A number of people have asked for clarifications or references
on the vertical tail vs spiral stability issue. There aren't
any that I'm aware of. Unfortunately it's a very complex subject.
Here's a writeup I did which expands only on the basic effects.
It's still kinda complicated, but I don't see any way to simplify
it further.
- Mark
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Whether an airplane is spirally stable or unstable depends
on a delicate balance of forces. After a yaw or bank upset,
some of these forces oppose the bank (resist spiralling in),
while some act in the direction of the bank (promote spiralling in).
Although the forces are varied and numerous, on a typical
glider there are four dominant ones, all comparable in importance:
Resist spiraling in:
roll moment due to yaw angle Cl_b (dihedral effect )
yaw moment due to yaw rate Cn_r (vertical tail's yaw damping)
Promote spiraling in:
roll moment due to yaw rate Cl_r (faster-moving tip has more lift)
yaw moment due to yaw angle Cn_b (vertical tail's yaw stability )
The airplane is spirally stable if the first two forces are greater
than the second two forces, all acting together. The symbols are
standard aero jargon for the forces. So we have...
Spirally stable if:
Cl_b x Cn_r > Cl_r x Cn_b (*)
After these four forces are estimated using the airplane's geometry,
the spiral stability criterion (*) above turns out to be approximately
the same as Blaine Rawdon's criterion after a bit of algebra:
EDA x (tail_length/span) > 5 CL (**)
So why doesn't the vertical tail area A_vert come into the picture?
Because it affects both the yaw stability and the yaw damping equally:
yaw damping Cn_r ~ A_vert x tail_length^2
yaw stability Cn_b ~ A_vert x tail_length
These are opposing forces which appear on the left and right sides
of criterion (*), so A_vert cannot influence the direction of the inequality.
Only the extra tail_length factor in the yaw damping force remains, and can
be seen in Blaine's form (**). The other quantities in Blaine's form come
from estimation of the other forces, e.g.
dihedral effect Cl_b ~ EDA x span^2
roll due to yaw rate Cl_r ~ CL x span^3
One can also influence the spiral stability criterion "artificially" by
using a rate gyro. This can be done in one of two ways:
1) Yaw gyro driving the rudder. Increases Cn_r (yaw damping)
2) Yaw gyro driving the ailerons. Decreases Cl_r (roll due to yaw rate)
In each case, the gyro feedback sign must be set correctly to move the Cn_r or Cl_r
number in the right direction. Otherwise spiral stability will get worse, not better.
Method 1) works because it increases yaw damping Cn_r, but DOES NOT increase
yaw stability Cn_b. Just adding vertical tail area increases both, which
then cancel each other out.
Blaine Rawdon and Bill Watson have demonstrated the effectiveness of method 2)
in artificially obtaining spiral stability on a full-house Open Class glider:
http://members.home.net/evdesign/pages/technical_articles.html
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