The Science of Welcome to Science of Stealth. ‘Big up’ National Science Week Hide slides depending on age and ability of group. There should be enough here to take to AS level. Let’s start with basic principles – gravity Next slide

Gravity (g) Gravity is a force of attraction between objects. The more massive the object, the greater the pull. However, the object has to be really massive, like Earth, for the pull to be obvious. Not afraid to poach from the NASA site. Until recently, all roller coasters relied on gravity. Use model and No Limits Roller coaster to demonstrate ( nominated pupil) NASA at the Amusement Park

g forces High g’s Any acceleration greater than free fall. > 9.8 m/s2 Low g’s Any acceleration less than free fall. < 1 g < 9.8 m/s2 Earth’s gravity = 1 g Provides a force of acceleration known as free fall (9.8 m/s2). With rides – we show the accelerations in terms of g forces No limits shows accelerations as part of the display. Point out g forces NASA at the Amusement Park

G forces In a theme park – you are likely to experience up to 5g The safe limit is 7g for a healthy person for a short period. Sustained levels of 10g will cause problems

Here are the basic facts for Stealth Stealth Facts Height 62 metres Launch time 2.3 seconds Train weight 8 tonnes (unladen) 10 tonnes (laden) Launch Speed 38 metres per second Dive Speed 35 metres per second Here are the basic facts for Stealth I’ve used these figures, the profile diagram from the manufacturers and a Physics book to work out the following

Stealth acceleration Acceleration = v – u (m/s) t (s) 2.3 Acceleration = 16.5m/s2 16.5 = 1.68 x gravity 9.8 (v = final speed, u = initial speed, t = time)

I’ve looked at representing the data in three ways – take your pick. Stealth v. Gravity Time 1s 2s 2.3s Gravity 9.8 19.6 22.5 Stealth 16.5 33.0 37.9 mps! I’ve looked at representing the data in three ways – take your pick.

S = distance, u = initial velocity, a = acceleration, t = time How far to reach 80mph? S = ut + 1/2 at2 S = (0 x 2.3) + (16.5 x 2.3 x 2.3) 2 S = 0 + 43.6 S = 43.6m S = distance, u = initial velocity, a = acceleration, t = time

Force to launch Stealth Force = mass (kg) x acceleration (m/s2) F = m x a F = 10000kg x 16.5m/s2 F = 165000kgm/s2 165 000N (Newtons) 10 tonnes = 10000Kg

Work done in launching Stealth Work = Force (N) x Distance (m) Work =165 000 x 43.6 Work = 719400Joules Work = 7 194 KJ Work = 7.19 MJ

The Power of Stealth Power = work (J) time (s) Power = 7194000 2.3 Power = 3127826Watts Power = 3.1MW

Potential energy needed= mgh As long as KE is greater than PE ……… Will you make it? – Potential energy needed= mgh PE = 10000 x 9.8 x 62 PE = 6 076 000J Kinetic energy = I/2mv2 KE = I/2 x 10000 x 382 KE = 7220000J As long as KE is greater than PE ………

………Stealth will make it over the top

On the way up! Curve radius = 35m Centripetal force = mv2 r Centripetal force = 100 x 38 x 38 on 100Kg rider 35 Centripetal force = 4125N Force of 1g on a 100Kg person = 1000N 4125N = 4.1g Total force on rider = 4.1g + 1.0g = 5.1g

On top of the world! PE = 6 480 000J KE = 7 220 000J KE – PE = 740 000J Surplus KE = 740 000J KE = I/2mv2 v2 = 2KE = 2x740000 = 148 m 10000 v = 12+ m/s

Force of 1g on a 100Kg person = 1000N On top of the world Outside curve radius 8m Centripetal force = mv2 r Centripetal force = 100 x 12 x 12 8 Centripetal force = 1800N Force of 1g on a 100Kg person = 1000N Resultant force 800N = 0.8g (almost weightless!)

On the way down! Curve radius 40m Centripetal force = mv2 r Centripetal force = 100 x 35 x 35 40 Centripetal force = 3062N Force of 1g on a 1000Kg person = 1000N Resultant force on rider = 3.1g + 1.0g = 4.1g

Nitrogen accumulators

Hydraulic fluid

The motors - Medusa

Cylinder block

Winch drum

The catch car

Wire cable and return drum

Magnetic brakes Fail safe – no power required. Efficient Maintenance free

Brakes! A metal plate moves through a permanent magnetic field. Eddy currents in the field produce a force to oppose the motion. The higher the speed – the greater the force. Magnetic brakes never stop you completely. Air brakes finish the job

Brakes!

Brakes!

Keeping on track

Vortex Manufactured by KMG Europe/Chance Rides 2001 Height 20m Max 120 degrees above vertical 4.5g max. Ride capacity 32 500 per hour Pendulum 9.2 rpm Carousel 7.5 rpm Duration 3 minutes

Pendulum

Vortex - Pendulum Length of arm 8.5m Period T = 2π√l /g = 2x 3.14√8.5/9.8 = 5.82s Frequency = 10.3 rpm Actual = 9.2 rpm

Vortex - Pendulum Data: 9.2 rpm Length, l = 8m Displacement, x = 8m Frequency of oscillation, f =9.2/60 = 0.15/s(Hz) Acceleration, a = (2Πf)2x = (6.28x1/6.5)2x8 = 7.46ms-2 (0.76g)

Motion in a circle

Vortex - Carousel Data: diameter, d= 8m, radius, r = 4m, Frequency, f = 7.5/60 = 0.125 /s (Hz) Angular velocity ω = 2Πf = 6.38 x 0.125 = 0.785 radians Linear speed, v = ωr = 0.785 x 4 = 3.14m/s (7mph)

Vortex - Carousel Centripetal acceleration a = v2/r = 3.142/4 = 2.46ms-2 (0.25g)

Salters Horners Jan 2008 A2 paper 6. On one type of theme park ride, a boat swings freely along a circular path from successively higher starting positions. As the boat moves through the lowest point on its swing, the riders are traveling at high speeds, and feel quite big forces on them. With some rides, such as Rush at Thorpe Park, the highest starting point is with the supporting arm horizontal as shown. Rush boat at starting point 18m Boat The length of the supporting arm of Rush is 18m. The mass of a typical rider is 70 kg. (a) Calculate the maximum "g-force" felt by a typical rider on Rush. “g-force" = force from seat weight of rider

Questions?