Xcelerator and Top Thrill Dragster Question

I don't seem to understand this very well. Xcelerator goes 82 on the launch to go up and over a 205 foot top hat. While Top Thrill Dragster goes 120 on the launch to go up and over a 420 foot top hat. You'd think that since the height was more than doubled that it would take two times as much speed to clear it. But instead, it is only 40 mph more instead of 80. Can someone explain to me why this is?

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Corey
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MF-26
TTD-11

I HEART OHIO

never thought about that, but it is a very good question

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I am one.
I am Turbo.
Top Thrill in the front row... anything else is lame
X...Whoa

Think about it this way, dragster carries more distance upward during the first few seconds of it's acent due it it's higher velocity. The negative acceleration of 9.8 m/s to air resistance and bearing friction is the same. At 215 feet i am willing to bet good money that it is traveling somwhere around 82 mph.

Think of it in reverse, how fast do you reach FALLING 420 ft?

Assuming you start with no initial velocity, the calculation to solve for the time to fall the 420 ft is

d(meters) = (0 m/s)*(2.6 s)+ 0.5*(9.8 m/s^2)*(2.6 s)^2

420ft / (3.28 ft/m) = (0 m/s)*(X s) + .5*(9.8 m/s^2)*(X s)^2

128.016m = 0 + 4.9 m/s^2 * X s^2

26.13 s2 = X s^2

5.11 = X seconds

Then, taking the theoretical fall time of 5.11 seconds, you can solve the speed at the terminus as follows

vf = vi + a*t

vf = 0 + (9.8 m/s2)*(5.11 s)

vf = 50.1 m/s

Multiply by 0.0006214 to convert meters to miles

vf = .03111 miles/s

Then multiply by 3600 (60sec*60Mins)

vf = 111.96 miles/hr

The calculation is close, but again remember, this is assuming that you carry no velocity going over the top.

The readers digest version for xcellerator -

205ft / (3.28 ft/m) = (0 m/s)*(X s) + .5*(9.8 m/s^2)*(X s)^2

3.57 seconds to fall 205 ft.

vf = 0 + (9.8 m/s2)*(3.57 s)

vf = 34.98 meters/sec = 78.2mph

For more info go to

http://www.glenbrook.k12.il.us/gbssci/phys/Class/1DKin/U1L5a.html

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--George H
Currency Tracking Experiment...Where's George.com
*** This post was edited by redman822 10/7/2003 10:42:41 PM ***
*** This post was edited by redman822 10/8/2003 12:08:15 AM ***

The short answer is because potential energy is linear in height, but kinetic energy is polynomial in speed.

Conservation of energy:

mgh = 1/2m*v^2

I guess if you want a layman's explanation that may be clearer than Arlok's, think about it this way: (and yes, I know this is an over simplification but it gets the point across)

Decceleration from gravity is 21.93 MPH/s. Thus, for every second that a train is traveling straight up, it slows down by 21.93MPH.

So, for the first second the dragster train travels 120MPH, for the second it travels 100MPH, for the third it travels, 80MPH, 60, 40, (which is about where I think it crests the top).

However, the Xcel train goes 80, 60, 40 (which is about where it crests).

Notice that the dragster train gets a LOT more time traveling at a faster speed than the xcel train, thus it can cover a lot more ground.

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Be polite and ignore the idiots. - rollergator
"It's not a Toomer" - Arnold Schwartzenkoph
"Those who know don't talk and those who talk don't know." -Jeff

Ahhhh!!!! Physics = Not Cool. ;)

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SWOOSH "proud to be a music major" HOLLON
MidwestInfoGuide.COM

The answer is simple and doesn't need all of the Physics and mathematic equations. Xcelerator doesn't need 82 mph to go through the top hat. Mr Freeze goes 72mph and can make it up to almost 205 feet, where the lims boost it up futher. Also the station on Xcelerator is elevated. I think think is right

The TTD and Xcelerator stations are both elevated about the same height- about 5 or 6 feet.

Your (non)reasons are bunk, jrhodes.
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- John
Homepark: CP Home-away-from-homepark: PKI
My Campusfish Blog
*** This post was edited by Michael Darling 10/8/2003 12:15:24 AM ***

Yeah, it seems that the physics *is* needed.

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As Mitch always said, "2-in-1 is a BS term, because 1 is not big enough to hold 2. That's why 2 was created.."
-Tomas

Distlling down the physics: height and speed don't have a linear relationship; its quadratic.

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http://www.eecs.umich.edu/~bnoble/

To put it simply, if you double the height of something, you double the amount of energy stored in it (potential energy). If you double the speed of something, you quadruple the energy stored (kinetic energy). As the coaster goes up a hill, it's kinetic energy is turned into potential energy. As it goes down a hill, it's potential energy is turned back into kinetic energy.

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2003 Parks: Cedar Point, SFWOA, Kennywood, PKI, MIA, SFGAM, SFKK and HW.
Still deciding where to go in 2004.