03-11-2012, 04:52 PM
Constructing & Simulating a Mathematical Model of Longitudinal Helicopter Flight Dynamics
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ABSTRACT
This paper will present detailed procedure of how to construct a basic mathematical model
that represents general longitudinal helicopter flight dynamics. The procedure will start from
linearizing the translational and rotational dynamics and rotational kinematics equations of
motion using the small perturbation theory. There are certain assumptions made for the sake
of simplifications. The next step is to construct the fundamental linearized form for describing
the stability and response of a small motion of a helicopter around a trim condition. In order to
simulate the results, basic input data from an existing helicopter will be used. The last step is
will be simulating the results using MATLAB Simulink program.
Introduction
HE helicopter is specific in regards to other transportation means, not just by its structure but also by its motion
possibilities. The helicopter can move vertically, float in the air, turn in place, move forward and lateral, and can
perform these movements in combinations. Because of this, helicopter dynamics modeling is a very complex problem.
In the present, problems in helicopter flight dynamics are mostly solved in aid of modern computers and software. 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 with the use
of simple formulas. Certain assumptions are taken into consideration in order to simplify the modeling procedure, such
as that atmospheric and other disturbances are ignored.
Helicopter Controllers
A helicopter is generally and mainly controlled by three operating controls. Those controls are throttle, the
collective pitch controller and the cyclic pitch controller. The collective pitch angle of a rotor blade is the angle
between the chord line and a reference plane determined by the rotor hub or the plane of rotation (Figure 1). The cyclic
pitch angle is between the rotor disk and the air speed caused by tilting the rotor disk either up (positive) or down
(negative) (Figure 2). The throttle main purpose is to control the angular speed of the main rotor. In this helicopter
model, we are going to assume constant angular speed in order to focus more on the effect of the other controllers.
The DRA (RAE) Research Puma, SA330 Input Data
For the purpose of simulating the above
mathematical model, the DRA Research Puma,
SA330 data will be used. The SA330 Puma is a
twin engine, medium support helicopter in the 6
tones category, manufactured by Eurocopter
France (ECF), and in service with a number of
civil operators and armed forces, including the
British Royal Air Force.
The stability and control derivatives predicted
by STAGE Helisim simulation software are
graphed as function of forward speed (knots). The
flight conditions correspond to sea level (ρ=1.227
kg/m3) with zero sideslip and turn rate, from hover
to 140 knots.
Conclusion
In this paper we have gone through the procedure of how to construct basic mathematical model that represents
general longitudinal helicopter flight dynamics. The procedure started with linearizing the translational and rotational
dynamics and rotational kinematics equations of motion using the small perturbation theory. The next step was to
construct the fundamental linearized form for describing the stability and response of a small motion of a helicopter
around a trim condition. In order to simulate the results, input data and derivatives from an existing helicopter was
used. The final step was simulating the results using MATLAB Simulink program. The design is still not fully
developed due to the fact that we don't have more information available about the performance specifications of the
Puma helicopter.