Aerodynamics: what about pitch stability?!

[PontiusPilotus]

As I was reading again the ATPL theory about Aerodynamics, in the chapter of Stability & control I kind of made a hold at the chapter about longitudinal stability. I do need some clarity about one specific topic.

First I have to say I'm reading the Oxford ATPL P.O.F. manual. I provide you with a scan of one page in the mentioned chapter to make myself clear.

Herein it states that to increase static longitudinal stability or in other words to have a more effective tailplane, engineers apply longitudinal dihedral between the wing and the tailplane. The tail is at a lower incidence than the wing. It states that by having this, it will generate a greater percentage increase of the tail lift than the wing lift in case of a vertical gust. Regarding the drawing they provide below I can not understand how this in any way could happen?

Thinking about the increase of downwash (as the angle of attack at the wing increase) this would decrease the effective angle of attack at the tail. Secondly, as the drawing shows the tail providing a nose down force for stability (lift upwards), the lower effective aoa would reduce the tail lift and so less static stability would be provided.

Secondly it writes that downwash reduces the longitudinal stability. In case the tailplane provides upwards lift (nose down) for stability, then I do confirm that downwash would reduce the effective aoa, so as reduce the lift.
In case the airplane though has a more aft CG (aft of the wing's AC), this means a nose up correction must be provided by the tailplane, then downwash at the tail would increase the nose up tendency. Am I right or do I somewhere miss the global picture?

Please some advice would be great! Thank you.

[PontiusPilotus]

Here is the scan.

Thank you

https://lh5.googleusercontent.com/---unRO6Okx0/UUn6TrXxSeI/AAAAAAAABVA/SSQ1WIo5PK0/s800/Aerodyn.long.stab.%252010-23.jpg

[Turbavykas]

It's pure mathematics. You can see in the image that angle of attack without gust is 4 degrees for the wing and 2 for the tail. When the gust hits angle of attack becomes 8 for the wing (100% increase) and 6 for the tail(200% increase). So tail will have twice as much lift and it will add to stabilizing effect.
You can imagine that airplane is designed so that for a level flight wing needs 4 degrees of angle of attack but tail requires only 2 degrees. So tail is more effective in producing lift as the wing. So as the gust hits it has more effect on the tail and the tail will not allow for airplane nose to pitch up.

[PontiusPilotus]

Thank you very much for your reply.
I do understand it in a mathematical way. Now if the tail provides a nose-up or nose-down stabilising effect depends on the CG and the contstruction of every aircraft. If I understand well, for the Oxford POF book it's just a matter of presentation that the Aerodynamical center of the wing is always in front of the CG (wether the CG is at AFT or FWD limit) ?

[Volume]

If I understand well, for the Oxford POF book it's just a matter of presentation that the Aerodynamical center of the wing is always in front of the CGThat is correct.
Keeping it to a simplified theory you could state, that an aircraft is stable in pitch if the wing loading of the forward wing is higher (in the mathematical sense) than the wing loading of the aft wing. If the Aerodynamical center of the wing is aft of the CG, the aft wing loading is negative, so it is definively smaller than the one of the front wing. So as long as the rear wing is large enough, it is OK if it produces some lift there, so the Aerodynamical center of the wing might be in front of the CG. For many high performance gliders this is the case, as large (negative) lift on the aft wing of course means additional drag.
If you make the aft wing even larger than the front one, you end with a canard configuration, which is stable in pitch if the wing loading of the canard is higher than that of the wing. In that case you can even use absolute numbers, as in any situation both wings will provide lift.

[PontiusPilotus]

Clear!

Thank you everybody for your help. I appreciate!

[Turbavykas]

That's not very correct. Keep in mind that image shows AC. There is also CP(center of pressure). AC has constant moment.For a positive cambered (http://www.grc.nasa.gov/WWW/k-12/airplane/geom.html) airfoil, the moment is negative and results in a counter-clockwise rotation of the airfoil. With camber, an angle of attack can be determined for which the airfoil produces no lift, but the moment is still present! So for airplanes with regular wings the tail has to press down because wings will try to rotate counter-clockwise and CG is aft of AC and opposes rotation. If we move CG even further to the tail we reach NP(neutral point) where tail will need to produce no any down force.Stick forces will be very light, drag from the tail will be low but it will be rather complex for humans to control airplane. So usually CG is somewhere between AC and NP for human controlled aircraft but for flyby wire CG can even move past NP for fighters. If you move CG forward past AC that will add very high load on the tail so it will produce a lot of drag or can even stall. So generally speaking CG oxford books are correct.

[Volume]

For a positive cambered airfoil, the moment is negative and results in a counter-clockwise rotation of the airfoil. With camber, an angle of attack can be determined for which the airfoil produces no lift, but the moment is still present! So for airplanes with regular wings the tail has to press down because wings will try to rotate counter-clockwise and CG is aft of AC and opposes rotation.The Moment coeficient however is constant over AoA, or therefore constant over Cl. So only at low Cl (low AoA, high speed) the moment is dominating requiring a negative stabilizer lift. At high Cl (high AoA, low speed) the lift of the wing dominates over the moment, so although the airfoil is positively cambered, lift might be produced at the stabilizer in this condition if the AC is ahead of the CG.
And by the way, being constant the pitching moment does only affect pitch equilibrum, but not pitch stability.

[Dick Whittingham]

Please go back to the original question, which was about longitudinal dihedral. The explanation given was that as tail alpha was a lower value than wing alpha a gust increase would give a greater proportional increase in tail alpha. so far so good. The explanation then went on to asume that this longitudinal dihedral had produced an extra element of positive stability because LD had produced "greater" tail lift. This is not so. LD does not significantly affect longitudinal stablity, only the balance of forces in level flight. It may (Wikipedia) affect phugoid movement in pitch

It is the use of percentages that leads you astray. Consider the case where ths pre-gust position has zero tailplane alpha. Any increase in a gust would give the tailplane an infinite percentage increase alpha. That would bring the nose down with a snap!

In fact, the tailplane, like the wing, has received the same finite increase in positive alpha and this would be the same with or without LD. I suspect the real reason for LD is to minimise trim drag in the cruise

[The Terminator]

I do prefer Dick's explanation. I can't come up with a real reason to believe the LD could increase pitch stability.

Also Why is lift going through the aerodynamic center? I don't want to confuse Pontius, but for me that explanation in manual does not make sense.

Besides the effective angle of attack for the tail plain is going to change based on elevator controls and actually in the case of an all moving tailplane.

[Owain Glyndwr]

LD does not significantly affect longitudinal stablity, only the balance of forces in level flight. ....

In fact, the tailplane, like the wing, has received the same finite increase in positive alpha and this would be the same with or without LD. I suspect the real reason for LD is to minimise trim drag in the cruise

That's pretty close :ok:

The tail receives the same increase in positive alpha from the gust as does the wing, but the effective increase in tail AoA is reduced because the wing generates more tail downwash as a result of its own AoA increase. As you say, this is independent of LD, which basically affects the forces in level flight.

Typically, the wing root may be set at 3 or 4 degrees nose up relative to the fuselage datum - this gives a more or less level cabin floor in cruise. The downwash generated at the tail by this wing AoA is roughly enough to generate the tail download needed to trim the aircraft with no elevator deflection and the tail set parallel to the fuselage datum. So you naturally get LD if you design the aircraft geometry to match cruise conditions.

Obviously these are ballpark numbers and the details will depend on the particular aircraft design and the actual CG position (I took a mid-CG), but the general principle is valid I think.

[Volume]

Also Why is lift going through the aerodynamic center? I don't want to confuse Pontius, but for me that explanation in manual does not make sense.This is due to definition. If we would produce lift at the center of forces, there would be no pitching moment. If you assume a constant pitching moment, then Lift (and especially any additional Lift due to gusts) always acts on the aerodynamic center.