From an engineering point of view, the calculation of skin friction is useful for estimating not only the total frictional resistance exerted on an object, but also the rate of convectional heat transfer over its surface.[8] This relationship is well developed in the concept of Reynolds analogy, which relates two dimensionless parameters: the coefficient of skin friction (Cf), which is a dimensionless frictional stress, and the Nusselt number (Nu), which indicates the magnitude of heat transfer per convection. Turbine blades, for example, require heat transfer analysis in their design process because they are imposed on high-temperature gas, which can damage them with heat. In this case, engineers calculate the skin friction on the surface of the turbine blades to predict the heat transfer that occurs across the surface.

A 1974 NASA study found that for subsonic aircraft, skin friction drag is the largest component of drag, causing about 45% of the total drag. For supersonic and hypersonic aircraft, the figures are 35% and 25% respectively.[9]​.

A 1992 NATO study found that for a typical civil transport aircraft, skin friction drag accounted for almost 48% of the total drag, followed by induced drag at 37%.[10][11]​.

There are two main techniques to reduce skin friction drag: delaying the boundary layer transition and modifying the turbulence structures in a turbulent boundary.[12]​.

One method of modifying turbulence structures in a turbulent boundary layer is the use of riblets.[13]​[14]​ Riblets are small grooves in the surface of the aircraft, aligned with the direction of flow.[15]​ Tests carried out on an Airbus A320 showed that riblets reduced aerodynamic drag by almost 2%.[13]​ Another method is the use of large eddy breaking devices. (LEBU).[13]​ However, some research on LEBU devices has found a slight increase in aerodynamic drag.[16]​.

• - Parasitic resistance.

Definition

The coefficient of surface friction is defined as:[2]​.

where:.

• - is the coefficient of surface friction.

• - is the density of the free current (far from the surface of the body).

• - is the free stream velocity, which is the magnitude of the fluid velocity in the free stream.

• - is the shear stress on the surface.

• - is the dynamic pressure of the free stream.

The coefficient of skin friction is a dimensionless skin shear stress that is not dimensioned by the dynamic pressure of the free stream. The coefficient of surface friction is defined at any point on a surface subjected to free flow. It varies depending on the position. A fundamental fact in aerodynamics states that.

.[3]​.

This immediately implies that the laminar skin friction resistance is less than the turbulent skin friction resistance, for the same inlet flow.

The coefficient of surface friction is an important function of the Reynolds number, and if it increases it decreases.

laminar flow

where:.

• - , is the Reynolds number.

• - is the distance from the reference point from which a boundary layer begins to form.

The above relationship is derived from the Blasius boundary layer, which assumes a constant pressure throughout the boundary layer and a thin boundary layer.[4]​ The above relationship shows that the coefficient of skin friction decreases as the Reynolds number () decreases.

Transient flow

The CPM, suggested by Nitsche,[5]​ calculates the surface shear stress of transition boundary layers by fitting the following equation to a velocity profile of a transition boundary layer. (Karman constant), and (surface shear stress) are determined numerically during the fitting process.

where:.

• - is a distance to the surface.

• - is a velocity of a flow at a given speed.

• - is the Karman constant, which is less than 0.41, the value for turbulent boundary layers, in transition boundary layers.

is the Van Driest constant, whose value is 26 in both the transitional and turbulent boundary layers.

• - is a pressure parameter, which is equal to when it is a pressure and is the coordinate along a surface where a boundary layer forms.

Turbulent flow

The above equation, which is derived from Prandtl's seventh power law,[6]​ provided a reasonable approximation of the drag coefficient of low Reynolds number turbulent boundary layers.[7]​ Compared to laminar flows, the skin friction coefficient of turbulent flows decreases more slowly as the Reynol number increases.

Resistance force due to surface friction

The total surface friction resistance force can be calculated by integrating the shear stress of the skin on the surface of a body.

From an engineering point of view, the calculation of skin friction is useful for estimating not only the total frictional resistance exerted on an object, but also the rate of convectional heat transfer over its surface.[8] This relationship is well developed in the concept of Reynolds analogy, which relates two dimensionless parameters: the coefficient of skin friction (Cf), which is a dimensionless frictional stress, and the Nusselt number (Nu), which indicates the magnitude of heat transfer per convection. Turbine blades, for example, require heat transfer analysis in their design process because they are imposed on high-temperature gas, which can damage them with heat. In this case, engineers calculate the skin friction on the surface of the turbine blades to predict the heat transfer that occurs across the surface.

A 1974 NASA study found that for subsonic aircraft, skin friction drag is the largest component of drag, causing about 45% of the total drag. For supersonic and hypersonic aircraft, the figures are 35% and 25% respectively.[9]​.

A 1992 NATO study found that for a typical civil transport aircraft, skin friction drag accounted for almost 48% of the total drag, followed by induced drag at 37%.[10][11]​.

There are two main techniques to reduce skin friction drag: delaying the boundary layer transition and modifying the turbulence structures in a turbulent boundary.[12]​.

One method of modifying turbulence structures in a turbulent boundary layer is the use of riblets.[13]​[14]​ Riblets are small grooves in the surface of the aircraft, aligned with the direction of flow.[15]​ Tests carried out on an Airbus A320 showed that riblets reduced aerodynamic drag by almost 2%.[13]​ Another method is the use of large eddy breaking devices. (LEBU).[13]​ However, some research on LEBU devices has found a slight increase in aerodynamic drag.[16]​.

• - Parasitic resistance.