Skin friction drag

Skin friction drag is a component of parasitic drag that occurs differently depending on the type of flow over the lifting body (laminar or turbulent). Just like any other form of drag, the coefficient of skin friction drag is calculated with various equations and measurements depending on the flow and then added to coefficients of other forms of drag to calculate total drag.

Flow and effect on skin friction drag

Laminar flow is when layers of the fluid move smoothly past each other, and turbulent flow has a fluctuating and irregular nature. Different types of flow affect drag because as each type of flow occurs, it changes the nature of the boundary layer on the body. To understand exactly how skin friction is created, it is advised to do research on boundary layer. In short, turbulent flow creates a much larger boundary layer than laminar flow and therefore creates more skin friction.

Calculation

The calculating of skin friction drag is heavily based on the Reynolds number of the body. For reference, Reynolds number (Re) is calculated with:

\mathrm {Re} ={\frac {{\mathbf {V} }{\mathbf {L} }}{\mathbf {\nu }}}\

where:

${\mathbf {V} }$ is the velocity of the flow
${\mathbf {L} }$ is the length of the body that the flow travels across
${\mathbf {\nu }}$ is the kinematic viscosity of the fluid

Now that Reynolds number is known, the coefficient of skin friction drag can be calculated.

Laminar flow

C_{f}={\frac {1.328}{\sqrt {\mathrm {Re} }}}\

, Also known as the Blasius Friction law

Note: if measuring skin friction from a certain point on the body, replace the ‘L’ in the Reynolds number equation with the distance from the leading edge that you want to measure ( $\mathrm {Re} _{l}$ ). Then use the following equation:

C_{fl}={\frac {.664}{\sqrt {\mathrm {Re} _{l}}}}\

Turbulent flow

C_{f}={\frac {.455}{log(\mathrm {Re} )^{2.58}}}\

, Also known as the Schlichting empirical formula

Drag

The total force on the body caused by skin friction drag in units of force can be calculated with:

F=C_{f}{\frac {\rho V^{2}}{2}}\ S_{wetted}

where ${\mathbf {S} _{wetted}}$ is the total surface area that is in contact with the fluid.

References

Fundamentals of Flight by Richard Shepard Shevell