B Y D I N E T H , J A E H O E N A N D Y A N N I

DISNEY STUDENT CHALLENGE

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

• Acceleration = 𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝑖𝐼 𝐼𝑠𝐼𝐼𝑠𝑇𝑖𝑇𝐼 𝑡𝐼𝑡𝐼𝐼

• 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 49 to get it into 𝑚/𝑠2.

• G-Force = 𝐴𝐼𝐼𝐼𝐴𝐼𝐼𝐼𝑡𝑖𝐴𝐼9.8

• So the g-force exerted is 26.679.8

which is equal to 2.72G. • 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.

(𝑎2 + 𝑏2 = 𝑐2) • 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)

• Using the Pythagorean theorem we can Calculate x. • 100.29722+352= 11284.52833 • 11284.52833 = x x = 106.2286606 • We can also use trigonometry calculate angle y.

100.2972

35

THE INCLINE (ALL UNITS ARE IN METRES)

y

ANGLE OF INCLINE

• We can use any of the trigonometry signs because we have all of the side values. • For this instance we are using Tan.

• Tan = 𝐴𝑠𝑠𝐴𝐼𝑖𝑡𝐼𝐼𝑠𝑎𝐼𝐼𝐼𝐼𝑡

• y = 𝑡𝑎𝑡−1(100.297235

)

• y = 70.76°

100.2972

35

THE INCLINE (ALL UNITS ARE IN METRES)

y

Acceleration (60mph in1seconds) 2.72g

ANGLE OF INCLINE 100.2972

35

THE ROLLERCOASTER SO FAR

70.76°

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

• 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 • The mass of the empty cart is related to THRC(theoretical hourly ride capacity)

ANGLE OF INCLINE

100.2972

35

POTENTIAL ENERGY

70.76°

z

POTENTIAL ENERGY

• PE = mgh • PE = 1880kg x 9.8 x 100.2972m • ∴ 𝑃𝑃 = 1847875.613 𝑗𝑗𝑗𝑗𝑗𝑠

VELOCITY

• V = 2𝑔𝑔 𝑑𝑑𝑠𝑡𝑎𝑡𝑐𝑗 𝑓𝑎𝑗𝑗𝑗𝑡 • 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=12𝑚𝑚2

• We will use the scenario from the last slide. • V= 4.427188724 m/s

• ∴ KE = 18802

x 19.6

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 𝑑𝑑𝑠𝑡𝑎𝑡𝑐𝑗 𝑓𝑎𝑗𝑗𝑗𝑡 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

𝐼

• 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.

• 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

𝐼

• a = 26.191601712

20

• a = 34.30000001

CENTRIPETAL ACCELERATION AND VELOCITY

• 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 = 𝐴𝐼𝐼𝐼𝐴𝐼𝐼𝐼𝑡𝑖𝐴𝐼9.8

• 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.

LOOP THE LOOP SAFETY

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.