As the vertical stabilizer keeps the gyroplane from wandering to the left or right. A horizontal stabilizer helps control the up and down pitch of a gyroplane. A horizontal stabilizer is a fixed structure and may be located far aft or at some mid-point on the empennage.
Some gyroplanes have been designed with no horizontal stabilizer. So where does this pitch control come from? It is designed into the main rotor and mast system to control the periodic swing of the rotor and airframe. Pretty cool, eh!
If the horizontal stabilizer was mounted in a fashion to allow it to move up and down and attached to the pilots control stick we would have a stabilator. Some gyroplanes use this flight element in their designs.
In the early days of gyroplane development the builders used modified airplane hulls as the stucture and many of them retained the horizontal stabilizer and elavators but scaled the sizes down for use in the gyroplane.
Due to previous and current discussions on the use and size of horizontal stabilizers I would like to make a small personal comment: To argue about what is right or wrong is like comparing a 172 to a Long-Eze or a Stealth bomber. They all use different methods to provide positive aircraft control. The sport will go farther if we support each other rather than bicker. This is after all one of the reasons we are in the experimental class-to experiment! To experiment we need verifiable data and then we can develop an engineering formula for the design. Were the Wright Bothers wrong in there design that used a canard and wing warping? Both are being used today. Support each other we are Bothers and Sisters of the air-help your sport move forward.
Glasgow University conducted a series of gyroplane tests starting with Project 1 and ending with Project 5. These studies involved a 1/3 scale model and actual flight data verification with proper test instrumentation. Provided here is the link to the summary of Project 5 with the final results of the affects of tail plane design and centerline of thrust on the buttline cg in regards to longitudinal stability.
Let's cruise on over to Aircraft Joysticks.
University of Glasgow