Points for Consideration (Includes Further Intense Maths & Physics

POINTS FOR CONSIDERATION

• In all designs, in which a fundamental aspect is formed of mechanical pistons, Gas Pressure Laws are a core principle. In any of the example designs featured, the compression of a piston is utilised so as to hinder the initial force implementing that compression, and hence bring it to a stop, before finally returning the system to its original state. • In the context of these designs, the tilting motion of the tower will exert a considerable downward force, thereby compressing the pistons on the side to which the tower is leaning. This compression leads to a reduction in the volume of the gas inside the piston, in turn leading to an increase in the frequency with which the gas molecules collide with the walls of the cylinder. • In addition, the exertion of the forces causing the compression will of course transfer a quantity of Mechanical Energy into the gas, raising its Internal Energy and in turn, therefore, its temperature. • This is because, as the gas absorbs this Mechanical Energy, its molecules each up-take a certain fraction of it, and so their average individual Kinetic Energy will increase (remembering that gas molecules are forever in a state of random motion, while ever they possess Kinetic Energy). • The combined effect of the increased temperature (Pressure Law) and the decreased volume (Boyle’s Law) will therefore lead to a drastic increase in pressure. • This is an Adiabatic Change, in which all of the gas’ gain in Internal Energy comes from the Mechanical Work originally done upon it, and no additional thermal energy is supplied or removed. • To add to this, bearing in mind that the gas stored inside the piston will not behave entirely like an Ideal Gas, the compression of its volume will eventually begin to strain the elastic intermolecular forces of the gas, and the Potential Energy of these forces will therefore increase as well. • This will add to the pressure of the gas as it pushes back out from the inside. Referring back to the context of these designs, this will have the effect of pushing back against the leaning of the tower, therefore beginning to convey it back into its original position.

PISTON COMPRESSION

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Retrieved: April 9th 2012

• Indeed, the pontoon on that same side will inevitably undergo some degree of submersion as well, meaning a greater volume of water will have been displaced in the process. The increased Buoyant Force that consequently arises from this will therefore add to the aforementioned effect of righting the tower back up.

Incidentally, attention must be drawn to one particular point raised in relation to the Internal Energy and Temperature:

• As a certain force acts to compress the gas inside the piston cylinder, it will do work upon that gas, and consequently cause it to absorb a certain quantity of Mechanical Energy equal to:

Where:

����= Mechanical Energy transferred into the system by external forces (Joules, J) ����= Pressure exerted (Pascals, Pa) ∆����= Resulting Volume Change due to compression (m3)

As aforementioned, this energy will lead to an increase in the gas’ temperature, due to the increase in average Kinetic Energy of the molecules, as follows:

Where:

���� = Total energy absorbed by the gas, equalling the Mechanical Energy (P ∆V) in the previous formula (J) ����= Mass of the gas inside the piston cylinder (kg) ����= Specific Heat Capacity of the gas (J.kg-1.K-1) ∆����= Arising Temperature rise (K) In view of this, it therefore becomes essential that the pistons are in some way kept cool, so as to prevent structural damage to these pistons in the form of thermal expansion or even hardening.

• One way in which this may be achieved is to use a heat-dissipating lubricant, which would of course simultaneously help to reduce friction as well, hence reducing the effect of over heating further. This does, however, lead us directly into the second detriment that is attributable to the use of pistons. Any lubricants used will be vulnerable to getting washed away or chemically-corroded by the salt water.

• Moreover, the seals on these pistons may also leak, and water droplets or vapour contaminating the gas inside the piston will of course impinge upon its performance, and subsequently damage the piston itself by causing corrosion, hence rendering the device useless for later applications. Therefore: ∆���� =����/(��������) =����

Tensile Steel Cables:

• Having a very high Young’s Modulus (Stiffness Co-Efficient in Tension and Compression in an elastic material) of 206GPa9, steel is far from ductile: though not necessarily brittle, it is certainly extremely stiff. Effectively, Young’s Modulus is the ratio, or constant of proportionality, between a material’s Strain, and the Stress causing it (which, due to Hooke’s Law, are directly proportional to one another). As such, with this ratio being so high, it is clear that a large degree of Stress will result in a small degree of Strain. That is, even very large forces will only stretch the steel by very small amounts.

• The Young’s Modulus can be calculated using:

Where:

����= Young’s Modulus (Pa) ���� = Stress (Applied Force per unit of cross sectional area perpendicular to the axis in the direction of theApplied Force, Pa) ���� = Strain (Change in length due per unit of original length: deformation due to applied stress, along the axis in the direction of the Applied Force)10

• As such, when stressed by the relative movement between tower and base, the cables will not afford any sort of give, and instead will come to an abrupt stop. Apart from failing an essential Specification point, on account of not slowing down the tower’s movements gradually, this will produce a sudden, sharp and hence intense impact force known as ‘Snatch’, the consequence of which is the frightening likelihood of the cable snapping.

• More to the point, in having such a high Modulus of Resilience (the quantity of Strain Energy absorbed by the steel per unit volume, for a given Stress Force acting upon it), a substantial quantity of energy will be absorbed by the steel cable before it finally snaps. This means that, when it does eventually go, all that energy is released, and the event is therefore highly dangerous. It is usually characterised by a high-speed recoil of the cable, capable of inflicting serious, even fatal injury to anyone in the way.

EFFECTS OF A CABLE-SNAP

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• Furthermore, the weight of the steel cable will Retrieved: April 4th 2012 unfortunately make it susceptible to sinking;in turn making recovery of the cable difficult once the tower has been sunk.