I think that the author felt that question had already been answered sufficiently by other papers -- his citations 1 and 2. The author was interested in adding

I think that the author felt that question had already been answered sufficiently by other papers -- his citations 1 and 2. The author was interested in adding pumping to the model, but as far as I can understand the pumping equations only work for low angles, so he restricted his work to those low angles. Within that range, the distance only increases as the angle increases. Someone can correct me if I've misunderstood.