Model Railroad System  2.2.2
Overall User Manaual
LocoPull Program Reference

Basis and Mathematics

This program is based on the information posted by Mark U. on the Yahoo XTrkCad list at the URL http://groups.yahoo.com/group/XTrkCad/message/4983 and the information supplied by rtroop on the TrainBoard forum in post no. 9 at the URL http://www.trainboard.com/grapevine/showthread.php?t=114497. This is a standalone program that incorporates the formulas presented in Mark U's spreadsheet and explained in rtroop's message. The formulas are as follows:

\begin{eqnarray} E_{unit} &=& W_{unit}{A} \\ E &=& E_{unit}{N} \\ R_{ave} &=& W_{ave}{F} \\ C_{0~Grade} &=& \Biggl\lfloor \frac{E}{R_{ave}} \Biggr\rfloor \\ R_{grade} &=& W_{ave}{G} \\ R_{net~at~grade} &=& R_{ave} + R_{grade} \\ R_{unit~at~grade} &=& W_{unit}{G} \\ D &=& \frac{5730}{\frac{rS}{12}} \\ C_{grade~and~curve} &=& \Biggl\lfloor \frac{ {E} - {N} {W_{unit}} ( G + F + D ) } { {R_{ave}} + {W_{ave}} ( G + {F_{per~degree}} {D} ) } \Biggr\rfloor \end{eqnarray}

Where:

$W_{unit}$
is the weight of each locomotive in ounces.
$A$
is the adhesion factor generally 25%.
$E_{unit}$
is the tractive effort per unit in ounces.
$E$
is the net tractive effort in ounces.
$N$
is the number of units.
$F$
is the resistance factor of each car, typically 4% for N scale cars.
$W_{ave}$
is the average weight per car, typically 1 ounce for N scale cars.
$R_{ave}$
is the average rolling resistance of each car.
$C_{0~Grade}$
is the capacity of the train on level, straight track.
$G$
is the percent of grade.
$R_{grade}$
is the added rolling resistance of each car due to grade.
$R_{net~at~grade}$
is the net rolling resistance of each car at grade.
$r$
is the track radius in inches.
$S$
is the scale factor (160 for N scale, 87 for H0 scale, etc.).
$D$
is the degree of curvature.
$F_{per~degree}$
is the resistance factor per degree of curvature, typically .04%.
$C_{grade~and~curve}$
is the capacity of the train on at grade on a curve.

The GUI

The main GUI screen of the LocoPull program is shown below. The GUI is broken down into sections:

  • The Scale section. The scale is selected here.
  • The Locomotive Information section. Information about the locomotives is entered here. The number of locomotives, how much they weigh each, and their adhesion factor. The tractive effort for each unit and the net tractive effort are computed and displayed here. It is assumed that all of the powered engines are the same, typically the same make and model, with the same weight and same adhesion factor.
  • The Consist Information. Information about the cars, including their average weight and their average resistance factor are entered and the rolling rolling resistance is computed and displayed.
  • The Zero-grade Capacity section. The maximum number of cars that can be pulled on a straight track on a level grade is computed and displayed here.
  • The Grade Information section. The percent of grade is entered and the added rolling resistance per car at grade, the net rolling resistance, and the added resistance per unit are computed and displayed here.
  • The Curve Information section. The radius of the curve in inches and the rolling resistance per degree of curve are entered and the degree of curvature is computed and displayed.
  • The Capacity at Grade and Curve section. This is the maximum number of cars that can be pulled at the grade and curve specified.
  • Calculate button. This button performs the calculation and updates all of the displayed values.

The Scale

The scale selection simply select the scale and is used to compute the degree of curvature.

Locomotive Information

This section of the GUI gathers information about the locomotives pulling the train. It is assumed that all of the locomotives have the same tractive effort, that is they are the same weight and have the same adhesion factor. This would generally be the case if the locomotives were the make and model. Three inputs are gathered in this section: the number of locomotives, the weight of each locomotive, and the adhesion factor of the locomotives. Two intermediate outputs are displayed here: the tractive effort of each locomotive and the net tractive effort of all of the locomotives together.

Consist Information

This section gathers two inputs and displays one intermediate result. The two inputs are the average weight of the cars and the average rolling resistance factor. The intermediate result is the average car rolling resistance.

Zero-grade capacity

This is simply the net tractive effort divided by the average car rolling resistance. The floor of the result is displayed as a whole number (since pulling a fraction of a car is not meaningful).

Grade information

One input is gathered and three intermediate results are displayed. The input is the percent of grade and the intermediate results displayed are the added rolling resistance at grade of each car, the net rolling resistance per car, and the added rolling resistance of each locomotive at grade.

Curve information

This section gathers two inputs and displays one intermediate result. The added inputs are the curve radius and the rolling resistance per degree of curvature and the intermediate result is the degree of curvature.

Capacity and Grade plus Curve

This is just the tractive effort less the tractive effort needed to pull the locomotives themselves divided by the combined rolling resistance of the average car: base rolling resistance plus the added rolling resistance due to grade, plus the added rolling resistance due to the curvature. The floor of the result is displayed as a whole number (since pulling a fraction of a car is not meaningful).