My SimulatorEngland / Engineering

Tower Bridge Simulator

Raise the bridge. Keep London moving.

Interactive 3D • London

Educational model: simplified dynamics and geometry, not engineering advice. Not affiliated with any operator.

Bascule leaf

Pivot and counterweight

High-level walkway

Next ship

Lab & science

Drag to orbit, wheel / pinch to zoom. Space = pause, R = reset, U = raise, D = lower, O = orbit.

0Ships passed

0 sAvg ship wait

0 sRoad delay / car

Presets

Drive and balance

Counterweight balance (moment ratio)

Max opening speed

Acceleration limit

Hydraulic power limit

Traffic and clock

Road traffic per direction

Simulation clock

Camera

Layers and graphics (High on every device; Low = lighter city, 1x pixel ratio)

Live readout (model values)

Missions

Mission 5: what is the smallest opening angle (degrees) that lets the Tall ship pass, centred 5 m off the middle line with 3 m of margin? Use the clearance equation.

The science

What you see

Two bascule leaves, each pivoting at a tower and balanced by a counterweight tail that swings down into the pier. A hydraulic drive turns the leaves up so a tall ship can pass between the towers; the high-level walkway stays fixed. Barriers and signals stop the road first, and an interlock refuses to raise the leaves unless the road is closed. Leaf and ship sizes follow the real bridge in round numbers (leaf 30.5 m, gap 61 m); masses and the drive are model values.

Equations

Leaf dynamics        I d2(th)/dt2 = tau_m - tau_g(th) - b w - tau_c tanh(w/w0)
Gravity torque       tau_g = (m_l r_l - m_c r_c) g cos(th) = (1 - k) m_l r_l g cos(th)
                     k = counterweight moment / leaf moment (balance ratio)
Potential energy     U(th) = (1 - k) m_l r_l g sin(th) ,  tau_g = dU/d(th)
Inertia              I = I_leaf + m_c r_c^2
Motion profile       w_ref = sign(e) min(w_max, sqrt(2 a |e|)) ,  tau_m = I a_ref + tau_g + Kp e + Kd de/dt
Power limit          |tau_m w| <= P_max
Energy balance       W_motor = Delta U + (1/2) I w^2 + W_friction
Clearance            leaf point at height z is at x(z) = D - z / tan(th) from the centre line (D = 30.5 m)
                     a ship part (width w, heights z0-z1, offset c) fits if
                     D - min(z1, L sin th) / tan(th) >= |c| + w/2 + margin
Tall rig (top above the leaf tip)   L (1 - cos th) >= |c| + w/2 + margin
                                    th_min = arccos(1 - (|c| + w/2 + m) / L)
Road queue (D/D/1)   closure T, arrivals lam, saturation flow mu: total delay = (1/2) lam T^2 mu / (mu - lam)
                     queue clears after T mu / (mu - lam) ,  max queue = lam T

Assumptions & honest simplifications

Both leaves are identical and move together as one rigid body about the pivot; masses, centres of mass and the hydraulic drive are round model values, not the real engines.
Each ship is a stack of boxes (hull, deckhouse, rig); real hulls and rigging are more complicated and a pilot would add a larger safety margin. The margin used is 3 m.
Wind, tide, ship manoeuvring and the exact leaf geometry are ignored; ships hold at a line before the bridge until the model says they fit.
Road vehicles follow a simple queue-discharge rule (one car every 2 s at the stop line); the analytic queue formula assumes a perfect D/D/1 queue.
The city, skyline and vessels are stylised, built in Blender for this page. Fixed model values, no timetable, no operating advice.

Independent numerical checks

Also in node: node check.js.

Sources

Classical rigid-body rotation about a fixed axis; bascule bridge design notes (counterweight balance, drive torque); public descriptions of the 1894 bridge (leaf span about 30 m, opening gap about 61 m, high-level walkways about 42 m above the river). Queue formula from deterministic queueing theory.

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