Run a virtual wind-tunnel test. Tilt a symmetric airfoil, probe both surfaces, and build the whole lift force from pressure around the wing.
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A wing interacts with the moving air around it. The flow changes, and pressure acts around the whole surface. Add those contributions and you can find a force across the incoming airflow: lift. A longer top surface and an equal-arrival rule are not required.
The upper and lower surfaces have equal lengths. Can this symmetric model produce lift?
Shape symmetry does not force flow symmetry at a nonzero angle of attack. Try +4° and −4°. Their ideal lift signs reverse.
A wing can move through air, or air can move past a held wing in a wind tunnel. The relative flow is the important input. Our fixture holds an ideal section still while air moves from left to right. Turning the air off removes dynamic wing lift in this model; buoyancy is outside this calculation.
The straight line from leading edge to trailing edge is the chord. Angle of attack is measured between that chord and the undisturbed relative airflow. At a positive angle in our view, the leading edge sits higher. The shape remains symmetric, but the surrounding flow no longer has upper/lower symmetry.
The flow solution supplies local speed. Under the assumptions used here, Bernoulli’s equation connects that speed to static pressure. The colors show pressure relative to upstream air. Negative values mean below that reference, not negative absolute pressure. A lower-surface reading can be below upstream pressure and still exceed the upper-surface reading.
Pressure acts normal to each little surface area. A uniform pressure around a closed body cancels in the total. Our force-building view sums the departures from that common reference. The final lift points perpendicular to incoming airflow. One probe or one part of the lower surface cannot tell the whole story.
Pressure and momentum are compatible descriptions of the same interaction between air and wing. Do not add a separate “Bernoulli lift” to a separate “Newton lift.” The model’s streamlines come from the same flow solution as its pressure values; paired tracers are never forced to meet again at the trailing edge.
The live section is an original mathematical Joukowski airfoil, not a NACA 0012 or an aircraft replica. A circle centered at −3/121 m with radius 3/11 m is mapped by z = ζ + b²/ζ, with b = 30/121 m. The result has a 1 m chord and about 11.785% thickness. The velocity uses the derivative of that same mapping.
An ideal flow around a sharp trailing edge needs a circulation choice. The Kutta condition selects the finite-velocity trailing-edge solution. With clockwise-positive circulation in our notation, Γ = 4πUR sin α. Lift per unit span is L′ = ρUΓ. The model uses ρ = 1.225 kg/m³ as a supplied example value.
Dynamic pressure is q = ½ρU². The pressure coefficient is Cₚ = (p − p∞)/q = 1 − (local speed/U)². For this fixed geometry, Cₗ = (24π/11) sin α and L′ = q c Cₗ. At 4° and 20 m/s, Cₗ is about 0.478 and L′ about 117.144 N/m. Doubling speed at the same angle multiplies force by four while leaving normalized pressure unchanged.
The result is force per meter of span for a two-dimensional section. The displayed extrusion helps you recognize a wing specimen, but the calculation has no finite-wing tips, induced drag or full aircraft. It does not predict whether an aircraft climbs, trims or carries a given weight.
This model assumes steady, incompressible, inviscid flow. Real air has viscosity and a boundary layer near the surface. Separation can change pressure and lifting behavior; an ideal smooth solution does not predict stall. The ±6° control range is a teaching boundary, not a measured stall angle. The separate Ladson data card identifies its own airfoil and test conditions.
A tunnel lets researchers hold a specimen, control the incoming flow, and measure pressures and forces. Our fixture borrows that idea. The actual tunnel walls, mount interference and measuring instruments are not part of the potential-flow calculation.
After release, a paper glider still interacts with moving air. Lift, drag and weight continue to act. Descending does not mean lift has disappeared, and the earlier push from your hand is no longer a continuing thrust force.
Designers have tested many shapes for different requirements. The NACA historical chart shows examples from 1908 to 1944. Our selected symmetric mathematical section is one teaching case; its result cannot rank every historical or modern wing.
Fold the paper lengthwise, open it, then fold the two top corners to the center crease. Fold those slanted edges toward the center again. Fold the paper closed along the center, then fold matching wings down on each side. Keep it light; no clips or added weights.
From a low height, give the glider a gentle release toward a clear floor area, away from people, pets, stairs and breakable objects. Use broadly similar releases. Record the path: a glide, turn, dive or other motion. A varying throw can change the result.
Sketch one part of the flight. Draw the glider’s travel arrow and an opposite relative-airflow arrow. Add weight downward. Lift is defined across the relative airflow, not necessarily vertically. After release, the earlier hand push is not a continuing force.
Optionally turn up the trailing 2–3 mm of both wings by a small matching amount and repeat three gentle trials. Write what changed and one thing you did not measure. The fold can affect trim, shape, drag and motion; it does not isolate lift alone.
Can a glider have lift while it is going downward?
A gentle paper observation, not an aircraft-performance test. No sharp parts, forceful throws or launches from heights. A flexible finite glider is not our rigid 2D airfoil; a changed path does not measure pressure, lift coefficient or an exact stall angle.
Wing chord and undisturbed relative airflow The incoming air is the reference. Aircraft attitude relative to the horizon is a different angle.
Upward lift in the horizontal-wind view Inclination makes the flow asymmetric while the shape stays symmetric. Equal-path or equal-arrival rules are not the source of lift.
The lower surface, although both are below upstream −23.5 Pa is higher than −176 Pa. “Higher than the other surface” is different from “higher than upstream.” These readings sample only one chord location.
No, combine contributions around the whole surface Different panels have different pressures, sizes and normal directions. The whole-surface sum supplies the resultant.
The incoming relative airflow Local pressure forces are normal to local panels. Lift is a component of their resultant, defined across the incoming flow.
It becomes four times as large Dynamic pressure contains U². With coefficient, density and geometry fixed, doubling speed gives four times the force.
No; separation and viscous effects are outside it The slider limits are chosen for teaching. Measured or suitable viscous-flow evidence is needed for a particular real case, with its own conditions.
No; lift, drag and weight can act during descent A flight path is a result of forces and motion. Descending does not mean the aerodynamic lift force has vanished, and a glider need not have engine thrust.
Definitions of lift, relative motion and the distinction from misleading equal-transit explanations.
NASA Glenn · LiftThe lesson does not calculate velocity from path length or force equal arrival.
NASA Glenn · Incorrect equal-transit theorySupports whole-surface integration and force-direction interpretation.
NASA Glenn · Aerodynamic forcesThe velocity field is solved first; Bernoulli does not supply a longer-path speed rule.
NASA Glenn · Bernoulli equationEquations Bged9–17. Our clockwise-positive circulation convention and numerical pressure integration are documented in the research record.
Caltech / C. E. Brennen · Joukowski airfoilsUniversity-hosted mathematical explanation. No source-page diagrams or licensed flow movies are copied.
University of Sydney / Cambridge · Joukowski transformationThe fixed-angle speed challenge keeps this model’s coefficient constant.
NASA Glenn · Lift equationThese effects are outside our ideal solver and are not faked by random particle motion.
NASA Glenn · Boundary layersLadson, NASA TM 4074 (1988), NACA 0012, 80-grit series, Re 6 million, M 0.15. Local copy and provenance are available in the evidence card.
NASA TMR · Original Ladson force dataEstablishes provenance of the numerical data host used here.
NASA · Turbulence Modeling Resource migrationCredit: NACA / NASA. The source rendition is hosted locally without content alteration.
NASA / DVIDS · Airfoil history imageSupports the safe paper-glider observation and its limits.
NASA Glenn · Four forcesIndependent subject review is pending.
Read the sources and model assumptions
Interactive explorationLoad a tiny barge and watch its waterline rise along the hull. Then lower a block through a tank to connect water pressure with buoyancy.
Interactive explorationOpen a detailed engine, turn its crank, and take the assembly apart. Follow four different jobs hidden inside two very similar-looking turns.
Squeeze a hydraulic brake. See inside the caliper, change piston sizes, and discover how pressure becomes force.