gdaldem hillshade stop working with mercator?

Parallel to gdalwarp `-te -5.8 41 10 51.5 -ts 1980 0` not working with mercator? , my hillshade works with lat/long input :

gdaldem hillshade input.tmp.tif shadedrelief.tmp.tif -s 111120 -z 5 -az 315 -alt 60 -compute_edges

But stopped to work when input is in mercator :

gdalwarp -of GTiff -s_srs EPSG:4326 -t_srs EPSG:3857  input.tmp.tif reproj.tmp.tif #mercator
gdaldem hillshade reproj.tmp.tif shadedrelief.tmp.tif -s 111120 -z 5 -az 315 -alt 60 -compute_edges

While lat/long is in degree, mercator is in meters, I believe both z scales to be in m which requires -s 111120 (requires -s 370400 if in feet!). Also, what do I do wrong ?