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 Measuring distance
Measuring direction
Pros and cons |
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| Navigation is a problem that is almost as old as the hills |
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In order to complete this challenge successfully, the teams must devise ways of measuring the direction in which they are travelling and the distance they have travelled.
Measuring distance
Both teams employ a similar method to construct an odometer – a device that measures distance. They measure the circumference of one of their vehicle's wheels to determine how far the vehicle will travel on one complete turn of the wheel. Then all they have to do is count the number of complete rotations and multiply that number by the circumference of the wheel.
Perhaps the most obvious way of measuring the circumference of a wheel is to wrap a piece of string around it and then measure the string. However, this is a bit fiddly and might be tricky with a really big wheel.
The mathematical way of calculating the circumference of a circle is to use a number called pi (the Greek letter  ). Pi is arrived at by dividing a circle's circumference by its diameter. The ratio of a diameter to a circumference is always the same: 3.142 (to three decimal places). So, to calculate the circumference of a circle, you can measure its diameter and multiply it by pi.
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| TC Graham originally planned a version of the ancient Chinese south-pointing chariot |
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| It would require two matching sets of differential gears ... and a certain amount of maths |
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| In the end the team opts for a much simpler design based on a turntable |
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Measuring direction
The gyrocompass: inertia and momentum
The Hammerlocks hope to keep track of direction using a gyroscopic compass. This will be a simpler version of the gyrocompasses used on most ships and aeroplanes.
A gyrocompass consists of a spinning wheel mounted on moveable frames called gimbals. Gimbals support the gyro's weight but allow movement in both the horizontal and vertical planes. Newton's first law of motion states that an object in motion tends to continue in motion in a straight line (or about an axis, as is the case with our spinning gyro) unless acted on by an outside force. When a vehicle in which a gyrocompass is mounted changes direction, the gimbals move but do not transfer force to the spinning gyro, which holds its position, providing a constant against which the change in direction can be measured. See More Info for details of a more extensive explanation of how gyroscopes work.
The resistance an object has to a change of velocity (speed in a given direction) is called inertia. If an object is stationary, it 'likes' to stay still; if it's moving at a certain speed and in a certain direction, it 'wants' to keep going at that speed and direction. A gyrocompass is an inertial navigation system. It makes use of a gyroscope's inertia – its tendency to keep pointing in the same direction.
The Hammerlocks add weight to the circumference of their gyro wheel to increase its momentum. Momentum is a way of measuring inertia. It can be defined as 'mass in motion', and is equal to an object's mass multiplied by its velocity. (See Rapid Fire science for more about mass and velocity.) The more momentum a gyro has, the more inertia it has, and the better it is able to resist any torque (turning force) transmitted through the gimbals (see Mud Monster science for more about torque).
South-pointing chariots
TC Graham originally planned to build a version of the ancient Chinese south-pointing chariot. This uses an arrangement of gears to maintain an arrow pointing in a constant direction. As the chariot turns, the gears cause the pointer or arrow to turn by an equal and opposite amount, giving a fixed reference point and allowing blind navigation. Such machines were called 'south-pointing' because south was the favoured reference point for Chinese culture, as north is to us nowadays.
In the event, the team rejects Graham's idea and goes for the much simpler option of jacking up the whole vehicle and rotating it on a giant turntable. The turntable is mounted on a large metal plate, which remains fixed in position. A pole welded to that plate runs up through the centre of the turntable and into the bus. Handles are attached to the pole, giving the Academics a fixed point against which they can push to rotate the bus. Marks on the floor of the bus allow them to keep track of how far they have turned around the static pole.
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| It is difficult to calculate location if you are turning on an arc ... |
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| ... but much easier if you are turning on a point |
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Pros and cons
The Hammerlocks
The Hammerlocks have back-up plans for direction finding. Firstly they hang a pendulum from the bus's roof – the idea being that the pendulum will carry on swinging in the same direction regardless of the vehicle's direction. Secondly, they tune a radio to pick up a signal from an external radio transmitter. As the bus turns, the signal is lost. Turning the radio's aerial until the signal is picked up again should give the approximate angle of a turn. Thirdly, they have a long mechanical arm with which they can detect obstacles.
On the other hand ...
The team need back-ups because they doubt the accuracy of their gyrocompass. A gyrocompass is a precision instrument and it's a very tall order to build one from scrap.
When the Hammerlocks turn, they are moving forward as well as left or right. This makes pinpointing their position on the map after a turn difficult, even though they know the turning circle of their vehicle.
Academics Anonymous
Because the Academics are rotating their bus on a point, working out their position is much simpler. All they have to do is measure the angle of a turn and then measure the distance they travel in a straight line.
On the other hand ...
Turning the big, heavy bus proved extremely difficult, particularly because, from inside, the team were unable to detect when the bus was level.
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