Many people use smart phones on a daily basis, yet, their energy consumption is pretty high and the battery power lasts typically only for a single day. In the scope of the EnAct project, we investigate potential energy savings on smart phones by offloading computationally expensive tasks into the cloud. Obviously, also the wireless communication for uploading tasks requires energy. For that reason, it is crucial to understand the trade-off between energy consumption for wireless communication and local computation in order to assert that the overall power consumption is decreased. In this paper, we investigate the communications part of that trade-off. We conducted an extensive set of measurement experiments using typical smart phones. This is the first step towards the development of accurate energy models allowing to predict the energy required for offloading a given task. Our measurements include WiFi, 2G, and 3G networks as well as a set of two different devices. According to our findings, WiFi consumes by far the least energy per time unit, yet, this advantage seems to be due to its higher throughput and the implied shorter download time and not due to lower power consumption over time.