### AirfoilPrep - Du-Selig Modified TSR

Posted:

**Wed Jun 10, 2020 7:34 am**Dear all,

I have a question on the formula used in AirfoilPrep Excel Macro for the Modified TSR.

I have attached one of the latest version published on the forum: AirfoilPrep_v2p0_NACA64_A17.xls

In the macro the Modified TSR is calculated as follows:

Lambda = RPM * pi / 30 * R / (V ^ 2 + (RPM * pi / 30 * R) ^ 2) ^ 0.5

However, I have found that in some papers the Modified TSR is slightly different:

Lambda = RPM * pi / 30 * R / (V ^ 2 + (RPM * pi / 30 * r) ^ 2) ^ 0.5,

(source: Sven Schmitz - Aerodynamics of Wind Turbines - 2019)

so I have modified the Excel macro for my own calculation as follows:

Lambda = RPM * pi / 30 * R / (V ^ 2 + (RPM * pi / 30 * R * rOverR) ^ 2) ^ 0.5

Unfortunately, on the airfoil in this example the difference is not so important but in the cases that I am studying the difference is consistent:

For a CL2D = 1.20, I obtain:

CL3D_standard = 1.91

CL3D_MODIFIED = 1.51

Could you please give me indication on which approach is correct?

Thank you in advance.

Best regards,

Matteo Strada

I have a question on the formula used in AirfoilPrep Excel Macro for the Modified TSR.

I have attached one of the latest version published on the forum: AirfoilPrep_v2p0_NACA64_A17.xls

In the macro the Modified TSR is calculated as follows:

Lambda = RPM * pi / 30 * R / (V ^ 2 + (RPM * pi / 30 * R) ^ 2) ^ 0.5

However, I have found that in some papers the Modified TSR is slightly different:

Lambda = RPM * pi / 30 * R / (V ^ 2 + (RPM * pi / 30 * r) ^ 2) ^ 0.5,

(source: Sven Schmitz - Aerodynamics of Wind Turbines - 2019)

so I have modified the Excel macro for my own calculation as follows:

Lambda = RPM * pi / 30 * R / (V ^ 2 + (RPM * pi / 30 * R * rOverR) ^ 2) ^ 0.5

Unfortunately, on the airfoil in this example the difference is not so important but in the cases that I am studying the difference is consistent:

For a CL2D = 1.20, I obtain:

CL3D_standard = 1.91

CL3D_MODIFIED = 1.51

Could you please give me indication on which approach is correct?

Thank you in advance.

Best regards,

Matteo Strada