I believe a hay rick is a haystack. What Phil Lord has described is
usually called a hay rack.

     The State Library has a copy of Hay Racks by L.M. Roehl (Cornell
Extension Bulletin 244) published in 1932. It has photographs of hay
racks and also specific instructions on how to construct them.

                                         Melinda Yates
                                         NYS Library
                                         Albany, NY