Profile resistance

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Diagram of the drag coefficient

The profile drag is a force applied to a wing profile at flow around the wing by a fluid (e.g., air to the wing of an aircraft is produced). The drag acts against the direction of movement of the wing. ${\displaystyle W}$

The resistance is calculated from the formula:

${\displaystyle W=c_{W}\cdot A\cdot {\frac {\rho }{2}}\cdot v^{2}}$

With

• the size of the area of the wing ${\displaystyle A}$
• the density of the fluid ${\displaystyle \rho }$
• the flow velocity ${\displaystyle v}$
• the aerodynamic profile drag coefficient ${\displaystyle c_{W}=c_{P}+c_{R}}$
  • the pressure resistance coefficient ${\displaystyle c_{P}}$
  • the coefficient of friction . ${\displaystyle c_{R}}$

The following also have an influence on the profile resistance:

• the shape of the profile
• the type of flow (laminar or turbulent, see below)
• the viscosity of the fluid
• the boundary layer thick and
• the roughness of the profile surface.

The determination of the drag coefficients of different profiles is the subject of extensive wind tunnel measurements. So that the measurement results can be transferred from the model to the execution, the Reynolds number ( ) and the Mach number ( ) must be determined as the relevant comparison numbers . The measured drag coefficients are then plotted in diagrams for incompressible flows or in diagrams for compressible flows. ${\displaystyle c_{W}}$ ${\displaystyle Re}$ ${\displaystyle Ma}$ ${\displaystyle c_{W}/Re}$ ${\displaystyle c_{W}/Ma}$

Here, the following result: in the low speed range and at laminar flow ( ) takes the value with increasing Reynolds number from . This is explained by the increasingly greater energy of the flow, which allows it to follow the airfoil longer and release to move point along the tread surface to the rear. The turbulent wake of eddies behind the profile becomes smaller and reduces its influence on the coefficient of friction. ${\displaystyle Re<Re_{krit}}$ ${\displaystyle c_{W}}$

Above the critical Reynolds number ( ), the laminar flow changes into a turbulent one , accompanied by a greater boundary layer thickness. In the area just above, this results in a significant increase in the coefficient of friction resistance. In the following middle speed range the coefficient of friction remains almost unchanged. At higher speeds, the compressibility of the gas has an ever increasing influence on the coefficient of friction resistance and increases the value sharply. In this area, the value is plotted against the Mach number as a comparative number (not shown in the diagram). ${\displaystyle Re>Re_{krit}}$ ${\displaystyle Re_{krit}}$ ${\displaystyle c_{W}}$ ${\displaystyle c_{W}}$

Friction coefficient of a plate overflowing with flow

The drag coefficient of a laminar overflow plate can be determined using the following formula:

${\displaystyle c_{R,lam}={\frac {1,328}{\sqrt {Re}}}}$

If the flow over the plate is turbulent, the following calculation formula applies:

${\displaystyle C_{R,tur}={\frac {0,0725}{\sqrt[{5}]{Re}}}}$

See also

• Flow resistance

Individual evidence

1. ↑ tec-science: drag coefficient (friction coefficient and pressure coefficient). In: tec-science. May 31, 2020, accessed on June 25, 2020 (German).