Mike:
Here is excerpts from several posts in RMR about CP information related to ring tail cp stability that you might find useful.
Regarding the ring tail code, I took data from MIL-HDBK-762, that
states that a ringtail has twice the force moment as a rectangular
cruciform fin of the same chord length and span. (This also
apparently matches with data in Hoerner's fluid dynamics books.) Of
course this has *not* been verified by model flight tests - R&D
project for anyone interested.
So, let me attempt to re-iterate: I simulate a ring tail rocket by
calculating the CP as if it were a normal four-finned rocket (with 90deg
between fins). The four fins are rectangular, with the chord dimension
being the "height" of the ring piece, and the span being the radius of
the ring minus the radius of the body tube. Such a calculation of CP is
then overly conservative, because the ring tail is actually twice a good
as that. Is that what you're saying?
We've also played around a bit with ring-tails, and they are fun! The
stability of a ring-tailed missile is much, much better than that of a
fin-tailed missile with the same general dimensions. In other words, a
ring-tailed model with a ring diameter of 3" and a ring chord of 1.5" is much
more efficient than a fin-tailed missile with four fins of 1.5" and an overall
fin span of ??.
Stability of ring-tails increases rapidly with increasing outside diameter of
the ring, and also increases rapidly as the chord of the ring is increased up
to 1/2 the ring diameter. There is little if any increase to be gained by
making the ring chord greater than 1/2 the ring diameter.
Hmmm, Hoerner's Ring Wing equation can be used to work out a 'ring
tail' type of configuration too...
For a ring tail, I've used the information in MIL-HDBK-762 that says
that a ring tail is about twice as effective as a rectangular
cruciform tail with the ring tail chord = the rectangular fin chord,
and the ring tail diameter = the cruciform tip-tip span. If Hoerner's
data agrees with '762, then we'd get similar (CN)t for both of the
following examples:
______
| |
|______|__________ 4 fins, s = 1, a = b = 2,
|
|________________ d = 1
| |
|______|
______
| |
| |__________ ringtail, a = 2, tail dia = 3
| |
| |_________ d = 1
| |
|______|
For the ringtail I'd first assume that the 'ring' body interference is
negligible (as long as the ring diameter is >> the body dia), and
that we can ignore the ring supporting structure. With these
assumptions then,
(CN)frt = (CN)trt = pi * d/c (rt = ring tail)
So if this is going to match what the '762 says, then for the above
examples, the following should be true: (also assuming that the
fin/ring Xf's are similar)
(CN)trt = 2 * (CN)t
scratching that out, for that example, I get 4.7 ~= 4.4
fudge in some body-ring interference & that gets way too close for a
coincidence..
Normal Force = N
Surface Area of Ring Fin = S
Diameter of Ring Fin =D
Fin Span = r
Root Cord = b
N = (32 * (S/D)^2) / (1 + Sqrt( 1 + (r/b)^2))
Fin Cp location = 0.75 * b
The general rule appears to be that a ring fin of diameter X and chord Y
will give twice the aerodynamic effect as four fins of semi-span X/2 and
chord Y -- that is, it's twice as effective as a set of conventional
fins with the same projection.
I just wanted to add that using 4 "fins" with a ring tail is not absolutely necessary.....you can use 3 which would reduce the drag and you also might be able to even get away with only 2 "fins"....
