Synchronized moving aperture radiation therapy (SMART) is a new technique for treating mobile tumours under development at Massachusetts General Hospital (MGH). The basic idea of SMART is to synchronize the moving radiation beam aperture formed by a dynamic multileaf collimator (DMLC) with the tumour motion induced by respiration. SMART is based on the concept of the average tumour trajectory (ATT) exhibited by a tumour during respiration. During the treatment simulation stage, tumour motion is measured and the ATT is derived. Then, the original IMRT MLC leaf sequence is modified using the ATT to compensate for tumour motion. During treatment, the tumour motion is monitored. The treatment starts when leaf motion and tumour motion are synchronized at a specific breathing phase. The treatment will halt when the tumour drifts away from the ATT and will resume when the synchronization between tumour motion and radiation beam is re-established. In this paper, we present a method to derive the ATT from measured tumour trajectory data. We also investigate the validity of the ATT concept for lung tumours during normal breathing. The lung tumour trajectory data were acquired during actual radiotherapy sessions using a real-time tumour-tracking system. SMART treatment is simulated by assuming that the radiation beam follows the derived ATT and the tumour follows the measured trajectory. In simulation, the treatment starts at exhale phase. The duty cycle of SMART delivery was calculated for various treatment times and gating thresholds, as well as for various exhale phases where the treatment begins. The simulation results show that in the case of free breathing, for 4 out of 11 lung datasets with tumour motion greater than 1 cm from peak to peak, the error in tumour tracking can be controlled to within a couple of millimetres while maintaining a reasonable delivery efficiency. That is to say, without any breath coaching/control, the ATT is a valid concept for some lung tumours. However, to make SMART an efficient technique in general, it is found that breath coaching techniques are required.