Notice that the pattern is unidirectional, and somewhat wider in the plane perpendicular to the elements. This is true in general for Yagis, regardless of the number of directors used. However, as more directors are added, the forward gain will increase, and the beam width will become narrower in both planes.
You may wonder what would happen if additional reflectors are added. The answer is that nothing happens. The first reflector reduces the power radiated rearward to approximately 1% of the forward value. The additional directors cannot couple strongly to the driver because the radiated field passing by them is so small. Only 1 reflector is necessary to reduce rearward radiation.
The operating bandwidth (the range of frequencies over which the gain and FB ratio stay within design criteria) for a Yagi is generally quite narrow and can be altered to some extent through careful adjustment of the length and spacing of the elements. The chart below shows how the gain and FB ratio of the 3 element Yagi depend on frequency.
The one problem encountered with this approach is that if the user is standing no-where near the transmitter, or facing directly away from it. The hand held display will show display indicating that the user is pointing in the right direction. While this is a large potential problem we must remember that the user will have a general idea of where the disc landed and should not end up facing this predicament in any case