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Two-tiered networking architecture scheme has been used for over a decade in clustered wireless sensor networks for which an accurate localisation of the sink plays a critical role for maximising network lifetime. Solutions so far have been for over-simplified cases of single sink with upper and lower bounds for constant and uniformly distributed loads that mostly suffer from convergence issues in practice. In order to overcome this problem, the authors propose a new sink location estimating method that combines multi-hop inter-cluster routing with single-hop intra-cluster routing where the death of first cluster head counts as network lifetime. For doing this, the authors propose a geometrical solution for locating the optimum sink placement using an algorithm outlining the novel approach that has been demonstrated to be superior to other methods for its convergence and many other practical features such as data rates and cluster heads.