#### In this chapter

Drag force is a very large topic in aerodynamics. There are books and conferences entirely devoted to it, along with countless specialized publications.

From a physical point of view, drag is the resultant of forces acting normally and tangentially to a surface, the former ones being pressure terms, and the latter ones viscous terms. The mechanism under which these forces are created is ultimately related to the formation of vortices and shear layers.

### Importance of the Subject

Very narrow gains (1 % or less) can translate into a change of technology. It is widely assumed that the fuel crisis of the 1970s created the need to invest in drag reduction technology for aircraft transport. But the problem is wider than that, since all the aerodynamic systems use external power that is partially dissipated due to drag forces.

#### Effects of Drag Reduction

For example, a reduction in the drag coefficient of an ordinary passenger car from CD = 0.4 to CD=0.3 would improve the fuel consumption by 7.5 %. This saving multiplied by the number of road vehicles in Europe and North America yields a figure (at least 10 billion gallons/year) that could affect the price of the crude oil in the world markets.

The reduction of 10 % drag on a large military transport aircraft would save over 10 million gallons of fuel over the life time of the aircraft.

A 15 % drag reduction on the Airbus A340-300B would yield a 12 % fuel saving, other parameters being constant (Mertens, 1998).

See the Table of Drag Data for more details.

### Flow Physics

The fundamental mechanisms by which drag is produced in steady state conditions can be reduced to the following ones

#### Viscous Drag

Viscous drag is produced by the effects of viscosity on the aerodynamic systems, through the thrust that must be applied to overcome the shear layers due to the non slip condition.

#### Lift-induced Drag

Drag due to lift is the result of the downwash (vertical flow) and to the strength of the vortices produced at some particular locations (wing tips or other sharp edges) of many lifting systems.

#### Vortex Drag

Vortex drag can be created by both lifting and non lifting bodies (usually of the bluff variety, ex. road vehicles, airships). Vortices are released during flow separatio and trail downstream to form structured or unstructured wake patterns.

#### Interference

Interference is the effect of the presence of one body on the aerodynamics of a second body. The interference drag is a system drag that is present even in absence of viscous effects (ideal fluid) and non lifting conditions. Since interference occurs in many practical situations interference drag is a separate topic.

#### Wave Drag

Wave drag is created by radiation of disturbances in the fluid by a moving body. This is the case of transonic and supersonic flows; in hydrodynamics waves are produced by several means, the most important of which is probably the pattern of surface waves produced by boats, ships and submerged bodies.

The presence of one or more drag components, along with their respective amounts, clearly depends on the aerodynamic arrangement and the system operation.

#### Speed-induced Drag

Another classification sometimes used is that according to speed. The speed (e.g Reynolds and Mach numbers) have, in fact, one of the most important effects on both the drag build-up and the drag level.

### Methods of Computation

There are several methods used to compute the drag of a lifting body. For example:

• The drag of an airfoil at subsonic speeds can be computed by using the Squire-Young approximation. The method consists in evaluating the drag coefficient by using boundary layer quantities at the trailing edge.

• By using the axial momentumbalance on a large control volume (between two planes far upstream and downstream the body).

• By integration of the surface forces (CFD approach). There are two contributions: the tangential (due to skin friction) and normal (due to pressure) contributions. This is the approach followed most by the current research.

Other (simplified) methods include: Integration of circulation in the Treffz plane (induced drag of large aspect ratio wings); Hayes formula (for linearized supersonic flow); Munk’s stagger theorems (for linearized multi-body lifting systems), etc. A detailed review of CFD capabilities has been recently published by van Dam (1999).

#### Selected References

• Hoerner SF. Fluid Dynamic Drag, Hoerner Fluid Dynamics, 1965.

• AGARD, Special Course on Concepts for Drag Reduction, AGARD Report R-654, 1977.

• AGARD, Special Course on Subsonic/Transonic Aerodynamic Intereference for Aircraft, AGARD Report R-712, 1983.

• AGARD, Aircraft Drag Prediction and Reduction, AGARD Report R-723, 1985.

• Clift R, Grace JR, Weber ME. Bubbles, Drops, and Particles, Academic Press, New York, 1978.

• Sovran G, Morel T, Mason WT. (editors). Aerodynamic Drag Mechanisms of Bluff Bodies and Road Vehicles, Plenum Press, New York, 1978 (ISBN 0-306-31119-4).
Check the
reviews of these references.

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