Necolatis wrote in Tue Apr 11, 2017 3:22 pm:What I am looking for, will for example at low speed typically be higher than 1 since the engine sucks in more air than would be pushed in by the air if the engine inlet would just be a hollow tube with no engine.

I think I have a reasonable idea on this math.

The flow through the motor and intake velocityThe mass flow of air through the engine:

f= 45*(1+b)*ff

where b is the bypass ratio, ff the fuel flow and 45 comes from the

reasoning above.

The inlet velocity:

vi= f/(r*A)

r is the air density and A is the area of the inlet(s).

For the pitching effect I get:

Force due to air inertia:

F=f*v0*sin(a) ~ f*v0*a (a<pi/6)

v0 is the free flow velocity and a is the angle of attack

But we want to calculate the extra force compared to a hollow tube model. So:

free flow through motor f0=V0*A*r

DF=F - f0*v0*a=a*f*v0-a*A*r*v0^2=a*(vi*r*A*v0-A*r*v0^2)=a*r*A*(vi*v0 - v0^2)

using qbar= r*S*v0^2/2 where S is the wing surface area, kA=A/S and the flow ratio CA= vi/v0 gives

DF=2*a*kA*qbar*(CA-1)

The moment are then

DF*R=2*R*kA*qbar*(CA-1)

R is the distance from the inlet to CG

Using the span as standard for moment arm

kR = R/B where B is the wing span

M= a*2*kA*kR*B*qbar*(CA-1)

M is the force moment

Combining 2*kR*kA into one coefficient Cm gives the formula:M=a*Cm*qbar*B*(CA-1)

This agrees, as far as I can see, with the text and figures in the JA37 document.

Hope it helps!

*Edited due to missing factor (ff) in first formula