BackgroundExplore the contents of this article with a free Wolfram System Modeler trial. Today, many helicopters launch from and land on ships at sea. Some are conventional helicopters, both commercial and military, and some are drones. In Wolfram System Modeler, we now have a system for simulating helicopter landings and launches that includes waves and ships. The models have been used for the design of mechanical parts, autopilots, landing criteria, and operational limits.
Major components of the systemThe aim has been to develop a model with an accurate depiction of the waves, ship motion, and helicopters in such a way that the results can be used not only qualitatively but also quantitatively in real industrial applications. The first task is to calculate the motion of the landing platform mounted on the ship's deck. There is commercially available historical wave data for different seas and oceans. Since access to this data is expensive, we will instead describe the waves mathematically. A model of the forces on the ship's hull was developed with classical analytical theory. With the waves and ship hull forces, the motion of the ship's landing platform can be calculated. If we assume that the helicopter landing does not influence the landing platform motion, the system is simplified. We speed up the simulation by storing the motion in a database for the different wave heights, lengths, and directions, and the ship's speed. Typically the database will include wave heights of 1, 2, 3, and 4 m; wave directions 0, 30, 60, 90, 120, 150, and 180 degrees; wave lengths 100, 150, and 200 m; and ship speeds of 5 and 10 knots. The helicopter was modeled with the MultiBody library. It includes mechanical parts such as rotors with gyroscopic effects and landing gear with hydraulic dampers. Friction models for wheel-deck interface and flexible beams for the rotor blades have been developed. We have also developed a simple autopilot where the landing algorithm is implemented and tested. For one application, the model has been run with the actual autopilot as hardware in the loop.
Explore the contents of this article with a free Wolfram System Modeler trial. Mathematical modeling is not just used for understanding and designing new products and drugs; modeling can also be used in health care, and in the future, your doctor might examine your liver with a mathematical model just like the one researchers at AstraZeneca have developed. The liver is a vital organ, and currently there isn't really a way to compensate for loss of liver function in the long term. The liver performs a wide range of functions, including detoxification, protein synthesis, and secretion of compounds necessary for digestion, just to mention a few. In the US and Europe, up to 15 % of all acute liver failure cases are due to drug-induced liver injury, and the risk of injuring the liver is of major concern in testing new drug candidates. So in order to safely monitor the impact of a new drug candidate on the liver, researchers at the pharmaceutical company AstraZeneca have recently published a method for evaluating liver function that combines magnetic resonance imaging (MRI) and mathematical modeling---potentially allowing for early identification of any reduced liver function in humans. Last year, Wolfram MathCore and AstraZeneca worked together on a project where we investigated some modifications of AstraZeneca's modeling framework. We presented the promising results at the ISMRM-ESMRMB Joint Annual Meeting, which is the major international magnetic resonance conference. In this blog post, I'll show how the Wolfram Language was used to calculate liver function and how more complex models of liver function can be implemented in Wolfram System Modeler.
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