**5. Conclusion**

In this chapter, the authors have developed a method of discrete vortex cylinders based on the Shaydakov's disk vortex theory. The capabilities of the discrete vortex cylinder method are demonstrated using a helicopter balancing program based on a "semi-rigid" model of the main and tail rotors. Data from numerical calculations are proposed with experimental data from actual flights. Simulations have been conducted. We found the following:


3.The results showed, repeating the results of the classical impulse rotor theory on hover mode in the plane of the rotor and in the wake far behind the rotor.

*br* chord at the blade cross section

*сL*,*cD* section lift and drag coefficients *dJxb*, *dJyb* elementary sectional inertial forces

*Jh* helicopter moment of inertia *Mh*, *Gh* helicopter mass and weight *M*ð Þ *ξ*, *η*, *ζ* vortex elements location point *Mt* aerodynamic flap moment *K<sup>β</sup>* flap hinge spring constant

*dtr*, *dqr* elementary sectional aerodynamic forces *h* distance from disk to point A location plane *J*1, *J*<sup>2</sup> Shaidakov's integrals for a semi-infinite

*Discrete Vortex Cylinders Method for Calculating the Helicopter Rotor-Induced Velocity*

*Jg* blade rotational inertia, first moment of inertia

*RMR*, *RTR*, *Rf* , *MMR*, *MTR*, *Mf* main, tile rotors, fuselage forces and moments

*v*1*<sup>b</sup>* , *v*2*<sup>b</sup>* the induced velocity in hover (at the rotor disk, in the far wake)

*v*1*<sup>b</sup>*, *v*2*<sup>b</sup>* rotor induced velocity in hovering (at the rotor

*βb*,*β*0, *βc*1, *βs*1, … , *βcn*, *βsn* blade flap angle, Fourier series coefficients of *β<sup>b</sup>* Γ, *γ* vortex element circulation, circulation intensity

formula (*δ* 6¼ 0)

, *vz*<sup>1</sup> rotor-induced velocity in *Ox*1*y*1*z*<sup>1</sup>

disk, in the far wake)

calculated by the Shaydakov's transcendental

j j *δ*

*<sup>V</sup>*<sup>~</sup> , <sup>~</sup>*<sup>v</sup>* related speeds, *<sup>V</sup>*<sup>~</sup> <sup>¼</sup> *<sup>V</sup>=v*1*<sup>b</sup>*, <sup>~</sup>*<sup>v</sup>* <sup>¼</sup> *<sup>v</sup>=v*1*<sup>b</sup>*

*γh*, *ϑ<sup>h</sup>* the helicopter angles of pitch and roll *δ* the inclination angle of the vortex cylinder is

*v* : *vx*, *vy*, *vz* rotor-induced velocity in *Oxyz*

*α <sup>f</sup>* fuselage attack angle

*<sup>V</sup>*<sup>~</sup> <sup>¼</sup> 2 1ð Þ � sin j j *<sup>δ</sup>* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *sgn<sup>δ</sup>* sin <sup>2</sup>*α*þ2 sin *<sup>α</sup>* cosð Þþ *<sup>α</sup>*þ*<sup>δ</sup>* sin *<sup>δ</sup>* cos <sup>2</sup>ð Þ *<sup>α</sup>*þ*<sup>δ</sup>* ð Þ <sup>2</sup>� sin j j *<sup>δ</sup>* <sup>p</sup> , *sgn<sup>δ</sup>* <sup>¼</sup> *<sup>δ</sup>*

*ρ* air density

*ψ<sup>b</sup>* blade azimuth

*<sup>μ</sup>* <sup>¼</sup> *<sup>V</sup>* cos *<sup>α</sup>* rotor advance ratio

*θ*0, *θc*1, *θ<sup>s</sup>*<sup>1</sup> main rotor controls Ω rotor rotational speed *ψ* discrete cylinder azimuth

Δ*ψ*, Δ*r* discrete vortex dimensions

*ω* : ω*x*, ω*y*, ω*<sup>z</sup>* helicopter angular velocity

*ds* <sup>¼</sup> sin *<sup>τ</sup>* direction of the vector *ds*

elementary oblique vortex cylinder

*CDf* ,*CLf* ,*CQf* ,*CZf* ,*CMxf* ,*CMyf* , fuselage coefficients

*ds* vortex element

*DOI: http://dx.doi.org/10.5772/intechopen.93186*

*lg* flap hinge offset *Oxyz*, *Ox*1*y*1*z*1,*Oryψ* coordinate systems *R* rotor radius

*V* flight velocity

*v*<sup>1</sup> : *vx*<sup>1</sup> , *vy*<sup>1</sup>

*dξ*

**117**

*ds* <sup>¼</sup> cos *<sup>τ</sup>*, *<sup>d</sup><sup>ζ</sup>*

*r* the cross-sectional radius *S <sup>f</sup>* , *Lf* fuselage area and length *Sg* first moment of inertia


To study the effectiveness of the method of discrete vortex cylinder embedded in the helicopter trimming computer program. The calculations are performed with the original data of the helicopter "ANSAT." The program allows calculating the trimming characteristics of helicopter rotor: aerodynamic performance, the loading of the blades.

The method of discrete vortex cylinders is successfully used for calculating inductive velocities in the aeroelasticity blade model for ANSAT helicopter main rotor loads calculation (for example, see [7]).
