Inflight measurement is dependent on several parameters whose equations are derived further.
What Is Neutral Point?
- Aerodynamic centre of the whole aircraft.
- A point where resultant aerodynamic forces act.
- The moment about a neutral point doesn’t vary with changing the angle of attack.
- At Neutral Point,
Theoretical Expression For Neutral Point
For Stick fixed NP is that CG location where CMα = 0.
CMα = CLα,w ( X’cg – X’ac,w) + CMα,f – ηt . VH . CLα,t .(1 – dε/dα )
Substituting CMα = 0
0 = CLα,w ( X’cg – X’ac,w) + CMα,f – ηt . VH . CLα,t .(1 – dε/dα )
Now, taking X’cg is the location of stick fixed neutral point
X’cg = X’NP
X’NP = X’ac,w – CMα,f/CLα,w + ηt . VH . (CLα,t/CLα,w) . (1 – dε/dα )
From the above equation, we will substitute value of X’ac,w in eq. (1),
CMα = CLα,w (X’cg – X’NP)
Also, we know
Static Margin = X’NP – X’cg
dCM/dα = (dCLα,w/dα) . (-Static Margin)
dCM/dCLα,w = -Static Margin
Inflight Measurement of Stick Fixed Neutral Point
To find the inflight measurement of stick fixed neutral point, we need to know the elevator angle to trim the aircraft.
We know the linear expression for CM
CM =CMo + CMα . α + CM,δe . δe
At trim, CM = O,
[ δetrim = -(CMo + CMα . α) ] / CM,δe
From eq. (2) & (3), we derive
δetrim= δeo + (dδe/dCL) . CLtrim
δeo= CMo/ CM,δe
Therefore, shape of δe vs. CL curve is
[ dδeo/dCL = -(Static Margin)fix ] / CM,δe
When δeo is positive, negative elevator deflection is required to trim the aircraft at CL = O.
CMα = CMαLO . (dCM/dCL)fix
(dCM/dCL)fix = O
Therefore, for the location of stick fixed neutral point for inflight measurement,
dδeo/dCL = O
Inflight Measurement of Stick Free Neutral Point
To find the inflight measurement of stick free neutral point, we find the free elevator deflection.
He or CHe = f(αt, δe, δt)
Linear expression for hinge moment coefficient is
CHe = CHo + CHα,t . αt + CHδe . δe + CHδt . δt
For free elevator, hinge moment, Che = O & also assuming CHo & δt to be equal to O.
[ δe,free= CHα,t . αt ] / CHδe
Now the linear expression for tail lift coefficient with free elevator will be
CLt = CLαt . αt + CLδe . δe,free
From eq. (5),
CLt = C’Lαt . αt
C’Lαt = CLαt . f
The movement about CG of the aircraft with free elevator can be obtained in similar way as fixed elevator.
The only difference would be that CLαt would be replaced by C’Lαt.
Static Margin for stick free is