PPRuNe Forums - View Single Post - Longitudinal Dihedral
View Single Post
Old 21st Mar 2005, 18:47
  #48 (permalink)  
Dick Whittingham
 
Join Date: Oct 2000
Location: Bristol
Posts: 461
Likes: 0
Received 0 Likes on 0 Posts
I hesitate to intervene again, but let us use a bit of logic on the “percentage” argument, which seems to be:

Proposition 1: If wing alpha is greater than tail alpha then an increase in the same number of degrees on both wing and tail – a positive gust – will give a higher percentage increase of tail moment than of wing moment.

Proposition 2: If the aircraft was flying before the gust an with increased longitudinal dihedral, with tail alpha less than in Proposition 1, with wing alpha the same, then in the gust the percentage increase in tail moment over the percentage increase in wing moment will be even higher.

Proposition 3: The effect given in Proposition 2 must lead to a proportionally greater nose down tail moment over the nose up wing moment and therefore an increase in longitudinal stability.

Conclusion: Increased longitudinal dihedral increases longitudinal stability

The argument falls because relative percentage changes in wing or tail alpha in gusts do not affect the relationship of the wing and tail moments. An incremental increase in wing or tail alpha gives exactly the same incremental increase in the wing and tail moments whether the alpha increment is from 2deg to 4deg, 4deg to 6deg or 6deg to 8 deg. The conventional Cl/alpha graph is linear in this regime.

Now, the killer. Consider the case where tail alpha is at zero before a positive gust. any increase in tail alpha will then be an infinite percentage increase. Under the “percentage” argument this should lead to an infinite increase in longitudinal stability, and the aircraft should hold an unchanging and unchangeable attitude. Clearly this is nonsense.

For an argument to hold it must be true in all cases, including the extremes. The percentage argument gives a clearly false conclusion in the zero tail alpha case, and this destroys the whole theory

Dick W
Dick Whittingham is offline