The relationships between the mean Doppler terminal velocities V-r of the hydrometeors with different phases and the range-corrected VHF backscatter P from the corresponding precipitation particles are investigated by using the Chung-Li VHF radar. The radar precipitation data employed for the analysis were taken from four independent experiments conducted on different weather conditions. They show that the observed alpha and beta values in the power-law approximation V-T = npp above the melting layer are generally smaller than those below the layer, while in the bright band the values of beta (alpha) are enormously smaller (greater) than those above and below the bright band. Theoretical analysis shows that the mathematical relationship between alpha and beta can be approximated very well by a simple exponential function, which is in excellent agreement with the observations. A new method for estimating the coefficient A and exponent B in the fall speed-diameter relationship V(D) = AD(B) with respect to still air on the basis of the theoretical relation between alpha and beta is also proposed. A comparison of the estimations of A and B with those reported in the literature indicates that the former are smaller than the latter. The authors believe that the difference in the two is due to the different types of the clouds producing the precipitation. In addition, it is found that the value of A is proportional to the height of the 0 degrees C isotherm, implying that the air temperature plays a role in establishing the relationship between the fall speed and the diameter of the hydrometeors.