PHITS of N. Co. NAR Section#565; NAR# 71034SR565

www.pageplus.com/~cwbrown/phits/phits.htm

> >> > ....For an airfoil fin, lift is

> >> > generated when the fin assumes an angle of attack to the airflow.

For

> >> > small angles of attack - drag only increases slightly, so the

restorative

> >> > force is mostly lift - and the force is not very strong. With a

plate

> >> > fin, the drag increases rapidly - and fairly strong lift also

occurs.

> >> > 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,

they

> >> are additive only as vector forces. Lift force is acting in the

"proper"

> >> 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,

this

> >> 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

there

> >> > is a large increase in drag - which provides more restorative force

than

> >> > 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

> >longer.

> >The Naval Postgraduate School has online panel code for 4 & 5 digit naca

> >airfoils available at

> >http://atemi.aa.nps.navy.mil/panel/panel.html

> >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

flight

> >> 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

> $14.95

> 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 ;-)

> --

> ------------------------------------------------------------

> 1111 Seacoast Dr. Unit 41 | home: (619) 423-4451 |

> Imperial Beach, CA 91932 | |