Traction Elevator Energy and Ride

What is modelled

A traction elevator hangs the car and a counterweight on the two sides of a driven sheave, so the motor lifts only the difference in weight plus the acceleration forces. The ride is planned as an S-curve: acceleration is ramped with a limited jerk so passengers feel no sudden jolt. When the car is lighter than the balance point going up, or heavier going down, gravity drives the sheave and a regenerative drive returns energy to the grid.

Equations

• Motor force F = (mcar + L − mcw) g + M a + Ffriction, with M the sum of the moving masses.
• S-curve trip time T = d / v + v / a + a / j when the car reaches cruising speed, and a lower peak speed on short trips.
• Mechanical work over a trip W = (mcar + L − mcw) g d + Ffriction d.
• Grid energy ∫ P / η dt when drawing and ∫ |P| η dt when regenerating.

Checks run in the page

• Numerical integration of the jerk-limited profile against distance, final speed and limits.
• Trip time against the closed form.
• Integrated motor power against the potential-energy change.
• The balance load found by bisection against the counterweight setting.

Honest simplifications

The ropes and compensation chains are massless, the guide friction is a constant force, the drive has one fixed efficiency each way and the counterweight is set as a fraction of the rated load. Real lifts add rope mass and stretch, brake and door cycles, standby power and car ventilation, so this is a teaching energy model, not a sizing tool.

• Press Empty car up and watch the power bar turn green as the heavy counterweight falls.
• Press Short hop, one floor and see the peak speed stay below the rated speed.
• Press Gentle hospital ride to lengthen the trip with lower acceleration and jerk limits.