A Scherzer-type rolling lift bascule carries its leaf, segmental girders and counterweight as one rigid moving body. As a circular segment of radius R rolls without slip through opening angle θ, its centre retreats horizontally by s = Rθ while staying at constant height; the forward leaf simultaneously rotates upward.
Rolling Lift Bridge Interactive Calculator
Explore ideal no-slip rolling and rigid-body point motion for a selected rolling lift bridge geometry.
Equation Used
- The segment rolls on a straight horizontal track without slip.
- The rolling segment radius is constant and its centre remains at constant height.
- The forward tip and rear counterweight reference point are rigidly attached on the closed leaf axis.
- Distances L and C are measured from the segment centre in the closed pose.
- Balance, mass distribution, gearing, torque, power, acceleration, loads, stresses, clearances and locks are excluded.
The secondary figure uses the same selected opening angle, rolling radius, leaf distance and counterweight-point distance.
How the selected rolling-lift geometry works
The leaf is rigidly connected to curved segmental girders that roll on horizontal track girders. Retaining teeth, racks or pintles maintain alignment and prevent slip in actual designs. Unlike a simple trunnion bascule, the rolling centre translates as the rigid assembly rotates.
The selected schematic uses an ideal circular rolling radius and no slip. It shows the forward leaf and a rear counterweight reference point moving with the same rigid body; it is not a structural or drive design.
What this calculator demonstrates
Select opening angle θ, segment rolling radius R, forward leaf distance L and rear counterweight-point distance C, all measured from the segment centre in the closed reference pose. The calculator returns horizontal track travel, vertical tip rise, horizontal tip retreat and counterweight-point drop.
It does not calculate balance, centre of gravity, motor torque, power, gearing, rack force, acceleration, wind load, braking, structural stress, foundation reaction, clearances, locks or opening time.
Ideal rolling-body kinematics
For no-slip rolling of a circular segment through θ radians, centre translation along the horizontal track is s = Rθ. With the closed forward leaf directed horizontally from the centre, tip rise is ytip = L sin θ and its horizontal retreat from the closed tip position is Δxtip = Rθ + L(1 − cos θ).
For a reference point C behind the centre on the same closed axis, its downward displacement is ycw = C sin θ. These are point-kinematic relationships only; actual counterweight shape and mass distribution govern balance.
Selected example
For θ = 82°, R = 4 m, L = 30 m and C = 3 m, the model converts θ to radians, calculates Rθ track travel, and transforms the two rigidly attached reference points.
The dimensions are illustrative. They do not represent an identified bridge or establish clearances, balance, loads, power, operating speed or suitability.
Interpretation and correction boundary
A larger rolling radius produces more horizontal retreat for the same opening angle. Forward-tip rise depends on L and sin θ, while its total retreat combines centre translation with rotation about that translating centre.
The removed calculator treated a generic motor-to-output ratio as though it directly defined an actual bridge opening time, without rack/pinion geometry, acceleration, braking or load data. Unsupported tolerances, forces, weights, powers, operating diagnoses and named-project claims were also removed.
Questions
Does the bridge rotate about a fixed pivot?
No. In the selected idealization the segment centre stays at constant height but retreats by Rθ as the segment rolls.
Does counterweight-point drop prove the bridge is balanced?
No. Balance depends on the complete moving body's mass distribution and gravity moment throughout the motion.
Can this calculate opening time?
No. Timing requires the actual drive train and motion profile, including acceleration and deceleration.
Does the model include rack and retaining teeth?
No. They are identified as real alignment and no-slip features but are not dimensioned or analyzed here.
Primary technical references
- U.S. Department of Transportation, Bridge Inspector's Training Manual — rolling-lift bridge classification, rolling segment and translating leaf.
- Connecticut DOT Railroad Bridge Inspection Manual — Scherzer segmental girder, track girder, alignment and drive arrangement.
- US719153A, Rolling lift-bridge — curved bearer rolling on a horizontal plate and rack/pinion actuation.
- Library of Congress HAER, Monroe Street Bridge — documented Scherzer rolling quadrant and track.
- Nguyen Duc Thang, Rolling Lift Bridge — retained subject video.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
