PHITS of N. Co. NAR Section#565; NAR# 71034SR565
> >> > ....For an airfoil fin, lift is
> >> > generated when the fin assumes an angle of attack to the airflow.
> >> > small angles of attack - drag only increases slightly, so the
> >> > force is mostly lift - and the force is not very strong. With a
> >> > fin, the drag increases rapidly - and fairly strong lift also
> >> > The two are additive, and produce a strong restorative force.
> >> This is incorrect on several counts. First of all, at small AOA, the
> >> difference in behavior between flat fins and airfoiled fins is quite
> >> small. Second, it is incorrect that the lift force of an airfoil at
> >> small AOA is "not very strong." Do you have numbers to back up this
> >> statement? Third, while it is true that lift and drag are additive,
> >> are additive only as vector forces. Lift force is acting in the
> >> vector direction--since it is perpendicular to the long axis of the
> >> rocket, it is very effective in rotating the rocket around its CG back
> >> to zero AOA. Drag force, on the other hand, acts in the "wrong"
> >> direction--nearly parallel to the long axis. To calculate the net drag
> >> force available to rotate the rocket back to zero AOA, multiply the
> >> total drag force by the TANGENT of the AOA. For a five degree AOA,
> >> is less than 9%, which means that 81% of the drag force is wasted as a
> >> restoring force.
> >> > A plate fin will provide even better correction than an airfoil, as
> >> > is a large increase in drag - which provides more restorative force
> >> > can be produced as lift from an airfoil.
> >> Again, incorrect. Ask an aeronautical engineer to run the numbers for
> >> you. The lift restorative forces are HUGE compared to the drag
> >> restorative forces, stalled or not stalled.
> >Andy, you are right in everything you said, and well said, too. In the
> >range of 0 to 5 degrees AOA, both the flat and airfoiled fin will have a
> >lift slope of roughly 0.116, but the airfoiled fin will hang in there
> >The Naval Postgraduate School has online panel code for 4 & 5 digit naca
> >airfoils available at
> >Happy Thanksgiving to everyone. JimC
> >> fine. A slow-accelerating rocket leaving the launcher in a crosswind,
> >> however, can experience such a high AOA that airfoiled fins (that keep
> >> "working" longer) could make the difference between a successful
> >> and a cartwheel.
> All --
> Very cool thread. Like Andy and James said, a flat plate
> does generate lift at Non-Zero AoA. At very small AoA, the
> slope is even linear, exactly like an airfoiled fin.
> As a matter of fact, the Borrowman Equations are actually
> based on the assumption that the fins are thin, flat plates !
> At small AoA, the theoretical coeff of lift of a flat plate is:
> CL = 2 * Pi * sin ( Alpha ) # Alpha == AoA in Radians.
> When an angle is very small, the sine of the angle is the same
> as the angle itself, so:
> CL = 2 * Pi * Alpha
> This means that the slope of the Lift vs AoA curve at small AoA
> is simply 2 * Pi, or in Aero terms, dCL/dA = 2*Pi. When AoA is
> measured in degrees, the slope of the lift curve is:
> dCL/dA = ( 2 * Pi ) * ( Pi / 180 )
> = Pi^2 / 90
> = 0.110
> Which is pretty close to James' number above.
> The original question was 'How does fin thickness affect
> stability?'. That is pretty a complicated question but,
> ignoring drag, and assuming you put a good airfoil on the
> fins, you can 'get away with' a thickness ratio as much
> as 25 % of the chord length.
> OTOH, Hoerner shows in _Fluid_Dynamic_Lift_ ( pp 2-10,
> figure 17 ) that a NACA 0018 airfoil ( max thickness =
> 18% of chord length ) modified with a 'large trailing edge
> angle' actually develops NEGATIVE lift out to more than
> 5 Deg AoA before it finally starts 'working as expected' !
> You do need to be careful not to get 'too fat' -- it increases
> your drag and reduces your stall angle ( works for people too ;-)
> Here is a summary of some airfoil data from _Theory_of_
> _Wing_Sections_ ( see below )
> Desig Thickness CL Angle slope Max CL
> ===== ========= ==== ====== ====== ======
> Plate n/a 0.82 10 deg 0.110 From Hoerner
> DblWedge 4.3% 0.83 10 deg 0.113 From Hoerner
> ( note that I measured all these numbers from graphs in
> the books mentioned -- YMMV -- but I did double check ;-)
> G.H.Stine suggested 10% -- a pretty good trade-off between
> lift coefficient, stall angle and drag. Looks good to me ;-)
> If you are really interested in the subject, I suggest the
> following book:
> Theory of Wing Sections
> Ira H Abbott
> Albert E. von Doenhoff
> Dover Publications
> ISBN 486-60586-8
> This book is a bargain at $15 -- it includes a summary of NACA
> airfoil data and also the answers to your question ;-)
> If you are _really_really_ interested, call Mrs Hoerner and
> order _Fluid_Dynamic_Drag_ and _Fluid_Dynamic_Lift_:
> Hoerner Fluid Dynamics
> PO Box 65283
> Vancouver, WA 98665
> ph/FAX 360-567-3997
> FDD: $75 + 6 shipping.
> FDL: $70 + 6 shipping.
> Have fun !
> -- kjh
> p.s. Kites and ( Rockets & Planes ) are completely different
> animals. Kites fly at large AoA, ( Rockets and Planes )
> are supposed to fly near zero AoA ;-)
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