Hunting Prevention of High Speed Intermodals

[Junctionfan]

Hello Everybody,

UP and NS's Blue Streak service for the "Super Flyer", calls for 4hp per ton and to go to speeds of 78mph.

How does UP think they are going to do this? At that speed, won't trailers hunt? They say they are using TTRX 3 unit spine cars; how effective are they at high-speeds? Are they less likely to hunt versus the 5 unit TTAX spine car?

Andrew

[Overmod]

Junctionfan:

It isn't the 'trailers' that hunt, it's the trucks under the cars. Peter (M636C) will weigh in with his knowledge of this as well.

Keep in mind that hunting is a complex motion, not just the trucks swinging back and forth. Also keep in mind that measures that reduce hunting may have an impact on ride, lower-speed flexibility, curve wear, equalization, and other factors.

Some forms of articulation can be quite effective at eliminating truck hunting, even with three-piece truck designs -- in cases where that is so, the more articulated joints you have in the train, the fewer locations where careful anti-hunting methods and devices would need to be used. Let me refrain from answering your 3-unit vs. 5-unit question for a moment.

The problem is that conventional 'articulation' of two car ends over a common truck needs to involve two separate longitudinal points on the bolster or truck frame to give best 'anti-hunting' results. The principle is that the differential draft lines through the two relative car-end connections will act to 'steer' the bolster or frame, which in turn steers the axles and wheels, and in the process applies force that damps out a tendency for the truck frame to rotate freely under built-up oscillation force. This eliminates the nosing couple that helps drive hunting. Unfortunately, some container equipment is designed to run on conventional trucks that have a single center pivot; these have somewhat better lateral guiding but don't do any more than a conventional underframe in retarding nosing. So I'd expect a 5-unit articulated car to do better than a 3-unit (and a 10-unit better than either!) but not as much from a 'hunting' standpoint as general tracking.

There are other approaches that can mitigate problems with truck slew/lozenging, steering, and shock absorption. In my opinion, some form of outside bolster support is likely to become necessary, especially for stack trains, in order to operate well at higher speed. These approaches become much more practical for relatively reserved-service equipment with high utilization, as the incremental capital and maintenance requirements can be more easily arranged (compared to interchange cars) etc.

Keep in mind that merely stiffening things up won't work in the 'big picture' -- a method of reducing truck oscillation can't induce substantial additional wear on curves; a method of improving side bearing shouldn't have a negative effect on tracking or stability.

More later

[Mikeygaw]

an even better question... what exactly is 'hunting'?

[Overmod]

Hunting is periodic motion of the trucks (bogies), described as a combination of nosing (yaw) and rolling. A given truck will have fundamental 'frequencies' of oscillation, just as a spring does, and it will tend to move more and more if driven in the wrong planes at that frequency. Complex interactions and nonlinear forces are often involved -- which means that the onset of hunting may not occur until a critical speed or force range is reached, and then hunting action may become severe, even critical, within a fairly short time or with only a few more mph speed (remember that energy goes up as the square of the speed, so very small nominal increments have increasing importance)

Since modern freight trucks are almost all 'three-piece' designs, in which there is no explicit rigid frame, other forms of oscillation or distortion can occur. One of these is slew/lozenging, in which the sideframes and axles assume a parallelogram relationship, restrained only by the springing at the bolsters and the side clearances between frames and bolster (but leverage effects here are comparatively high) and, to a much lesser extent, by brake rigging. In most truck designs, the frame ends rest directly on the individual bearing shells, and gravity is the only vertical 'restoring force' and friction the only shock-dissipating force. This often becomes inadequate to damp out slew forces at high speeds, or when track profiles are worn or poorly lined. The problem would be particularly evident if some component of the slew's natural frequency became coordinated with any of the forces leading to hunting of the truck as a whole.

Peter (et al.), add to this discussion as you see fit.

[Junctionfan]

Why don't they give passenger trucks to the intermodal cars than and arm them with shock absorbers?

[dehusman]

Actually the UP's trains are now 70 mph, not 78 mph.

Dave H.

[Junctionfan]

QUOTE: Originally posted by dehusman

Actually the UP's trains are now 70 mph, not 78 mph.

Dave H.

Currently yes but I heard that this new Blue Streak Super Flyer between Memphis and Los Angelas was to go at 74mph (correction not 78mph-I goofed) at some places where the track is good I guess.

[Overmod]

Passenger trucks are considerably more complicated, less flexible, and co$t an enormous amount more per unit. The good modern designs also require extensive connections (for struts, dampers, etc.) best suited to a full-width carbody instead of a spine car. An additional issue is that parts for them would need to be stocked in the usual shop areas, which has historically been a problem for specialized rail equipment.

Since there's no objective reason why a three-piece design can't be modified for proper operation at any "economically-sensible" intermodal-train speed (cf. early UP practice, and Reading use of Taylor trucks) I think it makes better sense to concentrate design and development efforts there. The design on the MHCs appears to be a reasonable compromise, complete with shock absorber, although I have no information from FRA/DOT at hand on how well they track and perform. This, I think, would be the truck to spec on a fast intermodal that was either being built 'new' or modified specifically for high speed.

There are further improvements to three-piece trucks that make them better suited to high speed, many of which have already been discussed in threads here. I would start researching this area by e-mailing Peter (M636C) and having him bring you up to speed on his direct experience with this.

[Anonymous]

The max speed on the UP is 70 in places. The only trains permitted to run at 79 is Amtrak and UP passenger trains.Anything over 79 mph has to have ats/atc equipped power.

[Junctionfan]

If I remember correctly (I have to read the article over again) I seem to remember that they plan on using ats/ atc equipped power. I remember seeing those kind of symbols anyways.

[Junctionfan]

I wonder than if there already has been an announcement for the line to be upgraded for that than. I don't remember anybody on the forum talking about it though.

[Junctionfan]

I'd like to know what the heck they are talking about than. I must find the story again so I can hyperlink it.

[Overmod]

Clarification, please: If it's coming out of "Memphis" on UP, it almost certainly would be originating at the yard in Marion, Ark., not on the east side of the Mississippi (where Memphis is). To my knowledge, only BNSF, CSX, and to a limited extent NS have intermodal facilities on the east side of a cross-Mississippi connection; CNIC of course has sizable capacity but no river crossing in that area. It would be interesting to see whether there are transfer moves or connections across the river via rail, as opposed to rubber-tire moves via I-40/240 and I-55 which seem a much more direct way to accompli***ransfer from the various east-side facilities...

[Paul Milenkovic]

Overmod:

Tell me if I have a handle on this matter of truck hunting.

The basic "engine" of wheel steering and hence oversteer in the form of hunting is the cone taper of the wheels. A wheelset with a constant cone taper will steer back and forth in a sine wave pattern, and the width of the oscillation will only grow in proportion to disturbances -- it doesn't grow exponentially. If you tie a pair of axles into a truck, you should get some damping in the form of the forces required to rotate a wheel at a slightly different speed than it wants to rotate on its own.

So a pair of axles and a truck by itself shouldn't have a critical speed where it shakes itself off the tracks -- it should always be stable even if the damping is very poor. So I was never very clear on where the critical speed -- the speed where oscillations can grow exponentially -- comes from. From trying to understand some papers in Journal of Vehicle Dynamics, I think the added factor is that you have a carbody on top of the truck -- when the wheel steers left, the truck goes left, and the carbody goes with it, but when the wheel and truck steer right, some force is required to stop the carbody from going left and make it go right, and things are even more complicated when the carbody sits on top of springs.

The reason I think this is that I had a friend who misloaded a trailer on his car, and when he hit 40 MPH, the darned thing started swaying so bad it almost ran him off the road. He thought loading the trailer to the front so that his rear car springs were sagging looked "uncool", but he found out the hard way there is a reason you load a trailer that way.

It seems that the steering effect of the combined rail-wheel taper together with the stiffness of the truck is not enough to describe the behavior -- you have to take into account what is swaying around on top of the truck.

Given that there are so many factors that interact, it seems the only way you can predict the critical speed is to either 1) solve the equations on a computer, 2) put a train car on shaker rollers, or 3) put an instrumented train car on rails. But is it possible to come up with a simplified equation that you can solve without a computer that includes enough factors that it gives a critical speed -- a speed where the hunting grows exponentially? What factors need to go into that equation?

Part of the reason I ask is that in a lot of disciplines they have something called a "model" -- actually a whole set of equations describing the behavior. In the global warming debate, there are these climate models which are vast sets of equations that require a computer to solve for figuring out the temperature of the atmosphere.

One direction you can go with a model is to include the kitchen sink -- come up with as detailed a model as you know how and then use a computer to solve it. The other direction is to come up with as simple or cartoon-like a model you can -- if you make it simple enough, you may be able to solve it without a computer, but even if you need a computer, the simple model may only need a small number of "parameters" to describe the configuration of the model. The purpose of the simple model is to figure the bare minimum requirements to duplicate the behavior of the observed system in order to better understand it.

Do people have a simplified model (set of equations) to describe hunting, and what is the bare minimum of effects you have to include to get a hunting critical speed?

[Paul Milenkovic]

My understanding of the matter after doing a lot of Web surfing and looking at papers in the engineering literature is that a 1 in 20 taper is common for freight cars while anything from a 1 in 20 to a 1 in 40 taper is used for passenger car wheels. The Japanese use a 1 in 40 taper on the Bullet Train (Shinkansen).

Don't know of anyone who uses a flat tread on passenger cars unless you count Talgo, which lacks the solid axle connection between wheels and hence the self-steer. I am not clear on how Talgo avoids contacting the flanges a lot (one British Web site sneered that Talgo does ride the flanges), but it seems they use a hollow taper combined with the force of gravity to center the wheels. There are things you can do with the wheel profile to avoid an abrupt flange contact as well.

The advantages of 1 in 20 taper are 1) greater steering force reduces wear on curves and 2) maintains steering force as the wheel wears down. The advantage of the 1in 40 taper is that it has reduced steering force and can help reduce hunting at high speed in combination with other factors. The disadvantage of 1 in 40 is that it require more maintenance as the worn profile can be very bad.

A Japanese Web site was claiming that the newer Bullet Trains use some kind of non-conical taper that better approximates a worn profile to cut down on maintenance, and there is something called a Heuman profile along the same lines, but I don't much understand how they work.

[Overmod]

Whoa there big fella! The conical tread on car wheels is MUCH more important than providing draft... not that that matters too much since the wheels are chilled-iron in the tread area, meaning they'd come out with clearance even with zero taper!

My understanding was that the taper, in fact, is what provides the actual centering force in normal running, keeping the flanges and in some cases even the 'gauge-corner' fillet from contact. There is some good AREMA stuff on the precise interaction between the taper geometry on the wheels and the predictable wear of the railhead.

Look at a tapered roller bearing (I suspect the SKF style is a bit more 'apropos' than the Timken type) to see how the taper mechanics works in principle. The idea is not that different from progressively-loading side motion control on steam-locomotive trailing trucks: the further off center you go, the higher the restoring force, which acts to keep small-period oscillations from growing to large-period ones. You need more extreme force of some kind to overcome this -- and, I suspect, usually several forces which for some reason add long enough to get the truck into nonlinear oscillation, in the absence of meaningful damping forces.

Unfortunately, with railroad trucks, there is only so much excursion that you get with the tapered restoring-force effect -- then you hit the gauge fillet and the flange. Do this with much energy behind it and you'll get a reflected restoring force (metal rail to chilled-iron-tread wheel is pretty damn elastic!) that is rapidly nonlinear. This, I think, not any small-period harmonic instability, is the actual cause of observed 'hunting' -- and I think that there are a relatively large number of possible 'exciting events' that could get such an oscillation started or even 'periodically' pump it at a critical frequency until it becomes self-sustaining on its own.

With respect to hunting: Look for the major oscillating driver to come when the wheelsets begin to make fillet or flange contact with minimal damping about the center pivot; the leading wheelset in each truck is dynamically 'unstable' just as a leading Bissel truck would be, and kinetic shock forces that can 'knock' it across to the opposite gauge-corner or flange contact can easily induce yaw in the truck -- remember the cone gives a restoring force to all moments 'off center'. I strongly suspect (but haven't verified mathematically) that this is one of the principal drivers of slew/lozenging in normal service. Note that this would NOT be a principal cause of hunting in curves, but it might be in a properly lined and surfaced spiral (as this would be made to keep the wheels' coned treads 'on center' and hence allow the necessary bilateral swing that would build up to hunting.

I don't think that pure yaw of the carbody *contributes* substantially to hunting, as there's technically no 'yaw' of the center pivot as the truck oscillates, although it would be easy to speculate that something like a double-stack car might have enough mass to constitute a loaded oscillator to move the entire truck, both axles, laterally if the forward axle were swinging heavily -- and the difference between the lateral axle motions in this case might be a 'driver' of truck slew. One might think that lateral wind gusts might induce sufficient lateral and roll moments to start something like this; it seems clear to me that people are reporting greatly higher drag resistance on intermodal trains than on 'normal' freights, and the quartering and lateral drag on ISO-style outside-flanged containers might be much higher than on smooth-sided cars (I have not seen any papers discussing the aerodynamics of slipstream-to-wind interactions from a train of flanged-side containers, but I'd be very interested to see one!)

Remember that rolling is a component of hunting in the classical model; the energy pumping the roll has to go someplace, that 'someplace' is the bolster springing, and added 'thrust' on the coned face relative to the railhead can increase the restoring force and hence drive the truck into yaw oscillation.

There are some pretty sophisticated models of various kinds of 3-piece truck action 'out there', but they all suffer from a fundamental difficulty of the mechanics -- they're all but certainly nonlinear. Furthermore, they're either nondeterministic or outright chaotic, and therefore sensitive to initial conditions in a formally unpredictable way. When you think about the number of variables in a running intermodal train -- including those that are impossible to predict meaningfully, such as weather conditions, rail or wheel wear, or even precise spring rebound and center-pivot friction -- you can see how difficult it is to determine what the 'bad apple' cars are going to do, and how they'll do it. The recent thread about a single badly-hunting car observed on a high-speed intermodal train in Canada is a reasonable indication of the kind of 'outlier' that might easily crop up on a train with otherwise smoothly-running axles... but (oh dear, I feel a pun coming on!) ... it only takes one bad axle to spoil the whole bunch.

I'd comment that a truck with lousy center-pivot lubrication is probably a poor candidate for hunting, although it contributes more than its 'fair share' to a number of kinds of trackwork wear and damage. One way I have found to avoid this problem is to use a speed-sensitive viscoelastic damper, which firmly resists small-period oscillations but smoothly allows actual pivoting of the truck relative to the carbody or frame in curves. Very good secondary damping (and comparatively soft outside-bolster springing to the carbody) is likely to work on the roll component of hunting, or to allow 'breaking' any resonance between roll and yaw.

The car trailer is a poor analogy (no offense) because the dynamics are completely different. Sway is a result of coupled carbody roll and poor axle mounting -- but note that there is no 'leading' motion as in truck yaw. What I think you'll find is that as the springs load and release, the axle actually tramps fore-and-aft on the mountings (a geometric effect of the way the springs are mounted), and invariably you don't find any damping on these trailers other than gravity and rust (neither of which works very well). The fact that the effect is much more pronounced if the trailer is improperly loaded tail-heavy is not just a factor of polar moment of inertia! (It is valuable to note, however, how small an amount of damping correction is useful in reducing 'sail' at the drawbar or trailer tongue!)

An interesting aside on those 'sagging car springs' -- the CORRECT way to load a trailer is so that the weight is almost perfectly balanced relative to the axle (or center of beam suspension on tandems) so that the tongue weight is no more than about 100 to 150lb (the only reason it needs to be that much is to prevent unloading the hitch or the vehicle's rear axle on certain kinds of bumps or in heavy braking). That sure shouldn't cause springs in good condition to sag too far -- and a pair of air shocks is a simple way to fix that degree of sag for only a small amount of money.

With respect to the Blue Streak: I was ASSuming that the train would originate in the Memphis area with dedicated equipment, and would hence be loaded specially rather than be composed of interchange blocks. I accept without question that at least a substantial portion of UP's intermodal traffic through Memphis is routed via NS (presumably to Atlanta) -- in part because that's the way I see it running (over the ex-Southern route and the Hanrahan Bridge). I would also be delighted to see NS high-speed service (perhaps even from the port of Savannah?) run to meet the Blue Streak service at Marion; in fact, I would think that might constitute a reasonable potential traffic source.

[adrianspeeder]

Whoaaa, this is a good one. Hot dang Overmod, I'm going to reread this one later, lots of info you put out. What is it that you do?

Adrianspeeder

[Overmod]

"Engineering and technical consulting" -- line forms on the right, take a number, please keep your children from pulling the cat's tail... ;-}

[Junctionfan]

I don't think there would be a lot of hunting if it were single stacked would it? Those TTRX spines would only get a single stack so it should be o.k I think.

[Overmod]

Don't have time to run back through posts -- but there was a thread a week or so ago about hunting observed on a Canadian train going in this approximate speed range. If memory serves, that was a single-stack train.

In my opinion, hunting is much more a function of speed than it is of absolute carloading; in fact, I'd expect the greater weight of a stack car to impede some of the mechanisms that induce the damaging components of the oscillations. I didn't really intend for my comments on double-stack aerodynamic load to apply 'across the board' to hunting; remember that it is periodic roll, not tilt induced by wind pressure, that leads to the coupled motion. I have, in the past, wondered about lateral vortex shedding (see the Tacoma Narrows Bridge, then turn the deck up on edge, so to speak) but haven't seen any papers on that.

[oltmannd]

QUOTE: Originally posted by Junctionfan

Why don't they give passenger trucks to the intermodal cars than and arm them with shock absorbers?

Cost! Lots and lots of $$.

[oltmannd]

This is a bit off topic, but Conrail did install new cab signalling on several portions of main line. The Boston line was done first. Later, the Pittsburgh line from Pittsburgh through to Alliance and then on to Cleveland. The attraction was you could do it and remove the wayside block signals, leaving only the fixed approach and home signals.

These installations would qualify for >79 mph operation (but routes and track condition aren't up to it)

[oltmannd]

In no particular order-

1:40 is typical wheel taper in passenger service in the US - and it is hard to maintain. 1:20 is std. freight and a lot of wear is allowed before you reach condemning limits.

Truck hunting and car/trailer sway are both examples of instability, not vibration.

The proper way to load an automobile trailer is with 9-15% of the total weight on the hitch. A couple hundred pounds hitch weight on a 5000# travel trailer is a recipe for disaster. (been there, done that, bought the Tshirt!)

[Anonymous]

After reading all of the posts, I think I would like to toss my coin in.

Hunting, considering the taper of a wheel's tread, should be absolutely normal. And, it would seem to me, the degree or amount of angle of a wheel's taper would affect the period or frequency of hunting.

It also seems to make sense to me that this frequency in terms of actuall distance traveled down the track to move through a complete cycle of lateral oscillation will remain the same regardless of speed ( pendulums, eh? ). A truck will hunt the same amount in the same distance at 5 mph as it would at 50 mph. The only difference would be that at the higher speed, the cycle is completed more quickly.

Could it then be possible that as track speed increases, decreasing the amount of time for a cycle to be completed, a point is reached where inertia of the wheels, axels, truck frame begin to contribute to the amplitude of the oscillation?

What if the momentary inertia became so great as to affect contact between the rail and wheel. instead of "tracking", the wheel begines to be slid back and forth across the top of the rail? on second thought, this might actually increase the period, restoring stability.

What if the amplitude where gradually increased because of increasing inertia of truck and wheels, until a flange makes contact.

Wouldn't the smooth curve of a sine wave be suddenly clipped?

Wouldn't that suddenly reduce the period of the oscillation by at least 1/2 ?

Let's see, a truck, at the limit of it's coping ability, sudenly oscillating at twice the rate.

Could it be this is why passenger wheels have less taper? to give a longer period to their oscillation?

[Anonymous]

This truck, suddenly oscillating at double frequency, would suddenly be far above the critical speed of the oscillation it is currently experiencing, and would not stop until decelerated below the new critical speed.

It seems to me, a truck made of a single piece rigid design would transmit forces from one axel to the other very efficiently, so a moment upseting one axel would be quickly transferred to the other axel.

I would think a truck made of multiple parts with flexibility would break up the transfer of energy from one axel to the other, allowing each axel to move independently and disrupting any possible destructive interactions.

[oltmannd]

jruppert-

It's more a matter of stable vs unstable and at what speed threshold the instability occurs. For a given system, things may be stable at 5 mph meaning there can never be hunting. However at 70 mph, the system may be unstable. This does not mean there WILL be hunting, but there CAN be hunting, if something excites it. Some of the main variables in a railcar related to hunting are length (truck centers and overall), wheel taper, gauge "tightness", polar moment of intertia and speed. Short, empty cars are notorious as are bulkhead flats for hunting.

An example:

Amtrak tested their roadrailer equipment for weeks at speeds up to 110 mph on the NEC only to have it hunt like crazy in NM at 90 mph on the ATSF. The difference turned out to be the ATSF had slightly tighter gauge. The problem was fixed with constant contact sidebearings.

[Overmod]

Let me throw a bit more in, now that this topic is heated up again...

Don, you're right on all counts, BUT I may not have made clear that the oscillation in hunting isn't the same thing as 'vibration' and isn't directly related to the normal sorts of vibration encountered in train operations. Hunting will cause vibration, of course, and some of its initial excitation may have come from vibration sources.

With respect to the trailer: REAL travel trailers are goosenecks ;-} I had been referring to freight utility trailers -- and fairly short ones at that. Anyone thinking of trailering: listen to Don. Likewise, be sure if you have 5000# of travel trailer that you have BOTH a weight-equalizing hitch and a pair of good anti-sail devices... they make life much easier when keeping the tongue in place on the hitch and the trailer in place on the road.

jruppert, you have a fundamental problem in your physics -- pendula are driven by gravity as a restoring force, which is why their period is a function entirely of length and not mass. This is not the case with the yaw of a truck frame, although it will be true of that part of the roll component not driven by inertia and "return" spring rate (e.g., the bolster springs on the side in compression). The restoring force induced by the coned treads is gravitational, of course, but I suspect that any lateral speed built up through this action alone is likely to be minimal; there must either be some 'pumping' to lift the cones further and further up the railhead 'slope' (which is unlikely in pure lateral translation as from wind pressure) or repeated oscillations -- the period of which will not be substantially determined by gravity.

The point about speed increases is that all the accelerations in truck yaw are driven by momentum transfer. Kinetic energy increases as the square of the speed, and all the perturbing moments rise in the same proportion, while the mass and fixed constants (e.g. the taper) of the truck remain essentially constant. I do not think there is an objective proportion between the degree or frequency of yaw and track speed other than this, particularly with respect to any critical speed for the onset of hunting -- my research so far indicates that it's nondeterministic.

It is not my opinion that meaningful hunt-inducing yaw can be observed in normal 3-piece trucks with even normally-worn wheels at low speeds, which would indicate (to me) that a model which claims such yaw is inherent in the truck guiding or design is likely mistaken.

One of the points of my model of resonant excitation is that the "inertia" of the truckset is indeed coupled to increasing yaw under some conditions. If this is what you mean by 'contributory', I would concur, but I think you are suggesting that the truck's polar moment is somehow generating all the force involved, which would be something of a mistake.

Your 'second thought' needs a bit further rethinking: What happens in hunting is not just that the wheeltreads are being 'slid' across the railhead, they're being steered slightly (by the arc of the rotation relative to the truck centerline) but at the same time are constrained to rotate at exactly the same speed (by the very substantial axle). You may determine for yourself what the effects of applied weight on the tread and railhead metallurgy is likely to be in this situation. I don't think that 'restoring stability' is a likely deterministic outcome of such a process, though...

I'm not sure why you think 'clipping' a sine wave will result in frequency multiplication (you're not reasoning by analogy with electrical systems, are you?) Naturally, flange contact will start injecting much more substantial amounts of energy into the yaw-roll system, and one effect of this will be to decrease the time between flange-to-flange contacts if the truck is predisposed to oscillate between flange contacts -- I would draw the analogy to what happens to a dribbled basketball when you start hitting harder on a ball the same distance from the ground. I don't see anything other than this affecting the 'critical frequency' of the truck, however. It's just that much more energy is 'suddenly' being fed into the same system (with its other parameters relatively unchanged) -- if there is no way to remove that energy, it will show up as increased motion, which will be reversed each time a flange makes contact (it taking much, much more energy to lift the wheel up by the flange contact, or to break the flange, than to reflect the wheel's incident lateral motion and, by its connections, the relevant 'rest of the truck frame.'

It may be interesting to speculate on the bearing of rigid vs. non-rigid truck framing on the critical physics of hunting. One point of a pin-guided lead truck, for example, is that flange contact on one leading wheel due to frame yaw will involve contact by the opposite rear wheel, the couple tending roughly to cancel rotation about the center pivot rather than increasing by drag as is the case in a Bissel. There is some evidence that these trucks, when used as trailing trucks, proved unstable at about the critical speed range we're seeing for 3-piece trucks (about 79-81mph) -- I don't have precise data but would welcome anyone who has it (call ahead for best guest bedroom!)

A multiple-part truck with DAMPED flexibility will, of course, 'disrupt ... destructive interactions' -- although I'd stop short of saying "any possible". The question then becomes: Does keeping the axles strictly parallel to the truck frame convey an advantage relative to letting them rack OUT of self-steering positions relative to the track (as happens in truck slew/lozenging). The 'revealed wisdom' on this, so far, has been that parallelism is a Good Thing (hence the sorts of diagonal bracing Peter (M636C) has commented on in other threads.

Bear in mind that it is somewhat difficult to achieve damping of lozenging forces in a typical three-piece configuration that is 'loose' enough at the bolster/sideframe connection to give good equalizing. IIRC the Taylor truck gets around this by providing an explicit circular pivot as a bearing around the bolster-to-sideframe connection, which permits articulation of the sideframes vertically without allowing substantial skew motion.

[Anonymous]

I guess I started my reasoning with the thought "what if a wheel had no taper?"

A perfectly flat tread perfectly parrellel to a perfectly flat rail head, what would limit lateral motion of the wheel in relation to the rail other than contact by the flange? A truck would definately hunt all the time under these conditions, the leading axel would make contact on one side, then the trailing axel, then the leading axel would make contact on the other side, then the trailing axel, because there would be no natural balance point in the center of the tread. I imagine the period of this ocillation would be set by the distance between the axels.

The pendulum is the "arm" between the the center of rotation at the bolster and the point of wheel rail contact. The "arm" swinging in a horizontal plane as the truck wanders then corrects and returns.

It feels safe enough to say gravity acting on the taper of the wheel is a correcting force to maintain contact in the center of the tread, because for the flange to contact the rail head, the point of contact would have to climb the taper.

This is why I feel a pendulum is a good analogy, because for this model I assume a truck has a natural non destructive hunting, an ocillation with a corrective force from gravity, this pendulum having a very small amount of motion.

I think what Oltmand says makes sense, if for some reason the track of a truck is upset and the lateral path of the wheels across the width of the rail head were tracked as a wave would the wave have a decreasing amplitude and increasing period eventually returning to stability? or an increasing amplitude and decreasing period of an unstable system?

This would mean an unstable system doesn't necessarily hunt, but can if provoked.

I was not thinking of electronics when I mentioned clipping, I was thinking of clipping like when the peak of a wave exceedes the limit of a system. If a wave increases in amplitude to infinity beyond the limit of a system the resault is a square wave.

In the system of a rail/flanged wheel, the limit is the flange.

The lateral ocillation of a hunting wheel across the face of the rail being traced as a curve on a graph.

The length of the wave would be the period or frequency and the hight of the wave the amplitude.

The amount of movement provided by the guage width vs. flange width is the vertical limit of the system.

Such a curve should be long and smooth as long as the line stays within the limits (vertical limit of the graph) of the flange, and if the line meets the flange's limit at a very narrow angle be returned gently.

When I mentioned clipping, I meant the amplitude of the line representing the track of the wheel exceedes the vertical limit of the line representing the limit of motion from the flange. Because the wheel cannot actually track this curve, the peak is in effect "clipped". And if the amplitude continues to increase, the angle of the wheel's line and the flange's line intersection will increase, which in reality will mean the flange is hitting the side of the rail's head in a shorter distance and with greater force.

[Anonymous]

The reason I think the clipping of this wave would resualt in a division of the period is because when the flange meets the rail head, that markes the point of reversal. If this point is met with increasing force because of increasing speed, then the period of oscillation will become shorter, increasing the force of the next reversal, making the period shorter, more force, shorter, etc......

this is true if as I assumed, a truck has a constant natural period of long period low amplitude hunting to begine with, to which at a certain speed the force of the correction become destabilizing, causing each succesive correction to become more forcefull in a shorter distance.

But, acording to Oltmand, this speed can actually be greatly exceeded, so long as the system is not provoked. And, in fact this model is not correct, because stable trucks do not hunt at all.

[Anonymous]

I think Oltmand's remark about Amtrak roadrailers and constant contact sidebearings is a posible clue as far as debating frame design.

Could it be that lateral motion between the frame ant the axel at the wheel bearing can be a cause?