ESL Online Examples

The online examples are taken from the examples included with ESL-Lite, modified slightly for use online.

• ARRST1 - Aircraft Arrester Gear System
• BENCH3 - Van der Pols equation
• FRICT2 - Car Suspension System
• PHYSBE - Cardio-vascular Simulation

ARRST1 - Aircraft Arrester Gear System

The object of the 'Aircraft Arrester Gear' is to bring to a halt a moving aircraft that would otherwise over-run the end of the runway. It is similar in principle to the arresting gear used on aircraft carriers.

The original aims of this investigation were to determine the aircraft masses and speeds that could be accommodated without exceeding the working limits of the cables or the 'water squeezer' damper. From a simulation point of view, this problem is of particular interest because the damper is described by a table of 16 experimentally measured values, and discontinuities occur as the cables change from being slack to being under tension. The ESL second order function generator, AFGEN2.ESL, is used to model the non-linear damper and 'IF' statements to implement the discontinuities.

A plot obtained from running the program shows: aircraft position (x ft), speed (x' ft/s) and acceleration (x'' f/s/s) for two different initial aircraft speeds.

BENCH3 - Van der Pols equation

This program illustrates many of the features of ESL through a solution of the Van der Pol equation. A detailed line-by-line description of the program will be found in the 'ESL Development Guide' section 3.3.

A plot of x and x’ against time and a phase-plane plot of x’ against x are produced.

FRICT2 - Car Suspension System

This program demonstrates the use of the ESL COULOMB friction submodel in a practical situation. A vehicle suspension system example is considered. The behaviour of a leaf spring suspension arrangement at one wheel of the vehicle is simulated as the vehicle is driven over a small step in the road surface. It is assumed that there exists friction in the suspension arrangement between the wheel (unsprung mass) and the vehicle body (sprung mass). This friction is determined by the COULOMB submodel and fed into the equations of motion of the system.

Plots of the relative positions of the vehicle body (x) and the wheel axle (y) immediately after the step is encountered and effective force (force) and friction force (friction) are produced.

PHYSBE - Cardio-vascular Simulation

PHYSBE is a model of the blood circulatory system in the human body. Each element of the circulatory system (eg lungs, arms, etc and the various cavities of the heart) are described by lumped parameter equations, relating blood flow to pressure, inflow and outflow resistance and compliance. The four valves within the heart are included and the entire system is driven by changing the compliance of the left and right ventricles as a function of time (i.e. a simulated heart beat). The model allows analysis of blood flow at different positions in the body to be displayed.

PHYSBE is a well documented standard benchmark, and has often been used to compare different computer simulation techniques. A detailed description of PHYSBE is given by J McLeod in his paper 'PHYSBE: A Physiological Simulation Benchmark Experiment', Simulation, December 1966. The requirements for a non-linear driving function, discontinuous operation due to opening and closing of valves, and the modular construction of the system, allow the features of ESL to be displayed.

The plot obtained when this example is run shows right ventricle, P2, and lung, P3, pressure.