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Physics question about speed


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Maybe I'm just stupid, but I have a physics question that bothers me a bit . I'm not the smartest person, but for example: Goliath is 46 meters high, and goes 106 km/h. Millenium Force is 92 (?) meters high and goes 150 km/h. My question is: Millenium Force is almost twice the height of Goliath, but why does Millenium Force only go 150 km/h? Thanks.

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The conversion from potential to kinetic energy is not linear, so twice the height will not yield twice the speed:

 

mgh => 0.5mv²

(potential => kinetic)

 

For an example, if h = 1 m:

9.81 = 0.5v² -> v=4.43 m/s

 

Doubling the height:

19.62 = 0.5v² -> v=6.26 m/s

 

There is also friction and other energy losses, but this conversion is the primary reason.

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I've just been playing around on rcdb for a while and discovered that good design counts for more than I thought.

 

The max speed Goliath could reach without resistive forces in just over 108 km/h, (it gives up <2% of it's theoretical speed to air resistance, friction etc.) and MF gives up 3 km/h (still <2%) but a standard SLC gives up almost 13 km/h of it's potential speed (>14%) to friction and air resistance. So not only does rattle give you a headache, it also seriously impacts the speed of the coaster. Of course I could (and probably have) done something wrong, but I thought I would share this with the geeks of TPR.

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^Yes but the max speed is generally achieved at the bottom of the drop, before any inversions have taken place.

 

All the calculations are based on the max height and max speed of the coasters (from RCDB). I assumed that the max height is the drop height, and the max speed is achieved at the bottom of the drop, whoch does leave quite a large magin of error

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