To synthesize the three-arc trajectory, draw a unity circle Ci tangent to both C 0 arid C/ as in Fig. 8b. The center of Ci is the intersection of two arcs which are two radii from C 0 and C f , respectively. By using different combinations of initial and final circles in this construction, up to eight such centers can be found. At most, two of these can be used to draw circles that form confluent three-arc trajectories and that contain angles of more than TT radians. The shortest of these two is another feasible optimum trajectory.To construct the four-arc trajectory, denote by P m the midpoint of the line connecting the center of the circles C 0 and C f . Draw a unity circle Ci tangent to C 0 with center at the intersection of two arcs, the first arc being two radii from C 0 and the second arc one radius from P m , as illustrated in Fig. 8c. Similarly, draw a second circle (7 2 tangent to both the final circle C/ and the circle C\. This procedure guarantees that the two-interior arcs of the four-arc trajectory are of equal length. At most, two four-arc trajectories with interior arcs containing angles of more than TT radians can be drawn by using different combinations of initial and final circles.This concludes the construction of all feasible optimum trajectories. The globally optimum trajectory can now be determined by comparing the length of all feasible optimum trajectories, and choosing the one with the shortest arc length.An experimental study was conducted using flow visualization techniques to investigate the nature of the boundary layer on a model helicopter rotor. Hovering and forward flight data were obtained; however, efforts were concentrated on hovering when unanticipated boundary-layer behavior was revealed. The primary flow visualization technique involved the use of ammonia injected into the boundary layer at the leading edge. The blade surface was chemically coated, and as the ammonia moved with the local airflow, it formed a trace on the surface indicative of the boundary-layer flow. The hovering traces initially moved chordwise along the surface, and then abruptly turned outward. A short distance later, the traces moved inward and then continued aft along the blade in a somewhat diffuse pattern. Similar traces were found over wide ranges of pitch angles and rotor speeds. It is hypothesized that a standing laminar separation bubble exists on the blade surface aft of the peak pressure position. No indication of any separation bubbles could be found on the forward flight traces. Nomenclature c = blade chord length LI = separation point 1/2 = reattachment point P = pressure coefficient AP = differential pressure q = dynamic pressure, pF 2 /2 r = radius to local blade section R = blade radius si = stagnation point preceding the separation bubble «2 = stagnation point following the separation bubble V -flight speed Presented as Paper 69-197 at the AIAA/AHS VTOL Research