From: Kevin Caldwell Sent: Tuesday, May 13, 1997 10:12 AM To: davis@halcyon.com Subject: Polar Corrections Davis, Haven't had a chance to do this for the whole polar yet, but putting in the correction for the airspeed reduction that the instrument sees due to wing circulation gives about a 6% increase in best L/D. Measured Corrected WW Fusion 10.8 11.5 Icaro Laminar ST 10.7 11.4 Icaro Laminar 9.6 10.2 WW XC - 2 9.7 10.3 WW XC - 3 8.9 9.5 WW XC - 1 8.9 9.5 Ref: At long last I have an answer to exactly how much a HG wing effects the airspeed reading at a typical instrument mounting location. Never did manage to figure it out myself, but after a request to sci.aeronautics, Mark Drela at MIT was kind enough to answer. This guy is good! I think he answers 80% of the questions on sci.aeronautics. And he still has time to work on an ultralite sailplane design. I'm looking forward to that. Any more news Gary? From: drela@athena.mit.edu (Mark Drela) In article , kcaldwel@nortel.ca writes: |> |> I have been struggling to analyze the flow velocities near a wing, to |> determine the wing's effect on the airspeed indicated by an instrument |> deck on a hang glider. The formulas for the flow angle change and the velocity change caused by a wing are essentially the same: v -CL c delta(angle) = - = ---- - U 4 pi x u CL c fractional delta(vel) = - = ---- - U 4 pi y Again, these formulas assume that the wing is replaced by a vortex with the same circulation (i.e. the same lift) placed at the center of lift. x,y are measured relative to this center of lift, which is at (1/4 - CM/CL) c from the leading edge --- typically between 0.30 c and 0.40 c on most airfoils in flight. U is the freestream speed, and u,v are the horizontal and vertical velocity changes due to the wing. The static pressure to first order is influenced only by u: 2 2 2 p = po - 0.5 rho [(U + u) + v ] ~ po - 0.5 rho U - rho U u since u,v << U. So your pitot airspeed sensor mainly "sees" u, and the second formula at top applies. |> root chord = 6.333 ft. |> tip chord = 3.167 ft. |> The location of the instrument airspeed measurement is: |> |> 30" back from the nose apex of the planform |> 56" below the chord line of the root chord This is not too close to the airfoil, so the point-vortex model is quite accurate (I checked it versus an "exact" 2D panel solution). Using the average chord, y/c = -56"/57" = -1.0 , I get "true" CL airspeed error CL_measured ------------ -------------- ----------- 0.30 -2.6 % 0.32 1.00 -7.9 % 1.18 1.50 -15.8 % 1.93 which seems quite severe at low speeds. I added the third CL_measured column because this is what you calculate by using the "wrong" measured airspeed. The relation is 2 2 Lift/S = 0.5 rho CL_measured U_measured = 0.5 rho CL U and with U_measured/U = 1 + u/U , we get -2 | CL c | CL_measured = CL | 1 - ---- - | | 4 pi y | It seems the hang-glider crowd gets much lower true CLs on their gliders than they think. Mark Drela First Law of Aviation: MIT Aero & Astro "Takeoff is optional, landing is compulsory" Using the above, I calculated the following instrument readings that correspond with the actual through the air speed. This was all calculated at 5,000' density altitude, 'cause that is all the numbers I have handy today. The details of my generic hang glider analysis model are: Wing area = 154 sq. ft. span = 32 ft. taper ratio = 0.5 1/4 chord sweep = 23 degrees dihedral angle = 0 degrees washout angle, root to tip = 15 degrees flying weight = 280 lbs. root chord = 6.333 ft. tip chord = 3.167 ft. average chord = 4.75 ft. The location of the instrument airspeed measurement is: 30" back from the nose apex of the planform 56" below the chord line of the root chord 28" offset from the planform center line All speeds in mph: Here is a list of actual through the air airspeeds versus the airspeed at the instrument deck location, with the lift coefficient required to fly at that speed. All at sea level: Actual (mph) Instrument Location (mph) CL 20 17.30 1.781 (past stall) 21 18.43 1.616 (past stall) 22 19.54 1.472 23 20.65 1.347 24 21.75 1.237 (min sink) 25 22.84 1.140 26 23.92 1.054 28 26.07 0.909 30 28.20 0.792 (max L/D) 32 30.31 0.696 34 32.41 0.616 36 34.50 0.550 38 36.58 0.493 40 38.65 0.445 45 43.80 0.352 50 48.92 0.285 55 54.02 0.236 60 59.10 0.198 65 64.17 0.169 70 69.23 0.145 Summary: The airspeed at the instrument location is 2.5 mph slower than free stream velocity at stall, 2.25 mph slower at min sink, 1.8 mph slower at best L/D, and 1.3 mph slower at an actual inter- thermal cruise speed of 40 mph. Instruments will have other errors built in. Impeller types read "true" airspeed, meaning your stall speed, etc, will read higher at higher density altitudes. This wil make it very difficult to build a correction factor for the wing effect into the deck, since it is dependent on wing CL. Pitot type airpeed indicators could have a correction built in, although then they would need a PG setting with no correction, since a PG wing is very far from the instrument deck. Summary: About 2.7 mph difference at stall speed (23 mph actual airspeed, 20.3 at instrument), 2.5 at min sink (25 mph actual, 22.5 instrument), 1.9 at best L/D (33 actual, 31.1 instrument), and 1.6 mph at interthermal cruise (40 actual, 38.4 instrument). Now is someone going to build the correction into their computer instrument decks for real speeds-to-fly? Kevin Caldwell Calgary, Canada kevinc@nortel.ca