# Wave drag

Last updated

In aeronautics, wave drag is a component of the aerodynamic drag on aircraft wings and fuselage, propeller blade tips and projectiles moving at transonic and supersonic speeds, due to the presence of shock waves. Wave drag is independent of viscous effects, [1] and tends to present itself as a sudden and dramatic increase in drag as the vehicle increases speed to the Critical Mach number. It is the sudden and dramatic rise of wave drag that leads to the concept of a sound barrier.

Aeronautics is the science or art involved with the study, design, and manufacturing of air flight capable machines, and the techniques of operating aircraft and rockets within the atmosphere. The British Royal Aeronautical Society identifies the aspects of "aeronautical Art, Science and Engineering" and "the profession of Aeronautics ."

A shell is a payload-carrying projectile that, as opposed to shot, contains an explosive or other filling, though modern usage sometimes includes large solid projectiles properly termed shot. Solid shot may contain a pyrotechnic compound if a tracer or spotting charge is used. Originally, it was called a "bombshell", but "shell" has come to be unambiguous in a military context.

In aeronautics, transonic flight is flying at or near the speed of sound 343 meters per second, relative to the air through which the vehicle is traveling. A typical convention used is to define transonic flight as speeds in the range of Mach 0.72 to 1.0.

## Overview

Wave drag presents itself as part of pressure drag due to compressibility effects. It is caused by the formation of shock waves around a body. Shock waves create a considerable amount of drag, which can result in extreme drag on the body. Although shock waves are typically associated with supersonic flow, they can form at subsonic aircraft speeds on areas of the body where local airflow accelerates to supersonic speed. The effect is typically seen on aircraft at transonic speeds (about Mach 0.8), but it is possible to notice the problem at any speed over that of the critical Mach of that aircraft. It is so pronounced that, prior to 1947, it was thought that aircraft engines would not be powerful enough to overcome the enhanced drag, or that the forces would be so great that aircraft would be at risk of breaking up in midflight. It led to the concept of a sound barrier .

In thermodynamics and fluid mechanics, compressibility is a measure of the relative volume change of a fluid or solid as a response to a pressure change. In its simple form, the compressibility may be expressed as

In physics, a shock wave, or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a medium but is characterized by an abrupt, nearly discontinuous, change in pressure, temperature, and density of the medium.

In fluid dynamics, the Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound.

## Research

In 1947, studies into wave drag led to the development of perfect shapes to reduce wave drag as much as theoretically possible. For a fuselage the resulting shape was the Sears–Haack body, which suggested a perfect cross-sectional shape for any given internal volume. The von Kármán ogive was a similar shape for bodies with a blunt end, like a missile. Both were based on long narrow shapes with pointed ends, the main difference being that the ogive was pointed on only one end.

The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a given body length and given volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the Prandtl–Glauert equation. The derivation and shape were published independently by two separate researchers: Wolfgang Haack in 1941 and later by William Sears in 1947.

### Reduction of drag

A number of new techniques developed during and just after World War II were able to dramatically reduce the magnitude of wave drag, and by the early 1950s the latest fighter aircraft could reach supersonic speeds.

World War II, also known as the Second World War, was a global war that lasted from 1939 to 1945. The vast majority of the world's countries—including all the great powers—eventually formed two opposing military alliances: the Allies and the Axis. A state of total war emerged, directly involving more than 100 million people from more than 30 countries. The major participants threw their entire economic, industrial, and scientific capabilities behind the war effort, blurring the distinction between civilian and military resources. World War II was the deadliest conflict in human history, marked by 70 to 85 million fatalities, most of whom were civilians in the Soviet Union and China. It included massacres, the genocide of the Holocaust, strategic bombing, premeditated death from starvation and disease, and the only use of nuclear weapons in war.

A fighter aircraft is a military aircraft designed primarily for air-to-air combat against other aircraft, as opposed to bombers and attack aircraft, whose main mission is to attack ground targets. The hallmarks of a fighter are its speed, maneuverability, and small size relative to other combat aircraft. Although helicopters are sometimes used in similar roles, the term fighter is at present applied only to fixed-wing aircraft.

These techniques were quickly put to use by aircraft designers. One common solution to the problem of wave drag was to use a swept wing, which had actually been developed before World War II and used on some German wartime designs. Sweeping the wing makes it appear thinner and longer in the direction of the airflow, making a conventional teardrop wing shape closer to that of the von Kármán ogive, while still remaining useful at lower speeds where curvature and thickness are important.

A swept wing is a wing that angles either backward or occasionally forward from its root rather than in a straight sideways direction. Wing sweep has the effect of delaying the shock waves and accompanying aerodynamic drag rise caused by fluid compressibility near the speed of sound, improving performance. Swept wings are therefore often used on jet aircraft designed to fly at these speeds. Swept wings are also sometimes used for other reasons, such as structural convenience or visibility.

The wing need not be swept when it is possible to build a wing that is extremely thin. This solution was used on a number of designs, beginning with the Bell X-1, the first manned aircraft to fly at the speed of sound. The downside to this approach is that the wing is so thin it is no longer possible to use it for storage of fuel or landing gear. Such wings are very common on missiles, although, in that field, they are often referred to as "fins".

The Bell X-1,, is a rocket-engine–powered aircraft, designated originally as the XS-1, and was a joint National Advisory Committee for Aeronautics–U.S. Army Air Forces–U.S. Air Force supersonic research project built by Bell Aircraft. Conceived during 1944 and designed and built in 1945, it achieved a speed of nearly 1,000 miles per hour in 1948. A derivative of this same design, the Bell X-1A, having greater fuel capacity and hence longer rocket burning time, exceeded 1,600 miles per hour in 1954. The X-1, piloted by Chuck Yeager, was the first crewed airplane to exceed the speed of sound in level flight and was the first of the X-planes, a series of American experimental rocket planes designed for testing new technologies.

Fuselage shaping was similarly changed with the introduction of the Whitcomb area rule. Whitcomb had been working on testing various airframe shapes for transonic drag when, after watching a presentation by Adolf Busemann in 1952, he realized that the Sears-Haack body had to apply to the entire aircraft, not just the fuselage. This meant that the fuselage needed to be made narrower where it joined the wings, so that the cross-section of the entire aircraft matched the Sears-Haack body.

Application of the area rule can also be seen in the use of anti-shock bodies on transonic aircraft, including some jet airliners. Anti-shock bodies, which are pods along the trailing edges of the wings, serve the same role as the narrow waist fuselage design of other transonic aircraft.

## Other drag reduction methods

Several other attempts to reduce wave drag have been introduced over the years. The supercritical airfoil is a type that results in reasonable low speed lift like a normal airfoil, but has a profile considerably closer to that of the von Kármán ogive. All modern civil airliners use forms of supercritical aerofoil and have substantial supersonic flow over the wing upper surface.

## Mathematical formula

### For flat plate aerofoil

${\displaystyle cd_{w}=4*{\frac {\alpha ^{2}}{\sqrt {(M^{2}-1)}}}}$ [2]

### For double-wedge aerofoil

${\displaystyle cd_{w}=4*{\frac {\alpha ^{2}+(t/c)^{2}}{\sqrt {(M^{2}-1)}}}}$ [2]

## Notes

1. Clancy, L.J. (1975), Aerodynamics, Section 11.7
2. "How can I calculate wave drag in supersonic airfoil?". 2 February 2014. Retrieved 23 May 2019.

## Related Research Articles

Aerodynamics, from Greek ἀήρ aer (air) + δυναμική (dynamics), is the study of motion of air, particularly as interaction with a solid object, such as an airplane wing. It is a sub-field of fluid dynamics and gas dynamics, and many aspects of aerodynamics theory are common to these fields. The term aerodynamics is often used synonymously with gas dynamics, the difference being that "gas dynamics" applies to the study of the motion of all gases, and is not limited to air. The formal study of aerodynamics began in the modern sense in the eighteenth century, although observations of fundamental concepts such as aerodynamic drag were recorded much earlier. Most of the early efforts in aerodynamics were directed toward achieving heavier-than-air flight, which was first demonstrated by Otto Lilienthal in 1891. Since then, the use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations has formed a rational basis for the development of heavier-than-air flight and a number of other technologies. Recent work in aerodynamics has focused on issues related to compressible flow, turbulence, and boundary layers and has become increasingly computational in nature.

A wing is a type of fin that produces lift, while moving through air or some other fluid. As such, wings have streamlined cross-sections that are subject to aerodynamic forces and act as airfoils. A wing's aerodynamic efficiency is expressed as its lift-to-drag ratio. The lift a wing generates at a given speed and angle of attack can be one to two orders of magnitude greater than the total drag on the wing. A high lift-to-drag ratio requires a significantly smaller thrust to propel the wings through the air at sufficient lift.

The Whitcomb area rule, also called the transonic area rule, is a design technique used to reduce an aircraft's drag at transonic and supersonic speeds, particularly between Mach 0.75 and 1.2.

Supersonic travel is a rate of travel of an object that exceeds the speed of sound (Mach 1). For objects traveling in dry air of a temperature of 20 °C (68 °F) at sea level, this speed is approximately 344 m/s, 1,125 ft/s, 768 mph, 667 knots, or 1,235 km/h. Speeds greater than five times the speed of sound (Mach 5) are often referred to as hypersonic. Flights during which only some parts of the air surrounding an object, such as the ends of rotor blades, reach supersonic speeds are called transonic. This occurs typically somewhere between Mach 0.8 and Mach 1.2.

The delta wing is a wing shaped in the form of a triangle. It is named for its similarity in shape to the Greek uppercase letter delta (Δ).

Richard Travis Whitcomb was an American aeronautical engineer who was noted for his contributions to the science of aerodynamics.

Robert T. (Bob) Jones,, was an aerodynamicist and aeronautical engineer for NACA and later NASA. He was known at NASA as "one of the premier aeronautical engineers of the twentieth century".

In aerodynamics, the critical Mach number of an aircraft is the lowest Mach number at which the airflow over some point of the aircraft reaches the speed of sound, but does not exceed it. At the lower critical Mach number, airflow around the entire aircraft is subsonic. At the upper critical Mach number, airflow around the entire aircraft is supersonic.

A supercritical airfoil is an airfoil designed primarily to delay the onset of wave drag in the transonic speed range. Supercritical airfoils are characterized by their flattened upper surface, highly cambered ("downward-curved") aft section, and larger leading-edge radius compared with NACA 6-series laminar airfoil shapes. Standard wing shapes are designed to create lower pressure over the top of the wing. The camber of the wing determines how much the air accelerates around the wing. As the speed of the aircraft approaches the speed of sound, the air accelerating around the wing reaches Mach 1 and shockwaves begin to form. The formation of these shockwaves causes wave drag. Supercritical airfoils are designed to minimize this effect by flattening the upper surface of the wing.

Mach tuck is an aerodynamic effect whereby the nose of an aircraft tends to pitch downward as the airflow around the wing reaches supersonic speeds. This diving tendency is also known as "tuck under". The aircraft will first experience this effect at significantly below Mach 1.

In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers or a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, drag forces depend on velocity. Drag force is proportional to the velocity for a laminar flow and the squared velocity for a turbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity.

Adolf Busemann was a German aerospace engineer and influential Nazi-era pioneer in aerodynamics, specialising in supersonic airflows. He introduced the concept of swept wings, and after immigrating in 1947 to the United States invented the shockwave free Busemann's Biplane.

An anti-shock body is a pod positioned on the leading edge or trailing edge of an aircraft's aerodynamic surfaces to reduce wave drag at transonic speeds.

The drag-divergence Mach number is the Mach number at which the aerodynamic drag on an airfoil or airframe begins to increase rapidly as the Mach number continues to increase. This increase can cause the drag coefficient to rise to more than ten times its low-speed value.

In naval architecture and aerospace engineering, the fineness ratio is the ratio of the length of a body to its maximum width. Shapes that are short and wide have a low fineness ratio, those that are long and narrow have high fineness ratios. Aircraft that spend time at supersonic speeds, e.g. the Concorde, generally have high fineness ratios.

A supersonic airfoil is a cross-section geometry designed to generate lift efficiently at supersonic speeds. The need for such a design arises when an aircraft is required to operate consistently in the supersonic flight regime.

In aeronautics, the thickness-to-chord ratio, sometimes simply chord ratio or thickness ratio, compares the maximum vertical thickness of a wing to its chord. It is a key measure of the performance of a wing planform when it is operating at transonic speeds.