Supersonic airfoils - AbsoluteAstronomy.com

Supersonic

Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...

airfoil

Airfoil

An airfoil or aerofoil is the shape of a wing or blade or sail as seen in cross-section....

is a cross-section geometry designed to generate lift

Lift (force)

A fluid flowing past the surface of a body exerts a surface force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the surface force parallel to the flow direction...

efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime.

Supersonic

Supersonic

airfoils generally have a thin section formed of either angled planes or opposed arcs (called "double wedge airfoils" and "biconvex airfoils" respectively), with very sharp leading and trailing edges. The sharp edges prevent the formation of a detached bow shock in front of the airfoil as it moves through the air.. This shape is in contrast to subsonic airfoils, which often have rounded leading edges to reduce flow separation

Flow separation

All solid objects travelling through a fluid acquire a boundary layer of fluid around them where viscous forces occur in the layer of fluid close to the solid surface. Boundary layers can be either laminar or turbulent...

over a wide range of angle of attack

Angle of attack

Angle of attack is a term used in fluid dynamics to describe the angle between a reference line on a lifting body and the vector representing the relative motion between the lifting body and the fluid through which it is moving...

. A rounded edge would behave as a blunt body in supersonic flight and thus would form a bow shock, which greatly increases wave drag

Wave drag

In aeronautics, wave drag is a component of the drag on aircraft, blade tips and projectiles moving at transonic and supersonic speeds, due to the presence of shock waves. Wave drag is independent of viscous effects.- Overview :...

. The airfoils' thickness, camber, and angle of attack are varied to achieve a design that will cause a slight deviation in the direction of the surrounding airflow.

However, since a round leading edge decreases an airfoil's susceptibility to flow separation, a sharp leading edge implies that the airfoil will be more sensitive to changes in angle of attack. Therefore, to increase lift at lower speeds, aircraft that employ supersonic airfoils also use high-lift device

High-lift device

In aircraft design, high-lift devices are moving surfaces or stationary components intended to increase lift during certain flight conditions. They include common devices such as flaps and slats, as well as less common features such as leading edge extensions and blown flaps.-Purpose:Aircraft...

s such as leading edge and trailing edge flaps.

Lift and Drag

At supersonic

Supersonic

conditions, aircraft

Aircraft

An aircraft is a vehicle that is able to fly by gaining support from the air, or, in general, the atmosphere of a planet. An aircraft counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines.Although...

drag

Drag (physics)

In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

is originated due to:

Skin-friction drag due to shearing
Shearing (physics)
Shearing in continuum mechanics refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material...
The wave drag
Wave drag
In aeronautics, wave drag is a component of the drag on aircraft, blade tips and projectiles moving at transonic and supersonic speeds, due to the presence of shock waves. Wave drag is independent of viscous effects.- Overview :...

due to thickness (or volume) or zero-lift wave drag
Drag due to lift

Therefore the Drag coefficient on a supersonic airfoil is described by the following expression:

C_D= C_D,friction+ C_D,thickness+ C_D,lift

Experimental data allow us to reduce this expression to:

C_D= C_D,O + KC_L²
Where C_DO is the sum of C_(D,friction) and C_D,thickness, and k for supersonic flow is a function of the Mach number. Whereas the skin-friction component is derived from the presence of a viscous boundary layer which is infinitely close to the surface of the aircraft

Aircraft

body. At the boundary wall, the normal component of velocity

Velocity

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

is zero; therefore an infinitesimal

Infinitesimal

Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. The word infinitesimal comes from a 17th century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a series.In common speech, an...

area exists where there is no slip

Slip

- In science and technology :* Slip , an aqueous suspension of minerals, and frequently deflocculant.* Slip , a positional displacement in a sequence of transmitted symbols...

. The zero-lift wave drag

Wave drag

component can be obtained based on the supersonic

Supersonic

area rule which tells us that the wave-drag of an aircraft

Aircraft

in a steady supersonic

Supersonic

flow is identical to the average

Average

In mathematics, an average, or central tendency of a data set is a measure of the "middle" value of the data set. Average is one form of central tendency. Not all central tendencies should be considered definitions of average....

of a series of equivalent bodies of revolution. The bodies of revolution are defined by the cuts through the aircraft

Aircraft

made by the tangent

Tangent

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f...

to the fore Mach

Mach

Mach may refer to:* Mach , a lunar crater* Mach disk, diamond pattern seen in rocket exhaust* Mach number, a measure of speed* Gillette Mach3, a manual razor with three blades* Mach bands, an optical illusion...

cone from a distant point of the aircraft at an azimuthal angle. This average is over all azimuthal angles.. The drag

Drag (physics)

In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...

due-to lift component is calculated using lift-analysis programs. The wing

Wing

A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

design and the lift-analysis programs are separate lifting-surfaces methods that solve the direct or inverse problem of design and lift analysis.

Supersonic Wing Design

Supersonic flow resembles bizarre conditions to engineers, physicists and designers, years of research and experience lead to some interesting conclusions about wings in a supersonic

Supersonic

flow

Fluid dynamics

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

.Considering a rectangular wing, the pressure at a point P with coordinates (x,y) on the wing is only being defined by pressure

Pressure

Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...

disturbances originated at points within the upstream Mach

Mach

cone emanating from point P. As result, the wing tips modify
the flow. The remaining area of the wing does not suffer any modification by the tips and can be analyzed with two-dimensional theory.
For an arbitrary planform

Planform

In aviation, a planform is the shape and layout of a fixed-wing aircraft's fuselage and wing. Of all the myriad planforms used, they can typically be grouped into those used for low-speed flight, found on general aviation aircraft, and those used for high-speed flight, found on many military...

the supersonic leading

Leading

In typography, leading refers to the distance between the baselines of successive lines of type. The term originated in the days of hand-typesetting, when thin strips of lead were inserted into the formes to increase the vertical distance between lines of type...

and trailing

Trailing

Trailing can mean, among others:* Facing and trailing, in railroads* Trailing wheel* Trailing arm* Trailing edge* Hound Trailing* Trailing twelve months...

are those portions of the wing edge where the components of the freestream

Freestream

The freestream is the air far upstream of an aerodynamic body, that is, before the body has a chance to deflect, slow down or compress the air. Freestream conditions are usually denoted with a \infty symbol, e.g. V_\infty, meaning the freestream velocity...

velocity normal to the edge are supersonic. Similarly the subsonic leading and trailing are those portions of the wing edge where the components of the free stream velocity normal to the edge are subsonic.

Delta wings have supersonic leading and trailing edges; in contrast arrow wings have a subsonic leading edge and a supersonic trailing edge.

Summary

Aerodynamic efficiency

Efficiency

Efficiency in general describes the extent to which time or effort is well used for the intended task or purpose. It is often used with the specific purpose of relaying the capability of a specific application of effort to produce a specific outcome effectively with a minimum amount or quantity of...

for supersonic

Supersonic

aircraft

Aircraft

increases with thin section airfoils with sharp leading and trailing edges.
Swept wing

Wing

A wing is an appendage with a surface that produces lift for flight or propulsion through the atmosphere, or through another gaseous or liquid fluid...

s where the leading edge is subsonic have the advantage of reducing the wave drag

Wave drag

component at supersonic

Supersonic

flight speeds; however experiments show that the theoretical benefits are not always attained due to separation of the flow over the surface of the wing; however this can be corrected with design factors.
Double-Wedge and Bi-convex airfoils are the most common designs used in supersonic flights.
Wave drag is the simplest and most important component of the drag in supersonic

Supersonic

flow flight regions.
For the optimized aircraft nearly 60% of its drag is skin friction drag, little over 20% is induced drag, and slightly under 20% is wave drag, hence less than 30% of the drag is due to lift.

Lift and Drag

Supersonic Wing Design

Summary

See also