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=0.8 and given that C_m=0.02, determine the moment coefficient of the moment around the aerodynamic centre.
To determine the moment coefficient around the aerodynamic center (C_m0), we need to use the concept of moment equilibrium.
First, let's define the variables:
- C_L: Lift coefficient of the wing (given as 0.8)
- C_m: Total moment coefficient (given as 0.02)
- l_cg: Distance from the aerodynamic center to the center of gravity (given as 0.05c, where c is the chord length of the wing)
The equation for moment equilibrium is:
C_m = C_m0 + (l_cg / c) * C_L
Rearranging the equation to solve for C_m0:
C_m0 = C_m - (l_cg / c) * C_L
Substituting the given values:
C_m0 = 0.02 - (0.05c / c) * 0.8
Since the term (0.05c / c) simplifies to 0.05, we can further simplify the equation:
C_m0 = 0.02 - 0.05 * 0.8
Calculating the result:
C_m0 = 0.02 - 0.04
C_m0 = -0.02
Therefore, the moment coefficient around the aerodynamic centre (C_m0) is -0.02.
To determine the moment coefficient around the aerodynamic center, we can use the equation:
C_m = C_m0 + C_L * (x_cg - x_ac)
Where:
C_m is the moment coefficient around the aerodynamic center
C_m0 is the moment coefficient when the lift coefficient is zero
C_L is the lift coefficient
x_cg is the position of the center of gravity (measured from the leading edge of the wing)
x_ac is the position of the aerodynamic center (also measured from the leading edge of the wing)
In this case, we are given that:
C_L = 0.8
x_cg = 0.05c (where c is the chord length of the wing)
We also need to know the value of C_m0, which represents the moment coefficient when there is no lift (C_L = 0). This value is typically provided in aerodynamic data tables or can be determined through wind tunnel testing.
Assuming we have the value of C_m0, we can substitute the given values into the equation to calculate the moment coefficient:
C_m = C_m0 + C_L * (x_cg - x_ac)
Keep in mind that the position of the aerodynamic center (x_ac) can vary depending on the specific wing shape and airfoil section. Therefore, you would need to consult aerodynamic data or use computational methods to determine the value of x_ac for your specific wing design.
I hope this explanation helps you understand how to calculate the moment coefficient around the aerodynamic center for a flying wing aircraft.
To determine the moment coefficient around the aerodynamic centre (C_mac), we can use the equation:
C_mac = C_m - (l_cg / MAC) * C_l
Where:
- C_mac is the moment coefficient around the aerodynamic centre
- C_m is the moment coefficient given (0.02)
- l_cg is the distance from the centre of gravity to the aerodynamic centre (0.05c)
- MAC is the Mean Aerodynamic Chord of the wing
However, the equation requires the Mean Aerodynamic Chord (MAC) of the wing. Since this information is not provided, we cannot directly calculate the moment coefficient around the aerodynamic centre.