Aql X-1 is one of the most prolific low-mass X-ray binary transients (LMXBTs) showing outbursts almost annually. We present the results of our spectral analyses of Rossi X-Ray Timing Explorer/proportional counter-array observations of the 2000 and 2011 outbursts. We investigate the spectral changes related to the changing disk-magnetosphere interaction modes of Aql X-1. The X-ray light curves of the outbursts of LMXBTs typically show phases of fast rise and exponential decay. The decay phase shows a "knee" where the flux goes from the slow-decay to the rapid-decay stage. We assume that the rapid decay corresponds to a weak propeller stage at which a fraction of the inflowing matter in the disk accretes onto the star. We introduce a novel method for inferring, from the light curve, the fraction of the inflowing matter in the disk that accretes onto the neutron star depending on the fastness parameter. We determine the fastness parameter range within which the transition from the accretion to the partial propeller stage is realized. This fastness parameter range is a measure of the scale height of the disk in units of the inner disk radius. We applied the method to a sample of outbursts of Aql X-1 with different maximum flux and duration times. We show that different outbursts with different maximum luminosity and duration follow a similar path in the parameter space of accreted/inflowing mass flux fraction versus fastness parameter.