A Beam antenna is generally composed of a series of elements arranged to provide a high powered directional aerial.
The Yagi Beam antenna is made up of a Refelector element, a Driven element, and a series of parasitic elements.
The reflector preforms two jobs. First it launches the signal in a forward direction, and reflects signals coming in from the back side of the yagi.
The driven element is a broken dipole, and the parasitic elements act simular to a series of tuning forks in that the first one resonates the signal to the next one.
With each passing parasitic element the signal increases it's resonance by 3 dbi gain.
Each time you double the number of parasitic elements you double the signal strength up to about 12 elements.
After that the actual gain of doubling dimmishes by about 25% percent.
Formulas:
Length of Reflector Element: 492/frequency in MHz.
Length of Driven Element (1/2 Wave) : 468/frequency in MHz.
Each Leg of the broken Dipole: (1/4 Wave): 234/frequency in MHz.
Parasitic Elements (Director elements): 450/frequency in MHz.
Spacing between Reflector and Driven Element: 187/frequency in MHz.
Spacing between Driven Element and 1st Director: 98.4/frequency in HMz.
Spacing between 1st Director and second: 123/frequency in MHz.
Spacing of all other Director elements: 148/frequency in MHz.