# Subsonic flight aerodynamics

High Speed Flight - Aerodynamics of Flight. Subsonic Versus Supersonic Flow In subsonic aerodynamics, the theory of lift is based upon the forces generated on a body and a moving gas air in which it is immersed. At speeds of approximately knots or less, air can be considered incompressible in that, at a fixed altitude, its density remains nearly constant while its pressure varies. Under this assumption, air acts the same as water and is classified as a fluid.

In reality, air is compressible and viscous. While the effects of these properties are negligible at low speeds, compressibility effects in particular become increasingly important as speed increases. Compressibility and to a lesser extent viscosity is of paramount importance at speeds approaching the speed of sound. In these speed ranges, compressibility causes a change in the density of the air around an aircraft.

During flight, a wing produces lift by accelerating the airflow over the upper surface. This accelerated air can, and does, reach sonic speeds even though the aircraft itself may be flying subsonic. It is therefore entirely possible to have both supersonic and subsonic airflow on an aircraft at the same time.

When flow velocities reach sonic speeds at some location on an aircraft such as the area of maximum camber on the wingfurther acceleration results in the onset of compressibility effects, such as shock wave formation, drag increase, buffeting, stability, and control difficulties.

Subsonic flow principles are invalid at all speeds above this point. Figure 1. Wing airflow. The speed of sound varies with temperature. An aircraft traveling at the speed of sound is traveling at Mach 1. Aircraft speed regimes are defined approximately as follows:.

Subsonic—Mach numbers below 0. While flights in the transonic and supersonic ranges are common occurrences for military aircraft, civilian jet aircraft normally operate in a cruise speed range of Mach 0. The speed of an aircraft in which airflow over any part of the aircraft or structure under consideration first reaches but does not exceed Mach 1. Critical Mach number is an important point in transonic flight. When shock waves form on the aircraft, airflow separation followed by buffet and aircraft control difficulties can occur.

Shock waves, buffet, and airflow separation take place above critical Mach number. A jet aircraft typically is most efficient when cruising at or near its critical Mach number. At speeds 5—10 percent above the critical Mach number, compressibility effects begin.

Drag begins to rise sharply. Figure 2. Critical Mach. The VMO limit is usually associated with operations at lower altitudes and deals with structural loads and flutter.

The MMO limit is associated with operations at higher altitudes and is usually more concerned with compressibility effects and flutter.

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At lower altitudes, structural loads and flutter are of concern; at higher altitudes, compressibility effects and flutter are of concern. Adherence to these speeds prevents structural problems due to dynamic pressure or flutter, degradation in aircraft control response due to compressibility effects e. Any of these phenomena could prevent the pilot from being able to adequately control the aircraft.

Above this altitude, an MMO of 0. It is important to understand how airspeed varies with Mach number. As an example, consider how the stall speed of a jet transport aircraft varies with an increase in altitude.It is a sub-field of fluid dynamics and gas dynamicsand many aspects of aerodynamics theory are common to these fields.

### Subsonic Wings

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 flightwhich was first demonstrated by Otto Lilienthal in Recent work in aerodynamics has focused on issues related to compressible flowturbulenceand boundary layers and has become increasingly computational in nature.

Modern aerodynamics only dates back to the seventeenth century, but aerodynamic forces have been harnessed by humans for thousands of years in sailboats and windmills, [2] and images and stories of flight appear throughout recorded history, [3] such as the Ancient Greek legend of Icarus and Daedalus. InSir Isaac Newton became the first person to develop a theory of air resistance, [6] making him one of the first aerodynamicists.

Dutch - Swiss mathematician Daniel Bernoulli followed in with Hydrodynamica in which he described a fundamental relationship between pressure, density, and flow velocity for incompressible flow known today as Bernoulli's principlewhich provides one method for calculating aerodynamic lift.

### Subsonic aircraft

The Euler equations were extended to incorporate the effects of viscosity in the first half of the s, resulting in the Navier—Stokes equations. InSir George Cayley became the first person to identify the four aerodynamic forces of flight weightliftdragand thrustas well as the relationships between them, [10] [11] and in doing so outlined the path toward achieving heavier-than-air flight for the next century.

InFrancis Herbert Wenham constructed the first wind tunnelallowing precise measurements of aerodynamic forces. Building on these developments as well as research carried out in their own wind tunnel, the Wright brothers flew the first powered airplane on December 17, During the time of the first flights, Frederick W.

Lanchester[16] Martin Kuttaand Nikolai Zhukovsky independently created theories that connected circulation of a fluid flow to lift. Kutta and Zhukovsky went on to develop a two-dimensional wing theory.

Expanding upon the work of Lanchester, Ludwig Prandtl is credited with developing the mathematics [17] behind thin-airfoil and lifting-line theories as well as work with boundary layers. As aircraft speed increased, designers began to encounter challenges associated with air compressibility at speeds near the speed of sound.

The differences in airflow under such conditions lead to problems in aircraft control, increased drag due to shock wavesand the threat of structural failure due to aeroelastic flutter. The ratio of the flow speed to the speed of sound was named the Mach number after Ernst Mach who was one of the first to investigate the properties of the supersonic flow.

Macquorn Rankine and Pierre Henri Hugoniot independently developed the theory for flow properties before and after a shock wavewhile Jakob Ackeret led the initial work of calculating the lift and drag of supersonic airfoils. This rapid increase in drag led aerodynamicists and aviators to disagree on whether supersonic flight was achievable until the sound barrier was broken in using the Bell X-1 aircraft. By the time the sound barrier was broken, aerodynamicists' understanding of the subsonic and low supersonic flow had matured.

The Cold War prompted the design of an ever-evolving line of high-performance aircraft. Computational fluid dynamics began as an effort to solve for flow properties around complex objects and has rapidly grown to the point where entire aircraft can be designed using computer software, with wind-tunnel tests followed by flight tests to confirm the computer predictions. Understanding of supersonic and hypersonic aerodynamics has matured since the s, and the goals of aerodynamicists have shifted from the behaviour of fluid flow to the engineering of a vehicle such that it interacts predictably with the fluid flow.

Designing aircraft for supersonic and hypersonic conditions, as well as the desire to improve the aerodynamic efficiency of current aircraft and propulsion systems, continues to motivate new research in aerodynamics, while work continues to be done on important problems in basic aerodynamic theory related to flow turbulence and the existence and uniqueness of analytical solutions to the Navier-Stokes equations.

Understanding the motion of air around an object often called a flow field enables the calculation of forces and moments acting on the object. In many aerodynamics problems, the forces of interest are the fundamental forces of flight: liftdragthrustand weight.

Of these, lift and drag are aerodynamic forces, i. Calculation of these quantities is often founded upon the assumption that the flow field behaves as a continuum. Continuum flow fields are characterized by properties such as flow velocitypressuredensityand temperaturewhich may be functions of position and time.Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object.

Aerodynamics is a subfield of fluid dynamics and gas dynamicswith much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with the difference being that gas dynamics applies to all gases.

Understanding the motion of air often called a flow field around an object enables the calculation of forces and moments acting on the object. Typical properties calculated for a flow field include velocitypressuredensity and temperature as a function of position and time. By defining a control volume around the flow field, equations for the conservation of mass, momentum, and energy can be defined and used to solve for the properties. The use of aerodynamics through mathematical analysis, empirical approximation and wind tunnel experimentation form the scientific basis for heavier-than-air flight.

Aerodynamic problems can be identified in a number of ways. The flow environment defines the first classification criterion. External aerodynamics is the study of flow around solid objects of various shapes.

Evaluating the lift and drag on an airplanethe shock waves that form in front of the nose of a rocket or the flow of air over a hard drive head are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine or through an air conditioning pipe.

## Aerodynamics

The ratio of the problem's characteristic flow speed to the speed of sound comprises a second classification of aerodynamic problems. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present normally when the characteristic speed is approximately the speed of soundsupersonic when the characteristic flow speed is greater than the speed of sound, and hypersonic when the flow speed is much greater than the speed of sound.

Aerodynamicists disagree over the precise definition of hypersonic flow; minimum Mach numbers for hypersonic flow range from 3 to The influence of viscosity in the flow dictates a third classification. Some problems involve only negligible viscous effects on the solution, in which case viscosity can be considered to be nonexistent. The approximations to these problems are called inviscid flows.

Flows for which viscosity cannot be neglected are called viscous flows. InLeonardo da Vinci wrote the Codex on the Flight of Birdsone of the earliest treatises on aerodynamics. He notes for the first time that the center of gravity of a flying bird does not coincide with its center of pressureand he describes the construction of an ornithopterwith flapping wings similar to a bird's.

Sir Isaac Newton was the first person to develop a theory of air resistance, [ 3 ] making him one of the first aerodynamicists. As part of that theory, Newton believed that drag was due to the dimensions of a body, the density of the fluid, and the velocity raised to the second power.

These beliefs all turned out to be correct for low flow speeds. Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluid flow. Unfortunately, this equation is completely incorrect for the calculation of drag unless the flow speed is hypersonic.

Drag on a flat plate is closer to being linear with the angle of inclination as opposed to acting quadratically. This formula can lead one to believe that flight is more difficult than it actually is, and it may have contributed to a delay in human flight.

These empirical findings led to a variety of air resistance experiments on various shapes throughout the 18th and 19th centuries. Towards the end of this time period Gustave Eiffel used his Eiffel Tower to assist in the drop testing of flat plates.

Of course, a more precise way to measure resistance is to place an object within an artificial, uniform stream of air where the velocity is known. The first person to experiment in this fashion was Francis Herbert Wenhamwho in doing so constructed the first wind tunnel in Wenham was also a member of the first professional organization dedicated to aeronautics, the Royal Aeronautical Society of the United Kingdom.

Objects placed in wind tunnel models are almost always smaller than in practice, so a method was needed to relate small scale models to their real-life counterparts.At this Web site you can study high speed aerodynamics at your own pace and to your own level of interest.

Some of the topics included are: isentropic flowsobliqueand normal shock waves, and multiple shock interactions. Because high speed aerodynamics involves the generation of heat, there are several pages devoted to basic gas propertieshow those properties change through the atmosphereand some basic thermodynamics. This site was prepared at NASA Glenn to provide background information on high speed aerodynamics for undergraduates, professionals, and life-long learners.

There is a particular emphasis here on the math and science involved with high speed aerodynamics. High school students should be able to make sense of the math and science principles. We include many, small, interactive calculators and simulators which solve the flow equations and are provided to aid your understanding. This site has been intentionally organized to mirror the unstructured nature of the world wide web.

## High Speed Flight - Aerodynamics of Flight

There are many pages here connected to one another through hyperlinks and you can then navigate through the links based on your own interest and inquiry.

There is an index of topics that you can access from any page, so you are never more than two clicks away from any other Web page at this site. However, if you prefer a more structured approach, you can also take one of our Guided Tours through the site.

Each tour provides a sequence of pages dealing with some aspect of aerodynamics. Many of the pages contain mathematical equations which have been produced graphically and which are too long or complex to provide in an "ALT" tag.

For these pages, we have retained the non-compliant graphic at the top of the page and have provided a compliant text version of the equations in the body of the page. In many cases, because of the use of Greek fonts in the graphics, the purely English text version of the equations is slightly different than the graphic version.

The differences are noted in the text. Welcome to the Beginner's Guide to Compressible Aerodynamics. High speed aerodynamics is a special branch of the study of aeronautics. It is often called compressible aerodynamics because, in this flight regime, the compressibility effects of air can not be neglected. The flight regime is characterized by the Mach number which is the ratio of the speed of the aircraft to the local speed of sound.

Flight less than the speed of sound is called subsonicnear the speed of sound is transonicgreater than the speed of sound is supersonicand very much greater than the speed of sound is hypersonic. Different flow phenomenon are present in each of the various flight regimes.Let's use a wing to help get a better understanding of lift at subsonic speeds.

With a typical subsonic wing, the upper surface is more curved than the lower surface. The curved upper surface constricts the flow of air more than the flatter lower surface, causing the air above the wing to speed up more than the air below.

The faster the air speeds up, the lower its pressure becomes. So the faster moving air above has less pressure than the slower moving air below. The higher air pressure below pushes the wing up—lift. Any further increase in the speed of the air will increase the difference in pressure and increase the lifting force on the wing.

They use the angle of attack of their flat wings to create lift. The angle of attack is the angle at which oncoming airflow meets the airfoil.

Lift is generated from the same low pressure Bernoulli effect as with a curved wing although not nearly as much. Forces of Flight on this Page.

Subsonic Wings. What Makes a Wing Work?

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Related Images Downward Lift. Winging It on the Water. Ask an Explainer Q: Paper airplanes don't have the "classic" airfoil shape, so how do they fly? A: They use the angle of attack of their flat wings to create lift. Watch a Video. Did You Know? Pop Quiz Which of the following are examples of airfoil shapes?A subsonic aircraft is an aircraft with a maximum speed less than the speed of sound Mach 1.

The term technically describes an aircraft that flies below its critical Mach numbertypically around Mach 0.

All current civil aircraft, including airlinershelicoptersfuture passenger dronespersonal air vehicles and airshipsas well as many military types, are subsonic. Although high speeds are usually desirable in an aircraft, supersonic flight requires much bigger engines, higher fuel consumption and more advanced materials than subsonic flight.

A subsonic type therefore costs far less than the equivalent supersonic design, has greater range and causes less harm to the environment. The less harsh subsonic environment also allows a much wider range of aircraft types, such as balloonsairships and rotorcraftallowing them to fill a much wider range of roles. Subsonic flight is characterised aerodynamically by incompressible flow, where dynamic pressure changes due to motion through the air cause the air to flow away from areas of high dynamic pressure to areas of lower dynamic pressure, leaving the static pressure and density of the surrounding air constant.

At high subsonic speeds, compressibility effects begin to appear. The propeller is one of the most efficient sources of thrust available and is common on subsonic aeroplanes and airships.

Sometimes it is enclosed in the form of a ducted fan.

At higher subsonic speeds and at high altitudessuch as attained by most airlinersthe high-bypass turbofan becomes necessary. Pure jets such as the turbojet and ramjet are inefficient at subsonic speeds and not often used.

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The span and area of a wing are both important to the lift characteristics. They are related by the aspect ratiowhich is the ratio of the span, measured from tip to tip, to the average chordmeasured from leading edge to trailing edge. The drag of a wing consists of two components, the induced dragwhich is related to the production of liftand the profile draglargely due to skin friction which is contributed to by the whole wing area.

This is best achieved with a high aspect ratio, and high-performance types often have this kind of wing. But other considerations such as light weight, structural stiffness, manoeuvrability, ground handling and so on often benefit from a shorter span and, consequently a less efficient wing.

Small, low-altitude general aviation planes typically have aspect ratios of six or seven; airliners of 12 or more; and high-performance sailplanes of 30 or more. At speeds above the critical Mach number, the airflow begins to become transonicwith local airflow in some places causing small sonic shock waves to form.

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