There are many types of coaster out there. Those coasters are running many different kinds of trains. As riders, we usually only think about what is going on above the floorboards, but an understanding of what is happening underneath can be very useful in showing why coasters perform the way they do (or don't).
For the purposes of this document, directions and motions will be expressed as follows:
|X axis:|| A transverse or lateral axis running left to right from the rider's point of view. |
|Y axis:||An axis running vertically bottom to top from the rider's point of view. |
|Z axis:||A longitudinal axis running in the direction of travel.|
|roll:||A rotation around the Z axis|
|pitch:||A rotation around the X axis|
|yaw:||A rotation around the Y axis|
|The coaster car shown here normally runs on the Gemini at Cedar Point.|
A note about axis conventions...
My identification of the X, Y, and Z axes (above) is based on a classic Physics-class type model. If you talk to a schoolteacher about mechanics of this type, this is how the axes will be defined. But in the amusement industry, for reasons which are unclear, but probably related to the technical limitations of the accelerometers and related computer software used to measure ride accelerations, a slightly different coordinate system is used, where the axes are pitched and rolled 90 degrees from what I show here. The "pitch", "roll", and "yaw" designations are the same with respect to the ride vehicle, but the axis designations are different...so "pitch" is about the Y axis, "roll" is about the X axis, and "yaw" is about the Z axis. I find the industry designations to be counter-intuitive to my academic upbringing, but that's the designation that made it into the ASTM draft standard. Eventually I will probably update this document to reflect the amusement industry's ASTM-accepted coordinate system, but for the moment I shall leave the text alone so that I don't accidentally take something that is correct and make it wrong. For the purposes of this document, the coordinate system used is as described and shown in the illustrations above.
Thanks (I think) to Steve Elliott, Ride Actions Ltd., for pointing out the discrepancy.
Got that? Now that you know what the directions and the motions are, we can examine some coaster cars, their limitations, and the problems of each.
This train of straight cars is running on The Beast at Paramount's Kings Island.|
Of course the simplest cars are the four-wheel-truck boxcar models. The oldest wood coaster trains are this type. At each corner of the car there is a wheel assembly rigidly mounted to the car frame. The cars are then tied together with a drawbar assembly which allows the cars to pivot relative to each other with some independence.
Perhaps you can see the trouble with this arrangement. When the car approaches a curve, the car cannot exactly follow the track. The wheels must be able to slide sideways at a tangent to the curve, because the car frame is rigid. This requires some slop in the track gauge through the curve to keep the cars from binding, and the sliding action of the road wheels means the track must be lubricated, otherwise the wheels will wear out the road steel.
The other problem with this design is less obvious, but in some ways more problematic. The front and rear axles operate in a single plane, because the car frame is rigid. So the track can only be banked very gradually. You see, when the train enters a bank, the front wheels hit the banked portion of track first. Say the track banks to the left. The right wheel is lifted first by the banked track, and the whole car is rolled to the left. The rear wheels must remain in the same plane as the front wheels, so even though the rear wheels have not yet reached the banked track, the car still rolls. The outside (right) rear wheel lifts off of the track until the right rear upstop hits. Either that, or the inside (left) front wheel will lift up until its upstop catches. Either way, road wheels are lifting from the track, and if the bank is severe enough, the difference in elevation between the front and rear axles will be enough for the car to bind up in the track. The amount of roll that the car can handle between the front and rear axles is determined by the total clearance between the track and up-stop on opposite corners of the car. Usually, that clearance isn't very great...perhaps an inch or two total.
In addition, the car body can twist a little (okay, so the cars on the Kennywood Racer can twist a lot...) to take up some of the variation. But this complicates matters a bit, as twisting the cars is something that can tear them apart. PTC alleviated the problem by engineering some flexibility into the cars, for example, the seat boards are not rigidly fastened to the car frame...instead, they are held in place with sleeved bolts running through oversize (well, if they aren't to begin with, they will be by the end of the first season) bolt holes. This lets the (rigid) seat boards shift relative to the frame instead of splitting and breaking.
While that is all well and good, wouldn't it be better to just move the wheels so that the car doesn't have to flex?
PTC came up with a solution to the problem of banked track some years ago with the development of the articulated car. Most 2-bench PTC cars are of this type. Instead of attaching the rear wheels directly to the car chassis, the rear wheel assemblies are attached to a subframe assembly. This subframe assembly forms a rear axle, and it is attached to the car by means of a longitudinal shaft. If you sit in the back seat, the end of this shaft is right below you, just above the car floor. The subframe is only able to pivot a few degrees, but that's all that is needed for a short car. Tilting the back axle increases the possible differential between the front and rear axle enough that the car can take banked curves without lifting any wheels. The wheels are still rigidly aligned with respect to the car's longitudinal centerline...that is, the wheels point straight forward...and when the car is going around a corner, they are pointing at a tangent to the direction of travel. This is why track lubrication is still needed even with articulated cars. The wheels still can't follow curves in-line with the direction of travel, and must slide sideways around the curve.
|Shown here is the rear footwell of a PTC junior car. Here you can see the end of the pivot shaft beneath the seat.|
Much has been written about flanged-wheel cars, but I suspect that the most important points have been overlooked. Let me try to explain.
The most common flanged-wheel car operating today is the junior car from PTC. These cars have four road wheels and four up-stops, but no guide wheels, as the wheel flanges make the guide wheels unnecessary.
|This multi-hued junior car runs on the Beastie at Paramount's Kings Island.|
PTC's junior cars are articulated in the same way as the larger cars, in that the rear axle is mounted on a sub-frame which can rotate on a longitudinal axis relative to the car and its front wheels. But there are a couple of other differences. First of all, in order to increase the roll clearance, the running boards...which form the frame of these cars...are notched to allow the wheels more play.
|From the rear you can see the gap between the seat assembly and the car frame which allows room for the seat and rear axle to pivot.|
Second, the rear seat is not attached to the frame and running boards, but rather to the rear axle subassembly. So these cars can handle a fairly significant bank transition. But they have a problem. Because of the wheel flanges, the road wheels cannot slide laterally on the track steel. If the wheels are held rigid with the car, the wheel flange will cause it to attempt to derail on the first curve. The flanged wheels must be able to follow the curve exactly.
This means that the wheel must be able to pivot relative to the centerline of the car. The simplest way to do this is with a simple pivoting axle. The problem is that a pivoting axle requires space which is not available under these cars. And the pivoting axle is needed at both ends of the car, as all four wheels need to be able to follow the curves, since all four wheels are flanged. Well, another way to accomplish this is to do what your car does. Instead of yawing the entire axle, we can pivot the wheels to follow the curve. With flanged wheels, it is easy enough to do. But there are two pitfalls to watch out for. First of all, if you locate the pivot point directly behind the wheel spindle, then as the leading edge of the wheel flange hits the outside of the curve, the leading edge will be directed inward, away from the rail...but it won't be able to go anywhere because the trailing edge of the wheel flange will already be tight against the rail. This will tend to keep anything from moving, thus defeating the purpose of the pivot. You can see this on your car if you turn the wheels to one side. Notice that on the outside of the turn, the back edge of the tire protrudes from behind the wheel-well. On a car, this is no problem, as there is no track involved. But on a coaster, this can mean trouble. The solution is to move the pivot point to a location behind the road wheel. That way, when the wheel pivots, the whole wheel shifts sideways, clear of the rail. The rear wheels, which, you will recall, are also mounted on a roll axle, have their pivots mounted forward of the wheel, for much the same reason.
Moving the pivot point back also creates a new problem. So far, we've concentrated on what happens to the outside wheel when the track curves. The new problem is what happens to the inside edge wheel. Because the pivot point is behind the trailing edge of the wheel flange, the inside edge wheel will not even touch the rail as the car heads into the curve. There is nothing to 'encourage' the wheel to follow the track as happens on the outside rail. Instead, the wheel will plow straight forward until the road surface falls right off of the rail. That is, of course, a Bad Thing™. Fortunately, the solution is simple. A tie-rod is attached to the wheel assemblies on the end opposite the pivot. That way, when the track pushes the outside wheel inward, the tie-rod will also push the inside wheel inward, insuring that it stays on the rail.
There is one final complication. The rear wheels must also be allowed to pivot, in a mirror image of the front wheels...that is, the pivot points are forward of the wheels and the tie rod is behind. The reason for this can be seen by looking at the tire tracks of an automobile, with its steerable front wheels and fixed rear axle. The problem is that as the car goes around the curve, the rear wheels will follow a path inside the track of the front wheels. This is fine for an automobile, but on a coaster it means the rear wheels are not actually following the track. Allowing the rear wheels to steer solves this problem.
|Adventure Express is the Runaway Train at Paramount's Kings Island.|
Note: This arrangement is described in excruciating detail in the U.S. patent for the Runaway Train chassis, coincidentally also available on this website!
It's worth noting here that Arrow solved almost all of these problems 40 years ago when they developed the Bobsled which later became the Runaway Train. That car has two beam axles, both of which can yaw, and one of which (the rear) can also roll. They refined the setup a bit by using dual guide wheels on each wheel assembly. Because of the guide wheels (rather than flanged road wheels) the wheel position can be slightly inexact because if the road wheel slides sideways slightly, the penalty is significantly less than with the flanged wheel. Also, by using dual guide wheels, the axle is steered from both ends...as the leading guide wheel strikes the outside rail, the trailing guide wheel on the other side should catch the inside rail. Allowing both axles to steer fixes the "back wheels inside" problem, and allowing the rear axle to roll solves the banked turns problem.
Most of the steel coaster manufacturers are using a variation on Arrow's Runaway Train for their two-axle cars. The usual configuration is to attach wheel carriers to the ends of a straight axle, and connect that axle to the car with a spherical bearing. A spherical bearing can swivel in any direction. To control body roll, one of the two axles is fixed in the roll axis relative to the car body. Premier does this by attaching a large disc to the end of the axle just inboard of the wheel carrier. The bottom of the car body then rests on top of those discs. Simple and effective.
(Technically, B&M cars are trailered, but it's worth mentioning here...)
The B&M coasters (except for the inverted coaster) use a wheel assembly which has a lot in common with the PTC junior, except that it uses two road wheels and two guide wheels, and is pivoted on an axis centered between the two road wheels. They can do this, again, because they use guide wheels instead of road wheel flanges. Also, the use of double guide wheels and the position of the wheel pivot on the center of the road wheel assembly means that the wheel carrier will be steered even on the outside rail (note that B&M steer curves from the inside rail because their guide wheels are outside...just the opposte of the PTC and Arrow designs), so the tie rod is really not needed, though B&M use it on all of their designs except the inverted (which works fine without tie rods).
All of this is fine and dandy, but what if we want to make the turns tighter, the banks sharper and the drops steeper? At the moment we are limited by the length of the car, and by the length and action of the drawbar between the cars. One thing we can do to clean things up a bit is to trailer the cars. Each car has only one pair of wheel assemblies under the back end. At the front, the car is supported on the back end of the car ahead. Done properly, the hitch is a 3-axis assembly, capable of pitching, yawing, and rolling. This essentially makes each car independent of those around it. The car is supported in front by the hitch, located in space above the center of the track. In the rear, the car is supported by its own wheels. As the train starts around a curve, the hitch assembly (traditionally just a ball and socket arrangement) follows the direction of travel, and the car pivots on its rear wheels to exactly match the train's path. The arrangement is mechanically simple, and should allow for track configurations that no other type of car can easily handle. But there are some caveats.
First of all, the lead car has to be supported by something. And, the lead car needs to have at the very least a roll-axis articulation. None of the other cars needs any axle articulation because the roll axis pivot is in the hitch, and the whole car (sitting on a single axle) can pitch and yaw. Ideally, in the lead car, the roll pivot will be on the axle away from the hitch, since the hitch end has the articulation with respect to the adjacent car. That will provide consistent performance through the whole train. It is not necessarily desirable to have yaw-axis articulation on the lead axle because additional articulation on that axle would enable it to fail to follow the track properly...to twist sideways and derail. This can be avoided with the use of steerable wheels with tie-rods, or by using dual guide wheels, and in fact Arrow and B&M both use fully-articulated lead axles in this fashion.
Note also that my use of the term "lead axle" may be a bit misleading, as the 'lead' axle can be at either end of the train, in fact Arrow, Vekoma, and Miler (at least) put their 'lead' axles at the back of the train.
The other problem with trailering has to do with the position of the hitch and the wheels. To demonstrate, let's consider a simple trailer. It has two wheels under the back end, and a leading tongue to support the front end. Now, if we lift up the tongue and start moving it about, we will see first of all that the trailer will pitch back on its wheels. If we move the tongue left or right, the trailer will yaw about a vertical axis centered on the axle. So, effectively, as we move the trailer tongue around, there is a point on the trailer which rotates, but does not translate...does not move...in space. That point is the center of the axle, in line with and centered between the center spindles of the road wheels. We could attach another trailer's tongue to that point, and the second trailer's exact alignment would be unaffected by the first trailer. If we put the whole arrangement on a curved section of track, and we pull the first trailer around the curve, the second trailer will simply follow the centerline of the first car, tracking independently around the curve.
This is, of course, what we want. We still need to put a lead axle on this setup, but we will end up with a train which will handle just about any curve we throw at it. This is how trains built by Prior & Church, Harry Traver, Carl Phare, Dana Morgan, and Mike Boodley are constructed. Cars built by Anton Schwarzkopf, Bolliger & Mabillard, Vekoma, Miler, and Arrow Dynamics expand on the concept a little further by adding wheel or axle articulation to the cars and using dual guide wheels. This enables the axle to follow the track exactly, even if there is a slight misalignment as the car starts into a curve. The system works remarkably well, but it is not without its problems.
|This Morgan-built trailered train runs on the Jack Rabbit at Seabreeze park. Notice that the coupler, in this case a ball-and-socket hitch, is positioned in-line with the road wheels.|
The problem is that coaster cars are very heavy, and the entire weight of the car...and remember, this weight must include the weight of the passengers and is multiplied by forces exerted by the ride profile, which may be in excess of 4G at times...must be carried by the road wheels. Of course, by trailering, we have reduced the number of axles, so now the whole load of the car has to be carried on the single axle. Well, not exactly. Remember, the cars are tied together, so in theory at least, part of the load is carried on the hitch which supports the front end of the car. If that hitch is positioned at the axle, then the axle is carrying about half the weight of the car it is attached to, and about half the weight of the car attached to it. This means that not only does the axle and wheel assembly need to carry that full load (a back of the envelope computation says that can exceed 12,000 pounds) of the car, but the hitch needs to be able to carry at least half of that weight reliably.
Well, carrying a heavy load on a couple of wheels is dead easy. If you are using soft wheels, you can decrease the load on each wheel by using tandem wheels (Arrow, B&M, Schwarzkopf, and Vekoma all do this) on the axle. But engineering the trailer tongue to carry all of that load and still provide sufficient articulation is more of a problem. The solution? Reduce the tongue weight. That is easy enough to do...simply move the axle closer to the car's longitudinal center of mass. That is the point where the loaded car would balance on its axle if nothing moved. Since cars generally have footwells and seats at opposite ends and are therefore heavier at one end, the center of mass will usually be somewhere between the center and the back end of the car. Balance the car in this fashion, and the tongue load is significantly reduced. National Amusement Device, Philadelphia Toboggan, and Ben Schiff all did this. It works, but there is a trade-off: This configuration, especially on a longer car, will put the axle some distance from the back end of the car. This is a problem, because for trailering to work properly, the coupler to the next car needs to be aligned with the axle. The distance can be significant; on the PTC trailered car, for example, the axle is under the floorboard ahead of the back seat...actually ahead of the wheel position used for the 2-axle cars. This means that for the assembly to work properly, there needs to be enough clearance under the back seat to accommodate the movement of the hitch tongue...movement which is amplified by distance.
Philadelphia Toboggan and National Amusement Device have both produced trailered cars. NAD's trailers are on the Lil' Dipper at Camden Park; to the best of my knowledge the only remaining PTC trailers are on the Raging Wolf Bobs at Geauga Lake and on the Predator at Six Flags Darien Lake. The fact that such cars have been removed from (at the very least) Texas Giant, Hercules, and Thunder Run should indicate that there might be a design problem. And indeed there is, with this design.
What PTC did was to balance the trailered car on its own axle. As noted, this is well and good, and there are good reasons for doing that. But they also mounted the hitch point to the very back of the car, providing a point for the next trailer to rest on. The trouble with that arrangement is that when the car pivots on its axle to go around a corner, the hitch point, instead of remaining in the center of the track, slides sideways. If the car turns to the left, for instance, the hitch ball gets pushed to the right. This, in turn, drags the tongue for the next car to the right, causing it to become misaligned with the track. It can only go so far, though, before its wheels hit the side of the track, causing it to try and realign with the track. This tends to pull the tongue back the other way, taking the hitch ball with it, and causing the leading car to misalign. Add to this action additional cars trailered in back, each one going through this oscillating motion, and you can see that the whole train is going to shake back and forth all the way through the curve. Perhaps the best demonstration of this is the Lil' Dipper at Camden Park. Sitting in the last car of the train, you can see all the cars shuffling back and forth as the train goes through the third turnaround at the back end of the ride. I have a video clip which shows this action on Thunder Run, along with another clip which shows the difference with the articulated train.
Molina is a special case. On the Moli-Coaster, which is a faithful copy of the Ben Schiff kiddie coaster, the single-bench cars are built like the PTC trailers, with the weight of the car balanced on the one axle, and the coupler at the rear of the train. And yet, these trains do not shuffle when they go around an extremely tight curve. Why?
The answer lies in the hitch position, and a little fact about the Moli-Coaster. If you take a close look at one of these gems, you will see that the hitch is positioned off-center, almost all the way over to the left wheel. You see, when the car pivots on its axle, the center of the back end slides sideways. But closer to the edge, there is a point which does not move laterally, because the back of the car is not merely translating sideways, it is rotating. The problem is that there are two such points, and which one isn't moving is entirely dependent on which direction the car is turning. But that isn't a problem for Ben Schiff, because the coaster has an oval layout. All of the turns on the ride are to the left, and therefore the hitch is positioned so that it is optimized for left-hand turns. Of course the upshot of all this is that the cars on a Moli-Coaster are incapable of turning RIGHT. Not a problem so long as the ride only turns left!
Note: Molina has gone the way of Ben Schiff (out of business); that coaster is now sold by the "Great American Roller Coaster Company".
Incidentally, Wisdom has a similar "one-way" arrangement on their Dragon Wagon, but rather than being related to the hitch position, it is a matter of different guide wheel arrangement on the lead axle so that again, the train is optimized for turning left.
I think that pretty well sums it up. To recap...
I'd like to encourage comments, questions, corrections, and other insights on this subject. Send me your comments and I will try to address them here.--Dave Althoff, Jr.
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