Types of drag

Attempts have been made to rationalize the definitions and terminology associated with drag[3]. On the whole the new terms have not been widely adopted. Here we will use the widely accepted traditional terms and indicate alternatives in parentheses.

Total drag

This is formally defined as the force corresponding to the rate of decrease in momen­tum in the direction of the undisturbed external flow around the body, this decrease being calculated between stations at infinite distances upstream and downstream of the body. Thus it is the total force or drag in the direction of the undisturbed flow. It is also the total force resisting the motion of the body through the surrounding fluid.

There are a number of separate contributions to total drag. As a first step it may be divided into pressure drag and skin-friction drag.

Skin-friction drag (or surface-friction drag)

This is the drag that is generated by the resolved components of the traction due to the shear stresses acting on the surface of the body. This traction is due directly to viscosity and acts tangentially at all points on the surface of the body. At each point it has a component aligned with but opposing the undisturbed flow (i. e. opposite to the direction of flight). The total effect of these components, taken (i. e. integrated) over the whole exposed surface of the body, is the skin-friction drag. It could not exist in an invisidd flow.

Pressure drag

This is the drag that is generated by the resolved components of the forces due to pressure acting normal to the surface at all points. It may itself be considered as consisting of several distinct contributions:

(i) Induced drag (sometimes known as vortex drag);

(ii) Wave drag; and

(iii) Form drag (sometimes known as boundary-layer pressure drag).

Induced drag (or vortex drag)

This is discussed in more detail in Sections 1.5.7 and 5.5. For now it may be noted that induced drag depends on lift, does not depend directly on viscous effects, and can be estimated by assuming inviscid flow.

Wave drag

This is the drag associated with the formation of shock waves in high-speed flight. It is described in more detail in Chapter 6.

Form drag (or boundary-layer pressure drag)

This can be defined as the difference between the profile drag and the skin-friction drag where the former is defined as the drag due to the losses in total pressure and

Fig. 1.13 (a) The displacement thickness of the boundary layer (hatched area) represents an effective change to the shape of the aerofoil. (Boundary-layer thickness is greatly exaggerated in this sketch.) (b) Pressure-distribution on an aerofoil section in viscous flow (dotted line) and inviscid flow (full line)

total temperature in the boundary layers. But these definitions are rather unhelpful for giving a clear idea of the physical nature and mechanisms behind form drag, so a simple explanation is attempted below.

The pressure distribution over a body in viscous flow differs from that in an ideal inviscid flow (Fig. 1.13). If the flow is inviscid, it can be shown that the flow speed at the trailing edge is zero, implying that the pressure coefficient is +1. But in a real flow (see Fig. 1.13a) the body plus the boundary-layer displacement thickness has a finite width at the traihng edge, so the flow speed does not fall to zero, and therefore the pressure coefficient is less than +1. The variation of coefficient of pressure due to real flow around an aerofoil is shown in Fig. 1.13b. This combines to generate a net drag as follows. The relatively high pressures around the nose of the aerofoil tend to push it backwards. Whereas the region of the suction pressures that follows, extend­ing up to the point of maximum thickness, act to generate a thrust pulling the aerofoil forwards. The region of suction pressures downstream of the point of maximum thickness generates a retarding force on the aerofoil, whereas the relatively high – pressure region around the traihng edge generates a thrust. In an inviscid flow, these various contributions cancel out exactly and the net drag is zero. In a real viscous flow this exact cancellation does not occur. The pressure distribution ahead of the point of maximum thickness is little altered by real-flow effects. The drag generated by the suction pressures downstream of the point of maximum thickness is slightly reduced in a real flow. But this effect is greatly outweighed by a substantial reduction in the thrust generated by the high-pressure region around the traihng edge. Thus the exact cancellation of the pressure forces found in an inviscid flow is destroyed in a real flow, resulting in an overall rearwards force. This force is the form drag.

It is emphasized again that both form and skin-friction drag depend on viscosity for their existence and cannot exist in an inviscid flow.