We study Michael Weiss “orthogonal tower”
of the
functors VBO(V) and
VBU(V). We describe the Weiss derivatives
of these
functors and calculate the homology
of the layers. The orthogonal tower studied here is related to the Goodwillie tower
of the identity functor in various ways. Most
of our results are Weiss-tower analogues
of previous results
of Arone–Mahowald and Arone–Dwyer on the Goodwillie derivatives
of the identity, but we believe that there are new things to be learned from the Weiss tower.