A meshed network with N transport paths can be effectively protected against single link failures using network coding and protection cycles (p-cycles). This so called 1+N protection scheme provides instantaneous recovery from single link failures. The performance of this scheme has thus far been considered for a network with unit traffic demands, and the reported results were based on simulations. In this paper, we give an analytical upper bound on the required transport capacity for 1+N protection in full-meshed networks with unit traffic demands. Next, we consider networks with uniform and exponentially distributed traffic demands, and derive more realistic bounds for the achievable network performance of 1+N protection in full-meshed networks.We will show analytically that the gains decrease significantly relative to a unit-traffic demand distribution, independent of the protection mechanism used.