Drayton Manor Theme Park: Centrepedial Force

Drayton Manor Theme Park.

On the 20th October 2004 I visited the Drayton Manor theme park, the park having many exciting opportunities to explore the scientific principles of speed, energy and force. I have identified two aspects of physics relating to two different rides.

1st Aspect of physics – centripetal force on the ride Cyclone.

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I get into my carriage, an attendant comes round and slides the door across, the first thing I notice about the inside is that there are no seat belts, this worried me as I had seen the ride in-action and did not want to fall about the carriage as the ride spins upside down. The ride began to spin round and build up speed and I felt as though I was about to fly out of my seat, as it got faster it began to lift off the ground and turn so that you were eventually vertical. When you were at the top of the circle the carriage was completely upside down, as shown in the picture below, I did not fall about the cage as I had thought but felt almost glued to the floor. I found it difficult to move my arms, legs and even to catch my breath.

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The fact that I did not fall about the carriage as I had originally thought can be explained by a physics concept called centripetal force.2

Newton’s first law of motion states that ‘Every object in a state of uniform motion tends to remain in that state of motion unless an external force is applied to it.’3 This means that objects like to keep doing what they’re doing, if an object is at rest it will stay at rest unless acted on by a resultant force and an object travelling in a certain direction will carry on travelling in that direction at the same velocity unless acted on by a resultant force. When moving in a circle the direction you are travelling is at a tangent to the curve, when moving clockwise around the circle shown below the direction you are travelling in at points A, B, C and D is shown by the red arrows.

As you can see, the direction is different at points A, B, C and D, so when moving in a circle you are constantly changing direction, this means that you are constantly changing velocity hence constantly accelerating.

To accelerate a force is required, this force is called centripetal force or “centre-seeking” force, as it is always directed towards the centre of the circular motion.2 Without this centripetal force the passengers of Cyclone would fly off at a tangent to the curve.

The reason I feel almost glued to the floor of the carriage and do not fall about the carriage is because of my inertia.

Consider being sat in a car at traffic lights, when the lights turn green and the car accelerates, the car moves forward but you move back into the seat, there is no force pushing you backwards, this is merely a result of your inertia, the tendency for you to stay at rest as you were when waiting for the lights to turn green, as Newton’s first law of motion tells us.4

The direction of inertia is always opposite to the direction of force, as centripetal force is directed towards the centre of circular motion the inertia therefore must be directed away from the centre. The inertia in regards to circular motion is also known as centrifugal force, it is this that holds the passengers of cyclone in place.4

2nd Aspect of Physics –microgravity on the ride Apocalypse.

When going on Apocalypse you have to stand on a platform and an attendant comes round a pulls a restraint over your shoulders, this and a small seat seem to be your only means of support. As you start ascending the tower about a metre up the ‘launch shuttle’1 is tilted forward at an angle of 20º, this meant that during the ascent the only way to avoid looking down was to close your eyes, and I did just that.

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When you reach the top of the tower the ‘launch shuttle’1 is held there for a few seconds, I ...

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When you reach the top of the tower the ‘launch shuttle’1 is held there for a few seconds, I opened my eyes and I could see for miles around. Then suddenly, the tower was dropped. During the fall I could feel myself lift off the seat, before I had felt the restraints holding me back; but now I could feel no pressure at all. As the ‘launch shuttle’ reached the bottom of the tower the speed was suddenly reduced with a jolt and I fell forward into my restraints, it was then slowly lowered to a stop.

When the attendant came and let me off I found it difficult to walk as my legs were shaking and I felt slightly nauseas but this was over within a few minutes. So what were these feelings? And why was I experiencing them?

Why do I feel weightless when the ‘launch shuttle’1 is being dropped?

On the way down the tower, the launch shuttle and I were falling towards the earth with only the force of gravity acting upon us. Objects in this situation can be described as being in ‘free-fall’.6 Anyone in free-fall will experience weightlessness and as I mentioned before I could feel myself lift off the seat, this is similar to astronauts when in space, you can see in the picture below astronauts floating and you have probably seen footage of astronauts floating around space shuttles, this is because they too are in free-fall but are travelling so fast horizontally they never come in contact with the earth.7

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A common misconception about weightlessness, more properly termed microgravity7, is to think of things being weightless when there is no gravity acting upon them, this is not the case. With apocalypse it is easy to see that although I feel weightless, gravity is still acting upon me because I am falling towards the earth. Free-fall was a term first used by Galileo Gallei (1564-1642), a scientist famous for dropping different objects off the leaning tower of Pisa and finding they hit the earth at the same time.6 Although according to Steven Hawkins this legendary experiment almost certainly did not occur, however, Gallei did roll balls of different masses down slopes and found that no matter what the mass they all reached the end of the slope in the same time, from this and a serious of other experiments Gallei concluded that all objects no matter what the mass fall at the same rate.5

So while falling down the Apocalypse tower I am falling at the same rate as the launch shuttle and the same rate as other riders even though they probably weigh different amounts, this is what gives me feeling of weightlessness, I’m not in contact with anything stable.8

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When you’re sat in a chair it is not the gravity that gives you a feeling of weight but the effect of the chair acting against gravity, gravity is pulling you down (Fgrav) but the chair is pushing you up with a force equal to this(Fnorm).8

Another example is to imagine you are stood on a set of scales, in your bathroom these scales will give you a measure of your weight but if you jump off a cliff still stood on these scales they would show that you weighed nothing, this is because neither yourself or the scales are in contact with anything stable that is counteracting the effect of gravity. You still have a mass, gravity is still acting on this mass but it appears you are weightless.8

These ideas were further defined in 1687 when Sir Isaac Newton (1642-1727) published the ‘Philosophiae Naturalis Principia Mathematica’ , this report is considered by many to be the greatest in modern science, in it Newton was able to explain much previously unrelated phenomena, such as the orbit of the moon, the action of tides, the erratic orbit of comets and the precision of the Earths axis with some simple laws. Newton’s law of gravitation, ‘All matter attracts all other matter with a force proportional to the product of their masses and inversely proportional to the square of the distance between them’3 explains what was happening in Gallei’s experiments, an objects mass and the force of gravity are connected in such a way that makes the action of gravity the same for objects of differing masses.

Newton’s laws are not the most up to date, Einstein’s theories on relativity predict the influence of gravity more accurately but this has little effect on calculations except when talking about the orbit of planets and Newton’s laws are considerably simpler so they are still widely used today.5

Newton’s laws also tell us that as something falls, it will not fall at a constant velocity but will get faster; this rate of acceleration is the same for all objects falling towards the earth and has been calculated at 9.8ms-2. Therefore I can assume the launch shuttle is falling down the tower at a rate of 9.8ms-2.3

The force on an object can be compared to gravity (9.8Nkg-1) and is often referred to as the number of G’s. When an object is in free fall it is under the influence of 1G, although as explained earlier it feels as though there is no force acting on the object so when free falling it feels as though you are in a 0G environment. The Drayton Manor website states that the launch shuttle ‘falls at the mercy of Gravity at over 4Gs’1, I think this is very misleading and as the launch shuttle is not falling at 4G’s, this figure is probably in reference to the point of breaking. Below I have calculated the number of G’s while the launch shuttle is breaking.

First I need to calculate the total force acting on the launch shuttle; the total force is equal to the resultant force and the force of the mass.11

In the diagram the two forces can be seen, the downward arrow represents the mass due to gravity, mass = an objects weight × gravity, the weight of the launch shuttle is 500kg,3 when I was on the ride there was myself and one other person so I’m estimating our combined weights at about 130kg therefore the combined weight is 630kg, this multiplied by 9.8Nkg-1 to get the value in Newton’s. 630 × 9.8 = 6174N.

I can then calculate the resultant upwards force using the equation Force = mass × acceleration (F=ma) 11. I have the mass but do not have the acceleration.

To calculate the acceleration I need to know the velocity of the launch shuttle and myself at the point of breaking. I can use the equation v2 = u2 + 2as.11

v = velocity at the point of breaking

u = initial velocity, as the launch shuttle was dropped rather than pushed down the tower the initial velocity was 0.

a = acceleration, the rate of acceleration being the same for all free falling objects, 9.8ms-2

s = displacement, the distance free fell was quoted by Drayton Manors technical Manager as 48m. 12

v2 = 02 + 2(9.8 × 48)

v2 = 940.8

v = √940.8

v =30.7ms-1 (3 s.f.)

Now I have calculated the velocity at which the launch shuttle begins to decelerate I can calculate the rate of deceleration, using the same equation.

v = this time the final velocity is 0 as the launch shuttle is being brought to a halt.

u = this time the initial velocity is 30.7ms-1

s = displacement while braking, if the total height of the tower is 54m1 and the distance free fell is 48m12 it is reasonable to presume that the other 6m are when the breaks are on.

a = the rate of deceleration.

02 = 30.72 + 2(6)a

0 = 940.8 + 12 a

-940.8/12 = a

a = -78.4ms-2

Now I can use the equation F = ma, I do not need to include the – sign in this calculation as this was simply telling us the launch shuttle was decelerating and not accelerating.

F = 78.4 × 630 = 49392N

The total forces is these two forces combined 49392 + 6174 = 55566N

I now need to calculate how many Newton’s are acting on each kg, 55566N/630kg = 88.2Nkg-1

I can now compare this figure to that of gravity to calculate the number of G’s, 88.2/9.8 = 9G’s

Limitations

This figure is over double that quoted on the website, I think perhaps the biggest source of error in this case is the dropping and breaking distance, the dropping distance was just an approximation made by the Technical Manager at Drayton Manor and the breaking distance was an estimate I made knowing the full height and the dropping distance. It is possible of course that the website is wrong and my 9G’s is more accurate although I think this is unlikely, if someone were under the influence of 9G’s they would be most likely to black out, heart attacks and aneurisms are also possible. Astronauts and pilots are often put in environments with high G levels yet they wear what is known as a ‘G’ suit, to dampen the effects of G’s.8

While at the park I did take some measurements, I used a stopwatch to time how long Apocalypse was in free fall, I took 3 measurements, 2.15s, 2.58s and 2.71s. I did not use these figures in the above calculation as I felt they were not very accurate as it was hard to tell exactly when Apocalypse began to slow down and also my reaction time and the fact that the stopwatch only recorded seconds to 2 decimal places limited how accurate these measurements can be. However, I can use these figures to make some checks as to how accurate the figures quoted to me were.

I will check that the distance free fell was approximately 48m,

I need to first calculate the final velocity,

v = final velocity.

u = initial velocity, 0.

a = 9.8ms-2

t = (2.15 + 2.58 + 2.71)/3 = 2.48s

v = u + at

v = 0 + 9.8 × 2.48

v = 24.304 = 24.3ms-1 (3 s.f.)

Now I can calculate the total displacement

u = 0

v = 24.304ms-1

a = 9.8ms-2

v2 = u2 + 2as

24.3042 = 02 + 2(9.8)s

590.684416 = 19.6s

s = 590.684416/19.6 = 30.13696 = 30.1m (3 s.f.)

This is a difference of almost 18m from the figure quoted by the Technical Manager at Drayton Manor; this could be where my calculation was wrong.

Why do I feel ‘strange’ when coming off the ride?

As you well know astronauts have to be physically fit. Before being put into space they are put through strenuous exercise regimes and intensive training. This is because weightlessness places great demands on your body. Your head and sinuses swell, your legs shrink, muscles can weaken and your bones become brittle. This will only occur over long term exposure but a few seconds of micro gravity on a ride is enough to leave you feeling shaky, dizzy, disorientated and nauseated.

Future Developments.

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Hershey Park in Hershey PA, Pennsylvania, is planning to build a new ride, claiming it will be the ‘world’s first free-falling tower coaster’. At just over 45m it is not as tall Apocalypse and the design is slightly different, being more like a roller coaster. In stead of having one drop, it has five 6m drops. You ascend the tower in a car designed for 4, 2 passengers facing opposite directions, at the top of the ride the car slides across a track, then suddenly plunges 6m, the car then slides in the other direction, plunging another 6m, the cars rocking from side to side throughout, sometimes turning upside down. If the funding is available then ‘Turbulence’ should be up and running in 2005.10

Other Applications: 13

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or ‘vomit comet’ as it’s better known, is a plane, used by NASA to simulate a microgravity environment. The plane is flown in arcs or parabolas, similar to that of a roller coaster and works on the same principle as Apocalypse.13 The pilot flies the plane up at a 45˚ angle at the peak of the flight the engines are turned off for 20-30 seconds, then the plane is flown down, again at angle of 45˚. For those few seconds, when the engine is off, passengers experience 0G.14

Astronauts have been trained on board this plane in order to experience weightlessness over a short period before actually going into space but that is not the only use, experiments for both research and teaching purposes have been conducted on the vomit comet.13

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Its nickname is self explanatory with 1 in 3 passengers being sick.13

Bibliography

Drayton Manor Website last updated 2004
Centripetal Force http://hyperphysics.phy-astr.gsu.edu/hbase/cf.html last updated 1998.
Newton’s laws .
Centripetal Force .
Stephen Hawking, The Illustrated, A Brief History of Time, published 1996.
Amusing Physics, free fall
Microgravity last up dated 2004.
Weightlessness
Photos .