Airfoil Lift and Drag: Definition, Coefficient, Formula, Relationship

An airfoil is a streamlined shape that generates significantly more lift than drag when exposed to airflow. The section lift coefficient Cl measures the differential lift produced per unit length of chord. The lift coefficient Cl is the dimensionless ratio of lift to dynamic pressure times reference area. Drag acts parallel to the incoming flow and equals the parallel unit of force through the center of pressure. The drag coefficient Cd is the corresponding dimensionless measure.

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Jim Goodrich

Jim Goodrich is a pilot, aviation expert and founder of Tsunami Air.

What is lift force in an airfoil?

Lift is an aerodynamic force produced by the motion of a fluid past an object. Lift is the part of this force that is perpendicular to the oncoming flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, and it is the force that holds an aircraft in the air. Lift depends on airfoil shape.

Lift is the part of the total force vector that works through the center of pressure and is perpendicular to the incoming flow. It is the upward force on the wing acting perpendicular to the relative wind and perpendicular to the aircraft's lateral axis. As a vector quantity, lift directly opposes the weight of an airplane and is required to counteract the aircraft's weight, holding the airplane in the air.

Lift force is generated by the interaction and contact of a solid body with a fluid and is transmitted through pressure. Air pressure greater below the airfoil than above creates lift force, and this pressure difference is the source of the upward force. Lift force equals the time rate of change of momentum of the air, reflecting Newton's laws that describe how downward deflection of air creates upward lift force. The airfoil upward force is equal and opposite to the downward acceleration of air.

Maximum lift force generated by an airfoil at a given airspeed depends on the amount of camber and on the angle of attack, which also creates drag. Lift is a function of freestream velocity, fluid density, and wing area, and it requires sufficient density and velocity to maintain flight. Center of pressure is where lift acts, and any solid surface deflects flow to produce this mechanical force.

How does an airfoil generate lift?

An airfoil generates lift through a combination of Bernoulli’s principle and Newton’s laws. The angle of attack causes air over the top of the wing to travel faster than the air beneath the wing, and downward accelerated air produces upward lift.

According to Bernoulli's equation, higher velocities produce lower pressures. Upper air flow is faster which leads to lower pressure on top. Lower flow is slower which results in higher pressure. The interaction of forces generates lift. Deflected downward flow creates upward force. The wing changes the momentum of the air and the deflection of flow momentum flux produces lift according to Newton's second and third laws.

Angle of attack is the angle between chord line and oncoming air. Negative lift occurs at a negative angle of attack, with the pressure gradient simply reversed. Except at the extremes, lift varies nonlinearly for higher angles of attack. At the critical angle, upper surface flow separates and stall occurs.

What is the lift coefficient in thin airfoil theory?

Thin airfoil theory gives the lift coefficient as C_L = C_L0 + 2π α, where C_L0 is the lift coefficient at α = 0 and the slope 2π per radian holds for any thin cambered airfoil. For a symmetric airfoil Cₗ₀ equals zero, so the expression reduces to Cₗ = 2πα; for a cambered section Cₗ₀ is set by the camber‑line integral Cₗ₀ = 2 ∫₀^π (dz/dx)(cosθ − 1) dθ and is close to 0.228 for the NACA 4‑digit profiles commonly used. Thickness is assumed infinitesimal in the derivation, but wind-tunnel data show that the same linear slope remains valid up to about 12 % thickness, while the zero-lift angle and hence C stay practically unchanged, thus thickness has a very small effect provided the airfoil is thin enough for the theory to apply. Typical thin-airfoil predictions are C 0.675 at = 2 for both NACA 4412 and NACA 4410, and C 0.658 for the symmetric NACA 0012, again confirming that camber dominates C whereas thickness merely preserves the 2 slope. The highest attainable lift coefficient in the theory is therefore limited only by the stall angle rather than by thickness, before stall, C continues to grow linearly with from its camber-determined value C .

How does airfoil shape affect lift?

Airfoil shape influences lift by determining how much the flow is turned. Camber, the curvature of a wing, influences lift, and increasing camber increases lift. A cambered airfoil has a larger curve on the top than on the bottom, while a symmetric airfoil has the same curve above and below the chord line. Because of this, a symmetric airfoil produces less lift than an asymmetrical airfoil at the same angle of attack. Most foil shapes require a positive angle of attack to generate lift. The angle of attack increases lift until stall occurs. Thicker airfoils increase lift and thickness influences stall characteristics. Trailing-edge shape influences lift: a sharp trailing edge prevents upward spill, whereas a rounded trailing edge causes upward spill of flow. Leading-edge shape influences flow turning, and the state of the boundary layer affects the attainable lift of an airfoil. Airfoil shape determines the pressure distribution on the top and bottom surfaces, and that pressure distribution affects lift. Each airfoil has a different flow pattern that depends on its shape.

How does a symmetrical airfoil create lift? A symmetrical airfoil creates lift only when set at a positive angle of attack. At zero angle of attack it produces zero lift because its camber line equals the chord line, giving identical curvature above and below. Once the wing is inclined to the airflow direction, the angle of attack turns the flow, establishing a pressure difference that generates lift. A symmetrical airfoil generally experiences less lift-induced drag at zero angle of attack because lift is zero. When angle of attack is increased to produce lift, induced drag appears, but for comparable lift a symmetrical airfoil requires a higher angle of attack than a cambered shape, slightly increasing drag.

What is a high lift airfoil?

A high-lift airfoil enhances the lifting force at low speeds, and its objective is to create maximum lifting force. High-lift airfoils play a key part in creating high lift-to-drag ratios, and they are responsible for creating high-lifting force without affecting high-speed aerodynamic efficiency.

A high-lift airfoil is a geometry or system that produces a larger lift force at low speed. It is a single-element shape like the S1223 airfoil or LI 003, or a two-element slotted layout. All variants are equipped with a flap system, frequently supplemented by leading-edge slats, whose extra camber and boundary-layer control raise the maximum lift coefficient and lower stall speed so that take-off and landing distances are shortened.

The best low-speed high-lift airfoil for small unmanned aircraft is the S1223 section. A symmetric airfoil mounted at zero incidence serves as a high-lift device when combined with large trailing-edge flaps, although cambered profiles are more common. The maximum lift of an airfoil is defined by the peak lift coefficient reached before separation. The value is highly sensitive to flap or slat placement and to maintaining correct rigging during maintenance.

A reflex high-lift airfoil combines aft camber with a slight upward bend at the trailing edge to reduce pitching moment, a feature valued for tailless designs and helicopter rotors where low pitching moment is required. Liebeck pursued the classic high-lift philosophy that employs concave pressure recovery with aft loading. This approach extends the low-lift end of the polar and is still a topic of considerable interest for modern UAV, rotorcraft, ESTOL, and hydrofoil applications.

How to calculate lift coefficient of airfoil?

The lift coefficient is defined by the ratio of lift force L to dynamic pressure multiplied by reference area; Cl = L / (0.5 x r x V2 x A). To obtain the numerical value for a given airfoil, one sets velocity, density, and area in a controlled setting, then measures the lift produced giving the quotient Cl.

What is the lift curve slope of an airfoil?

Lift curve slope is the gradient of lift coefficient versus angle of attack. It is denoted in two-dimensional flow (CL) and is measured in units per degree or radian angle of attack. For an incompressible flow airfoil the lift curve slope equals 2 per radian, which is 0.11 per degree. Most airfoils have a value within 10% of 2 per radian, so a practical working figure is 0.105 per degree. NACA 4- and 5-series airfoils with thickness ratios below 10% have measured lift slopes near 0.1097 per degree, whereas thicker airfoils with thickness ratios near 24% approach 0.10 per degree (5.73 rad). The simple approximation 2 per radian holds for both symmetric and cambered thin airfoils because camber changes the zero-lift angle but not the slope itself.

What is the lift slope equal to for a cambered thin airfoil? A cambered thin airfoil still has a 2-D section lift curve slope of 2 per radian. Camber shifts the lift curve sideways so that the zero-lift angle is negative, but the slope of the straight-line portion is unchanged.

What is the lift curve slope of an airfoil at stall? Below the stall angle (typically 10-15 for conventional airfoils) the lift curve slope is linear and close to 0.11 per degree. As stall is approached CL decreases, and after the maximum lift coefficient the slope becomes markedly smaller or even negative.

What is drag on an airfoil?

Aerodynamic drag is the fluid drag force that acts on any moving solid body in the direction of the air's freestream flow. Lift and drag act on an aerofoil-design body moving through air. The part of the aerodynamic force that is opposed to the motion is the drag, which is aerodynamic resistance to the motion of the object through the fluid.

Drag is the unit of the total force vector that acts parallel to the direction of the incoming flow. It is an aerodynamic force known as air resistance. It is generated by the interaction and contact of a solid body with a fluid, and it is a term used to describe the aerodynamic resistance produced by several interacting forces.

Pressure drag on an airfoil is created by air pressure acting on the airfoil. It results from pressure differences around the object and is also called form drag. Form drag is a function of shape and how the shape is presented to the airflow. It depends directly on the object's shape and frontal area, and it is generated by the disruption of the airflow around the body. Flow separation on the wing increases this pressure drag, because separation of the boundary layer creates additional pressure differences.

Induced drag occurs whenever a moving object redirects the airflow. It is generated by the creation of wingtip vortices and is also known as vortex drag. Induced drag increases as angle of attack increases, but decreases as speed increases. Higher aspect ratio reduces induced drag.

How is drag reduction achieved on a transonic airfoil?

Transonic drag reduction is achieved by weakening the shock wave that forms where the local airflow reaches the speed of sound. A supercritical airfoil delays the onset of this wave drag by flattening the upper surface and increasing aft camber, which moves the supersonic point farther aft and forms a smaller, weaker shock. The resulting shock wave almost disappears on one face of the airfoil during part of an oscillation cycle, so static-pressure rise and adverse pressure gradient downstream are reduced, suppressing flow separation and further lowering viscous pressure drag.

Active flow-control methods supplement this geometric strategy. Circulation-control blowing at the trailing edge, investigated on the FAST-MAC model, modifies the shock wave and produces thrust that must be removed from balance data to quantify the net drag decrease. Hybrid suction-and-loaded-leading-edge control redistributes surface pressure, while local suction downstream of the shock decreases skin-friction in the favourable pressure-gradient region. Cooling datum biconvex flow-control aerofoils show similar benefits, alleviating buffeting and delivering an overall drag decrease of 7.5%, with an 8.6% viscous-drag reduction, without increasing baseline viscous drag.

What is the drag coefficient of an airfoil?

Drag coefficient (Cd) is a dimensionless quantity aerodynamicists use to model the dependencies of drag on shape, inclination, and flow conditions. For a typical airfoil at low angle of attack Cd is about 0.045.

This profile drag coefficient (Cd) equals the sum of the friction drag coefficient (Cf) plus the pressure drag coefficient (Cp); thus Cd = Cf + Cp. Friction drag coefficient (Cf) puts wall shear stress (w) in relation to undisturbed external flow velocity (v), while pressure drag coefficient (Cp) accounts for the pressure difference between upstream and downstream faces.

Cd decreases almost inversely proportional to Reynolds number when Re is low, but at high Reynolds number Cd becomes nearly constant. Engineers plot Cd versus Re to analyze this trend.

How to calculate drag coefficient of airfoil?

The airfoil drag coefficient formula is Cd = Fd / A (ρV2 ÷ 2) where Fd is the drag force, A is the reference area, ρ is the density of the fluid, and V is the flow velocity relative to the object.

What is the relationship between airfoil lift and drag?

Lift and drag are components of the resultant force vector that act perpendicular and parallel, respectively, to the incident freestream fluid. They are aerodynamic forces measured in newtons, and their magnitudes are governed by the angle of attack - the angle between the incident freestream fluid and the chord line that extends from the leading edge to the trailing edge. At small angles drag is nearly constant, but it quickly rises above five degrees while lift initially increases. A polar curve shows lift versus drag and reveals that the ratio L/D reaches a maximum where the glide angle, equal to arctan(D/L), is minimized. Beyond a critical angle the airfoil stalls: the lift coefficient decreases and drag increases sharply, because the flow separates and the center of pressure, the point where the resultant force acts, shifts abruptly. Reynolds number and the relative thickness of the airfoil influence the exact magnitudes of lift and drag, yet the fundamental trend - lift grows then falls while drag keeps rising - defines the coupled behavior of these forces on every wing.

What is the lift-to-drag ratio of an airfoil?

Lift-to-drag ratio is the quotient of lift and drag for an aerodynamic body moving through air. It equals the ratio of lift coefficient to drag coefficient. Because lift must equal weight in steady-state level flight, the ratio doubles as glide ratio. The best glide ratio is achieved only at the optimal angle of attack, is independent of weight, and gives a lower glide angle when L/D is high.

Practical airfoils that combine Cl = 1.2 with Cd = 0.10 reach about 120:1 L/D, already placing them among the most efficient designs. Genetic-algorithm optimization of an ideal two-dimensional section pushes the theoretical limit to 300,000:1, far above any real surface. A cambered plate operating at Cl = 0.8 shows a maximum of roughly 23:1, whereas normal light-aircraft wings deliver between 15 and 20:1. A high L/D ratio indicates an efficient aerodynamic design. It is a dimensionless parameter that quantifies how much lift an airplane produces for each unit of drag it must overcome.

What is the drag polar of an airfoil?

The drag polar is the relationship between the drag on an aircraft and other variables like lift, the coefficient of lift, angle-of-attack, or speed. It specifies the drag coefficient Cd for a given lift coefficient Cl and vice versa. In graphic form the drag polar plots Cd versus Cl and summarizes the most important features of the airfoil's drag characteristics in one plot. A simple and widely used algebraic model is the parabolic drag polar Cd = Cd0 + KCl , where Cd0 is the zero-lift drag coefficient and the term KCl represents the lift-induced drag coefficient. The two key parameters in this equation, Cd0 and K, respectively quantify the profile drag present at zero lift and the sensitivity of induced drag to lift. Together they define the shape of the polar and hence the performance of the airfoil.

What is the pressure coefficient (CP) of an airfoil?

The pressure coefficient is a dimensionless number used in aerodynamics, and it describes relative pressures throughout a flow field. Every point in a fluid flow field has a unique pressure coefficient (CP).

The pressure coefficient CP is the difference between the local static pressure and the free stream static pressure divided by the free stream dynamic pressure (U). CP is dimensionless and for subsonic airfoils its values lie between -2 and 1. At a stagnation point the local velocity is zero, so CP equals 1.0, while CP equals 0 wherever the local velocity equals the free stream velocity. Engineers obtain CP from static-pressure ports drilled along the surface. Odd ports supply the upper-surface distribution and even ports supply the lower-surface distribution, and the data is collapsed into a single CP versus x/c curve for each angle of attack.

The center of lift, called the center of pressure, is the average location of the pressure variation around the airfoil. It moves back and forth along the surface as the angle of attack changes: forward as angle of attack increases and aft as it decreases. Determining this center requires calculus, but if the functional form is unknown engineers numerically integrate the equation CP = ( x p(x)dx) / ( p(x)dx) using a spreadsheet divided into small segments. For many low-speed airfoils the aerodynamic center - the quarter-chord point where the aerodynamic moment remains nearly constant with angle of attack - serves as a convenient reference for pitching-moment calculations.

CDp in airfoil terminology is the pressure-drag coefficient, the contribution of the pressure distribution to the total drag coefficient. It is set equal to the local section drag coefficient Cdp at a representative spanwise station halfway between root and tip.

What is airfoil suction?

Airfoil suction is the suction surface, which is typically the upper surface, generally associated with higher velocity and lower static pressure. This suction creates an artificial negative pressure gradient that allows the flow to remain attached around the shoulder of the airfoil, and suction is provided to the upper latter part of the airfoil accelerating the flow along the upper surface.

Suction is the artificial withdrawal of a small amount of mass-flow from the main flow into the airfoil near the trailing edge. The low-pressure source produces a local vacuum at the suction slot, creating an artificial negative pressure gradient that counteracts the adverse pressure gradient. In this way suction keeps the turbulent boundary layer attached behind the suction point and allows the flow to remain around the shoulder of the airfoil farther than on a conventional profile.

What happens to lift and drag post-stall in an airfoil? After the angle of attack exceeds the critical value, lift decreases and drag increases dramatically. The pressure on the upper surface becomes almost flat, and the airfoil stalls at about eighteen degrees. This lift loss and drag rise continue as the angle grows, so post-stall performance is dominated by separated flow and high form drag.

What is a low drag airfoil?

A low drag airfoil is an airfoil that generates lift with less drag, and these airfoils are highly-efficient lifting shapes. Low camber reduces drag divergence. A low-drag airfoil is designed so that a laminar boundary layer remains thin over the forward surface while a turbulent layer undertakes pressure recovery aft. Long laminar runs cut skin-friction losses and overall drag. The benefit is confined to a narrow band of lift coefficients and angles of attack nick-named the drag bucket. Outside this window the drag rises quickly like that of a conventional section. The number 3 in a NACA 6-section designation indicates, in tenths, how far above and below the design lift coefficient the bucket extends. Charts for the NACA 65, 3-418, deemed a conservative low-drag section, and for the NACA 65(216)-222, viewed as unconservative, illustrate the principle. Roughness or early transition erases the bucket and reverts the airfoil to ordinary performance. The Roncz/Marske-7 flying-wing airfoil, with 2.8% camber at 39% chord and 12.1% thickness at 43% chord, is a modern example that applies the same long-laminar-run strategy to achieve low drag for sailplane-type missions.