a long nonstop flight, we need to consider the forces acting on the aircraft.

First, let's break down the equation for drag force (fD):

fD = (1/2) * CD * rho * S * v^2

Where:
- CD is the drag coefficient
- rho is the air density
- S is the wing area
- v is the velocity of the aircraft

The drag force acts opposite to the direction of motion and opposes the forward thrust. The engine power required to overcome drag force is given by:

P = fD * v

Now, let's expand the equation to calculate the engine power required for level flight:

P = ((1/2) * CD * rho * S * v^2) * v
P = (1/2) * CD * rho * S * v^3

To proceed further, we need to know the values of the lift coefficient (CL), drag coefficient (CD), air density (rho), wing area (S), velocity (v), and aircraft mass (Mg).

The lift coefficient (CL) and drag coefficient (CD) could depend on various factors such as the angle of attack, Mach number, and Reynolds number, among others. These coefficients can be obtained from aerodynamic testing or performance data provided by the aircraft manufacturer.

The air density (rho) varies with altitude but can be estimated using standard atmospheric models or obtained from weather data. The density typically decreases with increasing altitude.

The wing area (S) is a geometric property of the aircraft and can be obtained from the aircraft specifications.

The velocity (v) is the speed at which the aircraft is flying. This also varies during different phases of flight.

The aircraft mass (Mg) includes the weight of the aircraft and its contents (fuel, passengers, payload). This mass reduces during the flight due to fuel consumption, so it would vary depending on the distance traveled.

To calculate the engine power required for level flight as a function of distance traveled, you would need to determine all the above parameters at different points during the flight and evaluate the equation for engine power (P) using the numerical values.

It's important to note that this calculation assumes level flight with no changes in altitude. In reality, the aircraft may climb or descend during different phases of the flight, which would affect the engine power required.