In this work, we utilized a parameterization model of ektacytometry to quantify the bulk rigidity of the rigid red blood cell (RBC) population in sickle cell disease (SCD) patients. Current ektacytometry techniques implement laser diffraction viscometry to estimate the RBC deformability in a whole blood sample. However, the diffraction measurement is an average of all cells present in the measured sample. By coupling an existing parameterization model of ektacytometry to an artificially rigid RBC model, we formulated an innovative system for estimating the average rigidity of the rigid RBC population in SCD blood. We demonstrated that this method could more accurately determine the bulk stiffness of the rigid RBC populations. This information could potentially help develop the ektacytometry technique as a tool for assessing disease severity in SCD patients, offering novel insights into the disease pathology and treatment.