Permeability is important in many geotechnical applications. The current (cone penetration test that gathers piezometer data (CPTu)) practice to obtain permeability values relies on dissipation tests, which are frequently slow and only linked to permeability through compressibility measures. On-the-fly methods offer an alternative approach in which permeability is directly linked to CPTu penetration measurements. Several on-the-fly methods have been proposed and their applicability and relative advantages are not fully clear. Numerical effective stress simulation of CPTu testing is used here to explore in a simplified but realistic setting the relative merits of different on-the-fly methods. It is found that for partly drained materials, the original simpler relation between cone metrics and normalised permeability works reasonably well. A continuous generalisation of Elsworth and Lee method to the full permeability range is proposed, noting the connection to the backbone normalised pore-pressure curve that describes the partly drained transition of cone penetration. The importance of an undrained limit beyond which the method produces large errors is emphasised.