ROLLER COASTER KS3 MATHS
FILE 2
‘DESIGNING OUR OWN RIDE’
1. MAKING THE RIDE FIT THE AVAILABLE SPACE
We look at the issue that the ride must be designed to fit in a certain area of the park. Explain that at Alton Towers, no ride must go above tree-height, because of planning restrictions. This means that the park has to be ingenious – and use existing environment elements, eg hills, valleys, etc.
The height restriction at Alton Towers is actually a useful constraint. Without it, students will tend, in designing their own rides, to go for the tallest/fastest possible. With the height restriction, they will need to think more precisely about use of hills etc to create the height needed for the ride.
Look at an aerial image of the Nemesis ride – this image can be shared as a handout, or projected on the whiteboard. (Images can be obtained using google earth, or at www.webaviation.co.uk)
Also look again at the following image – and at the new version of the ride plan, below:
Examine these images together, highlighting how the landscape has been shaped to fit the ride. A pit or quarry hollow has actually been dug (visible on the sketch), to create a deeper drop for the ride.
A hill is used for the first hill of the ride; there are two other, smaller hills that are used to create some height. What becomes clear is that the ride almost seems to be ‘suspended’ between these points on higher ground. It travels from ‘A’ – the station; to ‘B’, at the top of the lift hill; to ‘C’ (the bottom of the first drop). Then there are three sections:
Section 1: from ‘C’ to ‘D’
Section 2: from ‘D’ to ‘E’
Section 3: from ‘E’ to ‘F’
(Students have previously made side-elevation views of these three sections)
The pattern of the ride, then, may look entangled but it is basically simple.
The ride also uses lines between trees etc (Trees in the park are subject to preservation orders.)
PLANNING OUR RIDE
We distribute a map of the given area in Alton Towers, where our new ride will be situated. (See below.) This includes details of heights of hills, and natural obstacles (trees; lake; buildings, a monorail etc.).
Reveal the map arrived with a memo about the site from Alton Towers:
Merlin Entertainments, Alton Towers Resort
TO ALL RIDE DESIGNERS
Please find enclosed a map of the site for the new roller coaster ride at Alton Towers. Your ride must fit into this space.
Points to remember:
· The new ride will be gravity-driven. The lift hill has to take the train up to a certain height, so it can get the momentum it needs to take it around the track and over all the different elements. So you must make sure the lift hill is high enough.
· Planning restrictions mean that no ride at Alton Towers can go above tree-height.
· It is essential that you do not disturb existing trees, ponds, buildings, or excavate any hills on the site. The monorail can also not be moved.
When we built Nemesis, we had to get permission to dig a pit in the ground, to get the height and depth we needed for the ride; and you might decide it is be necessary to do this for your ride as well. It is possible to dig to a maximum depth of 16.5m at this site. (We will, of course, need exact details of the size and depth of any excavations you propose.)
Best wishes,
John Wardley
Alton Towers Resort
TRACK LAYOUT FOR OUR RIDE DESIGNS
We now need to decide the track layout for our rides – section by section:
Where will we place the ride station, and the lift hill?
Again refer to the Nemesis model:
LIFT HILL
What is the height difference there between the station, and the top of the lift hill, on Nemesis? What is the length of the lift hill?
Our measurements will need to be a similar height / length.
With these figures in mind, mark a possible place for a station on our map, and a route for a lift hill. At this stage, we should mark our plans in pencil, so we can change them later, as we work on the rest of the design.
Students need to recognise that the station should be placed close to one of the hills. (They should be able to work this out themselves!)
Stress that we are creating a gravity-driven ride with a conventional chain lift-hill – ie we are not going to be using the LIM system (’Linear Induction Motor’) which is used on some rides (such as ‘Rita’) to achieve high-speed acceleration from the very start of the ride. All speed and acceleration on our ride will be gravity-generated.
FIRST DROP
Looking at the Nemesis model: what is the difference between the top of the lift hill, and the lowest point reached on the first drop? What is the length of the track for the first drop?
Our measurements will need to be a similar height / length.
Again, mark in pencil a possible route for the first drop. If it appears that we will need to dig some kind of quarry pit to give us the depth we need for the first drop, we should mark that on the map, too.
STATION AND BRAKE RUN
We also need to have enough space for the station, and the brake run into the station. This needs to be a long straight line of track (as in Nemesis), or it could have a single bend in the centre (so the first half is the brake run, then the track bends into the station, as in Oblivion).
The track must be long enough for one train to pull in to the waiting area outside the station, while another train is in the station. Again, students should use the Nemesis side-elevation as a guide. (In reality, I’m not sure the side-elevation view is accurate here – but as I have said, we can use it as a working guide for our purposes, as if it is accurate.)
This work can be done in teams, pairs, or as individuals.
We should record on the map the height we want at different points, eg the station, the bottom of the first drop.
We have to remember that, whatever we do with the rest of the track, it will have to end at the brake run – so where we put the brake run is crucial.
OTHER KEY POINTS IN THE TRACK
We now have a station/starting point for the ride; a high point (top of lift hill); and a point at the bottom of the first drop.
We now need to determine the rest of the track layout.
1. SECTION ONE
On Nemesis, the first stretch of track, after the first drop, is from point C to point D. It covers a distance of roughly 83m. (This refers to distance, not to track length – which is longer, of course, because of the different ride elements that are added.)
From point C - the low point at the bottom of the first drop - to point D, there is a height difference of some +18m.
So we now need a stretch of track from the bottom of the first drop on our plan, to another point on the map – roughly as long, and with a similar height difference, as the Nemesis track.
Note that, on Nemesis, the stretch of track is pretty straight; and ours should be, too.
(The golden rule is: head for the hills! So as you exit the first drop, head straight for a hill; it will give you the height point you need.)
2. SECTION TWO
On the Nemesis plan, the next stretch of track goes from point D to point E. The height difference between point D and point E is about minus 5m.
It covers a distance of some 82m. Again, it is pretty straight.
So we now need a similar stretch of track on our plan – similar in length, and with a similar height differential. It should also be basically straight. (We could again use a hill to head towards.)
3. SECTION THREE
On Nemesis, the next section of track goes from point E to point F. The height difference here is minus 4m.
It covers a distance of some 103m.
Again, it is pretty straight – it curves but it is basically headed in one direction.
It is designed so that, on turning at the end, it takes us into the brake run.
So we now need a similar stretch of track on our plan – similar in length, and height difference; and basically straight.
We will now have ‘vector’ diagrams for our track layouts. The distances covered should be similar to the ‘Nemesis’ model – ensuring that the ride will be a similar length. It is important for future tasks that this is the case.
THINGS TO NOTE
· At points where the ride changes direction, tight bends are good, both to reduce the space taken up by the ride, and to add to the ‘thrill’ factor. It would be a useful exercise for students to measure the angle of the bends on the Nemesis track, and to use this as a guide – specifying in their own designs the angles.
If we do this properly, then achieving a track layout that produces a satisfying/exciting ride experience should actually be a challenge in itself, and we may have to do several drafts before we arrive at a final solution.
· Students will be inclined to want to use the pond in some way in their ride. They might want to take the ride over the water, or even under the water.
The map we have given them actually makes this very difficult to do, as long as we use the Nemesis model and create basically three quite straight sections of track after the first drop.
Students should not be allowed to find an easy way out of this (i.e. by making the track bend round, rather than go straight) – if they are determined to use the water, they will need to find a way to do it!
(The only way I can see is to use the hill, top left of the map, as the lift hill, rising on the left hand side – and then either going outside the trees at the top of the hill, or through the avenue between them. The first drop will then be on the right side of the hill. If it descends through the avenue of trees, it will have to go into a bend – as the Nemesis ride does on the first drop - to avoid another crop of trees on the hillside. The bottom of the first drop will then be in a quarry pit at the bottom of the hill, to the left of the pond. From there, you could shoot across to one of the hills, for the first stretch of track, in part crossing over the pond. Even so, students have to be aware that Alton Towers is a historic site; so they can’t do anything that might be seen as damaging the environment (e.g. they couldn’t build concrete supports for the ride in the pond itself); and also, if they are going to take the ride over the pond, they will have to bear in mind the tree-height restriction: so they have to calculate, how high above the water will the ride need to be – and does this take them above tree height?)
The design work undertaken so far can be marked on the basis of (a) does it meet the various restrictions and criteria; and (b) is the maths work accurate? I sometimes feel that it is odd in ‘Mantle’ projects, to mark work – after all, we don’t ‘mark’ people’s work in real life contexts, do we? But I see no problem here in the teacher, working as a kind of ‘project supervisor,’ assessing the work so far, and pointing out things that will need to be improved before the work is submitted to Alton Towers (‘We need to make sure that everything is accurate – we can’t submit a plan that isn’t accurate, they just won’t accept it, will they?’)
THE SHAPE OF THE RIDE
Looking again at the side-elevation graphs we did of Nemesis, students may observe a pattern.
There are two ride elements on the first drop: the barrel roll and the helix
Then, the three sections that follow all rise in the middle to another element (loop/zero-g roll/barrel roll).
For the turns from one section to another, the ride uses stall turns.
CHOOSING RIDE ELEMENTS
Distribute the ‘Ride Elements’ pack of cards (below). We have to choose up to five different elements we will include in our ride.
Students should ONLY choose ride elements from the cards given out – i.e. they should not try to invent completely new elements. (There are limits to what roller coasters can do. The basic elements that every ride uses are known. Roller coaster designers do try to invent new things – eg the ‘free-fall drop’ on the ‘Thirteen’ ride at Alton Towers; but that of course demands great technical know-how and years of research. If you do not restrict students to the ride elements on the cards, but allow them to invent things, you will find that they come up with ride elements that are (a) impossible to build from a technological point of view, and (b) would probably kill the passengers.)
We have to consider, not just what we’d like to include in the ride, not just what looks exciting – but what will fit in with the site we are using in the park (always remembering the height restriction!), and the overall shape of the ride track which we have mapped out so far.
We can now choose ride elements for our rides – following the Nemesis pattern:
We first select two elements for the first drop – one half-way (or 2/3) down, and one at the bottom
Then, we choose one element to be placed in the middle of each section – be it a loop, a corkscrew etc.
(We can’t add too many elements because of space/length/cost, and the fact it is a gravity-driven ride - and so the momentum gathered from the first drop will only take you over a certain number of loops and rolls etc).
Remember that we can’t add any element that is above tree-height.
We should also choose ride elements for the turns between sections (banked curve/stall turn)
Students should be aware that creating a good ride does not depend on having lots of different elements, or choosing the biggest and most extreme elements; after all, the ride elements for ‘Nemesis’ are quite simple - a loop, a helix, a couple of barrel rolls, and a zero-g roll – but it is still an exciting ride.
Students should also be discouraged from choosing a ‘big’ element (such as a loop) for half-way down the first drop – where the ride hasn’t really got up much speed yet.