Below you see a figure of a flying wing, so an aircraft without a tail. Its centre of gravity is situated behind the aerodynamic centre of the wing, with l(cg)=0.05c. If you are given that the wing flies with C_L =0.8and given that C_=0.02, determine the moment coefficient of the moment around the aerodynamic centre.
To determine the moment coefficient (Cm) around the aerodynamic center, we can use the equation:
Cm = (C_L)*(X_cg - X_ac)/c
Where:
- Cm is the moment coefficient
- C_L is the lift coefficient (0.8 in this case)
- X_cg is the distance from the aerodynamic center to the center of gravity (0.05c in this case)
- X_ac is the distance from the reference point (usually the leading edge of the wing) to the aerodynamic center
- c is the chord length of the wing
Since the figure given doesn't specify the distance X_ac, we can't calculate the moment coefficient without that information.
To determine the moment coefficient around the aerodynamic center (Cm), we can use the pitching moment equation:
Cm = Cm(ac) + (l(cg)/c) * CL
Where:
Cm(ac) = Moment coefficient around the aerodynamic center
l(cg) = Distance between the center of gravity and the aerodynamic center (0.05c)
c = Chord length of the wing
CL = Lift coefficient (0.8)
Substituting the given values into the equation, we have:
Cm = Cm(ac) + (0.05c/c) * 0.8
As for the value of C_, it doesn't seem relevant to the given question about determining the moment coefficient (Cm).
To determine the moment coefficient (Cm) around the aerodynamic center, we need to use the equation:
Cm = (Cm0 + cmα * α) + (Cm' * C')
First, let's calculate the position of the center of gravity (cg) with respect to the wing chord (c). Given that l(cg) = 0.05c, we can determine that the center of gravity is located 5% of the wing chord length behind the aerodynamic center.
Since we are given the lift coefficient (CL) as 0.8, we can assume that α (angle of attack) is also known since CL is determined by the angle of attack.
Now, let's determine the moment coefficient around the aerodynamic center using the equation above.
1. Calculate the position of the center of gravity (cg):
l(cg) = 0.05c
2. Use the given lift coefficient (CL) and calculate the moment coefficient due to the aerodynamic forces (Cm0):
Cm0 = -C_L * l(cg) = -0.8 * 0.05
3. Determine the moment coefficient due to the angle of attack (cmα):
Since the value of cmα is not given, we cannot calculate it without additional information.
4. Calculate the moment coefficient due to the change in the center of gravity (Cm'):
Since the value of Cm' is also not given, we cannot calculate it without additional information.
Given the information provided, we are unable to determine the moment coefficient (Cm) around the aerodynamic center without knowing the values of cmα and Cm'.