Inflight Measurement of Stick Fixed & Stick Free NP

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 C_Mα = 0.

We know,

C_Mα = CL_α,w ( X’_cg – X’_ac,w) + CM_α,f – η_t . V_H . CL_α,t .(1 – dε/dα )          

— (1)

Substituting  C_Mα = 0

We get,

0 = CL_α,w ( X’_cg – X’_ac,w) + CM_α,f – η_t . V_H . CL_α,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 – C_Mα,f/C_Lα,w + η_t . V_H . (CL_α,t/C_Lα,w) . (1 – dε/dα )

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

We get,

C_Mα = C_Lα,w (X’_cg – X’_NP)

—-(2)

Also, we know

Static Margin = X’_NP – X’_cg

Now,

dC_M/dα = (dC_Lα,w/dα) . (-Static Margin)

Therefore,

dC_M/dC_Lα,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 C_M

C_M =C_Mo + C_Mα . α + C_M,δe . δ_e

—–(4)

At trim, C_M = O,

[ δ_etrim = -(C_Mo + C_Mα . α) ] / C_M,δe

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

δ_etrim= δ_eo + (dδ_e/dC_L) . C_Ltrim

where,

δ_eo= C_Mo/ C_M,δe

Therefore, shape of δ_e vs. C_L curve is

[ dδ_eo/dC_L = -(Static Margin)_fix ] / C_M,δe

When δ_eo is positive, negative elevator deflection is required to trim the aircraft at C_L = O.  

Also,

C_Mα = C_MαLO . (dC_M/dC_L)_fix

(dC_M/dC_L)_fix = O

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

dδ_eo/dC_L = 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

H_e or C_He = f(α_t, δ_e, δ_t)

Linear expression for hinge moment coefficient is

C_He = C_Ho + C_Hα,t . α_t + C_Hδe . δ_e + C_Hδt . δ_t

For free elevator, hinge moment, C_he = O & also assuming C_Ho & δ_t to be equal to O.

We get,

[ δ_e,free= C_Hα,t . α_t ] / C_Hδe

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

CL_t = C_Lαt . α_t + C_Lδe . δ_e,free

From eq. (5),

C_Lt = C’_Lαt . α_t

C’_Lαt = C_{Lαt .} 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 C_Lαt would be replaced by C’_Lαt.

Static Margin for stick free is

(dC_M/dC_L)_free = – SM’