Understanding Pendulums A Brief Introduction
Despite their apparent simplicity, the behaviour of pendulums can be remarkably complicated. Historically, pendulums for specific purposes have been developed using a combination of simplified theory and trial and error. There do not appear to be any intr
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Engineering
7.1 Introduction Pendulums are an essential component of some engineering structures. Three of these are described in this chapter. These are the Watt steam governor, cable cars, and tension leg platforms. The Watt steam governor, also known as a centrifugal governor or fly ball governor, and in French r´egulateur a` boules (ball governor) was invented by James Watt to regulate the supply of steam to his steam engines and hence keep the speed reasonably constant, irrespective of the load (Lineham 1914). A Watt steam governor fitted to a Boulton and Watt steam engine ca. 1810 is shown in Fig. 7.1. It is not clear when James Watt started to use his steam governor. Denny (2002) states that it was in 1788, but the Science Museum in London have a Boulton and Watt steam engine, dated 1781, which is fitted with a Watt steam governor. Other applications for what is then known as the Watt governor include windmills, lighthouses and telescope drives (Denny 2002; Tobin 2003). Figure 7.2 shows a Watt governor fitted to a corn mill. Cable cars are widely used in mountainous areas for transporting people and freight up and down mountains. A cable car has an inline set of grooved wheels that run on a fixed cable between two stations (Fig. 7.3). A fixed cable is usually supported by pylons between the stations so that it follows the contour of the mountain (Fig. 7.4). A gondola is suspended below the wheel set by a girder that is fixed to the gondola, but pivoted to the wheel set. The gondola is therefore the bob of a pendulum. The pendulum must be correctly designed for satisfactory operation of the cable car. An important design requirement for the platforms used offshore for oil and gas exploration and production is to avoid excitation of structural resonances at wave passing frequencies. These are typically in the range 0.08–0.4 Hz (Pook and Dover 1989; Patel and Witz 1991). A fixed platform is a structure standing on the sea bed. Avoidance of structural resonances in fixed platforms becomes increasingly difficult as the water depth increases, and they are not normally used if the depth is L.P. Pook, Understanding Pendulums: A Brief Introduction, History of Mechanism and Machine Science 12, DOI 10.1007/978-94-007-1415-1 7, © Springer Science+Business Media B.V. 2011
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100 Fig. 7.1 Watt steam governor fitted to a Boulton and Watt steam engine ca. 1810
Fig. 7.2 Watt governor fitted to a corn mill
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Engineering
7.1
Introduction
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Fig. 7.3 Cable car and station at Aiguille du Midi, France
Fig. 7.4 Cables and pylon for cable cars at Stresa, Italy
greater than about 200 m. For deeper water tension leg platforms are now widely used. A tension leg platform is a floating platform which is held to the seabed by tethers. Tension in the tethers holds the platform below its equilibrium floating level. A tension leg platform is therefore an inverted pendulum. A typical tension leg platform is shown schematically in Fig. 7.5. A tension leg platform was first used to produce oil in 1984 (Patel and Witz 1991).
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