MF/Magnum Number Chrunching
I was calculating the speed of both coasters per 100 feet of their lift drops. Here's what I came up with. (all numbers rounded to the nearest 100th)
Magnum
72mph / 2 (for 200)=apprx. 36 mph per 100 feet.
MF
92mph / 3 (for 300)=apprx. 30.6mph per 100 feet.
Therefore Magnum is faster than MF by 5.4mph per 100 feet.
For a coaster that is 100 feet taller than Magnum it seems that MF should be the faster one per 100 feet than Magnum, right? It also seems that MF should go faster than 92mph as well. Why is this? Here's what I concluded with in my number crunching.
MF was intentionally designed to be slower per 100 feet than Magnum. When Magnum was designed, it was designed with a second hill straight in front of it. MF has a low, narrow turn. Magnum has a short pull in on the top of it's lift hill. MF has a long, wide pull in on the top of it's lift hill. The large pull in on MF's lift hill explains why it is slower than Magnum (apprx. 5.4mph) per 100 feet. The MF pull in causes the train to take longer to get set into motion, thus reducing the trains speed to a lower speed than a 300 foot tall coaster would allow for. Magnum was designed to go as fast as a 200 foot coaster can go because of the second hill in front of it to absorb it's speed. MF can't go much faster than the engineers designed it for because it doesn't have the luxury of a second hill in front of, but a low narrow turn. If MF was designed with a short pull in like Magnum for total speed allowable, the positive G's on the first turn would be too high for humans to endure. Other than what physics classes I took in HS, I don't know a lot about this stuff, but that is what I can up with. Everything that I can up with here is purely speculation. Correct me if I'm wrong.
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Vince "cpboy"Albertson
http://home.att.net/~vcalbertson/index.htm
*** This post was edited by Vince on 1/9/00. ***
Magnum
72mph / 2 (for 200)=apprx. 36 mph per 100 feet.
MF
92mph / 3 (for 300)=apprx. 30.6mph per 100 feet.
Therefore Magnum is faster than MF by 5.4mph per 100 feet.
For a coaster that is 100 feet taller than Magnum it seems that MF should be the faster one per 100 feet than Magnum, right? It also seems that MF should go faster than 92mph as well. Why is this? Here's what I concluded with in my number crunching.
MF was intentionally designed to be slower per 100 feet than Magnum. When Magnum was designed, it was designed with a second hill straight in front of it. MF has a low, narrow turn. Magnum has a short pull in on the top of it's lift hill. MF has a long, wide pull in on the top of it's lift hill. The large pull in on MF's lift hill explains why it is slower than Magnum (apprx. 5.4mph) per 100 feet. The MF pull in causes the train to take longer to get set into motion, thus reducing the trains speed to a lower speed than a 300 foot tall coaster would allow for. Magnum was designed to go as fast as a 200 foot coaster can go because of the second hill in front of it to absorb it's speed. MF can't go much faster than the engineers designed it for because it doesn't have the luxury of a second hill in front of, but a low narrow turn. If MF was designed with a short pull in like Magnum for total speed allowable, the positive G's on the first turn would be too high for humans to endure. Other than what physics classes I took in HS, I don't know a lot about this stuff, but that is what I can up with. Everything that I can up with here is purely speculation. Correct me if I'm wrong.
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Vince "cpboy"Albertson
http://home.att.net/~vcalbertson/index.htm
*** This post was edited by Vince on 1/9/00. ***
(*&^%!!! Hit the wrong button and lost it!)
I don't know where you got all that stuff up there, but what you need to look at are simple physics.
Let us assume for the moment that the drop on the coaster is not 60 or 80 degrees, but rather 90 degrees. It turns out that it doesn't make that much difference in ultimate speed, though it changes the timing a bit.
Acceleration is a,
time is t,
velocity is v,
distance is d, and
acceleration of a falling object is 32 ft/sec/sec.
You can verify this with a couple of simple experiments, but I don't want to get into that here. Just take my word for it that when things fall, they accelerate at 32 ft/sec/sec. :)
Now, we have an object which is undergoing continuous acceleration. So its velocity is
v = at
...that is, v = 32t ft/sec. So after one second, we're going 32 ft/sec; after two we're going 64 ft/sec; after three we're clipping along at 96 ft/sec.
Distance is a little different. Because we are accelerating continuously, we don't make it the whole 32 feet in the first second. In fact, we only make 16 feet in that first second. But we're moving at 32 feet per second, so in the second second we get the whole 32 feet. Because we're accelerating at the same rate, we also get another 16 feet, so in the second second we travel a total of 48 feet, giving us a total distance of 64 feet. In the third second, we get the whole 64 feet, plus another 16 feet for a total of 80 feet, plus the 64 feet we already covered, for a total distance of 144 feet after three seconds. It just so happens there is a formula for this:
d = (1/2)at^2.
Again, rather than sit here and derive it, I'll let you take my word for it...and notice in the breakdown above that yes, it works.
Notice that as a function of time, velocity is linear, while distance increases quadratically. Now, when building a coaster, ?? ????? ???????? ??????? ??? ????? ??? ??? ??? ??????? ??? ????????? ?? ???? ??? ???? ?????? ? ???? ??? ??? ??? ???? ?? ???? ??? ??? ??????? ??? ???? ??????? ????? ??? ??? ??????? ??? ???? ?? ????? ??? ??? ????? ??????? ??? ???? ??? ????? ???????????? ??? ???????? ?? ? ???????? ?? ?????????? ???????????? ?? ????????? ?? ?? ?? ??????? ??? ???? ?? ???? ??????? ????? ?? ?? ?? ??????? ??? ???? ?? ???? ?? ????? ?? ?? ?? ??????? ??? ???? ?? ???? ??? ????? ???????????????? ???????????? ??? ?????????? ??? ???? ???? ?? ????? ???? ??????? ?? ???? ? ? ????? ??? ??? ??????? ?? ???? ?? ????? ??????????? ???? ?? ????? ?? ??? ? ? ?? ???? ???? ??? ??? ?????????? ?? ?????? ?????? ????? ???? ????? ? ?? ???? ???? ????? ??? ?? ?? ?????? ??? ????? ???? ??? ?????????? ???? ????? ??????? ??? ? ??? ????? ?? ????? ?? ???? ???????? ?????? ??? ????????????????? ?????? ????? ??????????? ?? ????????? ??????? ????????????? ???? ????? ???? ???? ?????? ???? ? ???? ??? ??? ??????? ?????? ????? ?????????????????? ???? ???? ????? ????????? ???? ??????????????????????? ???????? ?????????????????? ???????? ?????? ??? ???? ???? ??? ?????? ?? ??????? ?? ???? ? ???
I don't know where you got all that stuff up there, but what you need to look at are simple physics.
Let us assume for the moment that the drop on the coaster is not 60 or 80 degrees, but rather 90 degrees. It turns out that it doesn't make that much difference in ultimate speed, though it changes the timing a bit.
Acceleration is a,
time is t,
velocity is v,
distance is d, and
acceleration of a falling object is 32 ft/sec/sec.
You can verify this with a couple of simple experiments, but I don't want to get into that here. Just take my word for it that when things fall, they accelerate at 32 ft/sec/sec. :)
Now, we have an object which is undergoing continuous acceleration. So its velocity is
v = at
...that is, v = 32t ft/sec. So after one second, we're going 32 ft/sec; after two we're going 64 ft/sec; after three we're clipping along at 96 ft/sec.
Distance is a little different. Because we are accelerating continuously, we don't make it the whole 32 feet in the first second. In fact, we only make 16 feet in that first second. But we're moving at 32 feet per second, so in the second second we get the whole 32 feet. Because we're accelerating at the same rate, we also get another 16 feet, so in the second second we travel a total of 48 feet, giving us a total distance of 64 feet. In the third second, we get the whole 64 feet, plus another 16 feet for a total of 80 feet, plus the 64 feet we already covered, for a total distance of 144 feet after three seconds. It just so happens there is a formula for this:
d = (1/2)at^2.
Again, rather than sit here and derive it, I'll let you take my word for it...and notice in the breakdown above that yes, it works.
Notice that as a function of time, velocity is linear, while distance increases quadratically. Now, when building a coaster, ?? ????? ???????? ??????? ??? ????? ??? ??? ??? ??????? ??? ????????? ?? ???? ??? ???? ?????? ? ???? ??? ??? ??? ???? ?? ???? ??? ??? ??????? ??? ???? ??????? ????? ??? ??? ??????? ??? ???? ?? ????? ??? ??? ????? ??????? ??? ???? ??? ????? ???????????? ??? ???????? ?? ? ???????? ?? ?????????? ???????????? ?? ????????? ?? ?? ?? ??????? ??? ???? ?? ???? ??????? ????? ?? ?? ?? ??????? ??? ???? ?? ???? ?? ????? ?? ?? ?? ??????? ??? ???? ?? ???? ??? ????? ???????????????? ???????????? ??? ?????????? ??? ???? ???? ?? ????? ???? ??????? ?? ???? ? ? ????? ??? ??? ??????? ?? ???? ?? ????? ??????????? ???? ?? ????? ?? ??? ? ? ?? ???? ???? ??? ??? ?????????? ?? ?????? ?????? ????? ???? ????? ? ?? ???? ???? ????? ??? ?? ?? ?????? ??? ????? ???? ??? ?????????? ???? ????? ??????? ??? ? ??? ????? ?? ????? ?? ???? ???????? ?????? ??? ????????????????? ?????? ????? ??????????? ?? ????????? ??????? ????????????? ???? ????? ???? ???? ?????? ???? ? ???? ??? ??? ??????? ?????? ????? ?????????????????? ???? ???? ????? ????????? ???? ??????????????????????? ???????? ?????????????????? ???????? ?????? ??? ???? ???? ??? ?????? ?? ??????? ?? ???? ? ???
My brain hurts now. :)
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Scott W. Short
sshort@mediaone.net
http://welcome.to/midwestcoastercentral
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Scott W. Short
sshort@mediaone.net
http://welcome.to/midwestcoastercentral
What are you talking about? There's no such unit as "mph/feet." That unit leaves nothing but time, which as far as we know is constant.
If what you're talking about is average speed, then Magnum would be slightly faster through the whole course (that is, assuming that the estimated ride time for MF is indeed 2:45). Magnum's average speed is about 29 mph while MF's will be about 27 mph. However, that's not a fair comparison when including the length of the lift hill and time it takes to climb it.
I would suspect that you might close the gap when you remove these factors, but there are so many factors that would affect the outcome (namely various kinds of friction).
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Jeff
Webmaster/Guide to The Point
If what you're talking about is average speed, then Magnum would be slightly faster through the whole course (that is, assuming that the estimated ride time for MF is indeed 2:45). Magnum's average speed is about 29 mph while MF's will be about 27 mph. However, that's not a fair comparison when including the length of the lift hill and time it takes to climb it.
I would suspect that you might close the gap when you remove these factors, but there are so many factors that would affect the outcome (namely various kinds of friction).
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Jeff
Webmaster/Guide to The Point
that's why i just leave it all up to the designers...but i AM curious now, so i will run this by my cousin who is an astrophysisist(SP?) and see what he can come up with...i mean, who understands space/time/speed better than a rocket scientist?
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"I think I scrambled my brain!!"
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"I think I scrambled my brain!!"
Well, I just ran this by my brother and he agrees with rideman, hes taken physics in high school. Well, hopefully I will understand this stuff soon if I want to be a roller coaster designer.
Scratch the math and physics for a moment. I put together that bogus math unit late at night while comming down with the flu and simply was just not thinking correctly. What I was trying to get at was the reasons for the large pull in at the top of the lift. Possibly to reduce it's speed because of the narrow turn at the bottom of the hill.
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Vince "cpboy"Albertson
http://home.att.net/~vcalbertson/index.htm
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Vince "cpboy"Albertson
http://home.att.net/~vcalbertson/index.htm
Two things.
mph/ft change of mph/ft could theoretically be used as a form of acceleration. miles/hour/ft = 5280ft/hour/ft = hours/5280. It's a unit of time, in this case.
Now, in a nutshell, the reaosn Magnum has a higher speed to height ratio is that distance to speed is not linear, it's a square value.
Thus, to be 2x as fast as Magnum's 72mph, you must be 4x (2*2) as high, or, somewhere in the neighborhood of 140mph. Of course, it's not even that simple given friction and air resistance.
mph/ft change of mph/ft could theoretically be used as a form of acceleration. miles/hour/ft = 5280ft/hour/ft = hours/5280. It's a unit of time, in this case.
Now, in a nutshell, the reaosn Magnum has a higher speed to height ratio is that distance to speed is not linear, it's a square value.
Thus, to be 2x as fast as Magnum's 72mph, you must be 4x (2*2) as high, or, somewhere in the neighborhood of 140mph. Of course, it's not even that simple given friction and air resistance.
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