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,

C= 0

Neutral point

Theoretical Expression For Neutral Point

For Stick fixed NP is that CG location where C = 0.

We know,

CMα = CLα,w ( X’cg – X’ac,w) + CMα,f – ηt . VH . CLα,t .(1 – dε/dα )          

— (1)

Substituting  C = 0

We get,

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

We get,

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),

We get,

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,= -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 + C . α + CM,δe . δe


At trim, CM = O,

[ δetrim = -(CMo + C . 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,

eo/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.

We get,

[ 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

inflight measurement

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

(dCM/dCL)free = – SM’

Stati margin of stick free
stick fixed
Inflight measurement
Cl vs alpha curve
Ekta Singh Chandel

Ekta Singh Chandel

Ekta Singh is an Aerospace Engineer. She likes to read and talk about books. She loves to write and aspires to be an author and an entrepreneur.
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