Bounce on Grass vs. Turf

Introduction

Pitch surface is one of the underappreciated variables in football. The game on a freshly-watered short-cut grass pitch behaves differently to the same game on a dry artificial surface — passes skid further, bounces sit up at unexpected heights, and a half-cleared ball can roll out of play instead of rolling back to the goalkeeper. Players adapt instinctively; the physics behind why is the topic of this page.

Two coefficients do most of the work: a coefficient of restitution that determines how much vertical energy survives each bounce, and a rolling-friction coefficient that determines how quickly a rolling ball slows down. The accompanying simulation lets you set the drop height, the horizontal launch speed, and the surface, and watch how bounce count and roll distance change.

The Physics Explained

When a ball strikes the ground, it deforms and the surface under it deforms in turn. Some of the kinetic energy that was carrying the ball downward is stored briefly as elastic strain in both the ball and the turf, and most of it is returned as the surfaces spring back. The fraction of vertical speed returned by the surface is called the coefficient of restitution, written e. A perfectly elastic surface has e = 1; a perfectly soft one has e = 0. Real grass and turf surfaces sit between 0.4 and 0.7 depending on grass length, soil moisture, and ball pressure.

Rolling friction is the steady drag that slows a ball down once it is on the ground and no longer bouncing. It comes from a combination of micro-deformation in the surface, the small pushing-up the ball must do to climb out of the dent it makes, and any turbulence in the air around the ball. The deceleration is to a good approximation a constant μ_r·g — independent of speed, but very dependent on the surface. A heavy, freshly watered grass pitch has a rolling-friction coefficient roughly twice that of a hard, dry artificial-turf pitch.

Together the two coefficients determine the entire post-flight trajectory. A high-e, low-μ_r surface — typical of artificial turf — keeps the ball alive for many bounces and a long roll. A low-e, high-μ_r surface — typical of long, wet grass — kills the bounce after one or two contacts and stops the roll quickly. The simulation makes that contrast visible by letting you switch between three preset surfaces while everything else stays fixed.

Key Equations

Vertical bounce v_y' = −e · v_y

Horizontal speed after bounce v_x' = v_x · (1 − ½·μ_r)

Rolling deceleration a_roll = −μ_r · g · v̂

Bounce-height series h_n = h_0 · e^(2n)

Energy retained per bounce η = (v_after / v_before)²

Total roll distance from speed v d_roll = v² / (2·μ_r·g)

Key Variables

Symbol	Name	Unit	Meaning
e	Coefficient of restitution	dimensionless	Vertical energy retained per bounce; 0.45–0.70 for the surfaces here
μ_r	Rolling friction coefficient	dimensionless	Lateral deceleration as a fraction of g; 0.20–0.45 here
g	Gravitational acceleration	m/s²	9.81 near Earth's surface
h_0	Drop height	m	1–5 m in the simulation
v_x	Horizontal speed	m/s	0–15 m/s; sets how far the ball rolls before stopping
v_y	Vertical speed at contact	m/s	√(2·g·h) at first contact, then attenuated by e on each bounce
η	Energy retained	dimensionless	Fraction of incoming kinetic energy that survives a bounce
n	Bounce count	integer	Number of surface contacts before transitioning to roll

Real World Examples

Skidding passes on dry turf: A driven pass on a dry artificial surface keeps almost all of its horizontal speed across 30 m. The same pass on long grass loses noticeable pace before reaching the receiver.
Heavy wet grass after rain: Wet grass slows the rolling phase aggressively and damps each bounce, producing a deadened, low-bouncing game that asks players to drive the ball through.
Turf and the long throw: A long throw-in on artificial turf can travel further after landing than it did in the air, because the bounces stay alive and the roll runs out slowly.
Goalkeeper distribution choice: On heavy grass keepers favour driven goal kicks and rolled distribution; on dry turf they can afford soft chips into space and trust the bounce to settle.

Historical Examples

Geoff Hurst's hat-trick goal — World Cup Final, 30 July 1966

The most famous bounce in football history was Hurst's third goal at Wembley: the ball struck the underside of the bar, bounced down on the goal-line area, and flew up and out. Whether it crossed the line is still debated, but the bounce itself was a textbook elastic interaction with grass — a high-e contact returned most of the ball's downward speed back upward, almost vertically. The match-day grass at Wembley was wet but well-cut.

BC Place artificial turf controversy — Women's World Cup 2015

Players publicly objected to the all-turf 2015 tournament, citing — among other complaints — the way the ball bounced. The artificial surface had a higher coefficient of restitution than the natural pitches the players were used to, producing taller bounces and more skidding rolls. The simulation reproduces this: switching from grass to turf at the same drop height roughly doubles the bounce count.

Mineirão pitch, Brazil vs Germany — World Cup 2014

The Mineirão pitch on the night of the 7-1 semi-final was firm and dry, with low rolling friction. Several of Germany's incisive through-balls used the surface to advantage, with the ball running smoothly into the receiver's stride. A heavier or wetter surface would have slowed those balls noticeably; the firm surface kept the geometry clean.

How the Simulation Works

The simulation is a side-on view of a ball dropped from a chosen height with a chosen horizontal velocity. While the ball is in flight the only force is gravity; the trajectory is therefore a parabola. The instant the ball reaches the ground, the bounce helper from the soccer physics module is applied: the vertical component of velocity is reversed and scaled by the surface's coefficient of restitution, and the horizontal component is damped by a small fraction tied to the surface's rolling-friction coefficient.

After enough bounces the ball's vertical velocity drops below a threshold and the simulation transitions to a rolling phase. In this phase the bounce equations are no longer used; instead the rolling-friction helper applies a deceleration vector opposite the ball's velocity at every step. The ball stops when its speed falls below a small threshold or it leaves the viewport.

The readouts show the elapsed time, the cumulative bounce count, the rolling distance accumulated since the bounce-to-roll transition, and the energy retained at the most recent bounce. The energy retained is reported as a percentage so the bounce-by-bounce decay is easy to follow. Toggle the surface slider between Grass, Turf, and Wet Grass to see how a single change of surface — every other variable held constant — reshapes the entire post-flight phase.

The simulation deliberately omits ball spin: real bounces transfer energy between rotational and translational modes, and the spin coupling at impact is sensitive to surface conditions in ways that resist a clean closed-form treatment. Adding a stylised spin would muddy the headline result that surface alone is enough to change the game.