Alright, well the coaster's done and I've just finished uploading to youtube. Here's the ride from a few offride and onride angles. I hope you've enjoyed this overview of rollercoasters. Again if you have any coaster related questions send me an email and I'll be happy to answer them. Good luck on finals!
Tuesday, May 5, 2009
Monday, May 4, 2009
Part 5: The Little Things
We'll start today with a description of one more element, then to a brief overview of energy dissipation methods, and conclude with talk of supports, ride colors, and themeing.
The last element on our ride is the helix. The helix is simply a turn that keeps on going, generally over more than 360 degrees of rotation. A helix can be as simple as a constant radius, slowly descending curve. This element's been around pretty much forever, and has a lot of unique examples. Here's a pretty cool one as Busch Gardens Williamsburg.
Notice how the designer used the changing height of the helix and adjusted the radius and banking angles to create a really unique diving exit. For our ride I'd like to make an intense helix inside of the first turn off of the launch. This will save space and create a few near misses along the way. After the corkscrew the track is right at the ground, so I'll build an ascending helix up and over the first turn. I'll also make the radius decrease as the track ascends, to keep the g forces constantly high.
Cool, now we've got the last element of our design done and finished. What to do now but slow the train to a stop! For a long time coaster brakes were mechanical clamps which dissipated the train's final energy by grabbing metal fins on the bottom of cars. Here's a picture of these brakes on the track. The fin on the underside of each car passes through the gap in the middle of the gray blocks, which are computer controlled to precisely manipulate the coaster's speed (or stop it completely).
A revolution occurred in 1999 when Millennium Force (still my favorite ride in the world) opened at Cedar Point. This ride broke some 13 world records, but the important one was the first use of a magnetic breaking system. This technique uses permanent magnets mounted on the track to oppose the motion of the cars traveling past by simple magnetic repulsion. Because there is no longer physical contact the system is much easier to maintain and much quieter. Additionally, because the system imparts a force based on the velocity of the train (as opposed to a harsh static frictional force), the deceleration is much smoother. Here's a picture of some moveable magnetic breaks. With the help of pneumatics the assembly can rotate away from the track and completely remove themselves from affecting the ride's speed.
The discussion of brakes wouldn't be complete without a brief overview of blocks. Blocks on a rollercoaster refer to a section of track with a controllable entrance and exit. 2 trains should never be in the same block at the same time. This is because, as in any field, failures happen. If a wheel assembly were to fail and a train were to grind to a halt, there needs to be a way to make sure the next train won't plow full speed into the back of our unsuspecting riders. To achieve this, no train is allowed to enter a block until the one that preceded it has safely passed through the next block's control point. It's a complex topic, so here's an example on our ride. See here that a train is sitting at the launch, waiting to go (we'll call this train B). However, the train in front of it (train A) has not yet cleared the final brake of the ride.
This situation means that there is some slim possibility that train A will stall and get stuck on the circuit. To assure the safety of all the riders, train B must wait until the moment that train A has cleared the final brake. That way, even if train A were to fail immediately after clearing the brake, train B could be stopped by the final brake before a crash would occur.
At this moment train B is clear to launch. This type of blocking occurs for all coaster types across every block, which can include stations, holding brakes, lift hills and mid-course brakes. Mid-course brake runs (MCBRs) are used to allow greater capacity on longer rides. For example, here on Dragon Khan in Spain, there is a MCBR approximately half-way into the circuit time wise. You can see it here, it's the flat piece of track with catwalks. The catwalks allow riders to be evacuated if a major problem should occur.
In this example, 2 trains can be on the "live" part of the track at once. One can be between the lift and the MCBR, while another can be finishing up after the MCBR and towards the final brake. This allows for greater capacity, which means less lines, happier riders, and more revenue.
Well, our coaster is mostly complete. However, it seems to be floating in the air. Yep, we need some supports to hold it up. Unfortunately, this is one area where No Limits doesn't really excel. There is no simulation of the forces going into the supports, so creating them is largely an exercise in cosmetics. Honestly I just try and imitate real rides from photos. It'd be hard to analyze the dynamics of supports, especially with myself not having taken a materials class first. Anyway, let's move onto the final stuff, colors and themeing. I've never really been one to theme a ride, but it can significantly help pull people's attention to rides. Themes can make a mediocre ride interesting, but can't make up for a terrible ride path. Our ride doesn't really need a theme, as it's a pure thrill ride. However, I've decided that a Boilermaker Special badging is in order. Therefore, I'll prepare a special car texture and change the colors.
Colors are slightly important because they are a clear visual draw to a coaster and can create a small sense of distinction from ride to ride.
Alright, that's it for today's update. I'll have one more update, featuring a few pics of the final ride and a point of view video. As always, thanks for reading.As a side note I'll be updating the first entry to better cover launch systems and lift hills (it made more sense to put the discussion there).
The last element on our ride is the helix. The helix is simply a turn that keeps on going, generally over more than 360 degrees of rotation. A helix can be as simple as a constant radius, slowly descending curve. This element's been around pretty much forever, and has a lot of unique examples. Here's a pretty cool one as Busch Gardens Williamsburg.
Notice how the designer used the changing height of the helix and adjusted the radius and banking angles to create a really unique diving exit. For our ride I'd like to make an intense helix inside of the first turn off of the launch. This will save space and create a few near misses along the way. After the corkscrew the track is right at the ground, so I'll build an ascending helix up and over the first turn. I'll also make the radius decrease as the track ascends, to keep the g forces constantly high.
Cool, now we've got the last element of our design done and finished. What to do now but slow the train to a stop! For a long time coaster brakes were mechanical clamps which dissipated the train's final energy by grabbing metal fins on the bottom of cars. Here's a picture of these brakes on the track. The fin on the underside of each car passes through the gap in the middle of the gray blocks, which are computer controlled to precisely manipulate the coaster's speed (or stop it completely).
A revolution occurred in 1999 when Millennium Force (still my favorite ride in the world) opened at Cedar Point. This ride broke some 13 world records, but the important one was the first use of a magnetic breaking system. This technique uses permanent magnets mounted on the track to oppose the motion of the cars traveling past by simple magnetic repulsion. Because there is no longer physical contact the system is much easier to maintain and much quieter. Additionally, because the system imparts a force based on the velocity of the train (as opposed to a harsh static frictional force), the deceleration is much smoother. Here's a picture of some moveable magnetic breaks. With the help of pneumatics the assembly can rotate away from the track and completely remove themselves from affecting the ride's speed.
The discussion of brakes wouldn't be complete without a brief overview of blocks. Blocks on a rollercoaster refer to a section of track with a controllable entrance and exit. 2 trains should never be in the same block at the same time. This is because, as in any field, failures happen. If a wheel assembly were to fail and a train were to grind to a halt, there needs to be a way to make sure the next train won't plow full speed into the back of our unsuspecting riders. To achieve this, no train is allowed to enter a block until the one that preceded it has safely passed through the next block's control point. It's a complex topic, so here's an example on our ride. See here that a train is sitting at the launch, waiting to go (we'll call this train B). However, the train in front of it (train A) has not yet cleared the final brake of the ride.
This situation means that there is some slim possibility that train A will stall and get stuck on the circuit. To assure the safety of all the riders, train B must wait until the moment that train A has cleared the final brake. That way, even if train A were to fail immediately after clearing the brake, train B could be stopped by the final brake before a crash would occur.
At this moment train B is clear to launch. This type of blocking occurs for all coaster types across every block, which can include stations, holding brakes, lift hills and mid-course brakes. Mid-course brake runs (MCBRs) are used to allow greater capacity on longer rides. For example, here on Dragon Khan in Spain, there is a MCBR approximately half-way into the circuit time wise. You can see it here, it's the flat piece of track with catwalks. The catwalks allow riders to be evacuated if a major problem should occur.
In this example, 2 trains can be on the "live" part of the track at once. One can be between the lift and the MCBR, while another can be finishing up after the MCBR and towards the final brake. This allows for greater capacity, which means less lines, happier riders, and more revenue.
Well, our coaster is mostly complete. However, it seems to be floating in the air. Yep, we need some supports to hold it up. Unfortunately, this is one area where No Limits doesn't really excel. There is no simulation of the forces going into the supports, so creating them is largely an exercise in cosmetics. Honestly I just try and imitate real rides from photos. It'd be hard to analyze the dynamics of supports, especially with myself not having taken a materials class first. Anyway, let's move onto the final stuff, colors and themeing. I've never really been one to theme a ride, but it can significantly help pull people's attention to rides. Themes can make a mediocre ride interesting, but can't make up for a terrible ride path. Our ride doesn't really need a theme, as it's a pure thrill ride. However, I've decided that a Boilermaker Special badging is in order. Therefore, I'll prepare a special car texture and change the colors.
Colors are slightly important because they are a clear visual draw to a coaster and can create a small sense of distinction from ride to ride.
Alright, that's it for today's update. I'll have one more update, featuring a few pics of the final ride and a point of view video. As always, thanks for reading.As a side note I'll be updating the first entry to better cover launch systems and lift hills (it made more sense to put the discussion there).
Part 4: Rolling Over
Alright, unfortunately I'm fresh out of dynamics material to cover so from here on out it's all history, technique, and my own philosophy on design. First, I'll explore the rest of the basic inversion types, starting with corkscrews. Corkscrews were the first inversion that was actually ridable (barely). They beat modern loops by a single year (1975 at Knott's Berry Farm).The first company to make corkscrews was Arrow Dynamics, and they became a staple inversion on almost all of their rides through the 1990s. Corkscrews are named for a ride path that resembles the wine-cork removing implement of the same name, and are naturally shorter than loops. Originally corkscrews were perfectly circular, sort of like moving at constant speed and rotation around the outside of a barrel.
Old school:
This led to some funky transitions into and out of the corkscrew, and made for lateral forces in the bottom half of the inversion (not so fun). Modern corkscrews are a bit fancier, and generally involve rotating mostly around the apex and have very slightly banked entrances. This ensures the lateral gs are minimized. Here's the new fanciness:
Look at the banking of the last car in the train, half-way up the corkscrew. It's only about 45 degrees from the horizontal. If you look at the cars half-way up the old-style corkscrew, you can see they are already on their side, banked at 90 degrees. At this point, however, the ride path is still curving upwards and thus to eliminate lateral force the train needs to be banked at less than 90 degrees. It's a strange concept to get, but think of how uncomfortable it would be to begin curving vertically upwards from a sideways position. Due to the complex assortment of roll variations available today, corkscrews are now more generally defined as a rotating inversion with positive g force. There are so many manufacturers making so many sizes and shapes of corkscrews that it's kinda hard to keep things straight, especially when they start giving them different names (wing-overs, flat spins). I just call them all corkscrews to save myself the trouble. I'll be putting one on our ride, here it is.
Next, the roll! This is really as simple as it sounds. It was first made in 1985 (on this bizarre thing) and wasn't terribly exciting then. They're easy to make and require the least speed of all of the inversions, but I've never really liked them much. Moving on to something more worthwhile, the zero-g roll! This type of roll gets its name because, simply enough, it's a zero g hill that's warped into a roll. This gives riders a sensation of floating while rotating, a really cool inversion. They were first done well by Bolliger and Mabillard (who, to me, really began the modern design era in 1993 with Batman: The Ride at Six Flags Great America). Here's a side view of a sample zero-g roll.
Note how the yellow heartline follows a basic parabola to create the zero-g while the track rotates around it to create the roll. Here's a real-life version, on Scream at Six Flags Magic Mountain.
I'll put a slightly tweaked version of this into our ride, right after the loop and a turnaround. The turnaround was made 'by hand' meaning I placed each track node individually. This isn't very precise, but I'm on a steep time budget here. I've made the turn ascending, so we end up high in the air in the middle of the loop.
Now, Since we're already so high in the air, I'll skip the first half of the parabola and do a flat roll through the loop into a zero-g finish. This'll give us a distinctive element which is still within ridable limits and that seems feasible. This sort of cautious innovation is what I base most of my designs on. I like to see what a manufacturer does, then move to the next logical extreme. This gives my rides unique elements that push the envelope of technology, something that's always fun.
Anyway, now that we've covered the basic elements we can start to get into combos. Most compound elements consist of some combination of corkscrews, zero g rolls and loops. I'll give 4 of the most popular here. First, the dive loop. This consists of a zero-g roll that stops rolling at the apex and drops into a half-loop all the way to the ground. Bolliger and Mabillard do this really well, here's a good example on Mantis at Cedar Point.
I've decided to feature a dive loop on our ride, right after the complex roll. Our dive loop soars over the final brake run. I'm always a fan of tying a coaster in knots. Here it is in it's final placement.
An 'Immelman' is the exact reverse of the dive loop, starting with a half loop but then rolling over into a descent. Here's 'Dive Coaster' and its stupidly huge Immelman at Chimelong paradise in China.
The next inversion type is kinda like an Immelman and a dive loop combined. The 'Cobra Roll' features a half loop then a sort-of half corkscrew. Next, a half-corkscrew throws rides back upside down until a second half-loop points them back in the direction from which they came. This is kinda hard to illustrate with words so here's The Incredible Hulk at Universal Studios Florida to do it for me.
This element is supremely useful for turning a ride around, and is a great feature to play with pacing a bit. Next, the batwing was a favorite of Arrow Dynamics for a long while. Almost the opposite of a cobra roll, the batwing consists of a half-corkscrew into a half-loop, then a second half-loop leading into a second half-corkscrew sending riders, again, out the way they came. Here's Viper's batwing at Darien Lake.
Many other inversion types exist, but most are possible only in certain train configurations (some more bizarre than others). Others are simple changes on the ones listed above, and aren't really that important.
Now that we've got our inversions straight, let's move back to our coaster. Originally I had thought that, after the dive loop, 2 corkscrews over the launch would occur. This brings me to the next important part of coaster design, pacing. Pacing really amounts to the intensity of elements and the speed at which they are taken. While strong forces are good, it's not really fun to spend an entire ride squashed in your seat at 4 gs. It's important to give riders a break, both to allow time to enjoy the experience and because the human body can only enjoy so much disorientation. With this in mind, I scrapped my original plan to create 2 corkscrews in a row after the dive loop. After riding a rough version, I felt that there was far too much rotation going on over this small section. I based this largely on my experiences in coaster design and what I would theoretically enjoy most on a coaster. I thought there was simply too much rotation and not enough time for the passengers to reidentify what was up and what was down. Therefore, I made the first corkscrew into a simple airtime hill. Again, it suited the style of ride and kept up the speed while still allowing a little break from all the spinning. The hill is also thrilling in its own right, giving riders a bit of a head-chopper effect underneath the first airtime hill. A 'head-chopper' is a percieved near miss above the track. Fortunately, at high speeds it's difficult for the human brain to differentiate between what is dangerously close and what if just out of the way. Therefore while the track above the riders is quite safely out of reach, it appears to be dangerously near. I love making extremely cramped coasters simply to create such crossovers and near misses, raising excitement levels greatly.
Here's an overview of most of the layout of our ride. You can see the launch (in the closest tunnel), the airtime hill, the loop, the turnaround, the zero-g drop, the dive loop, the second airtime hill, and the corkscrew.
Anyway, now that we've got all of the inversions out of the way, I'll wait explore the miscellaneous other important info next time. Until then.
Old school:
This led to some funky transitions into and out of the corkscrew, and made for lateral forces in the bottom half of the inversion (not so fun). Modern corkscrews are a bit fancier, and generally involve rotating mostly around the apex and have very slightly banked entrances. This ensures the lateral gs are minimized. Here's the new fanciness:
Look at the banking of the last car in the train, half-way up the corkscrew. It's only about 45 degrees from the horizontal. If you look at the cars half-way up the old-style corkscrew, you can see they are already on their side, banked at 90 degrees. At this point, however, the ride path is still curving upwards and thus to eliminate lateral force the train needs to be banked at less than 90 degrees. It's a strange concept to get, but think of how uncomfortable it would be to begin curving vertically upwards from a sideways position. Due to the complex assortment of roll variations available today, corkscrews are now more generally defined as a rotating inversion with positive g force. There are so many manufacturers making so many sizes and shapes of corkscrews that it's kinda hard to keep things straight, especially when they start giving them different names (wing-overs, flat spins). I just call them all corkscrews to save myself the trouble. I'll be putting one on our ride, here it is.
Next, the roll! This is really as simple as it sounds. It was first made in 1985 (on this bizarre thing) and wasn't terribly exciting then. They're easy to make and require the least speed of all of the inversions, but I've never really liked them much. Moving on to something more worthwhile, the zero-g roll! This type of roll gets its name because, simply enough, it's a zero g hill that's warped into a roll. This gives riders a sensation of floating while rotating, a really cool inversion. They were first done well by Bolliger and Mabillard (who, to me, really began the modern design era in 1993 with Batman: The Ride at Six Flags Great America). Here's a side view of a sample zero-g roll.
Note how the yellow heartline follows a basic parabola to create the zero-g while the track rotates around it to create the roll. Here's a real-life version, on Scream at Six Flags Magic Mountain.
I'll put a slightly tweaked version of this into our ride, right after the loop and a turnaround. The turnaround was made 'by hand' meaning I placed each track node individually. This isn't very precise, but I'm on a steep time budget here. I've made the turn ascending, so we end up high in the air in the middle of the loop.
Now, Since we're already so high in the air, I'll skip the first half of the parabola and do a flat roll through the loop into a zero-g finish. This'll give us a distinctive element which is still within ridable limits and that seems feasible. This sort of cautious innovation is what I base most of my designs on. I like to see what a manufacturer does, then move to the next logical extreme. This gives my rides unique elements that push the envelope of technology, something that's always fun.
Anyway, now that we've covered the basic elements we can start to get into combos. Most compound elements consist of some combination of corkscrews, zero g rolls and loops. I'll give 4 of the most popular here. First, the dive loop. This consists of a zero-g roll that stops rolling at the apex and drops into a half-loop all the way to the ground. Bolliger and Mabillard do this really well, here's a good example on Mantis at Cedar Point.
I've decided to feature a dive loop on our ride, right after the complex roll. Our dive loop soars over the final brake run. I'm always a fan of tying a coaster in knots. Here it is in it's final placement.
An 'Immelman' is the exact reverse of the dive loop, starting with a half loop but then rolling over into a descent. Here's 'Dive Coaster' and its stupidly huge Immelman at Chimelong paradise in China.
The next inversion type is kinda like an Immelman and a dive loop combined. The 'Cobra Roll' features a half loop then a sort-of half corkscrew. Next, a half-corkscrew throws rides back upside down until a second half-loop points them back in the direction from which they came. This is kinda hard to illustrate with words so here's The Incredible Hulk at Universal Studios Florida to do it for me.
This element is supremely useful for turning a ride around, and is a great feature to play with pacing a bit. Next, the batwing was a favorite of Arrow Dynamics for a long while. Almost the opposite of a cobra roll, the batwing consists of a half-corkscrew into a half-loop, then a second half-loop leading into a second half-corkscrew sending riders, again, out the way they came. Here's Viper's batwing at Darien Lake.
Many other inversion types exist, but most are possible only in certain train configurations (some more bizarre than others). Others are simple changes on the ones listed above, and aren't really that important.
Now that we've got our inversions straight, let's move back to our coaster. Originally I had thought that, after the dive loop, 2 corkscrews over the launch would occur. This brings me to the next important part of coaster design, pacing. Pacing really amounts to the intensity of elements and the speed at which they are taken. While strong forces are good, it's not really fun to spend an entire ride squashed in your seat at 4 gs. It's important to give riders a break, both to allow time to enjoy the experience and because the human body can only enjoy so much disorientation. With this in mind, I scrapped my original plan to create 2 corkscrews in a row after the dive loop. After riding a rough version, I felt that there was far too much rotation going on over this small section. I based this largely on my experiences in coaster design and what I would theoretically enjoy most on a coaster. I thought there was simply too much rotation and not enough time for the passengers to reidentify what was up and what was down. Therefore, I made the first corkscrew into a simple airtime hill. Again, it suited the style of ride and kept up the speed while still allowing a little break from all the spinning. The hill is also thrilling in its own right, giving riders a bit of a head-chopper effect underneath the first airtime hill. A 'head-chopper' is a percieved near miss above the track. Fortunately, at high speeds it's difficult for the human brain to differentiate between what is dangerously close and what if just out of the way. Therefore while the track above the riders is quite safely out of reach, it appears to be dangerously near. I love making extremely cramped coasters simply to create such crossovers and near misses, raising excitement levels greatly.
Here's an overview of most of the layout of our ride. You can see the launch (in the closest tunnel), the airtime hill, the loop, the turnaround, the zero-g drop, the dive loop, the second airtime hill, and the corkscrew.
Anyway, now that we've got all of the inversions out of the way, I'll wait explore the miscellaneous other important info next time. Until then.
Friday, May 1, 2009
Part 3: Downside-up
Well, it's been a while since the last update. I spent a lot of time working on a fancy formula to generate a perfect ride path which, while very interesting to myself, doesn't really have a good bearing on the class. With that in mind, I've put the ridepath generator on hold and moved back to the coaster at hand. When we last left off I had built a formula to generate airtime hills. That's done and finished, so we can move on to the third element in our ride, the vertical loop. Loops are one of the easiest inversions, and one of the most popular elements. They provide a great wow factor and are relatively simple to work with. First, some history. Loops appeared as early as the 1800s. These loops, however, weren't exactly fun to ride on. For starters coasters didn't have wheel assemblies as we see them today, and were therefore held on the track solely by the normal force experienced by traveling along the path. Therefore, if the train were to go slower than expected (due to some mechanical failure or some weather condition) it would fall off of the track. This, of course, is very bad. An additional problem with early loops was the shape of the loop itself. Here's one of the early loops:
For simplicity, it's a nearly circular shape. Let's do some analysis to see why this doesn't really work. Starting at 20.83 m/s (the speed we left off at last time), we want a loop that generates 4 vertical g forces at the bottom to match the pull-up from the airtime hill. Calculation of the radius of loop required to generate this force is pretty trivial. We'll also see what the situation at the top is.
Well, we've got a big problem. To have rideable forces at the bottom of our circular loop, the coaster stalls before it can complete the loop. If we keep positive forces at the top of the loop, we see the force at the bottom raises to unsafe levels. The differences between N1 and N2 are too high in every case! So, what do we do now? Well, we wait until 1976 when Werner Stengel and Anton Schwarzkopf, both Germans, made the jump to modern design. Both men are largely credited with making modern loops work, and also pioneered the heart-lining concept which makes complex modern maneuvers possible as explained in part 1. Stengel still works in the coaster field today, completing almost every facet of design from ride path generation to structural analysis for the majority of rides built today (seriously, almost every new ride comes through his company). Anyway, the first real modern vertical loop was Revolution at Six Flags Magic Mountain. The only real change was using a radius of curvature that decreased as the cars turned through the loop (in a clothoid or euler spiral configuration). This allowed the force at the top of the loop to be much closer to that of the bottom, and for a much better overall experience. Here's the loop that started modern inversions:
Modern loops can have all sorts of shapes and sensations. There were loops by Arrow Dynamics, whose sharp teardrop shape created heavy positive gforce throughout. Here's an example of this, again at Six Flags Magic Mountain. Note the extreme change in shape from the circular loop.
Other types of loop are more passive, and give riders a small sense of floating over the crest. This can be desirable when a designer wants to slow down the pacing, and gives riders more time to notice that they are, in fact, very upside-down and very high in the air. Here's an example at Cedar Point. See how it curves less aggressively over the crest.
To suit the style of our ride, I want to make a loop with heavy positives at the bottom leading to about 1 g at the top. It's hard to show the dynamics of this problem due to the constantly changing radius, so I'll just highlight the method I used and the final result. To make our loop I utilized an alternate version of my airtime generator from the last update. I set a switch based on the value of the ascent angle. For the first and last quarters of the loop (0 < Theta < pi/2 and 3*pi/2 < Theta < 2*pi) I set the vertical g force at 4. For the top half of the loop, I set the gforce to vary as a sin function from 4 to 1 and back (Gforce=1+3*abs[sin[theta]]). Then I forced a constant offset to the side so the track does not cross through itself. This isn't really how loops are designed in the field, but I found it a fun use of my formulas and the results were very solid. This formula gave an intense, fast loop but still allowed for a little time to breathe. Here's a picture of the final loop, with a little preview of the next part of the layout.
That's it for today, tomorrow I'll get Part 4 (corkscrews and rolls) and Part 5(The little things) done tomorrow. I'll also have some video of the ride sometime over the weekend. To conclude, Here's a pic showing how silly a circular loop looks on a modern ride.
For simplicity, it's a nearly circular shape. Let's do some analysis to see why this doesn't really work. Starting at 20.83 m/s (the speed we left off at last time), we want a loop that generates 4 vertical g forces at the bottom to match the pull-up from the airtime hill. Calculation of the radius of loop required to generate this force is pretty trivial. We'll also see what the situation at the top is.
Well, we've got a big problem. To have rideable forces at the bottom of our circular loop, the coaster stalls before it can complete the loop. If we keep positive forces at the top of the loop, we see the force at the bottom raises to unsafe levels. The differences between N1 and N2 are too high in every case! So, what do we do now? Well, we wait until 1976 when Werner Stengel and Anton Schwarzkopf, both Germans, made the jump to modern design. Both men are largely credited with making modern loops work, and also pioneered the heart-lining concept which makes complex modern maneuvers possible as explained in part 1. Stengel still works in the coaster field today, completing almost every facet of design from ride path generation to structural analysis for the majority of rides built today (seriously, almost every new ride comes through his company). Anyway, the first real modern vertical loop was Revolution at Six Flags Magic Mountain. The only real change was using a radius of curvature that decreased as the cars turned through the loop (in a clothoid or euler spiral configuration). This allowed the force at the top of the loop to be much closer to that of the bottom, and for a much better overall experience. Here's the loop that started modern inversions:
Modern loops can have all sorts of shapes and sensations. There were loops by Arrow Dynamics, whose sharp teardrop shape created heavy positive gforce throughout. Here's an example of this, again at Six Flags Magic Mountain. Note the extreme change in shape from the circular loop.
Other types of loop are more passive, and give riders a small sense of floating over the crest. This can be desirable when a designer wants to slow down the pacing, and gives riders more time to notice that they are, in fact, very upside-down and very high in the air. Here's an example at Cedar Point. See how it curves less aggressively over the crest.
To suit the style of our ride, I want to make a loop with heavy positives at the bottom leading to about 1 g at the top. It's hard to show the dynamics of this problem due to the constantly changing radius, so I'll just highlight the method I used and the final result. To make our loop I utilized an alternate version of my airtime generator from the last update. I set a switch based on the value of the ascent angle. For the first and last quarters of the loop (0 < Theta < pi/2 and 3*pi/2 < Theta < 2*pi) I set the vertical g force at 4. For the top half of the loop, I set the gforce to vary as a sin function from 4 to 1 and back (Gforce=1+3*abs[sin[theta]]). Then I forced a constant offset to the side so the track does not cross through itself. This isn't really how loops are designed in the field, but I found it a fun use of my formulas and the results were very solid. This formula gave an intense, fast loop but still allowed for a little time to breathe. Here's a picture of the final loop, with a little preview of the next part of the layout.
That's it for today, tomorrow I'll get Part 4 (corkscrews and rolls) and Part 5(The little things) done tomorrow. I'll also have some video of the ride sometime over the weekend. To conclude, Here's a pic showing how silly a circular loop looks on a modern ride.
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