Greezed Lightnin' is a shuttleloop coaster featuring an elliptical
360-degree loop, instant acceleration and backward motion.
Riders are propelled from 0 to 60 mph (26.8 m/s) in four seconds,
circle the loop, then surge up a near-vertical 70-degree incline,
and then repeat the journey...backwards! 
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| Data: Height of front hill: 41.8 m Height of back hill: 33.5 m Height of loop (h): 24.7 m Horizontal diameter of loop: 13.7 m | 
| Vertical Acceleration:
Entering loop forward: ? g Top of loop forward: ? g Exiting loop forward: ? g |
Greezed Lightnin' is an example of a Klothoid loop.
This loop has a shape that controls the forces you experience as you go around the loop. |
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The radius of the circle is equal to the height of the loop divided by 2. | Calculate the minimum velocity
(vcircle-b) needed to maintain vertical motion. Assume that the diameter of the vertical circle is the same as the height of the loop in Greezed Lightnin'. | 
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The Law of Conservation of Energy: Energy cannot be created or destroyed.
What does that mean?
Simply stated, this means that whatever energy is put into a system, the same amount of energy will be gotten from the system. You might say, no way, that's not going to happen because we "lose" energy every day. Did you stop to think that the energy you think you are loosing is energy converted to heat? Friction generates heat and most energy is converted to heat due to friction. That's why you might think that energy is sometimes lost, but in reality, it isn't lost, it's converted to heat energy.
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For our purposes here, we will consider that all the energy we put into the system is given back to the system. In other words, when you reach the highest peak of a roller coaster, you have potential energy (PE). As you go down the peak of the roller coaster, the potential energy becomes kinetic energy (KE). Potential Energy = mass X gravity (9.81 m/s2 on earth) X height (PE = mgh)
Potential energy is converted to kinetic energy (KE). Kinetic Energy = 1/2 mass X velocity2 (KE = 1/2 mv2)
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If potential energy is equal to kinetic energy, then: Potential Energy = Kinetic Energy (PE=KE)
mass X gravity (9.81 m/s2 on earth) X height = 1/2 mass X velocity2 ( mgh = 1/2 mv2) Mass cancels out of the equation so: gh=1/2 v2
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Use the law of conservation of energy to determine the velocity (vcircle-bottom) needed entering the VERTICAL CIRCLE to provide the minimum velocity (vcircle-B) calculated above. Remember that mass cancels out. |
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| A thought: Circular loops on early rides failed because they created dangerously large centripetal forces at the bottom and too slow speeds (and centripetal forces) at the top. |
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 | Calculate the centripetal forces (Fc) both as you enter the loop and at the top of the loop (point B), using the data for a vertical circle. The actual mass of the loaded coaster is not known, but assume a mass (m) of 500 kg. Since we will only be comparing forces, this is an arbitrary measurement. |  |
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1 g = 9.8 m/s2 |
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What is the advantage of the Klothoid loop over a vertical circle? |
| Below is some accelerometer data from a coaster initially entering and exiting the loop. |
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| Where will you sit on the coaster? What do you think will be your accelerations? Link to interactive MS Excel Worksheet here! MS Excel Worksheet will have "built-in" formulas for calculations. Download a worksheet to take with you to the Greezed Lightnin' Coaster. |
