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## Longitudinal Dihedral

• student101
• Topic Author

### student101 created the topic: Longitudinal Dihedral

Hey guys, just a quick question regarding Longitudinal Dihedral: according to the Aerodynamics Bob Tait Textbook (Page 11.4, Fig 11.8) ...By setting the tailplane onto the fuselage at a slightly smaller angle of incidence than the mainplane, a nose-up pitch will always produce a bigger proportional increase in lift on the tailplane than it does on the mainplane... It is my understanding that an aerofoil flying at a higher AoA (mainplane) would mean more lift achieved in comparison to an aerofoil flying at a lower AoA (tailplane). My questions is, How can a lower angled aerofoil such as the tailplane achieve more lift than the higher angle of the mainplane aerofoil? Does it have to do with the relative airflow speed that hits both aerofoils? Any help on the subject would be greatly appreciated.

• Posts: 2297

### bobtait replied the topic: Longitudinal Dihedral

There's more to this than just the forces acting. When it comes to stability, what really matters is the moment generated by those forces.

The slope of the lift coefficient curve on most conventional aerofoils is close to a straight line until the the stalling angle of attack is approached. That means that any increase or decrease in angle of attack will produce about the same percentage increase or decrease in the forces generated.

Let's assume that the angle of incidence of the mainplane is 4° and the angle of incidence of the tailpane is 2°. If the aircraft is flying with its longitudinal axis parallel to the relative airflow, the angle of attack would be the same as the angle of incidence.

Now imagine that the nose suddenly pitches up by 1°. Inertia will keep the aircraft moving along the same flight path momentarily. So the angle of attack on the mainplane will increase from 4° to 5° - an increase of 25%. That will produce an increase in the moment generated by the mainplane about the centre of gravity of the same proportion.

However the angle of attack of the tailplane will increase from 2° to 3°, an increase of 50%.

The stabilizing moment generated by the tailplane increases by a greater proportion that the destabilizing moment generated by the mainplane. This contributes to longitudinal stability.

Also it is sometimes the case that, because of the downwash from the mainplane, the relative airflow arrives at the tailplane at a lower angle of attack anyway. There may be no need to set the tailplane at a lower angle of incidence, since the downwash from the mainplane produces the same effect.

• student101
• Topic Author

### student101 replied the topic: Longitudinal Dihedral

Thank you so much for the detailed response Mr Tait. I clearly missed a few things while reading up on the subject, especially the proportional side of the Lift increase percentage. Thank you.

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 702

### John.Heddles replied the topic: Longitudinal Dihedral

I don't have access to a copy of Bob's text so without knowing what that text says specifically, it is not appropriate for me to enter the discussion in detail.

However, the following old thread from PPRuNe is of relevance and may help with general understanding. I note that some of the posters in that thread are very well-credentialed experimental test pilots and aircraft OEM design engineers - there is even some input from the odd UK ground school specialists.

www.pprune.org/tech-log/166667-longitudinal-dihedral.html

Engineering specialist in aircraft performance and weight control.

• student101
• Topic Author

### student101 replied the topic: Longitudinal Dihedral

Thank you Mr Heddles. There was a post on the link you gave me which defined longitudinal dihedral almost exactly as Mr Tait did, using a similar example.

• Posts: 2297

### bobtait replied the topic: Longitudinal Dihedral

Stability is a 'can of worms' with dozens of influences operating simultaneously. Almost every attempt at an explanation has to begin with assumptions. There are some areas in the CASA syllabus that lead to endless discussion but have absolutely nothing to do with your ability to safely fly an aeroplane.

I have often made myself unpopular at conferences by suggesting that flying training does not belong in the science faculty. Flying training is industrial education - we are teaching someone to operate a machine. You can be capable of driving a car perfectly safely without being able to draw a diagram illustrating the principle of automatic transmission.

That is why I devoted only two paragraphs to longitudinal dihedral in the Aerodynamics book and then only because it is in the CASA syllabus. My reference for that was A. C. Kermode's Mechanics of Flight 10th edition Page 277. In fact Kermode's explanation is also open to dispute.

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