We propose a new dynamical method to estimate binary mass ratios by using the period of superhumps in SU UMa-type dwarf novae during the growing stage (the stage A superhumps). This method is based on a working hypothesis in which the period of the superhumps at the growing stage is determined by the dynamical precession rate at the 3:1 resonance radius, a picture suggested in our new interpretation of the superhump period evolution during the superoutburst (Osaki, Kato 2013, arXiv:1305.5877). By comparison with the objects with known mass ratios, we show that our method can provide sufficiently accurate mass ratios comparable to those obtained by quiescent eclipse observations. This method is very advantageous in that it requires neither eclipses, nor an experimental calibration. It is particularly suited for exploring the low mass-ratio end of the evolution of cataclysmic variables, where the secondary is undetectable by conventional methods. Our analysis suggests that previous estimates of mass ratios using superhump periods during superoutburst were systematically underestimated for low mass-ratio systems and we provided a new calibration. It suggests that most of WZ Sge-type dwarf novae have secondaries close to the border of the lower main-sequence and brown dwarfs, and most of the objects have not yet reached the evolutionary stage of period bouncers. Our result is not in contradiction with an assumption that the observed minimum period (~77 min) of ordinary hydrogen-rich cataclysmic variables is indeed the period minimum. We highlight the importance of early observation of stage A superhumps and propose a future desirable strategy of observation.
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