I had at the back of my mind something that I had seen about this stuff and I finally remembered it. Go to
http://www.desktopaero.com/appliedaero/appliedaero.html
There are no equations in this page, very basic assumptions - No fuselage, no wing section pitching moment, just basic stuff.
The definitions of the inputs in the figure are below
sm = static margin, the measure of stability based on the reference chord. Distance between the CG and the Neutral Point.
Wing AR and Tail AR = changes in the picture as you change the numbers. What you see is what you get
St/SW = the ratio of tail area to wing area, easy stuff.
The Figure changes to show the changes, you can click/drag the tail left and right and see how the changes occur.
If the Lt/Lw printed out is positive it indicates a tail up load.
e is the induced drag and is not too interesting.
I chose the following for an example of a aerobatic ship.
sm = .10
Wing AR = 6
Tail AR = 3
St/Sw = .25
Push the compute button.
Use the mouse and move the red horizontal tail left and right and see the load on the horizontal change. If the term Lt/Lw is positive then the load is up.
For the fun of it try a sm = .4 (really stable) and see the negative values appear.
Put in a sm = .25 and see the load change about half way back as you move.
It is a good tool to find out what is happening. Of course if the airfoil has a big moment input or the fuselage, flaps, etc it will change the answer. Sometimes not easy to guess at.
---------- Heaven help me.... Now I'm quoting my own stuff.... Looking around for items relating to center of pressure (totally forgotten during this morning's very early 1:30 AM ephiphany) I'm seening lots of conflicting stuff. It seems that the old way of looking at an overall aircraft center of pressure has been tossed out and this new Neutral Point method put into it's place. --------------
Well I argue with myself and I always lose or win depending on which of me wins. It gets worse late at night. My wife mentions something about looney toons as she walks by.
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The Neutral Point (NP) consideration calls for it to be fixed based on the geometry of the airplane. Similarly the CG is fixed. But something has to move or the airplane would not take any corrective action when upset in flight.
This brings me to the overall aircraft lift Center of Pressure (lets call it the CPa). This being the resultant point of all lift forces of the wing, tail and fuselage and (YES), even drag moments. So .................. center of drag. In fact in the diagram I've shown below even though I've shown the CPa moving forward and up it's equally possible that it could move up and BACK as long as there was still a positive righting force from the drag to overcome a rearward shift of lift. Strange but true as I see it.----------
No, you don't need to approach the problem with a CPa thing. The answers will fall out without it. Assume constant velocity.
When you are neutrally stable the upset motion (say increasing angle of attack) can be made without any restoring moment from the tail.
If you have a stable airplane the moment due to the stab INCREASES FASTER than the moment due to the wing. Thus you get the restoring moment.
How it works is for a neutrally stable airplane is this
Cmwing = Cmtail
Cmwing = (Clalphawing X alphawing X wingarea X dynamic pressure) X distancetoCGwing
Cmtail = (Clalphatail X alphatail X tailarea X dynamic pressure) X distancetoCGtail
crossing out things that can be equal we get
wingarea X distanceCGwing = tailarea X distanceCGtail
But if the airplane is stable the distanceCGwing number has decreased from the neutrally stable point and the distanceCGtail increased from that point. This means that if disturbed the tail moment will increase faster than the wing moment. It works for pylon free flight or Extras equally well.
If the velocity is increased and the airplane is stable then the fact that the tail moment increases faster than the wing moment gives a nose down and a possible tuck under if the wing incidence angle is close to the tail angle. To stop this make the wing incidence angle greater than the tail angle to get angle of attack stability, put in down thrust to counter a pitch up in the climb which is faster than the glide speed and you get an airplane that works. Of course the spiraling climb works better.