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In wireless sensor networks, with respect to a desired time deadline real-time data dissemination schemes achieve that by a spatiotemporal communication approach forwarding data from a source to a destination with a delivery speed. The delivery speed is typically obtained from both the static distance from the source to the destination and the interval of the time deadline. However, in case of real-time routing to a mobile sink, since the mobile sink randomly moves around, the distance from a source to the mobile sink would be dynamically changed. Hence, we propose a new real-time routing scheme considering the dynamic distances by the mobile sink. In the scheme, the source calculates an expected area of the mobile sink by the moving speed of the sink; then, the data delivery speed is obtained from the worst case distance from the source to the farthest position on the area. The source transmits data to expected area with the delivery speed, and the first sensor node within the area then floods in the area to deliver the data to the mobile sink that is dynamically located within the area.