Skin friction drag

Skin friction drag is a component of profile 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 in parallel lines. In nature, this kind of flow is rare. As the fluid flows over an object, it applies frictional forces on the surface of the object which works to impede forward movement of the object, in other words, create skin friction drag. Skin friction drag is often the major component of parasitic drag in objects experiencing laminar flow.

Turbulent flow has a fluctuating and irregular pattern of flow which is attributed to the formation of vortices. Turbulent flow suggests a faster rate of flow due to velocity increase and/or viscosity decrease relative to laminar flow. This results in a thinner boundary layer which, relative to laminar flow, depreciates the magnitude of friction force as the fluid flows over the object. This suggests that the total parasitic drag observed in turbulent flow is minimally impacted by skin friction drag.

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:

${\displaystyle \mathrm {Re} ={\frac {{v}{L}}{\nu }}\ }$

where:

• ${\displaystyle {v}}$ is the velocity of the flow
• ${L}$ is the length of the body that the flow travels across
• ${\nu }$ 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 (${\mathrm {Re}}_{x}$). Then use the following equation:

${\displaystyle C_{fx}={\frac {0.664}{\sqrt {\mathrm {Re} _{x}}}}\ }$

Turbulent flow

${\displaystyle C_{f}={\frac {0.455}{log(\mathrm {Re} )^{2.58}}}\ }$, 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:

${\displaystyle F=C_{f}{\frac {\rho _{f}v^{2}}{2}}\ S_{wetted}}$

where ${\displaystyle {\rho _{f}}}$ is the fluid density, ${\displaystyle {v}}$ is the fluid velocity and ${\displaystyle {S_{wetted}}}$ is the total surface area that is in contact with the fluid.

See also

• Parasitic drag

References

Fundamentals of Flight by Richard Shepard Shevell