Does a Higher Frame Rate Improve the Measurement of g? Precision and Accuracy in Video Analysis

Abstract

This study investigates the influence of frame rate, expressed in frames per second (FPS), on the experimental estimation of the acceleration due to gravity, g, using video analysis with Tracker. Two different dynamical systems were analysed: free fall and a simple pendulum. Starting from original recordings acquired at 120 FPS, equivalent 60, 30, and 10 FPS series were generated by uniform temporal decimation, preserving the same physical trajectory within each realisation. The analysis included ten independent realisations for free fall and eight for the pendulum. For each condition, the mean estimate of g, the standard deviation across realisations, the relative error with respect to g_ref = 9.81 m s^-2, and the RMSE were calculated. For free fall, the 120 FPS condition exhibited the lowest dispersion and RMSE, whereas the mean estimates obtained at 10 and 30 FPS were closer to the reference value. For the simple pendulum, by contrast, the mean value of g, dispersion, relative error, and RMSE remained essentially unchanged between 10 and 120 FPS. An additional analysis of the 12 possible subsampling phases at 10 FPS showed that this stability does not critically depend on a particular choice of decimation phase and that the variability associated with phase is small compared with the dispersion observed across realisations. The results show that a higher temporal sampling rate does not necessarily provide both greater precision and closer agreement with the reference value. The influence of FPS depends on the temporal characteristics of the system and on the procedure used to estimate the physical parameter. In particular, a higher temporal sampling density may reduce dispersion or increase robustness to sampling without necessarily yielding an estimate closer to the expected value.