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_m=0.02, determine the moment coefficient of the moment around the aerodynamic centre.
To find the moment coefficient (C_m) around the aerodynamic centre, we can use the following formula:
C_m = (l(cg) / c) * C_L
Given:
l(cg) = 0.05c (distance from the centre of gravity to the wing's aerodynamic centre)
C_L = 0.8 (lift coefficient)
Substituting the given values into the formula, we have:
C_m = (0.05c / c) * 0.8
C_m = 0.05 * 0.8
C_m = 0.04
Therefore, the moment coefficient (C_m) around the aerodynamic centre is 0.04.
To determine the moment coefficient (Cm) around the aerodynamic center, we can use the following relationship:
Cm = Cm_ac - (X_cg/X_ref) * CL
Where:
- Cm_ac is the moment coefficient around the aerodynamic center
- X_cg is the distance between the center of gravity (CG) and the aerodynamic center
- X_ref is the reference length, which is typically the mean aerodynamic chord (c) of the wing
- CL is the lift coefficient
Given:
- X_cg = 0.05c (distance between CG and aerodynamic center)
- CL = 0.8 (lift coefficient)
- Cm = 0.02 (moment coefficient)
We can plug the given values into the equation to find Cm_ac:
Cm_ac = Cm + (X_cg/X_ref) * CL
Since X_cg is given as a fraction of the mean aerodynamic chord (c), we can substitute X_cg with 0.05c. Therefore,
Cm_ac = 0.02 + (0.05c/c) * 0.8
Cm_ac = 0.02 + 0.05 * 0.8
Cm_ac = 0.02 + 0.04
Cm_ac = 0.06
Therefore, the moment coefficient around the aerodynamic center (Cm_ac) is 0.06.
To determine the moment coefficient (Cm) around the aerodynamic center, we can use the equation:
Cm = Cm(ac) - CL(distance)
Here, Cm(ac) is the moment coefficient around the aerodynamic center when the aircraft is at its reference point, and CL(distance) is the change in lift coefficient (CL) multiplied by the distance between the center of gravity (CG) and the aerodynamic center (AC).
Given:
- Cm(ac) = 0.02
- CL = 0.8
- Distance between CG and AC (d) = 0.05c
Substituting the given values into the equation, we have:
Cm = 0.02 - (0.8 * 0.05c)
Now, to fully calculate the moment coefficient, we also need the value of the chord length (c). Please provide the value of 'c' in order to compute the final result.