HENFOIL
An airfoil knowledge base for HENFOIL, in reading order: geometry and forces, analysis and design, boundary layers, theory and computation, then named families, wind-tunnel method, geometry repair, optimization, and the workflows that keep a polar traceable. Product field guides sit after the lessons. These are teaching notes, not certification reports.
220 articles · 38 topics
Product
HENFOIL and HENSYNTH product notes: what each workspace adds, who it is for, and what it does not claim.
How-to
Field guides for HENFOIL features and HENSYNTH loops — geometry, requirements, synthesis, Mission, Performance, Trades, Optimize and Reports.
Airfoil fundamentals
Chord, camber, thickness, NACA names, angle of attack, and how shape creates lift.
Airfoil analysis
Polars, Reynolds and Mach number, L/D, drag, pitching moment, and how to compare sections.
Airfoil design
Choosing, drawing, and optimizing a section for a UAV or another real mission.
Advanced aerodynamics
Boundary layers, stall types, roughness, icing, pressure plots, and airfoil noise.
Airfoil applications
Wind turbines, electric aircraft, CFD, and the step from a 2D section to a 3D wing.
Airfoil geometry
Coordinates, chord, camber, thickness distribution, leading-edge radius and named NACA profiles.
Lift and drag
How to calculate CL and CD, read the lift slope, zero-lift angle, CLmax and the best angle.
Analysis methods
Lift curves, low Reynolds number, Cp plots, potential flow, convergence and compressibility.
Design and modification
Editing a section, parameterization, design variables, optimizers and a comparison matrix.
Applications and validation
HALE and racing aircraft, altitude, gliders, wind-tunnel tests and checking a computation.
Boundary layers
Thickness, laminar bubbles, adverse gradients, transition, roughness and skin friction versus pressure drag.
Stall and flow control
Stall type, post-stall polars, slats, flaps, vortex generators and dynamic stall.
Coordinates and numerics
Bad points, interpolation, resampling, panel methods, resolution and why two codes disagree.
Operating conditions
Reynolds-number sweeps, temperature, yaw, critical Mach, shocks and off-design flight.
Design workflows
Databases, CAD sketches, performance maps, high-lift selection and the step from a polar to a wing.
Geometry models
NACA camber lines, 5-digit and 6-series sections, coordinate equations, CST and Bézier curves.
Aerodynamic theory
Thin-airfoil lift, the lift slope, the Kutta condition, circulation and the aerodynamic center.
Computational methods
Panel methods, viscous coupling, XFOIL settings, failed polars, CFD meshes and RANS.
Stability and integration
Pitching moment and stability, tailplanes, flaps, control surfaces and finite-wing effects.
Specialized applications
Solar UAVs, human-powered aircraft, wind-turbine stations, small electrics and performance maps.
Airfoil families
Clark Y, NACA 23012 and 4415, symmetric thicknesses, and Eppler and Selig low-Reynolds-number sections.
Flow phenomena
Pressure recovery, leading-edge suction, camber and zero lift, compressibility corrections and three-dimensional flow.
Wind-tunnel testing
Balances and wakes, data reduction, uncertainty, oil flow, pressure taps and a validation workflow.
Geometry processing
Self-intersections, area and ordering, transforms, DAT to DXF, and a quality check before the loft.
Optimization and workflows
Robust and multi-point design, surrogates, machine learning, morphing sections and an automated analysis loop.
Geometry parameters
Leading-edge radius, thickness ratio, trailing-edge thickness, reflex camber, and comparing two sections.
Performance reading
Best lift-to-drag angle, glide ratio, reading lift with drag and moment, hysteresis, and polar trade-offs.
Analysis workflows
Reynolds-number sweeps, consistent databases, sensitivity, outliers, solver benchmarks, and reproducible reports.
Aircraft and propulsion
Trainers, flying-wing UAVs, propeller blades, electric VTOL, high-altitude flight, and slow mapping aircraft.
Research methods
Uncertainty, Bayesian search, physics-informed models, flow control, bio-inspired sections, and digital twins.
Latest
Product
HENSYNTH targets aerospace OEMs, Tier-1 suppliers, UAV and eVTOL manufacturers, design bureaus, research labs and aeronautical students — with one honest conceptual-design product.
HENDOI · 30 October 2026
How-to
How to download the latest HENSYNTH analyze PDF, list stored runs, and mail a conceptual screening summary from the Reports page.
How-to
After Requirements and Synthesize, open HENSYNTH Mission, Performance, Trades and Optimize for stored predictions, mission-opt grids, sweeps and conceptual range search.
How-to
End-to-end HENSYNTH help path: dashboard project, Aircraft geometry, Requirements, Run screening, compliance, Synthesize, candidate apply, zip report, HEN-AI.
How-to
Read synthesis candidate cards, apply geometry with Use this aircraft, open the Aircraft page and CAD continuity after a style search — screening handoff, not auto-certification.
Aircraft
Walk through a fixed-wing electric UAV in HENSYNTH: payload and endurance requirements, battery cap and reserve SOC, geometry, Run screening, synthesis, candidate apply.
Product
HENFOIL is the airfoil and section loop; HENSYNTH is geometry, requirements, run, compliance, and synthesis. One HENDOI login, handoff from the dashboard, no merged solver fantasy.
How-to
Zip reports from the requirements run and candidate cards: PDF, PNG figures, stored metrics, download icon, and email share with CC/BCC limits.
Aircraft
Static margin on the requirements run is a pitch stability screen in MAC fractions — neutral point, CG, tail volume — from the ? help modal, not flight-test stability approval.
Aircraft
Takeoff limit and landing limit on Requirements map to predicted ground roll plus obstacle clearance — how HENSYNTH documents the screening formulas in help modals.
Aircraft
How HENSYNTH predicts range and endurance against requirements — electric energy bookkeeping, cruise speed link, reserve SOC, and compliance rows without wind claims.
Aircraft
How HENSYNTH builds MTOW and empty mass for conceptual screening — component groups, electric UAV vs heavier GA paths, and why weight drives every later metric.
How-to
The compliance table compares each mission requirement to predicted screening values — target, predicted, margin, status chip, and confidence — on Requirements and in reports.
How-to
Run Synthesize candidates after feasibility: minimum MTOW, maximum endurance, minimum energy, and balanced design — style searches with wing loading, AR, and battery fraction.
How-to
After Run screening, the Requirements run report lists MTOW, range, endurance, stall, field lengths, climb, L/D max, static margin, compliance rows, and ? modals with formulas.
How-to
Enter range, endurance, cruise, field lengths, payload, span cap, and battery limits on the HENSYNTH Requirements page — with feasibility check and handoff to synthesis.
How-to
How to use the Aircraft page in HENSYNTH: planform inputs, fuselage dimensions, tail arms, propulsion, 3D view, section plots, and save-before-run discipline.
Product
HENSYNTH is live. Geometry, requirements, Run, synthesize, Mission, Performance, Trades, Optimize and Reports — conceptual analysis only, not certification.
Product
XFOIL is a free local viscous solver. HENFOIL is the section workspace around a C++ engine: geometry, several methods, reports, and a handoff to rotors. This page compares the jobs, not a made-up error table.
Product
XFLR5 is the airplane workbench. QBlade is the rotor workbench. HENFOIL is the section workspace that feeds both, with a marked 360° polar and the same files those tools already read.
Airfoil fundamentals
Chord, camber, thickness, leading edge and trailing edge — the geometry that lets a wing, blade or fin make lift with controlled drag.
Airfoil fundamentals
A symmetric section lifts only when it is at an angle. A cambered section lifts at zero chord angle — and it brings a pitching moment with it.
Airfoil fundamentals
The four digits are maximum camber, where that camber sits, and thickness. NACA 2412 is 2% camber at 40% chord and 12% thick.
Airfoil fundamentals
Geometric angle of attack tilts the chord to the freestream. Lift rises almost linearly, drag rises faster, and then the section stalls.
Airfoil fundamentals
Lift is the integral of pressure and shear around the section. Camber and angle of attack decide where the suction sits.
Airfoil analysis
A polar is the section’s lift, drag and pitching moment against angle of attack — or drag against lift — at one stated flow condition.
Airfoil analysis
Reynolds number says how large viscosity is relative to the section. Mach number says how much the flow notices that air is compressible. State both.
Airfoil analysis
L/D is lift divided by drag at the same condition. The best section is the one whose maximum L/D sits on your mission lift coefficient.
Airfoil analysis
The drag polar plots CD against CL. Minimum drag, the laminar bucket and maximum L/D are three different points on that curve.
Airfoil analysis
CM is the section’s pitching moment, usually about the quarter-chord. It sets tail load, trim drag and how the nose feels near stall.
Airfoil analysis
XFOIL couples a panel method to an integral boundary layer and an eⁿ transition model. It is fast and serious — and it is not a stall certificate.
Airfoil analysis
Hold Reynolds number, Mach number and transition fixed. Then compare CL, CD, L/D, CM and the stall break at the lift you actually fly.
Airfoil design
Cruise speed, chord, endurance and how gently it stalls decide the section. A name that worked on a light aircraft is not automatically a UAV section.
Airfoil design
Optimization changes the shape on purpose: variables, an objective, constraints, and a method. A lower drag number is not a result unless the constraints survived.
Airfoil design
Endurance is a high-lift efficiency problem at modest Reynolds number. The section has to hold that efficiency after the leading edge gets dirty.
Airfoil design
A section is a list of x and y. The file format, the order of the points, and the chord scaling decide whether the next tool sees the shape you designed.
Airfoil design
Thickness is the structural budget and a stall and Mach trade. Camber is the zero-lift angle and the pitching moment. They are not free decorations.
Airfoil design
Cruise drag, pitching moment and stall do not share a single winner. The Pareto front is the set of shapes that trade those goals honestly.
Advanced aerodynamics
Separation is the boundary layer leaving the wall because the pressure rise is more than its momentum can climb. Lift, drag and moment all change when it does.
Advanced aerodynamics
Laminar skin friction is lower. Turbulent flow resists separation. Transition is where that choice is made, and it moves when the day, the bugs or the Reynolds number change.
Advanced aerodynamics
Stall is the lift break after separation wins. Trailing-edge stall arrives gradually. Leading-edge stall arrives as a burst. Thin-airfoil stall is a long bubble. They are not the same event.
Advanced aerodynamics
A rough leading edge trips the boundary layer, raises drag, and can cut maximum lift. Laminar sections feel it first. The polar you owe the operator is the dirty one.
Advanced aerodynamics
Past a point, the forces on the way up in angle of attack are not the forces on the way down. Dynamic stall adds a leading-edge vortex that steady polars never show.
Advanced aerodynamics
A Cp plot is the surface pressure versus chord. The suction peak, the rooftop and the recovery explain the lift, the boundary layer and the Mach limit.
Advanced aerodynamics
An airfoil in clean flow still makes noise. The turbulent boundary layer scattering off the trailing edge is usually the main broadband source, and the edge geometry changes it.
Advanced aerodynamics
Ice on the leading edge is a shape change: more drag, less maximum lift, an earlier stall, and a pitching moment the clean polar does not contain.
Airfoil applications
A turbine blade is many airfoils. The root is a thick structure, the outer board is a high-lift machine, and the tip has to stay efficient when it is dirty and quiet enough to site.
Airfoil applications
Battery energy makes cruise L/D expensive to waste. eVTOL adds a second problem: sections and rotors that must behave in hover, in transition and in wing-borne flight.
Airfoil applications
A viscous panel polar and a Navier–Stokes solution are different instruments. Use the fast one to search. Use the expensive one when the physics leaves the fast one’s assumptions.
Airfoil applications
A wing is a spanwise family of sections, twisted and tapered, flying in its own induced flow. The section polar is the input. It is not the airplane.
Airfoil geometry
A useful polar starts as a clean polyline: unit chord, leading edge at the origin, no loops, and a trailing edge you can explain.
Airfoil geometry
Chord is the reference length of the section. It scales the drawing, the Reynolds number and every coefficient that uses a length.
Airfoil geometry
Camber is how far the mean line bends away from the chord. Thickness is how far the upper and lower surfaces stand apart. They peak in different places and do different jobs.
Airfoil geometry
Maximum thickness is one number. The thickness distribution is the whole function t(x), and it is what the spar, the stall and the panel code actually see.
Airfoil geometry
The nose radius decides how hard the flow turns at high angle. The trailing edge decides how cleanly the upper and lower streams leave, and how much base drag you pay.
Airfoil geometry
All three are 12% thick 4-digit sections. The first digit changes the camber: 0%, 2% and 4% at 40% of the chord. That is the whole comparison.
Lift and drag
Section lift coefficient is lift per unit span divided by dynamic pressure and chord. The same letters on a wing use area instead of chord.
Lift and drag
Section drag coefficient is drag per unit span divided by dynamic pressure and chord. In two dimensions that drag is profile drag: skin friction plus pressure, not induced drag.
Lift and drag
Lift curve slope is how fast section lift coefficient grows with angle of attack. Thin-airfoil theory says 2π per radian. Real sections sit a little lower, and a finite wing sits lower still.
Lift and drag
The zero-lift angle is the geometric angle at which section CL is zero. It is about zero for a symmetric section and negative for ordinary positive camber.
Lift and drag
CLmax is the highest section lift coefficient on the polar before stall wins. It moves with Reynolds number, nose shape, camber, roughness and Mach number.
Lift and drag
The best angle is where the section’s lift-to-drag ratio peaks for your mission, not where lift is highest and not where drag is lowest.
Analysis methods
A lift curve is a sweep of one section at one Reynolds number and one Mach number. The step size, the range and the failed points are part of the result.
Analysis methods
Below a few hundred thousand chord Reynolds number, laminar separation bubbles dominate the drag and can dominate the stall. A section designed at three million will not automatically survive there.
Analysis methods
A Cp plot is the surface pressure from one solved angle of attack, drawn with suction upward. Build it from a real run, then read the peak, the rooftop and the recovery.
Analysis methods
Potential flow can set the lift of an attached section. It cannot set the drag. Viscous analysis exists because the boundary layer is where drag, transition and stall live.
Analysis methods
A polar point is finished only if the iteration settled. Oscillation, a negative drag, a one-point spike or a trailing-edge explosion is a failed point, not a feature of the airfoil.
Analysis methods
Above a section’s critical Mach number the suction peak goes sonic, a shock can form, and drag rises. Thickness, camber and lift all move that Mach number.
Design and modification
Change camber, thickness or the nose through a parameterization, then re-normalize and re-check curvature. Dragging individual points is how a section grows wrinkles.
Design and modification
Cruise speed and chord fix the Reynolds number and the Mach number. Wing loading fixes the lift coefficient. The section is designed at that point, not at a famous one.
Design and modification
A parameterization is the small set of numbers that generates the coordinates. NACA digits, CST coefficients and spline control points are three different bargains between freedom and smoothness.
Design and modification
A new section is a legal point in a design space: variables inside bounds, constraints that reject unbuildable geometry, and only then a polar.
Design and modification
A gradient method follows the local slope and finishes quickly near a good start. A genetic algorithm searches more widely and spends many more evaluations. The airfoil problem decides, not a fashion.
Design and modification
A comparison matrix is a table with one row per section and one column per requirement, filled at the same Reynolds number, Mach number and transition setting.
Applications and validation
At altitude the air is thin, so the same chord and true speed give a much lower Reynolds number. A HALE section has to be efficient there, light, and willing to stall gently.
Applications and validation
A racing multirotor is a set of propeller blades. A fixed-wing UAV is a cambered wing. They do not share a design lift coefficient, a Reynolds number or a stall requirement.
Applications and validation
The section coefficients do not contain altitude. Altitude changes density, viscosity and the speed of sound, and through them the Reynolds number, the lift coefficient you must fly, and the Mach number.
Applications and validation
A sailplane wing is a high-aspect-ratio device, so section drag matters. Maximum glide ratio and minimum sink are two different points on that polar.
Applications and validation
A section test is useful when Reynolds number, trip, wall corrections and the drag method are stated. An uncorrected balance run at the wrong Re is not a referee for a computation.
Applications and validation
Validation means the same geometry at the same Reynolds number, Mach number and transition, compared with the uncertainty of the test — not a tuned curve that matches one plot.
Boundary layers
The boundary layer starts thin at the stagnation point and grows as it travels. A pressure rise makes it grow faster. Thickness, displacement thickness and momentum thickness are three different measures.
Boundary layers
A laminar bubble is a short separated patch: the laminar layer leaves the wall, transitions in the shear layer, and reattaches turbulent. If it fails to reattach, the section stalls.
Boundary layers
An adverse gradient is a pressure rise in the flow direction. It slows the near-wall fluid. Separation is that fluid stopping and reversing.
Boundary layers
Transition is not one switch. Tollmien–Schlichting waves, crossflow, bypass, separation and roughness are different routes from a laminar layer to a turbulent one.
Boundary layers
Roughness moves transition forward when a grain is large compared with the thin layer near the nose. Below a threshold it can sit inside the laminar layer and do little.
Boundary layers
Skin friction is the streamwise pull of shear on the wall. Pressure drag is the streamwise push of normal pressure. Stall is mostly a pressure-drag event. Cruise of a clean section is mostly friction.
Stall and flow control
Thickness, nose radius and camber choose the stall pattern. A thicker, blunter nose tends to stall from the trailing edge. A sharper nose tends to stall from the leading edge.
Stall and flow control
A post-stall polar continues past CLmax: lift after the break, the drag rise, and the moment change. Simulators, spins and some UAVs need that branch. A cruise solver usually does not provide it.
Stall and flow control
A slat is a small airfoil ahead of the main nose. The slot feeds high-energy air onto the main element and the slat’s own shape softens the peak. Stall angle and CLmax both rise.
Stall and flow control
A trailing-edge flap adds camber. Lift rises at a given angle, the zero-lift angle goes more negative, the moment goes nose-down, and drag rises. Fowler flaps also change the chord.
Stall and flow control
A vortex generator is a small vane that sheds a streamwise vortex and mixes high-speed air down to the wall. It can delay separation. It always adds some cruise drag.
Stall and flow control
When angle of attack changes quickly, lift can overshoot the static maximum and the return path is a different curve. Reduced frequency says whether the motion is fast enough to matter.
Coordinates and numerics
A zero-length panel, a repeated trailing edge, a crossed surface or a point that jumps backward will quietly ruin a panel solution. Detect them before the solver runs.
Coordinates and numerics
Interpolating an airfoil is how you add points or build a CAD curve. Linear interpolation facets the nose. An unconstrained spline can loop. A shape-preserving fit stays between the points.
Coordinates and numerics
Resampling places a new point set on the same curve. Cosine clustering protects the nose. Uniform spacing in x does not. Always compare thickness and leading-edge radius afterward.
Coordinates and numerics
A panel method replaces the airfoil with panels carrying source or vorticity. Lift can be accurate with a modest set. The nose, the trailing edge and the pressure peak show the discretization first.
Coordinates and numerics
There is no universal panel count. A cosine distribution of on the order of 100 to 200 panels is a sane start for section lift. Drag and the nose peak decide whether you need more.
Coordinates and numerics
Two trustworthy codes can print two polars for one DAT file because they did not solve the same problem. Geometry closure, transition, panel count and the meaning of CD are the usual gaps.
Operating conditions
As Reynolds number rises, attached skin friction usually falls, transition moves, and maximum lift often rises. One polar cannot stand in for the range.
Operating conditions
Viscosity sets the Reynolds number together with density and speed. Temperature changes viscosity and the speed of sound. It does not change a coefficient by itself.
Operating conditions
A yawed wing meets the section with the velocity component normal to the leading edge. An airplane in crosswind is mostly a sideslip problem. A 2D polar does not contain either effect until you say which one you mean.
Operating conditions
Critical Mach number is when the peak local speed first reaches sonic. Drag divergence is the later freestream Mach number where drag actually rises. They are not the same Mach number.
Operating conditions
A transonic shock is a sudden pressure rise on the upper surface. Wave drag is the momentum lost through that shock. If the rise is too sharp, the boundary layer separates and the moment breaks.
Operating conditions
The design point is one dot on the polar. Climb, gust, high-speed dash, a dirty leading edge and a second Reynolds number are the rest of the airplane’s life.
Design workflows
An airfoil database stores a geometry, its provenance and the polars that were actually run. A folder of unnamed DAT files is not a database.
Design workflows
A CAD sketch of an airfoil is the normalized section, scaled to the real chord, drawn in a plane normal to the leading edge or the spar, and closed on purpose.
Design workflows
A performance map shows a coefficient over two operating axes, such as lift coefficient and Reynolds number. Comparing sections on one polar hides the axis where they actually differ.
Design workflows
A high-lift airplane needs a cruise section and a deployed high-lift system. Selecting only for CLmax, or only for cruise L/D, designs half the flight.
Design workflows
A lifting-line or strip estimate takes section polars, applies the local induced angle, and integrates. Profile drag comes from the polar. Induced drag comes from the wake. Stall is the first station that runs out of CL.
Design workflows
A wing CAD model is a loft through several scaled, twisted section sketches. The loft is faithful only if every sketch is the airfoil you analysed, at the chord and twist of that station.
Geometry models
The mean camber line is the midline between the upper and lower surfaces. For a NACA 4-digit section it is two parabolas. For a coordinate file it is the average of the two surfaces, done carefully.
Geometry models
A 5-digit NACA name puts the camber farther forward than a 4-digit section of similar design lift. NACA 23012 means a design lift coefficient of 0.3, maximum camber at 15% chord, and 12% thickness.
Geometry models
A 6-series section is drawn around a pressure distribution: a favorable gradient back to a chosen point, to hold a laminar run, and a design lift coefficient on a separate mean line.
Geometry models
Thickness is laid perpendicular to the camber line, not stacked vertically on the chord, except when the camber line is straight. The slope of the camber line is part of the coordinate.
Geometry models
CST writes each surface as a class function, which sets the nose and the trailing edge, times a shape function, which is a short polynomial. A handful of coefficients replaces a cloud of points.
Geometry models
A Bézier curve feels every control point globally. A B-spline feels only the nearby ones. Neither one knows what a leading-edge radius is unless you constrain it.
Aerodynamic theory
Thin-airfoil theory replaces the section with a vortex sheet on the chord line. It predicts lift slope, zero-lift angle and the moment from camber, and it predicts none of the drag.
Aerodynamic theory
In thin-airfoil theory the section lift slope is 2π per radian, about 0.110 per degree. A finite wing is shallower. The units are where most calculations go wrong.
Aerodynamic theory
Potential flow allows many circulations around one shape. The Kutta condition chooses the one that lets the flow leave a sharp trailing edge smoothly, at finite speed.
Aerodynamic theory
Lift per unit span equals density times freestream speed times circulation. The Kutta condition chooses the circulation. This theorem converts it into a force, and it still predicts no drag.
Aerodynamic theory
Moment depends on the reference point. About the quarter-chord it is nearly constant with lift. About the leading edge it grows more nose-down as lift rises, by about CL/4.
Aerodynamic theory
The aerodynamic center is the point about which pitching moment does not change with lift. In thin-airfoil theory it is the quarter-chord. The center of pressure is a different point, and it moves.
Computational methods
A panel method solves the inviscid flow with unknowns only on the surface. Sources and vorticity enforce a streamline body and the Kutta condition. Drag is not one of the outputs until viscosity is added.
Computational methods
The boundary layer thickens the shape the potential flow sees and takes momentum out of the wake. Iteration between those two facts is what turns an inviscid lift into a viscous polar.
Computational methods
An XFOIL polar is not defined until Reynolds number, Mach number and the transition setting are chosen. Those three inputs move the drag as much as a modest shape change.
Computational methods
A failed polar is a tooth in the lift curve, a negative drag, or a point that never settled. Fix the geometry and the case before you smooth the plot.
Computational methods
A RANS airfoil mesh has to resolve the boundary layer, not only the outline. Independence means lift and drag stop moving when you refine, including the wake.
Computational methods
A panel method with a boundary layer is the right tool for a matrix of attached polars. RANS is the right tool when the flow has a shock, a slot or a separation the integral layer cannot carry. Cost follows that split.
Stability and integration
A nose-down section moment changes the tail load required to trim. It does not, by itself, make the airplane stable. Stability is the slope of moment with angle, set by where the center of gravity sits.
Stability and integration
A tailplane usually wants a symmetric section, because it must lift both ways. Its Reynolds number is not the wing’s, and its stall is a control failure, not just a drag item.
Stability and integration
Small flap angles move lift, drag and moment almost together. Larger angles keep adding drag and moment after the lift increment has flattened, because the flap itself has separated.
Stability and integration
A control surface is a flap on a particular section. Ailerons change wing lift asymmetrically. Elevators change tail lift. The hinge moment and the stall of that flap are the control limits.
Stability and integration
A preliminary performance model reads CL and CD from the section polar at the lift the wing is flying, then adds induced drag. Using the section L/D as the airplane L/D skips that second term.
Stability and integration
A finite wing flies at a lower effective angle than the geometric angle, pays an induced drag the section never had, and stalls where some station reaches its section limit first.
Specialized applications
A solar UAV spends the day’s collected energy on drag. The section has to be efficient at low speed and low Reynolds number, and the upper surface is also a solar array that must stay smooth.
Specialized applications
A human can produce a few hundred watts for a long effort. The airplane only closes if airplane L/D is very high, which means a large aspect ratio and a section whose profile drag is small at low speed.
Specialized applications
Root, mid-span and tip are different airfoils at different Reynolds numbers. The rotor works only if each station is analysed at its own speed, chord and thickness.
Specialized applications
A small electric airplane has a wing section at a modest Reynolds number and a propeller section at a different one. Battery energy makes both drags expensive, and they are not the same airfoil.
Specialized applications
A short-field airplane needs a high maximum lift coefficient at low Reynolds number and a climb gradient after liftoff. Cruise efficiency still has to survive once the devices retract.
Specialized applications
A performance database is a set of polars indexed by Reynolds number, Mach number, flap setting and surface condition. One curve at one condition is a sample, not the map.
Airfoil families
The Clark Y is a moderately cambered section with a flat lower surface over the rear half. It was drawn so a builder could set that flat on a board. It is not a laminar-flow section.
Airfoil families
NACA 23012 asks for a design lift coefficient of 0.3 with the camber crest at 15% chord and 12% thickness. The forward camber is why the pitching moment stays milder than a 4-digit section asked for the same lift.
Airfoil families
NACA 4415 is 4% camber at 40% chord and 15% thick. It carries more design lift than a 2412 and more spar depth than a 4412. Both of those choices have a drag and a moment attached.
Airfoil families
Both sections are uncambered. NACA 0018 is thicker, so the leading-edge radius, the spar and usually the stall margin grow, and low-lift drag and critical Mach usually pay for it.
Airfoil families
Eppler sections were designed by prescribing the velocity distribution, with the low-Reynolds-number boundary layer in mind. A model-sailplane polar is not a full-scale polar.
Airfoil families
Selig sections for models and small aircraft were developed by designing a shape, testing it at low Reynolds number, and publishing the result. The wind-tunnel Reynolds number is part of the design.
Flow phenomena
Recovery is the rise in pressure from the suction peak back toward the trailing edge. A short, steep recovery separates. A longer recovery can stay attached and keep the wake, and the drag, thin.
Flow phenomena
Suction around the nose has a component pointing forward. In attached flow that leading-edge thrust offsets pressure drag. Stall is, in large part, the loss of that thrust.
Flow phenomena
More camber makes the zero-lift angle more negative and rearranges the chordwise load. The lift slope stays nearly the same. Spanwise distribution is a wing question that starts from this section lift.
Flow phenomena
The Prandtl–Glauert rule stretches incompressible lift and pressure by 1 over the square root of 1 minus Mach squared. It is a small-disturbance, subsonic correction. It is not a shock model.
Flow phenomena
Two tests represent the same airfoil only when geometry, Reynolds number, Mach number and relative roughness match closely enough that the boundary layer is the same kind of flow. High-Re coefficients change slowly. Low-Re coefficients do not.
Flow phenomena
A real wing has a spanwise direction. Sweep, taper, the tip vortex and a stall cell all move air sideways, so a 2D polar is the section input, not the wing result.
Wind-tunnel testing
Lift is usually a balance reading. Drag is a balance reading or a wake survey. Both are useless until dynamic pressure, angle and the wall corrections are part of the same record.
Wind-tunnel testing
Data reduction turns voltages into coefficients. The test condition is the Reynolds number, the Mach number, the trip and the wall corrections — not the fan setting you remember.
Wind-tunnel testing
A coefficient inherits the uncertainty of the load, the dynamic pressure and the area. Repeatability is the scatter you measured. Bias is the alignment and the corrections you did not scatter.
Wind-tunnel testing
A thin film of pigmented oil follows the surface shear. It piles up where the shear vanishes, which is separation, and it often changes texture where the boundary layer becomes turbulent.
Wind-tunnel testing
A tap reads static pressure at a point. Integrated, the taps are a lift and a moment. They miss whatever happened between the taps, and the leading-edge peak is exactly where the gaps hurt most.
Wind-tunnel testing
Validation is a sequence: same geometry, same Re, same Mach, same trip, then lift slope and zero-lift angle, then drag and moment, and only then the stall. Matching a drag curve by tuning a transition knob is not the end of that list.
Geometry processing
A self-intersection is a curve that crosses itself, usually a bad ordering, a spline loop or a trailing-edge fold. Delete the loop and rebuild the station. Do not scale it and hope the panel code copes.
Geometry processing
Area is a shoelace sum on a closed polyline. Perimeter is the length of that polyline. Thickness, camber and a leading-edge radius estimate come from the same points, and all of them move if the chord is not really 1.
Geometry processing
Selig order walks in from the trailing edge along the upper surface and back along the lower. Lednicer lists each surface from the leading edge. A panel code needs one winding, and it needs a trailing edge that is either one point or an honest gap.
Geometry processing
Scale about the origin, rotate about a stated point, then translate. Do that for a drawing. For an analysis file, put the leading edge back at the origin and the chord back on the x-axis, and apply angle of attack in the solver.
Geometry processing
A DXF profile is the same polyline as the DAT file, in declared units, with an explicit closure. Spline it only after the points are clean. The CAM system will cut whatever you write, including a reversed surface.
Geometry processing
A loft will faithfully turn a bad section into a bad wing. Check closure, thickness, leading-edge radius, point order and the trailing-edge rule on every station before you generate the solid.
Optimization and workflows
A robust section stays good when Reynolds number, Mach number and transition move a little. Optimize the expected value or the worst case over that neighborhood, then recompute the winner as a real polar.
Optimization and workflows
A surrogate is a fit to a set of real aerodynamic evaluations. It can propose the next shape. The shape you keep is one you recompute with the real solver, inside the range the fit was trained on.
Optimization and workflows
A model can propose a shape or a polar only inside the cases it was trained on, and only inside the geometry constraints you still enforce. The number you publish is a solver or a test, not a network output.
Optimization and workflows
A wing section has to work at more than one lift coefficient. Multi-point optimization states those points, weights them on purpose, and refuses a cruise bucket that cannot climb or land.
Optimization and workflows
A morphing section changes camber or thickness in flight so the same wing can sit in more than one polar. Each shape is still an airfoil you have to analyse. The mechanism does not create lift by itself.
Optimization and workflows
An automated workflow accepts a coordinate file, rejects geometry that fails the gate, runs a declared method at declared conditions, and stores the polar with its inputs. A run that needed a human to nudge a hidden setting is not automated.
Geometry parameters
The leading-edge radius is the circle that fits the nose. On a coordinate file it is a local fit, and a coarse or faceted nose makes that fit a guess. A NACA four-digit section also has a closed-form estimate.
Geometry parameters
Thickness divided by chord buys spar depth and usually a milder nose peak. The same ratio usually costs low-lift drag and critical Mach. Quote it only after the chord in the file is the chord you mean.
Geometry parameters
A mathematical trailing edge has zero thickness. A part does not. The gap you leave is base drag, a closure rule for the panel model, and a loft constraint from root to tip.
Geometry parameters
Reflex turns the mean line back up near the trailing edge. That rear curl adds a nose-up couple, which is why flying wings use it. In this series a positive moment is nose-up.
Geometry parameters
Two outlines are hard to compare. Split each into a camber line and a thickness distribution, on a unit chord, and the difference becomes a pair of curves instead of a visual impression.
Geometry parameters
A conventional camber line asks a tail to trim a nose-down moment. A reflexed line spends some lift-to-drag to bring that moment back. Pick the one whose moment the airplane can actually trim.
Performance reading
Maximum section efficiency is the peak of CL/CD, not maximum lift and not minimum drag. On a drag polar it is where a straight line through the origin touches the curve.
Performance reading
In a steady glide the airplane’s lift-to-drag ratio is its glide ratio. The airfoil’s lift-to-drag ratio is higher, because the section does not carry induced drag or the rest of the airframe.
Performance reading
One angle of attack produces three coefficients. Lift says whether the wing can carry the weight, drag says what it costs, and moment says whether the tail can hold the attitude.
Performance reading
Past an abrupt stall, the lift on the way down in angle is often not the lift on the way up. The loop is a history effect. A single sweep, or a steady solver marched in one direction, can draw only one branch.
Performance reading
A polar is a trade already drawn. The cruise point, the climb point and the stall are different places on the same curve, and a shape that helps one of them moves the others.
Performance reading
Section efficiency is CL/CD at a stated lift coefficient, Reynolds number, Mach number and surface condition. Across a flight it is a table of those values, not the peak of one polar.
Analysis workflows
A Reynolds-number sweep is a matrix: one geometry, one method, one transition policy, many Re. Automation stores every converged point with its Re, and it leaves the failed points failed.
Analysis workflows
A useful airfoil database is a set of runs that share a chord definition, a moment reference, a Mach number and a transition policy. A folder of polars from different tools, with those choices unspoken, is not a database.
Analysis workflows
Sensitivity is the change in CD, CL or CM when you change one geometric quantity and rerun the same case. It is a local slope. It is not an optimum, and it is not a license to stack several changes and add the slopes.
Analysis workflows
A negative drag, a lift slope nothing like attached flow, or a point the solver did not converge is not a quirky airfoil. Flag it. Do not fair a curve through it.
Analysis workflows
A fair benchmark holds the geometry, the Reynolds number, the Mach number, the transition policy and the angle list fixed. Then it compares zero-lift angle and lift slope before it compares drag.
Analysis workflows
A reproducible report is one a colleague can rerun from the record: geometry hash, method, freestream, transition, residuals, and the table the figure was drawn from.
Aircraft and propulsion
A trainer section is judged on a gentle stall, a moment a simple tail can trim, and behavior with a rough leading edge. Cruise lift-to-drag is a later column.
Aircraft and propulsion
A flying-wing section has to trim at a positive lift coefficient without a tail. Reflex, sweep and the center of gravity do that together. The section moment is necessary and not sufficient.
Aircraft and propulsion
A propeller blade is a stack of sections. Each radius has its own speed, Reynolds number and inflow angle. A wing polar pasted along the whole blade is the wrong map.
Aircraft and propulsion
A wing-borne electric VTOL section lives in at least three problems: a high-lift transition, a quiet cruise, and a structure thick enough to carry people. No single polar covers all three.
Aircraft and propulsion
At altitude the density drops. Chord Reynolds number can be low even when true airspeed is high, and Mach number can rise at the same time. The section has to be chosen for both.
Aircraft and propulsion
A slow mapping airplane lives at a high lift coefficient and a low Reynolds number for a long time. Evaluate the section at the loiter condition, including a rough leading edge and a mild stall.
Research methods
A polar is a number conditional on geometry, Reynolds number and transition. Uncertainty quantification says how those inputs, and the numerical error, move the number. A band without a stated input is not confidence.
Research methods
Bayesian optimization fits a surrogate, often a Gaussian process, and chooses the next real aerodynamic evaluation where the surrogate is either promising or still unsure. The shape you keep is recomputed by the real solver.
Research methods
A physics-informed model is trained to match measured or computed data and to keep a residual of the governing equations small. Its output is still a model. It becomes a polar only after a declared aerodynamic method, or a test, agrees.
Research methods
Suction, blowing and a synthetic jet change the boundary layer by adding or removing momentum. The actuator power is part of the drag accounting. A lower section CD that ignores that power is not a better airplane.
Research methods
Bird wings change camber, use a small leading-edge feather like a slat, and fly at low Reynolds number. Those are lessons for devices and schedules. A traced bird outline is not an airfoil polar.
Research methods
A digital twin of an airfoil is one geometry identity, a simulation at the same condition as the test, and a stored discrepancy. A plot archive without those links is a slide collection.
How-to
How to fill Import — airfoil name, Selig/Lednicer text, Inspect vs Import, normalize — and what conditioning results mean before Geometry Doctor.
How-to
How Team plan seats work — own logins, shared monthly meters, admin visibility, ACL grants and email notices when access changes.
How-to
What t/c, camber, LE radius, TE state, CST residual, polar readiness scores mean — and why you should fix FAIL before climbing the analysis ladder.
How-to
What every Optimization control means — max L/D objectives, NACA/CST/Bayesian search, t/c and Cm limits, multi-point Re/Mach/CL weights — and what results to trust.
How-to
How to fill geometry filters, Re, cruise CL and ranking inputs — and what scored candidates, why lists and confidence mean.
How-to
Kind, M/P/T, 5-digit design CL, 6-series family, Joukowski μ, CST — purpose of every Create field and the coordinates and reports you get.
How-to
Sweep type, Re, Mach, Ncrit, trip stations, roughness, AoA range — purpose of each Polars field and the CL/CD/Cm results you should expect.
How-to
Brightness, threshold, LE/TE, detect mode, TE/fit/panel options — purpose of each Digitize field and the results you should expect before Create Airfoil.
Plans
All three plans unlock the same HENFOIL tools. Here is how monthly budgets, HEN-AI requests and team sharing change as you move up.
Product
Create an account, pick a plan, import or digitize a section, pass the geometry gate, run a VIC polar and export a datasheet — the practical first path.
Product
How geometry, mesh, CFD and FEA packs report gate status with method IDs — and why labelled screens beat pretty lies.
Product
Student USD 9, Professional USD 29, Team USD 89 — every plan unlocks all tools; monthly quotas differ. Why the prices look like this.
Product
Tool-calling explanations of stored HENFOIL results, billed by monthly requests — never fabricated polars.
Geometry
NACA families, CST / PARSEC, Selig / Lednicer DAT, and image digitize — then the same quality gate for every source.
Optimization
Target CL / Cp screens, NACA and CST grid or gradient search, Bayesian optimize — then robustness before you crown a winner.
Selection
Weighted compare, envelopes, ranking and export — so the winning section has a reason you can show in review.
Analysis
VIC is the production polar engine for compare and select. Deep notes on use cases, limits, envelopes and honesty labels.
Geometry
Thickness, camber, LE radius, TE, curvature and CST/PARSEC fit checks — PASS, WARNING or FAIL before you climb the analysis ladder.
Analysis
Thin-airfoil → Hess–Smith panel → Thwaites–Head IBL → VIC polars — and optional Euler / IB / RANS-SA screens. Escalate only when the decision needs it.
Product
A deep look at HENDOI’s browser-based airfoil design, analysis, selection and optimization platform — methods, honesty gates, and who it is for.