**3.1 Mathematical models of helicopter flight dynamics**

The helicopter is specific in regards to other traffic-transportation means, not just by its structure but also by its motion possibilities. The helicopter can move vertically, float in the air,

It is assumed =0 and that the blade is moving forward in relation to the vertical hinge by the lead-lag angle amount . The vertical hinge is placed at distance eR from the shaft axis.

<sup>2</sup> 2 / *M J z z*

2 2 <sup>2</sup> *<sup>z</sup>*

 

It is assumed that flutter and lead-lag angles are equal zero. The blade step is the angle between the blade cross section chord and the plane of the hub, designated as k. Figure 22

 

*d d M d J d*

*z*

 

 

**3.1.1.2 Equations of blade lead-lag** 

Fig. 21. Blade lead-lag scheme

**3.1.1.3 Equation of blade climb** 

 

**3.1.2 Rotor forces** 

The coordinate system is placed as in the previous case.

If the azimuth angle is described as =t, then follows:

shows the coordinate system attached to the blade. Equations of blade motion about longitudinal axis are:

Fig. 22. Coordinate system at blade cross section

<sup>2</sup> / sin 2

to the rotor plane, that is, to the plane on which reside blade tips, and shaft axis.

 cos cos <sup>0</sup> *y k k yk k J J*

To project forces the following axis may be use: control axis, rotor disc axis which is normal

*k k xx MJ J M z kkz*

2

 

From this follows the equation for blade lead-lag:

turn in place, move forward and lateral, and can perform these movements in combinations. Because of this, helicopter dynamics modeling and testing is a very complex problem.

In the present, problems in helicopter flight dynamics are mostly solved in aid of modern computers. Though inevitable in many complex problems, computers do not make it possible to understand the physical nature of the problem. Fortunately, many problems considering helicopters can be analyzed without overly complex calculus and usually it is possible to obtain simple formulas. Though not suitable for calculus, these formulas, when designing the helicopter, enable a satisfactory interpretation of required aerodynamic and dynamic phenomena.

The mathematical model described in this paper is related to three-dimensional (space) geometry and kinematics, and rigid body dynamics and fluid dynamics through which it moves.
