A kite weighs 9.8N having an area of 1m square makes an angle of 7.5 degree to the horizontal
when flying in a wind at speeds of 35km/h. If the pull on the string attached to the
kite is 50N and is inclined to the horizontal 45 degree. Determine the lift and dras
coefficients. The density of air is 1.2kg/m3.
To determine the lift and drag coefficients, we need to calculate the lift and drag forces acting on the kite.
1. Calculate the lift force (L):
The lift force can be calculated using the equation:
L = 0.5 * ρ * A * v^2 * Cl
Where:
L = Lift force
ρ = Density of air (given as 1.2 kg/m^3)
A = Area of the kite (given as 1 m^2)
v = Velocity of the wind (35 km/h = 35,000 m/3600 s = 9.72 m/s)
Cl = Lift coefficient (to be determined)
Plugging in the values, we get:
L = 0.5 * 1.2 * 1 * (9.72)^2 * Cl
L = 0.5 * 1.2 * 1 * 94.5744 * Cl
L = 56.7446 * Cl
2. Calculate the drag force (D):
The drag force can be calculated using the equation:
D = 0.5 * ρ * A * v^2 * Cd
Where:
D = Drag force
ρ = Density of air (given as 1.2 kg/m^3)
A = Area of the kite (given as 1 m^2)
v = Velocity of the wind (35 km/h = 35,000 m/3600 s = 9.72 m/s)
Cd = Drag coefficient (to be determined)
Plugging in the values, we get:
D = 0.5 * 1.2 * 1 * (9.72)^2 * Cd
D = 0.5 * 1.2 * 1 * 94.5744 * Cd
D = 56.7446 * Cd
3. Calculate the lift coefficient (Cl):
The lift coefficient can be calculated using the equation:
Cl = L / (0.5 * ρ * A * v^2)
Plugging in the values, we have:
Cl = 50 N / (0.5 * 1.2 kg/m^3 * 1 m^2 * (35,000 m/3600 s)^2)
Cl = 50 N / (0.5 * 1.2 * 94.5744)
Cl ≈ 0.888
4. Calculate the drag coefficient (Cd):
The drag coefficient can be calculated using the equation:
Cd = D / (0.5 * ρ * A * v^2)
Plugging in the values, we have:
Cd = 50 N / (0.5 * 1.2 kg/m^3 * 1 m^2 * (35,000 m/3600 s)^2)
Cd = 50 N / (0.5 * 1.2 * 94.5744)
Cd ≈ 0.888
Therefore, the lift coefficient (Cl) and drag coefficient (Cd) are approximately 0.888 each.