Trailing Edge Technology's
Transition Spiral Calculator
Line-by-Line Explanations

Input Section
From Radius The track radius (in feet) at the start of the spiral.  For straight track, leave blank.  For left turns, enter a positive radius.  For right turns, enter a negative radius.
To Radius The track radius (in feet) at the end of the spiral.  For straight track, leave blank.  For left turns, enter a positive radius.  For right turns, enter a negative radius.
Speed The equilibrium, or balance, speed (in MPH).  When traveling at this speed, the train will experience no side forces.  This is usually between 71% and 80% of the maximum speed (see accompanying Primer).
C-C Rail Spacing The distance between the rail centers (in inches).  This is the where the rail superelevation is measured.
C-C Tie Spacing The distance between tie centers (in inches).  This is used to determine the interval between the tie locations and does not need to be the same as the actual tie locations but it is helpful.
Tie Length The length of the tie (in inches).  This is used to determine the superelevation of the tie end.  It may be more accurate to use tie superelevation than rail superelevation to set superelevation when using plastic ties.  This is because plastic ties tend to be quite flat and the tie-end height difference is about twice the rail height difference.


Initial Results
From Superelevation The superelevation of the right rail with respect to the left rail at the start of the transition spiral (in inches).  Negative numbers should be interpreted as raising the left rail, not lowering the right.
To Superelevation The superelevation of the right rail with respect to the left rail at the end of the transition spiral (in inches).  Negative numbers should be interpreted as raising the left rail, not lowering the right.
From Bank Angle The angle across the track with respect to the horizontal plane at the start of the transition spiral (in degrees).  This is not normally used but is provided for informational purposes.
To Bank Angle The angle across the track with respect to the horizontal plane at the end of the transition spiral (in degrees).  This is not normally used but is provided for informational purposes.
Twist Length The minimum length of the transition spiral (in feet) as determined by the twist criteria.  In a left spiral, the front right wheels are higher than all the other wheels and this puts a twist on the car suspension and body.  The recommended limit for twist is 400 : 1.
Jerk Length The minimum length of the transition spiral (in feet) as determined by the jerk criteria.  “Jerk” is the rate of change in acceleration and is particularly annoying to humans (equipment is affected by acceleration, not jerk).  The “Jerk Length” is calculated to prevent discomfort to passengers as the spiral is entered or exited.
Proposed Length This is simply the maximum of the twist length and the jerk length.  If not overridden in the next section, this is the length used to calculate the Transition Spiral.
Transition Type This is a text string which describes the type of Transition Spiral.  This is provided as a check so that input errors may be easily detected.


Length Override
Override Transition Length To override the Proposed Length, enter the desired length of the spiral (in feet).  Otherwise leave blank and the Proposed Length will be use.  This is typically done to have the transition be an integral number of ties or track panels. Reducing the Transition Length to less than 80% of the Twist Transition Length is normally not advisable.


Final Results
Length This is the measure, in feet, of the start (From) and end (To) of the transition spiral.  The measure is from the straight (tangent) track and may not be zero at either end.  In a spiral between sections of same-handed curves, zero will not be in the range at all.
X Pos The length of a line from the tangent track to the start (From) and end (To) of the spiral.  This is measured from the tangent, along the tangent line, and is in inches.
Y Pos The offset of the start (From) and end (To) from an extension of the straight (tangent) track.  This is measured perpendicularly from the extension and is in inches. Positive numbers are to the left of the extension and negative numbers are to the right of the extension, both taken in the direction of travel.
Angle The angular offset of the start (From) and end (To) with respect to the straight (tangent) track.  These angles must be subtracted from the constant-radius curve that the transition is joining.


Tie-by-Tie Track Location Table
Tie No. An integer tie number counted from the straight (tangent) track. If this field is blank this row represents constant-curvature track at the from or to end of the Transition Spiral.
Distance The distance (in feet) from the straight (tangent) track at the specified tie.  This is measured as if on a center (Lionel™) rail.
X The distance (in inches) from the straight track to the tie on an extended straight line.  See the diagram below.
Y The perpendicular distance to the center of the specified tie.  This distance is measured at right angle to the extended straight lines mentioned in the previous entry.  Positive numbers are to the left; negative numbers are to the right.
Rail SE The superelevation of the right rail with respect to the left rail at this tie in the transition spiral (in inches).  Negative numbers should be interpreted as raising the left rail, not lowering the right.
Tie SE The superelevation of the right end of this tie with respect to the left end of this tie in the transition spiral (in inches).  Negative numbers should be interpreted as raising the left end of this tie, not lowering the right end.
X' The distance (in inches) to the center of the specified tie measured along a line from the "From" end to the "To" end.
Y' The perpendicular distance to the center of the specified tie.  This distance is measured at right angle to the straight line mentioned in the previous entry.  Positive numbers are to the left; negative numbers are to the right.

Measuring X, Y, and Length

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