Stability and control characteristics of model helicopters

Visagie, Jonathan Gerhardus (2004-12)

Thesis (MScEng)--University of Stellenbosch, 2004.

Thesis

ENGLISH ABSTRACT: A need exists for the development of an unmanned rotorcraft capable of autonomous flight, as would be required for the survey of high voltage electricity supply lines. A program was initiated at the University of Stellenbosch in December 2002 in order to develop such an aircraft. The first goal of this thesis was the development of software that could calculate the stability and control derivatives of a model helicopter. These derivatives could then be used in the formulation of an appropriate helicopter control strategy. The second goal of the thesis was an investigation of the stability and control characteristics of model helicopters. The trim settings of the helicopter were required in the calculation of the stability and control derivatives. A computer program was developed to determine the trim settings of a helicopter in forward flight. Another program was developed to calculate the stability and control derivatives, using the results of the trim analysis. The trim analysis was based on the assumption of negligible coupling between the longitudinal and lateral modes of motion. The method proposed by Bramwell (1976) was used to perform the trim analysis. The stability and control derivatives were calculated by obtaining the trim settings from the trim analysis. These derivatives were then used to solve the roots of the characteristic equations of the longitudinal and lateral modes of motion. The stability of the helicopters were investigated firstly by examining the stability derivatives and secondly through root-loci analyses. The most important results were the following: • The root-loci analyses indicated that a helicopter without a horizontal stabiliser suffered from instability of the phugoid mode. It was also found that the short-period motion of these helicopters was heavily damped. Fitting a horizontal stabiliser to these helicopters caused the phugoid motion to become stable even at low speeds. This was achieved at the cost of a reduction in short-period motion damping. • The periods of the lateral and longitudinal motions were smaller than those found on full-scale helicopters. This was attributed to the small mass and inertia properties of the model helicopters. An increase in speed is generally accompanied by an increase in the stability of the helicopters. This could be attributed to the effective operation of the tail surfaces at higher speeds. • The axial climbing speed of a helicopter is influenced by the rotor speed. A low rotor speed allows higher climbing velocities at a given power setting. This was due to lower induced power losses at low rotor speed, assuming that no blade stall occurs. • The rotor speed does not influence the incremental amount of power (M:,) required to achieve a certain climbing velocity, due to the fact that the profile power losses are constant for a certain rotor speed. • The simplified horseshoe-vortex theory can be used to analyse the downwash angle at the horizontal stabiliser if the helicopter is in high-speed forward flight.

AFRIKAANSE OPSOMMING: Daar is tans 'n vraag na die ontwikkeling van onbemande rotor-vlerk vliegtuie wat die vermoë beskik om hulself te beheer. Hierdie tipe vliegtuie sal gebruik word om byvoorbeeld hoë-spannings elektrisiteitverskaffingsdrade na te gaan. 'n Program is in Desember 2002 by die Universiteit van Stellenbosch begin om sulke vliegtuie te ontwikkel. Die eerste doel van hierdie tesis was om sagteware te ontwikkel wat die stabiliteit- en beheerafgeleides van 'n model helikopter kon bereken. Hierdie afgeleides kan dan gebruik word om 'n gepaste helikopter beheerstrategie saam te stel. Die tweede doel van die tesis was om die stabiliteit- en beheerseienskappe van model helikopters te ondersoek. Die berekening van die stabiliteit- en beheerafgeleides van die helikopter berus op die beheerinsette benodig om die helikopter in ewewig te hou (trim). 'n Rekenaarprogram is ontwikkelom hierdie beheerinsette vir 'n helikopter in voorwaartse vlug te bereken. 'n Ander program is ontwikkelom die stabiliteit- en beheerafgeleides te bereken met behulp van die ewewig beheerinsette. Die analise van die helikopter in ewewig berus op die aanname dat die grootte van die koppeling tussen die longitudinale en laterale beweginsmodusse weglaatbaar klein is. Die beheerinsette van die helikopter in ewewig tydens voorwaartse vlug is bereken deur van Bramwell (1976) se metode te gebruik. Die stabiliteit- en beheerafgeleides is bereken deur van hierdie beheerinsette gebruik te maak. Die afgeleides is gebruik om die wortels van die karakteristieke vergelykings van die longitudinale en laterale bewegingsmodusse te bereken. Die stabiliteit van die helikopters is eerstens beoordeel deur die stabiliteitsafgeleides te ondersoek en tweedens deur middel van 'n wortel-lokus analise. Die belangrikste resultate is as volg: • Die wortel-lokus analise toon dat 'n helikopter sonder 'n horisontale stabiliseerder phugoid-onstabiliteit (Iangperiode onstabiliteit) het. Die kort-periode beweging van hierdie helikopters het verder groot hoveelhede demping aangetoon. Die phugoid-beweging kon selfs teen lae snelhede gestabiliseer word deur 'n horisontale stabiliseerder aan te heg. Hierdie stabiliteit is egter bereik ten koste van die demping van die kort-periode beweging wat verminder is. • Die periodes van die longitudinale en laterale bewegings is kleiner gewees as vir volskaal helikopters. Dit kan toegeskryf word aan die klein massa en inersie van die model helikopters. • Die stabiliteit van die helikopter is in die algemeen verbeter soos die snelheid verhoog. Dit kan toegeskryf word aan die beter werking van die stert teen die verhoogde snelhede. • Die klimtempo van die helikopter word beïnvloed deur die hoofrotor snelheid. 'n Lae hoofrotor snelheid laat 'n hoër klimptempo toe teen 'n spesifieke drywinginset. Dit is as gevolg van die laer geïndusseerde drywingsverliese teen die laer hoofrotor snelheid. Daar word aanvaar dat die lugvloei oor die lem nie staak nie. • Die hoofrotor snelheid beïnvloed nie die inkrimentele drywing (M,,) wat benodig word om 'n sekere klimtempo te bereik nie. Dit is as gevolg van die konstante drywings verliese teen 'n sekere hoofrotor snelheid. • Die vereenvoudigde perdeskoenwerwel teorie kan gebruik word om die afspoel hoek by die horisontale stabiliseerder te bereken indien die helikopter in hoë-spoed voorwaartse vlug is.

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