In article ,
Jim Logajan wrote:

Alan Baker wrote:
In a glide in a low wing aircraft:

Total aerodynamic force (lift and drag!)
^
|
|
M (Centre of Mass)
|
C (Centre of Aerodynamic Pressure)
|
|
Weight (no down arrow head... ...sorry)

Now remember, the aircraft must be descending to make this work.

The above diagram is simplified too soon in the analysis. You may as well
have dispensed with the weight and aerodynamic forces too, as they
contribute nothing to your subsequent argument since you never vary them.

No, it's not.

It represents all the forces on an aircraft in a trimmed glide: total
aerodynamic force perfectly balancing weight.


Now if you add thrust at the "drag line" (the line through the CoP
parallel to the aircraft's motion):

Total aerodynamic force
^
|
|
M (Centre of Mass)
|
(Thrust)--C (Centre of Aerodynamic pressure)
|
|
Weight

You can align the engine any way you want and it will still create a
pitch up, right?

Sure - and the object will rotate about M until it reaches a rotation
speed in equilibrium with air drag (by definition, the only point where
we are allowed to add that drag component is at point C):

It will never reach such an equilibrium. That's the problem. With the
increased thrust, the aircraft will both: pitch up and gain airspeed.
Remember: drag is notional. It is just the component of the total
aerodynamic force anti-parallel to the motion of the aircraft. In this
situation of a low wing aircraft, if you add thrust at the CoA, the
aircraft will pitch up, and that will rotate the craft and you'll have
to trim the aircraft. No waiting for drag to grow will do it.


Total aerodynamic force
^
|
|
M (Centre of Mass)
|
(Thrust)--C--(air drag) (Centre of Aerodynamic pressure)
|
|
Weight


But:

Total aerodynamic force
^
|
|
(Thrust)--M (Centre of Mass)
|
C (Centre of Aerodynamic Pressure)
|
|
Weight

Add the thrust at the centre of mass, and you get no pitching moment.

The diagram above is of a system that isn't in equilibrium. Furthermore,
there is no vector we can anchor at C that brings it into equilibrium -
if we add a vector so that we get a pure couple, like so:

So, what do you expect an aircraft in a stable glide to do when you add
thrust: accelerate. The natural consequence of a system that isn't in
equilibrium.


Total aerodynamic force
^
|
|
(Thrust)--M (Centre of Mass)
|
C--(air drag) (Centre of Aerodynamic Pressure)
|
|
Weight

...then the _couple_ rotates the aircraft around M in a counterclockwise
direction (i.e. pitch down!) Your force diagram is flawed because it
makes incorrect assumptions about the location of C at equilibrium and
the direction of the total aerodynamic forces.

Sorry, but no.

By definition, an aircraft in a stable glide has a *total* aerodynamic
force acting on it that must be precisely equal to the aircraft's weight
and *must* be acting through the centre of mass. You're suddenly adding
a new force as if it isn't accounted for in the previous diagram.


Running the thrust line through M does _not_ guarantee you wont get any
couple.

It guarantees you won't get a couple from the thrust. You say you have a
B.SC: from where?


In fact none of the diagrams you or I drew are complete and do not
accurately capture the reality. Center of mass changes with each flight
and even during flight, and center of pressure changes with aircraft
orientation.

So? The point I've been trying to make is that if you're trying to keep
the aircraft's flight characteristics, what you need to consider is
orientation of the thrust line with respect to the CoM. For the
purposes of argument, I've been using a thrust line through the centre
of mass to illustrate my point, but at no time have I argued that it is
the only place you can have the thrust line and have a stable aircraft.

But by using the zero point, I can illustrate it well. If you have an
airframe with an engine installation where the thrust line goes through
the centre of mass, then you're noting going to have a pitching moment
generated by thrust, period. So if you install a new engine and have to
adjust it's mounting point such that it maintains the CoM in the same
location, but moves the thrust line up or down, all of sudden you *will*
have a pitching moment generated by changes in thrust.

That is a change in the aircraft's flying characteristics, period.

To remove that change, simply reangle the engine to once again have the
thrust line pass through the CoM. Then once again, you will have no
thrust induced pitch changes.

Do the same reasoning for an aircraft with a thrust line above the CoM,
where a new engine lowers it to coincide with the CoM. You'll once again
change the flying characteristics from one where increased thrust causes
a pitch up, to one where thrust does not. Reangle the engine and you'll
restore the original flying characteristics.

Period.

--
Alan Baker
Vancouver, British Columbia
http://gallery.me.com/alangbaker/100008/DSCF0162/web.jpg