DISNEY STUDENT CHALLENGE BY DINETH, JAEHOEN AND YANNI

DISNEY STUDENT CHALLENGE BY DINETH, JAEHOEN AND YANNI

OUR RIDE- THE BUZZATRON We have decided to base our rollercoaster on the theme Toy Story specifically Buzz light year. We think this to be a good financial decision because Toy story is the second highest grossing animated film. Second only to Frozen. The world wide gross has accumulated $1,063,171,911. We were also looking to use the words Too infinity and beyond to represent a quick acceleration much like the Rock n Rollercoaster. This could maybe be played nearing the acceleration to increase the tension and increase the enjoyment of the ride. This ride, will be a big thrill so height restrictions and people with medical conditions won t be able to go on to the ride.

THE ACCELERATION IIIIIIII ii sssss Acceleration = TTTT ttttt We are planning for the ride to increase 60mph in one second. To try and calculate the g force exerted you first need to times 60 by 4 to get it into 9 m/s2. G-Force = AAAAAAAAAAAA 9.8 So the g-force exerted is 26.67 which is equal to 2.72G. 9.8 This about the same as many Disneyland rollercoasters. The next slide goes into detail about acceleration safety and the consequences of too high a g-force.

ACCELERATION SAFETY When designing a rollercoaster it is extremely important to consider the safety of the ride. As well as curtailing to the enjoyment of the ride the safety is paramount. Here are examples of what can happen at high accelerations 4g-start to lose colour vision 4.5g-start to lose vision altogether 5-6g-lungs start to collapse and blood rapidly escapes your brain resulting in memory loss 7-8g-stomach bursts and blood escapes your veins 8-9gbrain stops functioning altogether and you pass out 10g for more than 60 seconds is guaranteed death That s why the maximum g-force allowed on a rollercoaster is 2-3g for a substantial period over time. However you are allowed high amounts of g-force over a very short period of time.

THE INCLINE Pythagoras Theorem states that in a right angle the hypotenuse is equivalent to the square root of the sum of the squares of the other two sides. (a 2 + b 2 = c 2 ) We can calculate the length of the incline by using this theorem. As this is a big thrill ride we would like to make the height at the top of the incline vey high. The height at the top of the incline will be 329 feet (100.2792 metres)

THE INCLINE (ALL UNITS ARE IN METRES) Using the Pythagorean theorem we can Calculate x. 100.2972 2 +35 2 = 11284.52833 11284.52833 = x x = 106.2286606 We can also use trigonometry calculate angle y. y 35 100.2972

THE INCLINE ANGLE (ALL OF UNITS INCLINE ARE IN METRES) We can use any of the trigonometry signs because we have all of the side values. For this instance we are using Tan. Tan = oooooooo aaaaaaaa y = ttt 1 ( 100.2972 ) 35 y = 70.76 y 35 100.2972

THE ROLLERCOASTER SO FAR ANGLE OF INCLINE 100.2972 Acceleration (60mph in1seconds) 2.72g 70.76 35

THRC Theoretical Hourly Ride Capacity This is very important, it is how many people can travel on the ride in one hour. It is crucial because it determines the economic revenue of the ride and how much profit the company makes for an hour. That is why the mass of each cart is critical as it affects the THRC. The mass of our empty cart is 800kg(this is the average mass of a rollercoaster car withought riders) To increase the THRC we will try and fit 12 people in one car. Lets assume that every person is 90kg (just to be on the safe side in case the riders are slightly overweight ) Thus making the estimated total mass 800+12(90) = 1880kg

POTENTIAL ANGLE OF INCLINE ENERGY We want to find out the potential at point z. We can use this equation to find out the potential energy PE=mgh M=mass of empty cart G=gravitational force H=height of incline 70.76 The mass of the empty cart is 35 related to THRC(theoretical hourly ride capacity) z 100.2972

POTENTIAL ENERGY PE = mgh PE = 1880kg x 9.8 x 100.2972m PP = 1847875.613 jjjjjj

VELOCITY V = 2gg dddddddd ffffff The distance fallen is the differentiation in height from the highest point of the rollercoaster. For example we can use this equation to calculate the speed of the rollercoaster a meter after the incline. The distance fallen is 1m. V= 2ggg The rollercoaster will be travelling at 4.427188724 m/s when the rollercoaster is a meter after the incline.

KINETIC ENERGY KE= 1 2 mm2 We will use the scenario from the last slide. V= 4.427188724 m/s KE = 1880 x 19.6 2 KE = 18424 J

LOOP THE LOOP Another key part of our ride is the loop the loop. When you travel around a circle, there is centripetal acceleration pulling you towards the centre of the circle. You can also use the equation V = 2gg dddddddd ffffff to calculate the speed at any point inside the loop. The loop the loop is another hazardous part of the rollercoaster.

LOOP THE LOOP SAFETY As always the safety is paramount. If a perfectly spherical shape was used then it would be extremely dangerous. The diagram perfectly represents why the clothoid shape is used. At the bottom the loop has a larger radius which means that at the top there is much less length for the rollercoaster to go through. Reducing the chance that the rollercoaster will collapse and fall.

LOOP THE LOOP The centripetal acceleration can be calculated by using this equation. This equation can calculate the centripetal acceleration at any given point the loop a = v2 r Remember you can use the calculation v = 2g x distance fallen to calculate the speed at any point in the loop. We also need the radius, I have made the radius 20 meters.

CENTRIPETAL ACCELERATION AND VELOCITY We are going to calculate the centripetal force at the top of the loop. v = 2g x distance fallen The highest point = 100.2972m 65m = distance fallen Making v = 26.19160171 m/s Centripetal force = a = v2 a = 26.191601712 20 a = 34.30000001 r

LOOP THE LOOP SAFETY Again safety is paramount, the g-force has to be enough for the body to cope and enough for the rider to enjoy. We will use the same scenario as the last slide (at the top of the loop.) G-Force = AAAAAAAAAAAA 9.8 G-Force = 34.30000001 9.8 G-Force = 3.500000001 g This an acceptable g-force that will not jeopardise the safety of the riders.

CONCLUSION Our ride includes a sudden acceleration of speed, an incline and a loop the loop. It is a fast paced action adventure that includes big thrills. It is extremely enjoyable and also complies with all the safety protocols. The G-Forces are completely safe, the g-forces do spike at some points but only for split seconds.