This study provides guidance for researchers who work with functional (curve) data and aim to perform a prior sample size estimation. Focusing on the two-population framework, we test mean differences between two populations — a scenario common in fields such as human movement science. Through simulations, we examine how standard deviation and smoothness influence sample size requirements to achieve 0.80 statistical power, using four methods with control the family-wise error rate: interval-wise testing (IWT), threshold-wise testing (TWT), F-max, and Extreme Rank Length (ERL) global envelope. For instance, increasing the standard deviation from 5 to 10 can raise the sample size from approximately 10 to over 30. Adjusting the smoothness parameter from 5 to 45 can lead to varied outcomes: the required sample size may increase to over 50, remain near 10, or even decrease, depending on the method and data characteristics. Three key findings are: (1) higher noise levels require larger sample sizes, (2) smoother data necessitate more samples when mean differences span larger domains, and (3) TWT and IWT are more efficient for large-domain differences, while ERL and F-max performbetter for differences on narrower domains.