Gravity Energy Storage: Crane Tower, Concrete Blocks and the m g h Round Trip (2D Elevation)

Presets

Live readouts

Graphs

State of charge against time

Net electric power (+ buying, - selling)

Tower capacity against the number of levels

Round trip against block mass

Numerical checks

running...

How to use

Pick a preset and press play. Cranes carry blocks from the yard to the shelves (charge) or lower them back (discharge) while the state of charge, power and round trip are read live. Try: (1) Ideal machine and see only the handling energy remain; (2) double the block mass and watch the hook slow down at the power limit; (3) add cranes and see the power rise; (4) raise the friction and the winch losses and read the round trip; (5) Daily schedule and watch the sun, the surplus window and the evening peak. Space pauses, R resets, hover a part for its numbers.

The science

Idea. Raising a block of mass m by h stores potential energy; lowering it later drives the winch as a generator.

E = m g h (stored) E_tower = m g dh W NL (NL + 1) / 2 (full tower, W blocks on each of NL levels spaced dh apart)

Losses in this model. Hoisting needs E_in = m g h / (eta_m (1 - f)), lowering returns E_out = m g h eta_g (1 - f), with eta_m, eta_g the drive efficiencies and f the rope, sheave and guide friction as a fraction of m g h. Every pick and set-down takes the handling time and a little trolley energy (rolling resistance 0.02 over 12 m). A standby load runs all the time.

round trip = E_out / E_in ~ eta_m eta_g (1 - f)^2 (minus handling and standby)

Speed and power. The hook speed is limited by the maximum speed and by the crane's electrical power limit: v = min(v_max, P_max eta_m (1 - f) / (m g)). Heavy blocks therefore move slowly and the empty hook returns at twice the speed.

Dispatch. The automatic schedule charges in the surplus window and discharges in the evening peak. The highest blocks are lowered first and the lowest shelves are filled first.

Honest simplifications. Constant efficiencies (real drives vary with load), no rope stretch or sway, no wind limits, no block-to-block variations, trolley travel is a fixed 12 m, the empty-hook return costs no energy (a counterweight is assumed). Real systems with 35 t blocks are tens of MWh; this tower is a teaching size. The 3D scene is not a product model and is not affiliated with any company.

Checks in the page. (1) the summed m g h of a full tower equals the closed form; (2) the electrical energy of one lift equals m g h / (eta_m (1 - f)); (3) with ideal drives the round trip is exactly 1 once handling is removed; (4) the first law E_in - E_out = dPE + losses closes with blocks in flight.