# Inflight Measurement of Stick Fixed & Stick Free NP

Inflight measurement of stick fixed and stick free neutral point is derived in this article.

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 doesnâ€™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 CMÎ± = 0.

We know,

CMÎ± = CLÎ±,w ( X’cg â€“ X’ac,w) + CMÎ±,f â€“ Î·t . VH . CLÎ±,t .(1 â€“ dÎµ/dÎ± )

— (1)

Substituting  CMÎ± = 0

We get,

0 = CLÎ±,w ( X’cg â€“ X’ac,w) + CMÎ±,f â€“ Î·t . VH . CLÎ±,t .(1 â€“ dÎµ/dÎ± )

Now, taking X’cg is the location of stick fixed neutral point

X’cg = X’NP

We get,

X’NP = X’ac,w â€“ CMÎ±,f/CLÎ±,w + Î·t . VH . (CLÎ±,t/CLÎ±,w) . (1 â€“ dÎµ/dÎ± )

From the above equation, we will substitute value of  X’ac,w  in  eq. (1),

We get,

—-(2)

Also, we know

#### Static Margin = X’NP – X’cg

Now,

dCM/dÎ± = (dCLÎ±,w/dÎ±) . (-Static Margin)

Therefore,

### 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 + CMÎ± . Î± + CM,Î´e . Î´e

—–(4)

At trim, CM = O,

[ Î´etrim = -(CMo + CMÎ± . Î±) ] / CM,Î´e

From eq. (2) & (3), we derive

#### Î´etrim= Î´eo + (dÎ´e/dCL) . CLtrim

where,

Î´eo= CMo/ CM,Î´e

Therefore, shape of Î´e vs. CL curve is

[ dÎ´eo/dCL = -(Static Margin)fix ] / CM,Î´e

When Î´eo is positive, negative elevator deflection is required to trim the aircraft at CL = O.

Also,

CMÎ± = CMÎ±LO . (dCM/dCL)fix

(dCM/dCL)fix = O

Therefore, for the location of stick fixed neutral point for inflight measurement,

dÎ´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.

Since

He or CHe = f(Î±t, Î´e, Î´t)

Linear expression for hinge moment coefficient is

CHe = CHo + CHÎ±,t . Î±t + CHÎ´e . Î´e + CHÎ´t . Î´t

For free elevator, hinge moment, Che = O & also assuming CHo & Î´t to be equal to O.

We get,

#### [ Î´e,free= CHÎ±,t . Î±t ] / CHÎ´e

Now the linear expression for tail lift coefficient with free elevator will be

CLt = CLÎ±t . Î±t + CLÎ´e . Î´e,free

From eq. (5),

CLt = Câ€™LÎ±t . Î±t

#### Câ€™LÎ±t = CLÎ±t . 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 CLÎ±t would be replaced by Câ€™LÎ±t.

Static Margin for stick free is

#### Ekta Singh

Ekta Singh is an Aerospace Engineer. She is the Founder of The Enigmatic Creation. She loves to read and talk about books. She loves to write and aspires to be an author and an entrepreneur.

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