A trailer doesn't react to a tractor's backing up until 10 feet of travel

256bits · Sep 18, 2016

sophiecentaur said:

As far as I can see, the rule is followed by most TT combinations because the other dimensions are much the same, not surprisingly because they are probably near optimal. Overhang, wheelbases and positions of axles (and even the limits of the tractor steering, probably) will be what governs the locus of all the wheels.

Three types of tractors, each with its own version of the rule guidline ( for new drivers )
Sleeper - the longest tractor wheelbase - most dificult to back up with.
Regular - for day trips - medium whellbase - what most one will see on the road.
Shuttle - shortest wheelbase - easy connect diconnect - open view - used around yards to manipulate the trailers around - excessively productive compared to the other types.

256bits · Sep 18, 2016

256bits said:

Three types of tractors, each with its own version of the rule guidline ( for new drivers )
Sleeper - the longest tractor wheelbase - most dificult to back up with.
Regular - for day trips - medium whellbase - what most one will see on the road.
Shuttle - shortest wheelbase - easy connect diconnect - open view - used around yards to manipulate the trailers around - excessively productive compared to the other types.

PS. trailers. 53 foot.
Rear three axle and two axle.
Rear axle can be on a dolly that can be moved ( just do the release and push the trailer box back or forth on the locked rear axles ) from most rear to about 1/3 from the rear, depending upon weight distribution.
Dolley position will affect the "ten foot rule" and driver will have to adjust.

EnumaElish · Sep 18, 2016

sophiecentaur said:

As far as I can see, the rule is followed by most TT combinations

256bits said:

Dolley position will affect the "ten foot rule" and driver will have to adjust.

Are you all referring to a rule in the sense of a physics theorem, or as folklore regardless of what physics says about it?

sophiecentaur · Sep 18, 2016

EnumaElish said:

a rule in the sense of a physics theorem,

This isn't 'Physics'. It's Maths (Geometry), at least to a first approximation. You would get similar results if you treat everything as 'idea' and with no slippage or drag. The patterns will be derived from combinations of cycloid and tractrix type curves.

EnumaElish · Sep 18, 2016

sophiecentaur said:

This isn't 'Physics'. It's Maths (Geometry), at least to a first approximation. You would get similar results if you treat everything as 'idea' and with no slippage or drag. The patterns will be derived from combinations of cycloid and tractrix type curves.

Great. Now read the OP. Either point to a proof (sketchy is okay) or abandon all pretense.

I'll go first. My railroad analogy was posted under the false presumption that the OP was about backing up. I've gone back and reviewed it. I realize that it's about a change of direction while backing up. So my RR analogy totally misses the point. Thanks for pointing that out.

jim hardy · Sep 18, 2016

The angle between tractor's axis and trailer's axis drives itself toward zero when moving forward
and away from zero when moving backward.

When backing , the rate of angle increase per foot of travel depends on the angle. At zero angle it's zero. At any other angle it increases , proportional to magnitude of angle.
Anything whose rate of change is proportional to its magnitude is suffering exponential growth.

When moving forward , the rate of angle decrease per foot of travel depends on the angle. At zero angle it's zero. At any other angle it decreases, proportional to magnitude of angle. That's exponential decay instead of growth.

A perfectly aligned tractor and trailer with angle = 0 would be able to back clear across the Seven Mile Bridge were it not for that dogleg.
.

Exponential growth begins imperceptibly.
So while it might take something like ten feet for the rate of change of angle to become perceptible, rest assured it started much earlier.
Forward motion is the opposite - angle approaches zero asymptotically.

I recently moved the axle of my 12 foot long utility trailer eight inches rearward for two reasons.
1) make it easier to back up. It was overly prone to jacknife , as all short trailers are. Look at the geometry above.
2) move axle behind center of gravity to stop divergent side to side oscillations on the highway.
That dramatically improved its "user friendliness" on both counts.

old jim

sophiecentaur · Sep 18, 2016

EnumaElish said:

Great. Now read the OP. Either point to a proof (sketchy is okay) or abandon all pretense.

I am not after a "proof" because that would certainly be very complicated but the basic behaviour of back and front wheels on a car will follow the same sort of argument as is used in the derivation of the tractrix curve. (with modifications that make it more or less impossible for me).
The following is "sketchy" but I think it heads on the right direction. The behaviour of the tractor when backing up and turning is, I reckon, based on the tractrix curve - see this link and the animation half way down (pushing part). That curve shows what would happen if the front wheels were steered to follow a straight path backwards but when there has been a slight deviation (i.e. it chooses between right or left) It will produce a jackknife, eventually and the curvature increases rapidly towards that condition. But the driver will prevent this condition by chasing a better path. This involves keeping to the same point on a newly positioned tractrix with a different pair of exes. It seems that for all steered vehicles, the tractrix curves are dependent only on the wheelbase and the direction of the steering motion relative to the axis. he shorter the vehicle, the sooner it will turn by a specified angle. The long trailer must move back further than the tractor, to achieve a given angle and, of course, the pivot will always be on the opposite side of the axis from the tractor steered wheels. So the reasoning in the OP would seem to be correct when it says that the reverse steering for the trailer, is always in the other direction but much smaller with a long trailer. Looking at the animation, the deviation from straight is very little until the movement of the driven end is something like the length of the string / bar / wheelbase. At this point the trailer will not deviate by much (tractrix applies here too, I think) - just enough to be noticed by the driver. The lateral movement of the pivot divided by the trailer length would give you the angle
The ten foot 'rule' is obviously very crude but it was probably thought up when rigs became all of fairly similar proportions (related to a Standard Container, these days) and the resulting error is actually not very great.
I know it would never apply to the situation of a saloon car and a short, general purpose trailer that's used for trips to the local dump or for camping because the trailer length is about half the wheelbase of the vehicle. It will jackknife in about one metre of bad reversing.
Edit: The 10 ft rule is only approximate but it must relate to the wheelbase of the tractor (and they will all be pretty similar). Using a specific number of turn of the wheels may be a better rule because (I imagine) the bigger tractors will also have bigger wheels (?) so there will be some compensating factor doing it this way.

EnumaElish · Sep 19, 2016

I think the rule can be seen in the attached video, mainly between 1:46 and 1:48 and up to 1:52. At 1:46 the trailer is halfway jackknifed. As the tractor backs up, the trailer pretty much pivots at the same spot. At 1:49 it starts to move back. So my thinking is, an actual tractor would have moved about 10 feet between 1:46 and 1:49. Hence the "10-foot rule."

http://www.loveyourrv.com/back-fifth-wheel-trailer/

P.S. Had the trailer fully jackknifed with a 90-degree angle, no amount of backing up could have pushed it back; it would merely pivot on its wheels. I suppose in that case the applicable rule would be the "no good rule" instead of the "ten foot rule." But then, a 90-degree angle is probably not part of an optimal trajectory when backing up a trailer.

P.P.S. Just realized @OCR had already explained this. And with a real-life video. Minus above hilarity.

jim hardy · Sep 20, 2016

Can a Tesla do this ?

http://www.usatoday.com/story/money/cars/2015/05/21/ford-f-150-backup-assist/27705471/

OCR · Sep 20, 2016

EnumaElish said:

But then, a 90-degree angle is probably not part of an optimal trajectory when backing up a trailer.

In certain circumstances a 90°, or even more, angle can be useful to get the tractor in a better position for making pull-ups, for instance... I've used the technique when forced to make a u-turn on narrow roads.

I have even unloaded our dozer, and "dozed" the back end of our lowboy into a better position... that might not work too good in an RV park, though.[COLOR=#black]..[/COLOR] lol

Just a couple pictures of dozer on lowboy... I was in the Big Horns, heading home from a fire.

sophiecentaur · Sep 21, 2016

Shame there's only a 'like' available for the above post. It would be nice to put in a 'heart'.

DaveC426913 · Sep 21, 2016

New Series: The Littlest Dozer. (spin off from The Littlest Hobo*)

Goes across country, town to town, doing good deeds and helpin' folk outta trouble.