it is necessary to modify the moment equations to achieve the desired goal of estimating the various boundary layer thickness locations. The peaking behavior of the velocity profile means the area normalization of the moments becomes problematic. To avoid this problem, it has been suggested that the unbounded boundary layer be divided into viscous and inertial regions and that the boundary layer thickness can then be calculated using separate moment integrals specific to that region. That is, the inner viscous region of laminar and turbulent unbounded boundary layer regions can be tracked using modified moments whereas the inertial boundary layer thickness can be tracked using modified and moments. The slow rate at which the peak asymptotes to the free stream velocity means that the calculated boundary layer thickness values are typically much larger than the bounded boundary layer case. The modified and moments for the inertial boundary layer region are created by: 1) replacing the lower integral limit by the location of the velocity peak designated by , 2) changing the upper integral limit to h where h is located deep in the free stream, and 3) changing the velocity scale from to . The displacement thickness in the modified moments must be calculated using the same integral limits as the modified moment integrals. By taking as the mean location, the modified 3-sigma boundary layer thickness becomes where is the modified width. The modified second derivative moments can be calculated using the same integrals as defined above but with replacing H/2 for the upper integral limit. To avoid numerical errors, certain calculation recommendations should be followed. The same concerns for the second derivative moments in regards to APG bounded boundary layers for the bounded case above also apply to the modified moments for the unbounded case. An example of the modified moments are shown for unbounded boundary layer flow along a wing section in Figure 3. This figure was generated from a 2-D simulation for laminar airflow over a NACA_0012 wing section. Included in this figure are the modified 3-sigma , the modified 3-sigma , and the locations. The modified ratio value is 311, the modified ratio value is ~2, and the value is 9% higher than the value. The large difference between the and compared to the value demonstrates the inadequacy of the boundary layer thickness. Furthermore, the large velocity peak demonstrates the problem with treating interior bounded boundary