Final answer:
To determine the speed at which the air must move over the upper surface of the wing to create the ideal lift, we can use Bernoulli's principle and the lift equation. The same principle and equation can be used to calculate the air speed over the upper surface of the wing at a cruising speed and altitude with a different air density.
Step-by-step explanation:
To find out how fast the air must move over the upper surface of the wing to create the ideal lift, we can use Bernoulli's principle.
Bernoulli's principle states that the sum of the pressure and kinetic energy per unit volume of a fluid is constant along a streamline.
The ideal lift can be given by the equation:
Lift = 0.5 * density * velocity^2 * area * lift coefficient
Given that the lift coefficient is 1000 N/m^2 and the wing area is 250 ft^2, we can calculate the air speed:
1000 N/m^2 = 0.5 * 1.29 kg/m^3 * (60.0 m/s + v)^2 * (250 ft^2 * 0.092903 m^2/ft^2) * lift coefficient
where v is the air speed over the upper surface of the wing.
(b) Calculation of Cruising Speed:
Using the same equation, we can calculate the air speed over the upper surface of the wing at a cruising speed of 245 m/s and at an altitude where air density is one-fourth that at sea level:
1000 N/m^2 = 0.5 * (1.29 kg/m^3 /4) * (245 m/s + v)^2 * (250 ft^2 * 0.092903 m^2/ft^2) * lift coefficient