  Recent large eddy simulations have led to improved parameterizations of the
effective roughness height of wind farms. This effective roughness height can
be used to predict the wind velocity at hub-height as function of the geometric
mean of the spanwise and streamwise turbine spacings and the turbine loading
factors. Meyers and Meneveau (Wind Energy 15, 305-317 (2012)) used these
parameterizations to make predictions for the optimal wind turbine spacing in
infinitely large wind farms. They found that for a realistic cost ratio between
the turbines and the used land surface the optimal turbine spacing may be
considerably larger than used in conventional wind farms. Here we extend this
analysis by taking the length of the wind farm, i.e.\ the number of rows in the
downstream direction, into account and show that the optimal turbine spacing
strongly depends on the wind farm length. For small to moderately sized wind
farms the model predictions are consistent with spacings found in operational
wind farms. For much larger wind farms the extended optimal spacing found for
infinite wind farms is confirmed.
