Researchers at the University of Wisconsin conducted a study using a custom-designed footbath to test four different bath dimensions with two different step-in heights. The number of immersions per rear foot was counted for each footbath design for each cow passing through the bath on two consecutive days.
While a higher step-in height significantly increased the number of foot immersions, the effect was small compared to the effect of length. The probability of each rear foot receiving at least two immersions reached 95% at a bath length of 3.0 m, and a significant increase in the frequency of three and four immersions per foot was observed between 3.0 and 3.7 m. In order to optimize the number of foot immersions per cow pass, while limiting the footbath volume, this study recommends a bath 3.0–3.7 m long, 0.5–0.6 m wide, with a 28 cm step-in height.
source: N. B. Cook, et al., The Veterinary Journal 193:669 (2012) – full article here