How to calculate the amount of thrust of a autogyro during auto rotation? When a autogyro/gyrocopter is in a horizontal steady flight the rotor should be able to provide enough thrust using the auto rotation principle if the horizontal speed can be regulated by the vertical propeller. 

I was wondering how the amount of thrust provided by the main rotor of a autogyro during auto rotation can be calculated. All the characteristics of the autogyro and his blades are known. 

The horizontal speed of the gyrocopter can be regulated by additional engines and they do not need a specification.
In auto-rotation, either flying level, or with a constant sink speed, the vertical component of the thrust provided by the rotor is exactly the same as the weight of the gyro...

In Wikipedia  https://en.wikipedia.org/wiki/Disk_loading#Momentum_theory  you can find the derivation of the following expression:

$T = 2v^2· A·  rho$

where T is the thrust of the rotor, v the sink speed in vertical auto-rotation, A the 'disk area' (that swept by the blades) and rho the air density.