In order to determine the plane's drag coefficient, we need to calculate the drag force. The drag force can be calculated using the following formula:
Drag force = (1/2) * ρ * v^2 * Cd * A
Where:
ρ = air density
v = velocity of the aircraft
Cd = drag coefficient
A = wing surface area
First, let's convert the velocity from knots to meters per second:
116.6 knots = 60.27 m/s
Given that the plane's altitude is 850 meters, we can use the International Standard Atmosphere (ISA) to find the air density at that altitude. The air density at sea level (ρ0) is approximately 1.225 kg/m^3, and it decreases with altitude at a rate of -0.0065 kg/m^3 per meter. We can use this information to calculate the air density at 850 meters:
ρ = ρ0 * (1 + (L * h / T0)) ^ (-g / (L * R))
Where:
L = temperature lapse rate (0.0065 K/m)
h = altitude (850 m)
T0 = sea level temperature (288.15 K)
g = acceleration due to gravity (9.81 m/s^2)
R = specific gas constant for air (287.1 J/kg·K)
Using this equation, we find:
ρ = 1.225 * (1 + (0.0065 * 850 / 288.15)) ^ (-9.81 / (0.0065 * 287.1))
= 1.082 kg/m^3
Now we can calculate the drag force. Rearranging the formula for drag force, we can solve for Cd:
Drag force = (1/2) * ρ * v^2 * Cd * A
Cd = Drag force / ((1/2) * ρ * v^2 * A)
The mass of air accelerated by the propeller every second is 80 kg, and its velocity is 105.56 m/s. This mass and velocity represent the force produced by the propeller (thrust). At constant velocity, this thrust force must be equal to the drag force. Therefore, we can set the thrust force equal to the drag force:
Thrust force = Drag force
80 kg * acceleration = (1/2) * ρ * v^2 * Cd * A
Rearranging this equation, we can solve for the drag coefficient:
Cd = (2 * 80 kg * acceleration) / (ρ * v^2 * A)
Plugging in the given values:
Cd = (2 * 80 kg * 105.56 m/s) / (1.082 kg/m^3 * (60.27 m/s)^2 * 22 m^2)
Calculating this expression gives us the value for the drag coefficient Cd.
A general aviation aircraft (m = 1200 kg) flies (under ISA conditions) at 850 metres altitude, with a constant velocity (true airspeed) of 116.6 knots. Its wing surface area is 22 square metres.
Given that its propeller is able to accelerate 80 kilograms of air to a velocity of 105.56 m/s every second, determine the plane's drag coefficient .
1 answer
2 answers