Roller Coaster Speed Profile: Gravity's Rollercoaster

A coaster's speed isn't constant—it's a conversation between gravity, track geometry, and friction. Here's the anatomy of velocity.

Launch / Lift Hill: Energy Deposit

• Chain lift: 0.5–1.5 m/s climb. Potential energy = mgh.
• Launched (LIM/LSM/hydraulic/flywheel): 0 → 100+ km/h in 2–4 s. Kinetic energy injected directly.

First Drop: Maximum Velocity

Converts potential → kinetic. Speed at bottom: v = √(2gh) minus losses. Typical: 100–150 km/h (60–90 mph). Steepness (angle) matters less than height difference.

Subsequent Elements: The Energy Budget

• Airtime hills: Crest at lower height → slower. Negative Gs (floater/ejector).
• Loops/corkscrews: Centripetal acceleration. Speed must exceed √(gr) at top.
• Helixes/turns: Lateral Gs. Banking reduces lateral force.
• Mid-course brake runs (MCBR): Trim speed for block spacing / second half pacing.

Loss Mechanisms

1. Wheel friction: Polyurethane on steel. ~1–3% energy loss per element.
2. Air resistance: v² drag. Significant >80 km/h.
3. Track vibration: Energy into structure/sound.
4. Brake fins: Eddy current (magnetic) or friction. Controlled dissipation.

Weather & Load Factors

• Cold wheels: Harder polyurethane → less grip → slower (morning runs)
• Wind: Headwind on lift/hills = slower. Tailwind = faster.
• Train weight: Full train = more momentum, more friction. Empty = faster lift, less momentum.

Safety Control

Block zone system + PLC + magnetic trim brakes maintain design envelope. Speed sensors every block. E-stop if exceeded.

The speed you feel isn't the motor—it's gravity, borrowed and spent, hill by hill.