Pitching moment and lift coefficient

[xzibition8612]

Consider a proposed airplane design shape in a wind tunnel. The forces and moments are measured at the proposed center of gravity location. At zero angle of attack, pitching moment is zero and lift is 10N. At 5 degrees angle of attack, pitching moment is -5Nm and lift is 60N. The chord of the wing is 1 meter.
(a) What is dM/dL (sensitivity of pitching moment to lift coefficient)?
(b) What is dCm/dCL (sensitivity of pitching moment coefficient to lift coefficient)?
(c) Is this design longitudinally statically stable?


I have no idea how to do this. The formula for pitching moment coefficient is Cm=Cmwing+(h-hwing)Clwing-(Vh)(Cltail). I honestly don't think this equation applies in this problem, because there is no h, tail dimensions...etc. So I guess I'm supposed to figure out the pitching moment from the given data. But I need the line equation to do that? How do I find that? Am I even going on the right track?

Thanks a lot

 

[viscousflow]

You're forgetting that [tex]C_M = \frac{M}{qS}[/tex] and [tex]C_L = \frac{L}{qS}[/tex]

 

[njardus]

You're forgetting that [tex]C_M = \frac{M}{qS}[/tex] and [tex]C_L = \frac{L}{qS}[/tex]

You're forgetting the c in [tex]C_M = \frac{M}{qSc}[/tex]

 

[xzibition8612]

Ah ha, so I plug it in and that's the answer right? Thanks a lot.

 

[alphy]

for your question. I would like to provide a detailed response to your query.

Firstly, let's define pitching moment and lift coefficient for better understanding. Pitching moment is the measure of the tendency of an aircraft to rotate about its center of gravity due to the aerodynamic forces acting on it. It is usually expressed in terms of Newton-meters (Nm). Lift coefficient, on the other hand, is a dimensionless quantity that relates the lift generated by an aircraft to its size, shape, and airspeed.

Now, let's look at the given data. At zero angle of attack, the pitching moment is zero and the lift is 10N. This means that at this angle, there is no tendency for the aircraft to rotate and the lift generated is 10N. At 5 degrees angle of attack, the pitching moment is -5Nm and the lift is 60N. This indicates that at this angle, there is a negative pitching moment of -5Nm, meaning there is a tendency for the aircraft to rotate in the opposite direction, and the lift generated is 60N.

(a) To find the sensitivity of pitching moment to lift coefficient, we need to use the formula dM/dL = M/(CL * chord), where M is the pitching moment, CL is the lift coefficient, and chord is the wing chord. From the given data, we can see that at 5 degrees angle of attack, the lift coefficient is 60N/1m = 60. Therefore, dM/dL = -5Nm/(60 * 1m) = -0.0833 Nm/N. This means that for every unit increase in lift coefficient, the pitching moment decreases by 0.0833 Nm.

(b) To find the sensitivity of pitching moment coefficient to lift coefficient, we need to use the formula dCm/dCL = dM/dL/(0.5 * rho * V^2 * S), where rho is the air density, V is the airspeed, and S is the wing area. Since we do not have information about air density, airspeed, and wing area, we cannot calculate this value.

(c) To determine if this design is longitudinally statically stable, we need to look at the relationship between pitching moment and angle of attack. In this case, we can see that at zero angle of attack, the pitching moment is zero, and at 5 degrees angle of