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_{Mα}= 0

### Theoretical Expression For Neutral Point

**For** **Stick fixed NP is that CG location where C _{Mα} = 0.**

We know,

C_{M}** _{α}** = 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_{M}_{α}_{,f}/C_{L}_{α}_{,w} + η_{t }. V_{H }. (CL_{α,}_{t}/C_{L}_{α,}_{w}) . (1 – dε/dα )

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

We get,

#### C_{M}_{α} = C_{L}_{α,}_{w} (X’_{cg} – X’_{NP})

_{α}

_{α,}

—-(2)

Also, we know

#### Static Margin = X’_{NP} – X’_{cg}

Now,

dC_{M}/dα = (dC_{L}_{α,}_{w}/dα) . (-Static Margin)

Therefore,

#### dC_{M}/dC_{L}_{α,}_{w }= -Static Margin

_{α,}

### 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_{M}** _{α}** = C

_{M}

_{α}_{LO}. (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