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Tugs of War science
 Buoyancy
The Archimedes' screw
Paddles and slippage
Pros and cons |
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| Archimedes made his famous discovery in a public bath |
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| An object that is less dense than water will float |
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| An object that is more dense than water will sink |
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Buoyancy
Objects that float are described as being 'positively buoyant'. Objects that sink are negatively buoyant. Objects that neither sink nor float – in other words, that will stay at the same depth unless another force acts on them – are neutrally buoyant.
Buoyancy was explained by Archimedes, the Greek mathematician, in what is known as Archimedes' principle: any object that is wholly or partly immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by that object. Archimedes first got the hang of this, famously, when he stepped into a public bath and saw it overflow.
Whether an object floats or sinks, therefore, depends not only on its weight but also on the amount of water it displaces. A ship floats because the weight of water that it displaces is equal to the weight of the ship.
The force created by the displacement of water is called the buoyant force. It acts in the opposite direction to gravity, which is pushing the ship down. The strength of the buoyant force depends on an object's volume – the greater the volume, the greater the amount of water displaced, and the greater the buoyant force.
So the crucial factor in determining an object's buoyancy is its density: the relationship between its weight, which is pushing it down, and its volume, which creates the buoyant force pushing it up. An object that is more dense than water – in other words, that weighs more than an equivalent volume of water – will sink. An object that is less dense than water will float.
The Boat Buoys' tug consists of two steel skips and a heavy tractor also mainly made of steel. Steel is much heavier than water. But the vast majority of the skips' volume is taken up with air. The combined density of the skips and the air is much less than the density of water, so the tug floats – as long as the skips don't leak.
The same principle applies with purpose-built ships. Because a ship contains a lot of air, on average it is much less dense than water – the same weight is contained in a much greater volume. This and the broad shape of a ship's hull (or even a skip) mean that very little of a ship has to be submerged before it has displaced its own weight.
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| The Martial Mechanics make use of another of Archimedes' discoveries: the water-lifting screw |
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The Archimedes' screw
The Martial Mechanics decide to use another of Archimedes' famous discoveries: the water-lifting screw or auger. This consists of a spiral screw or helix which fits tightly inside a tube. If one end sits in water, rotating the screw will cause water to become trapped between the spiral curve and the inside of the cylinder, and as rotation continues, water will be drawn up the cylinder. This device was first used to get water from the river up the bank and into the fields. It is the forerunner of the modern wood-screw.
The Martial Mechanics plan to use two variants on this theme to propel their tug through the water. They attach two rows of oil barrels along each side of their chassis to provide buoyancy. But the helixes are attached outside the tubes, as the aim is not to collect water but simply to push it backwards. In other words it acts as a propeller. Because every force or action results in an equal and opposite reaction (Newton's third law of motion), the craft is propelled forwards.
The team needs to take care that the pitch of the vanes of their screws is just right. If the angle is too steep, the screws will just churn up the water; if too shallow, not enough water will be moved.
The screws will also provide the steering on the Martial Mechanics' craft: to turn, they will slow down the screw on one side. This is a bit like skid steering on land – see Mud Monsters science.
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| If the paddles are mounted too high, the craft will waste energy making spray |
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| If they mount the paddles too low, they'll waste energy |
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Paddles and slippage
The Boat Buoys decide to use paddle-wheels to power their craft. There are various factors they need to consider.
Firstly, a big paddle wheel is better than a small one because the power stroke of each blade through the water will be longer, therefore providing more thrust. Secondly, paddle wheels are most efficient when the blades make a relatively shallow stroke through the water, otherwise energy is wasted pushing the blade down through the water and pulling it back out again.
The team also faces the problem of slippage. A wheel on dry land will normally move forward a distance more or less equivalent to the circumference of the wheel for every rotation. This is because there is plenty of friction between the ground and the wheel. But water is much less dense than land and so doesn't provide such a good base to push against. So for every rotation of a paddle wheel, there is slippage. The bigger the paddle blades, the smaller the slippage. The team are aiming for the biggest blades compatible with the size of their wheels and the power of their engine.
It's also important that the paddle wheels don't turn too quickly. With each stroke, water is pushed backwards. Before the next blade begins its power stroke, it is important that new water has had time to take its place, or the blade will be pushing a mixture of air and water. Air and water is even less dense than water alone, so slippage will increase and less thrust will be generated.
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| The Martial Mechanics' design features a long and complicated drive-line ... |
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| ... which is vulnerable to failure at a number of points |
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Pros and cons
Boat Buoys
Paddle power is a tried-and-tested means of propulsion and is quite simple mechanically, so there isn't too much to go wrong.
A tractor is the perfect power source, and the paddles can be mounted straight onto the existing wheel rims.
On the other hand ...
The skips leak! If the Martial Mechanics hadn't generously agreed to allow the Boat Buoys to use a bilge pump, this machine would have sunk before it reached the start line.
The Boat Buoys have stability problems. Their craft's centre of gravity is initially much too high (see Monowheel science for more about the centre of gravity) – you need more weight at the bottom than the top, and skips have the opposite. Adding oil drums as stabilisers keeps the craft on an even keel, but also increases its overall buoyancy, so it sits higher in the water. This means that the paddles are just skimming the water and that the centre of gravity is even higher! To remedy this, extra ballast is added in the form of sandbags, making the craft even heavier than it was already and so reducing power.
Martial Mechanics
The Archimedes' screw provides continuous thrust along the whole length of the craft.
The Martial Mechanics' craft is lighter and quicker, and has more pulling power.
Its low centre of gravity ensures stability.
On the other hand ...
The design features a long and complicated drive-line, which is vulnerable to failure.
The screws provide propulsion, buoyancy and steering. Placing all your eggs in one scrap basket is always a high-risk strategy.
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