I am looking for information or any explanation, I want to know how this envelope is graphed, the limits (underlined in the image) from where they are obtained and what do they tell me? I want to know step by step how a graph is made as it is, specifically for a Helicopter, any idea where I can start I really appreciate it.
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The basis of CofG location for airplanes and helicopters is completely different. For airplanes, CofG location is equivalent to the pivot axis of a weathervane relative to the weathervane's aerodynamic center. Static stability is achieved by making sure the aft-most CofG is far enough ahead of the aerodynamic center to get a strong weathervaning tendency in flight, positive static stability (but not so far as to prevent the "weathervane" from being trimmed to operate at an angle off-axis to get the wings to make lift, which sets the forward limit).
A helicopter is more like a camping trailer suspended from a crane, the rotor disk being the crane, and the mast being the cable. If the CofG of the trailer is perfectly centered under the attachment point, the trailer will sit level. When you move the CofG forward and aft of that, the trailer will sit with a tilt.
The tilt means the vertical axis of the body is not parallel to the rotor axis in a hover (in still air). This angle-off-parallel uses up some of the range of movement available to the rotor disc, through the swash plate and control linkage, relative to the fuselage, needed to maneuver and to maintain a hover in various conditions, and to maintain a desirable nose attitude in cruise flight.
So, the helicopter's CofG limits are those beyond which there is not enough articulation range for the rotor, relative to the fuselage, to ensure control in all operating conditions.
The range tends to get narrower as the weight goes up as inertial effects of the higher mass can create dynamic effects in flight that further restrict how much articulation room can be given up in having the CofG off centre.
For example, aft CofG may be limited as weight goes up due to the need to have sufficient control authority to maintain nose attitude at maximum speed with some remaining forward cyclic margin, the more of this margin being used up the heavier the machine is, giving the slope at the back of the curve. Forward CofG may be limited until some fuel is burned off when the machine is heavily loaded, if the tanks are aft of the rotor axis, resulting in the slope at the front of the curve.
For that particular chart, the curves would have been determined by the designer initially, and validated and adjusted during development and certification test flying, where the machine is loaded to its limits at various weights and they see what happens.
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$\begingroup$ Behaviour of the helicopter with CoG change depends on the rotor hinge $\endgroup$– KoyovisJan 5 at 23:45
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$\begingroup$ Thank you very much for your answer. But then, is there a way that I can make this graph step by step or a description of what is done to trace each point. I understand that the designer is in charge, but then how does he determine the limits? From what I understood, data is also taken from various calculations for different helicopter weights? $\endgroup$ Jan 6 at 2:10
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$\begingroup$ @Koyovis Yes, if the rotor is teetering it's a completely free pendulous connection. If articulated it's more of a semi rigid flexible connection, but the CofG limits are still related to disc articulation limits one way or another. $\endgroup$– John KJan 6 at 4:23
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$\begingroup$ It will be done from initially from calculations that would estimate disc displacement off axis for various weight/CG configurations, then validated by experimental test flights. How much rotor margin is required for a rotor system will depend the type of rotor head and other things. Then you have external features to help. When you see tail rotors that are angled, it's being done to provide a vertical lift component that allows extension of the aft CofG limit by helping to hold the tail up. Horizontal stabilizers also add to the potential CofG range. $\endgroup$– John KJan 6 at 4:31