Airfoil Design “Airfoil optimization requires the application of science, intuition, and perseverance” When Burt Rutan designed the Vari-EZ in 1974, he selected NASA’s GA(W)-1 airfoil for the wing.  He modified the cusp to reduce its pitching moment, but the section remained a modern (at the time) laminar flow, high-lift airfoil.  Burt then designed the Long-EZ in 1978 and selected the Eppler 1230 airfoil, which he also modified to reduce pitching moment.  The E1230 is a forward loaded, turbulent flow airfoil with higher drag than the GAW1.  This choice puzzled some observers.  Why would Burt specify an older, draggier airfoil for the Long-EZ? I learned the answer while investigating the Cozy wing using Airplane PDQ.  A pattern developed in the aircraft’s response to different airfoils.  In short, the following airfoil qualities had a major affect on pitch stability and CG range: Lift curve slope.  The canard is a flapped airfoil and its lift coefficient (CL) increases at a faster rate than the wing as their angle of attack increases.  This moves the neutral point forward and decreases the stability margin.  To combat this, the wing’s airfoil should have the steepest lift curve possible.  For a given set of parameters, the wing’s lift curve determines how far the neutral point moves forward as alpha increases.  The steeper the curve, the farther aft the neutral point will remain. Pitching moment.  The wing’s pitching moment determines the aircraft’s forward CG limit.  An airfoil with a low moment coefficient (Cm) will allow the aircraft’s CG to be farther forward.  Airfoils with large pitching moments load up the canard and restrict the forward CG, or they require a larger canard which moves the neutral point forward. The E1230 airfoil has a steeper lift curve and smaller pitching moment than the GAW1.  This maximizes the Long-EZ’s CG envelope and minimizes the required wing sweep; whereas the Vari-EZ wing needs more sweep to keep the neutral point far enough aft with the GAW1 airfoil.  The Long-EZ is also more stable than the Vari-EZ at higher angles of attack. I didn’t realize how excellent Burt’s choice was until I searched for a replacement.  I used Airfoil Optimizer and Airplane PDQ to evaluate airfoils with low drag and high CL max.  Many of the laminar flow airfoils had large moment coefficients (Cm) that resulted in lower cruise speeds due to high trim drag on the canard.  After filtering these out, I found sections like the NLF0414F, GA40A315 and 65(2)-415 that increased cruise speed by 5 to 9 knots along with a small increase in stall speed.  I also found the Eppler 1212 airfoil (used on the Q2 and Q200) that lowered stall speed by 2 knots with no impact on cruise speed.  No single airfoil increased cruise speed and lowered stall speed simultaneously. It was around this time that I decided to abandon the Cozy wing, for reasons described on the Wing Geometry page.  Reconfiguring the wing to eliminate the strake would provide modest efficiency gains all by itself.  But the airfoil studies led to an insight that really improved performance: The wing root should have a laminar flow airfoil optimized for the larger operating RN and the tip airfoil should be a turbulent flow, high CL max airfoil optimized for the smaller RN! Using two different airfoils with a smooth transition from root-to-tip would ensure that every section of the wing was optimized for its respective RN.  The inboard span (the larger area) would be dominated by the laminar airfoil and would reduce total wing drag.  The outer span would be dominated by the stall resistant, high CL max, turbulent airfoil.  Both airfoils would have a low to moderate moment coefficient.  Later analysis confirmed this configuration was ideal. The Apollo’s wing area, taper, sweep and washout are similar to the Cozy, except the Apollo’s mean aerodynamic chord is 33% larger than the Cozy wing (without the strake).  The Apollo’s design lift coefficient at 195 mph is 0.187 after accounting for a 17% loss from wing sweep.  Washout reduces the wingtip CL to zero at cruise speed, so the root airfoil CL must equal 0.37 to approximate 0.187 for the entire wing.  The wing root incidence is tentatively set at +1.0 degree but downwash from the canard reduces this to zero or slightly less.  This means the root airfoil’s design lift coefficient at zero degrees alpha should be 0.37 or higher. Using Pazmany’s equation for Reynolds Number (RN), the Apollo’s 55” root chord operates at RN of 8.3 million at cruise speed and 3.0 million near stall.  Airfoil Optimizer was used to identify airfoils with low drag “buckets” at lift coefficients around 0.4 and with low to moderate moment coefficients.  Candidate airfoils were then analyzed in Airplane PDQ to determine their effect on the aircraft’s total performance.  Dozens of airfoils were evaluated against the Eppler 1230 baseline and each other.  The 65(2)-415 came close to being optimal.  For the Apollo application, the cusp was modified to reduce the pitching moment, the camber line was tweaked to increase CL and to fit the wing spar, and the nose was modified per Riblett’s design method.  The new airfoil has a higher L/D ratio at design CL than the 65(2)-415. The tip airfoil operates at RN of 4.2M at cruise and 1.5M near stall.  To approximate an elliptical lift distribution, the wing tip should produce zero lift at the design cruise speed.  We tentatively set wing twist at 3.2 degrees.  The root airfoil has +1.0 deg incidence, so the tip airfoil must produce zero lift at -2.2 degrees alpha.  The tip airfoil should also be stall resistant and achieve high CL max at a relatively small RN.  These requirements favor a forward loaded airfoil with a round nose.  Rutan’s modified Eppler 1230 provided a good baseline for the tip.  After analyzing dozens of alternatives, we found the Eppler 1212 was a strong contender.  But the NACA 2415 fit our spar design better, had less drag at cruise, and had less Cm than the Epplers.  After further analysis, the 2415 airfoil thickness was reduced to 14% to lower drag, the nose was updated per Riblett’s method, and the camber line was optimized for high CL max. All airfoil modifications were performed with XFLR5 software.  As a designer (and not an aerodynamicist) I found the following techniques invaluable: 1. XFLR5 allows the user to create airfoils by “interpolation”.  This function blends two different airfoils into one, with full control over the mixing percentage.  Designers use this method to combine airfoils with different desirable properties into a new airfoil with a mix of those properties.  The result is a compromise, the extent of which is controlled by the user.  One airfoil can be influenced by several others in this way. 2. The second technique is rather embarrassing.  If software did this, it would be called “parametric airfoil optimization using artificial intelligence”.  Since I did it manually, it’s called “the brute force optimization method”.  It involves raising or lowering the four airfoil quadrants (one surface at a time) by a small percentage and then analyzing the effect.  “Quadrant” refers to the forward and aft portion of the upper and lower airfoil surfaces.  I promise you will have an intuitive feel for airfoil design trade-offs after using this method a hundred times or so. These techniques are less sophisticated than what many aerodynamicists do, but they can still provide excellent results.  Airplane PDQ reports the new airfoils and wing planform increase cruise speed by 8 knots and reduce stall speed by 4 knots compared to the Cozy wing.  And that’s before adding the blended winglets, which PDQ can’t model. The following pictures (click to enlarge) show the Apollo’s airfoils for the wing root, wing tip and winglet: Site Map Email the Designer Copyright © 2012 Apollo Canard