Roller Coaster Steering

I've read numerous posts on this website and articles elsewhere talking about steering, vehicle joints, zero cars, etc., all having to due with how different styles of trains navigate through curves in the track. I was lead to RideMan's terrific 12-year-old article discussing the different manufacturers' styles of vehicles and axle/wheel assembly arrangements.

There's still one thing I'm getting hung up on, though. For cars that have wheel assemblies that can independently yaw, how do they steer through a section of curved track if the gauge remains constant (which I assume it always does)?

It's easy to understand for a car that has both wheel assemblies on each side fixed to a single axle, which itself can yaw with respect to the car. In this case, the wheels always remain parallel to each other and equidistant. But if the carriers on each side can pivot separately, I don't see how they can navigate a curve where the space between the rails remains constant. I've gone through the geometry several times, but it's not making sense. Any thoughts?

Rideman would probably know more about this, but I do remember reading that these types of wheel assemblies do have a system, such as a bar, that connects the two assemblies so that they turn in union with each other.

TGG has this video that shows the mechanism for their steering wheel carriers:

http://www.youtube.com/watch?v=xhg1B5UEMX0

As you pointed out CPcisco, there is a tie rod that connects the wheel assemblies, and they appear to resemble an Ackermann steering mechanism, in that they turn at different rates based on the geometry of the system, so that the wheels aren't pointing in the same direction when they are pivoted.

http://en.wikipedia.org/wiki/Ackermann_steering_geometry

Despite this, I still see a problem maintaining a constant track gauge. It's very difficult to describe without a picture, but I'll give it a shot and try to keep it short. Basically, when the track is straight, the road wheels are parallel and pointing straight forward. They are also a fixed distance apart. The idea is that as the car goes into a turn, the road wheels pivot to stay tangent to the radius of the curvature of the rail.

In the case where the curved rails are concentric, as on a coaster, the shortest distance between the two curves is a line that is perpendicular to both curves. If we take this line to be the connecting rod between the two wheel sets, then the wheels must be perpendicular to that rod and parallel to each other to remain tangent to the rails. This is exactly how wheels that are fixed to a common axle would behave, remaining the same normal distance apart and parallel to each other.

Wheels that steer independent of each other will by nature not be perpendicular to the connecting line, which means that the normal distance between them, if they stay parallel to each other, would have to shrink as the curve gets sharper. In addition, the straight-line distance between the yaw axes would have to increase, which as far as I know doesn't happen.

If the wheels can pivot at different angles, then in order to remain tangent to the curved rails, one wheel would have to be at a different swept angle than the other; in other words, it will have to be slightly ahead of the other wheel. But the story is the same in this case as well. The straight line distance has to increase in order to accommodate the curve.

Well, I utterly failed at keeping that short, but it takes a lot of words to paint the picture. It still seems like there's something missing to me.

Glad to see you found the information about the Ackermann geometry. That was one of the first places I was going to send you. 8-)

While the track gauge is kept constant, as is the distance between the road wheels, when the gauge is kept constant, the curve radius is *not*. The inside wheel has to track a much tighter curve than the outside wheel.

If you are doing beam steering, as Arrow does, you have to rotate the entire axle to follow the curve. In the Ackermann-style steering assembly used by Gravitykraft, the wheel carrier pivots relative to the axle (or in fact there doesn't even need to be an actual axle, but that's another issue). So the points directly behind the road wheel will be a constant distance from each other. The tie rod is located ahead of or behind the road wheel, and the distance from the pivot point to the steering knuckle, along with the difference between the length of the tie rod and the wheel gauge determining the difference in angle between the inboard and outboard wheel.

On a coaster, there is an added complication, and it is one of the difficulties with the Lost Coaster of Superstition Mountain (LoCoSuMo) train. For LoCoSuMo, the wheel carriers are a different design from that used on the Timberliner. Each wheel carrier has a conventional guide wheel located directly below (and obviously inboard of) the road wheel, then there is an additional pilot wheel located ahead of the road wheel on the leading axle, and behind the road wheel on the trailing axle. With that design, the guide wheel doesn't really do any guiding at all, it merely provides a side surface to ride against the rail, and because of its location, as the road wheel pivots, the guide wheel remains in the same location relative to the road wheel. Meanwhile, the pilot wheel catches the outboard side of the curve and actually steers the wheel on that side to follow the curve. The tie rod pushes the wheel carrier on the inboard side so that the inboard wheel also follows the curve. The end result of all this is that the steering input comes only from the outboard side of the curve, with the track on the inboard side merely limiting the excursion of the pilot wheel on that side. The upshot of all this is that if the train is running on a straight bit of track, there is no steering input on either side to insure that the wheel carrier goes straight. So while the LoCoSuMo train can handle a 6' radius curve without any trouble, it has some problems going straight. Fortunately, there is almost no straight track on that ride.

The Timberliner train borrows a page from Arrow's playbook to correct for this problem. The Timberliner axle uses two guide wheels, one located ahead of the road wheel, and another located behind it. The dual guide wheel serves to effectively provide steering input on both sides of the track, with both the leading guide wheel on the outboard side, and the trailing guide wheel on the inboard side. As B&M have demonstrated with their inverted coaster, it is a design that actually eliminates the need for a tie rod...on the inverted coaster, the two wheel carriers are completely independent of one another (apart from being attached to a common axle).

I'm going to have to double check a few things to make sure I am getting this right. But you're on the right track, so to speak. The steering arrangement is designed to allow the wheels to *not* pivot parallel to each other because while they are allowed to pivot, the axle is not held perpendicular to the track as the train enters the curve. The wheels are, but the axle is not.

--Dave Althoff, Jr.

But the track gauge on a wood coaster is not held constant. Since the axle restricts the wheel assemblies, the Timberliners will still not steer as well as steel coasters. (Try saying "still not steer as well as steel".)

The two wheel assemblies together will constantly be trying to find the rail it wants to use for steering, so to speak. You can hear this constant struggle on the testing video: http://www.youtube.com/watch?v=aLO0WAlJDtI (1:30 is best)

^Could this be one of the improvements Gravitykraft has/is making?

Sorry, I'm not sure what I'm hearing is a constant struggle to find the rail it wants to use.

How can you tell that that is the sound you're hearing?

Personally, I'm wondering if Mike from Gravitykraft ever mounted a video camera on the Timberliner to watch the wheel assemblies track the curves to see how they really operate in the real world. I am not convinced that the sound in the Raven testing video indicates any problem tracking, and in fact the low speed segments at the beginning and end of the ride, where the wheel carriers are most visible, do not seem to show any hunting at all. By comparison, have you ever watched the axle assembly on an Arrow mine train oscillate back and forth? The beam steering system actually requires a little bit of slop in the guide wheels to allow that axle assembly to turn, and on a Corkscrew or a Mine Train, that axle assembly is quite large; it looks to be about three feet between the front and rear guide wheels.

Somewhere I have seen some of the modeling data on the development of the Timberliner. I don't remember where I saw it, so it may have been proprietary, so I'll refrain from going into even as much detail as I remember (which isn't much). But I know that Gravitykraft experimented (at least in simulations) with a number of different configurations. While all the designs have a certain amount of tracking error...the difference between the "perfect" road wheel path, where the road wheel is always at a tangent to any curve and parallel to the rail...the steerable wheel carrier configuration on the single bench car had by far the least tracking error of any of the configurations they examined. That was the basis of the Gravitykraft configuration, and my understanding is that the testing on the Voyage indicated that they were able to reduce the lateral forces applied to the track (not what the rider feels, but what the track has to endure) by even more than they had predicted. So the empirical evidence, at least through anecdotal presentation, seems to be that the system does work.

--Dave Althoff, Jr.

Thanks for jumping in Dave! I was hoping a technical discussion like this would catch your attention.

I'm still having a problem understanding the geometry though. When you said in your first post that the curve radius is *not* constant, you meant that each running rail is a different radius, correct? Let me try to describe the problem I'm seeing with this, and please correct me if I'm wrong on any points:

1. Let's take a curve that is perfectly circular. The gauge remains constant, and all three radii (the spine and the two rails) are concentric, but not equal.
2. Take a set of wheel assemblies whose pivot (yaw) axes run vertically straight through the road wheels, and thus straight through the point of contact between the road wheels and the rail. Let's call the distance between the yaw axes the axle (even though there doesn't have to be a physical axle, as you mentioned).
3. Now, when the car is positioned on a straight section of track, the road wheels are parallel to each other and perpendicular to the axle, and thus the axle is perpendicular to the rails.
4. When the car enters a curved section, for the axle to remain the same length (which it has to), it has to remain perpendicular to both rails, correct? The shortest distance between two concentric curves is a line that is perpendicular to both, whose extension runs through the center of curvature for the rails/spine/track. This axle distance is essentially the track gauge, which is the same distance as it was when the track was straight and everything was nicely aligned. Therefore, I don't see how the wheels would ever pivot, since by definition an axle that is perpendicular to the rails would have perpendicular lines (road wheels) that are tangent to the rail, which is the intent of the design.
5. Another way to think about it is to look at the swept angle. Let's say the turn is 90 degrees to the left. If the wheels remain parallel to each other, then they will follow the same swept angle as they navigate through the turn. The radius of curvature of the wheel path will be the same as the radius of curvature of its corresponding rail.
6. Now consider if the wheels aren't parallel to each other (the Wikipedia Ackermann link I posted has a good picture of this). They will still follow the same radius of curvature as their rails, but now they're at different swept angles. In other words, the inner wheel is slightly ahead of the outer wheel. This forms a triangle, from the inner wheel to the center of curvature (inner wheel radius of curvature), out to the outer wheel (its radius of curvature), and back to the inner wheel (axle). As the swept angles of the wheels spread apart (tighter curve), the axle has to grow in length. How can this be?! The only way for the axle to remain the same length as it was on the straight section of track is for the swept angles to converge, which gets us back to wheels that are both tangent to the rails, parallel to each other, and perpendicular to the axle. Either this, or the track gauge has to change corresponding to the tightness of the curve.

See the conundrum?

I think I might have found the answer. Watching the video that Two Fifteen posted, I noticed how much wider the flat steel running rail is than the road wheel. This would allow the road wheels to follow their own radius of curvature, which would be slightly different than the true center of the running rail. I suppose that the road wheel still wouldn't have to skid laterally, that it would point in the direction of travel, but the extra width of the steel rail would allow for some play in the radius of curvature of the wheels.

That video provides a great look at the wheel assembly as it enters that first turn. At 0:11, you can see that the wheel appears to be riding right down the center of the rail, right along the scoring line (produced by the original PTC wheels?). A second or so later, from 0:12 to 0:13, you can see that when the wheels pivot, they ride slightly off center, on the inside of the center scoring line for the wheels that we can see.

Based on this, I would think that a steel coaster's track gauge would have to change according to the curve for cars that have independently pivoting wheel assemblies, since the road wheels are more precisely fitted to the tubular rails.

Two Fifteen's video of the "chatter" at 1:30 struck me as funny. I mean, seriously, there are WAY worse instances of that sort of "hunting" throughout a turn. For example - my main problem with Hades is that 180* turn after coming back out of the underground "return" section....the chattering starts and completely ruins a good 15-20 seconds of trackwork right near the end of the ride. Anyone who's ridden Hades after year one knows EXACTLY what part of the ride I'm referring to - and hates it.

I'm pretty sure Mike has mountains of data showing the forces exerted by the ride on the trains, and those graphs are incredibly smooth compared to those of a PTC. You don't need video to verify that. :)

I wasn't paying attention to the noise in the video, I was just trying to figure out how the cars actually steered through the curves, and it's pretty apparent that the road wheels don't follow the exact centerline of the running rails, hence the extra width of those rails compared to the wheels.

I'm not suggesting that the trains don't track smoothly because of this, I was just failing to understand how the mechanism worked, but I think I get it now. It still begs to question of what happens to the track gauge on steel coasters.

Link
http://de.wikipedia.org/wiki/Achterbahnfahrwerk#Rahmen

Hi! I enjoyed the discussion since I was already figuring out how this should work a time ago. I also arrived at 2 types, I called them Bogie and also Ackermann style. Bogie because of these things under train waggons, that steer them. I was so free to quote RideMan in my german Wikipediaarticle which has nice graphics about it!
Thx :) cocoo