Forces in the Cars

Your point #2 is correct.

In this situation, each locomotive carries whatever weight it is capable of. The coupler slack on the front of the train will be "stretched", while the coupler slack on the rear of the train will be "bunched." (Those are the terms used in railroading.)

At some point in the train there will be a coupler that is not stretched or bunched...it's just floating along with no strain on it at all. The couplers ahead of this point will be stretched and the lead locomotive is carrying the weight of those cars. The couplers behind this point will be bunched and the trailing helpers are carrying the weight of those cars.

Where do these helpers live that they can come dashing out to help a train up the curve?  I'm assuming there is a facility fairly close that they have some engines just waiting for this duty?

@gunrunnerjohn posted:

Where do these helpers live that they can come dashing out to help a train up the curve?

Most likely Altoona, which is the base of the grade.

I'm assuming there is a facility fairly close that they have some engines just waiting for this duty?

Correct. At least there was, prior to the use of DPUs.

The helpers work out of Altoona, which is at the bottom of the grade, or out of Cresson, which is at the top of the hill.

Most trains on this hill use helpers as far as Cresson. Then it's downhill all the way to Pittsburgh!

I guess after they pass Cresson, they need brakers and not helpers!

Well...it’s not a steep down grade to Pittsburgh, just a long, very gradual grade with stretches of level running, too.

West out of Altoona the railroad climbs out of a valley between two mountain ridges in a fairly short distance, then gradually descends into the Ohio River valley in Pittsburgh.

The Cresson engine facility is a bit below the top of the hill. It’s technically on the west slope. The crest is just shy of the tunnels in Gallitzin heading east.

The westbound grade from Gallitzin to Johnstown is still over a percent. Helpers are often called out of Conemaugh to assist eastbound trains as well.

Jack, you are asking about the node.

When mid-train and/or rear of train helpers are used, this creates a node.

A node is a location within the train which floats as the train passes over slight variations in gradient and negotiates curves, or as the road and helper engine consists slightly increase or reduce speed independently of each other.  At the node, on an ascending grade, the couplers of the cars ahead are stretched, while those behind the node are bunched.  At the node, one pair of couplers is neither pulling nor pushing, usually only for a moment while the node floats to the next pair of couplers.  On a descending grade, assuming that dynamic braking is in use on both the road locomotive and the helper(s), the coupler tension is the opposite ahead of and to the rear of the node, although, if the train air brakes are also in use, they can create extra nodes within the train.

When more than one helper engine is used (i. e., mid-train and rear) then there is more than one node, as each helper engine creates a node.  Each mid-train helper can create two nodes -- one ahead of it and the other behind it -- if there is also another helper to the rear.

Locomotive Engineers use elementary physics in order to learn techniques and develop skills used for managing the node to the degree that it is possible.  Every train is a little but different.

Jack, I'm answering this part of your query separately, as I did not want to add anything more to my post about the node.

There are two cases in which helper engines would be used:

1. The weight of the train exceeds the tonnage rating for the road locomotive consist.
2. The weight of the train exceeds maximum rated drawbar strength at the head end.

Railroads publish a tonnage rating for each class of locomotive on each portion of the railroad.  This is usually published in the Special Instructions of employee timetables, specifying track between two specific timetable stations.  Some cover 100 miles of mildly undulating prairie, while others cover a portion of the line where there is a significant ascending grade.  The tonnage rating is calculated by the Engineering and Mechanical Departments so as to compensate for the grade, curvature, and maximum rated drawbar strength.  It is primarily the responsibility of the Dispatching Office to assign a locomotive capable of ascending grades unassisted or to arrange for helpers to be used.  The Conductor and the Engineer are secondarily responsible for seeing to it that the tonnage of their train does not exceed the maximum allowable tonnage on their respective district.

In case 1, the locomotive rating, there are two factors:  horsepower and tractive effort.  Horsepower determines the speed at which the train will proceed toward the summit of the grade.  Tractive effort determines the amount of tonnage that a locomotive can start and continuously move on the grade.  DC locomotives such as the GE Dash9-44CW or the EMD SD70 have continuous traction motor amperage ratings.  When the locomotive is pulling a train in maximum throttle position, traction motor current increases as speed decreases.  When the speed has reduced to the point at which the ammeter indicates the maximum continuous amperage (normally around 13 MPH), the locomotive is at its tonnage rating for that location.  It is allowable to exceed the continuous amperage rating for short times and these are marked on or near the ammeter for the Engineer to use if necessary.  Usually there is a 15 minute rating, a 10 minute rating and a 5 minute rating.  These each stand alone and cannot be combined for their respective full values.  If the locomotive is pulling hard and uses up the short time rating, the train must be stopped and the traction motors cooled by placing the reverse lever in neutral, opening the generator field switch, and placing the throttle in Run-4 to use the traction motor blowers to air-cool the motors.  

Locomotive traction motors do not have windings like smaller electric motors.  Instead, they have copper commutator bars radiating outward from the center and held in place by a special plastic cement.  Excessive amperage can cause enough heat so that, when the motor eventually does cool back down, one or more of the commutators can become loose, move outward due to centrifugal force, and knock pieces off of the brushes, causing arcing and physical damage in the traction motor.  In reality, it is pointless to blow the traction motors cool and then try to start the same train to proceed onward, so, normally, the crew will have to secure the rear portion of the train with handbrakes and cut off a head portion sufficient to fit within a siding or other auxiliary track past the summit of the grade ahead, and then return for the rear portion of the train, coupling the two portions together again, to proceed to their destination.  This is called doubling the hill, and is time consuming.  Most main lines today are so busy that a train doubling the hill will cause trains for a considerable distance in both directions to come to a stop, and it can take a whole day for train traffic to again be fluid on that territory.

AC locomotives such as the EMD SD70MAC or the GE C-44ACi do not have a continuous amperage rating.  They can drag down to 1 MPH in Run-8 on good, dry, rail, and stay at that speed all day.  However, tractive effort is a greater consideration when AC locomotives are used.  They are more likely to be able to pull a train that exceeds the strength of the steel in the drawbars, leading to case 2, the drawbar rating.  

The formula commonly used to avoid exceeding the rating of the DC traction motors is horsepower per ton, and gross tonnage is used to calculate the rating for the drawbars.

In either case, the crew is required to set out cars at some point, if necessary, to comply with rated tonnage prior to entering the ascending grade.  That -- barring an unplanned event such as failure of one of the locomotive units -- avoids having to stop and double the hill . . . Or . . . helpers must be employed.

Your question, as I read it, pertained mainly to mountain grade territory, but the same considerations exist on the prairie.  When a train in the flatlands, with one or two diesel-electric units and a lot of cars (such as a branch line local during the summer wheat rush), encounters a slight ascending or descending grade as the track undulates, speed increases or decreases accordingly.  So there are tonnage ratings on all districts of a railroad, not just on the heavy grades and, yes, a train can stall on the great plains as well as in the mountains.  And, out on the plains there is a node it the train, and it floats.