longitudinal stability/aero.center vs. center of P

Question

longitudinal stability/aero.center vs. center of P

renfrew (Aeronautics)

(OP)

24 Oct 03 16:58

Ok guys and gals..I graduated 15 years ago and remember very little from Engineering School, so go easy on me. I'm doing a little light reading for fun and am getting very confused by something. I understand Aerodynamic center (Ac - as a convenience) and Center of Pressure (Cp - moves fwd as a.o.a. increases). Now, regarding how they relate to C.G to provide Longitudinal Stability - most literature says the CG should always be forward of Ac to provide stability.I'm reading a book by H.C. 'Skip' Smith that uses diagrams showing the CG AFT of the Ac? All the FAA books show the CG forward of the Ac, and some show the CG forward of the Cp? They seem to be jumping back and forth between Ac and Cp.. My resolution to this is that when the Ac convention is used, a positive, nose down pitching moment is always included. In this case, the tail downward lift and the wing upward Lift vector (through the Ac and FORWARD of the CG) causes a balancing (negative moment) of the positive moment due to lift. Now, most FAA manuals show a Lift vector AFT of the CG. This is balanced by a downward lift vector from the tail. Possibly, this is a simplified explanation used by the FAA to explain to us simpletons. Can anyone shed any light on this? To satisfy myself, I've concluded that the CG must always be between the Ac and the Cp to remain stable? Is this true? Also, does the pitching moment (airfoil only) due to lift always create a nose down momenton the wing, or are there times when a wing would pitch up? I am grateful for any help from anyone...Thanks, Scott

mohr (Aeronautics) · Answer 1 · 2003-10-26 00:07:07

Hi renfrew !!

Read " Stability and Control" by Perkins and Hage. It is
a classical book for your questions and is very easy to
understand.

Cheers

Mohr

renfrew (Aeronautics) · Answer 2 · 2003-10-26 06:02:15

Thanks Mohr.. I actually have Perkins and Hage and it only confused the issue some more. On page 10 they have a diagram of the summation of moments and they show the CG aft of the wing lift. They also show a vertical (up) component of lift from the tail, and a postive (or nose up) moment about the Aerodynamic Center. All three of these are in contradiction to what I'm reading and trying to sort out. I'm guessing that since this is a textbook, that this diagram is a generic summation diagram with no preference given to what is normal or desired for a stable aircraft. It is simply a mathematical diagram used to express all the 'possible' moments and it is up to the user to determine the actual directions (+ or -) of the forces shown. Can anyone confirm that? Thanks again for the reply

colinp (Mechanical) · Answer 3 · 2003-10-27 10:32:20

Hi Refnew and Mohr,

I keep seeing this question and it seems to have a parallel to longitudinal stability of stepped planing surfaces.

So let me take a crack at a possible answer:

If the lift curve slope of the tail is steeper than the lift curve slope of the wing than the origin of the net lift vector will move aft with increasing pitch attitude, causing a nose down moment. The opposite would occur with decreasing pitch attitude.

Does this seem resonable?

-colin

colinp (Mechanical) · Answer 4 · 2003-10-27 13:35:11

oops..

I said
"The opposite would occur with decreasing pitch attitude."

What I meant was that a moment of the opposite sign would be caused by a decrease in pitch attitude. (sounded like I meant the lift vector origin would move forward)

sorry about that.
-colin

DORD2002 (Aeronautics) · Answer 5 · 2003-11-17 16:42:16

I noticed the same thing about Skip's book. I have since thrown it away. I found it to be misleading.
There is another term that is missing from the picture. That is the Neutral Point (N.O.). The Neutral Point is located where the slope of the curve of pitching moment versus angle of attack equal zero. This is the rearmost location of the C.G. If the CG moves beyond this point (rearward) an airplane will exhibit negative static stability. The C.G. of an airplane should always be located forward of the Neutral Point.

Going back, the A.C. of a wing alone is defined as the point about which the pitching moment coefficient is constant at all angles of attack. So, the Neutral Point can be thought of as the A.C. for an entire airplane. It is a turning point so to speak. In front of the N.O. there is positive static stability. Behind the N.O. there is negative static stability. However, right at the N.O. there is no change in Pitching Moment when the angle of attack changes (due to a gust for instance). Having said all that, I should mention that this is all true only when the controls of an airplane are fixed.

So I guess this is the long way around to answering your question. The CG should be located forward of the AC. Any diagram that shows otherwise is probably indicating a "wing-only" situation.

Clear Prop!

cawiddison (Aeronautics) · Answer 6 · 2003-11-19 16:24:27

Colinp got it wrong insofar as horizontal tails are almost always of lower aspect ratio (and lower lift-curve slope) than the wing.

Renfrew's guess is correct : If the sign convention specifies Lift as positive UPWARDS all lift terms will be depicted as UPWARDS, the actual value (including sign) to be determined by the physical configuration.

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longitudinal stability/aero.center vs. center of P