As the resident pseudo-statistician I have occasionally performed sample size calculations for animal studies and often these have included multi-way ANOVA designs. I have seen these calculations performed by others using very basic powering for a t-test and extrapolating upwards. I have also seen recommendations for using more complex calculations using partial-eta-sqaured etc, however, it is often difficult to get hold of enough data to estimate these accurately, so I can see the benefit of the simpler approach.