Oliver Arend
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I don't know whether this has been discussed here before, but over at EURocketry we came across an interesting and disturbing fact concerning the stability of rockets with slotted fins such as the Thor design.
This is the thread I'm referring to: https://www.eurocketry.org/forum/german/viewtopic.php?t=650
Stefan found that doing the stability calc with two fins making up the slotted fin yielded much more optimistic results than doing the sim with one single large fin.
(what follows is a crude translation of the post I did this afternoon on the topic)
I had another look at Barrowman's original report (his dissertation that is, not Centuri's TIR-33), as well as at the NACA TN 2335 authored by Diederich, which served as a starting point for Barrowman's deductions.
The whole thing is based on the usual lifting-line-theory for subsonic flows (which Prandtl developed back in the days) and the correcting factors for swept wings.
It becomes clear quickly, that two separate fins will be treated as wings with rather high aspect ratios each, whereas the entire fin has a rather low aspect ratio. The lift gradient varies a lot given wings or fins with low aspect ratios such as we are commonly using, so this change has a strong effect. It's also no longer surprising that the aft fin all by itself yields a better result than the entire, larger fin (another sim which Stefan ran), due to its comparatively high aspect ratio and aft position.
The coefficient for body-fin-interference stays the same throughout all calculations, since body tube radius and semi-span do not change.
What Barrowman did or could not consider are closely neighboring fins, as these are rarely found on sounding rockets or missiles (and wind tunnels can be used for tests on these...) and even today can only be treated numerically at rather high costs (-> multi-element airfoils).
I would regard the given fin configuration as a wing of low aspect ratio with a probably lift-increasing slot (like slotted or Fowler flaps on airplane wings), which would not show any effect except at high angles of attack (non-linear, boundary layer transition and separation etc.), and hence can be ignored when studying stability.
Ultimately (in short ;-), one should treat slotted fins as one large fin, not only because it's more conservative, but also because it corresponds to the assumptions Barrowman made when deriving his equations, which is not the case when the fin is treated as two separate ones.
Oliver
This is the thread I'm referring to: https://www.eurocketry.org/forum/german/viewtopic.php?t=650
Stefan found that doing the stability calc with two fins making up the slotted fin yielded much more optimistic results than doing the sim with one single large fin.
(what follows is a crude translation of the post I did this afternoon on the topic)
I had another look at Barrowman's original report (his dissertation that is, not Centuri's TIR-33), as well as at the NACA TN 2335 authored by Diederich, which served as a starting point for Barrowman's deductions.
The whole thing is based on the usual lifting-line-theory for subsonic flows (which Prandtl developed back in the days) and the correcting factors for swept wings.
It becomes clear quickly, that two separate fins will be treated as wings with rather high aspect ratios each, whereas the entire fin has a rather low aspect ratio. The lift gradient varies a lot given wings or fins with low aspect ratios such as we are commonly using, so this change has a strong effect. It's also no longer surprising that the aft fin all by itself yields a better result than the entire, larger fin (another sim which Stefan ran), due to its comparatively high aspect ratio and aft position.
The coefficient for body-fin-interference stays the same throughout all calculations, since body tube radius and semi-span do not change.
What Barrowman did or could not consider are closely neighboring fins, as these are rarely found on sounding rockets or missiles (and wind tunnels can be used for tests on these...) and even today can only be treated numerically at rather high costs (-> multi-element airfoils).
I would regard the given fin configuration as a wing of low aspect ratio with a probably lift-increasing slot (like slotted or Fowler flaps on airplane wings), which would not show any effect except at high angles of attack (non-linear, boundary layer transition and separation etc.), and hence can be ignored when studying stability.
Ultimately (in short ;-), one should treat slotted fins as one large fin, not only because it's more conservative, but also because it corresponds to the assumptions Barrowman made when deriving his equations, which is not the case when the fin is treated as two separate ones.
Oliver
