Stone Skipping Tom as Cruz Lu s Cebola Stone Shape Angle With - - PowerPoint PPT Presentation

Stone Skipping

Tom´ as Cruz Lu´ ıs Cebola

Stone Shape

Angle With Water

Spin

Children’s Game?

Children’s Game?

Physics of Everyday Life

“Physicists have figured out some extremely fine details of the universe, from the radius of black holes to the behavior of subatomic particles - neither of which we can even see. It may surprise you to learn, then, that they lack explanations (or have

• nly recently stumbled upon them) for many common phenomena

we observe in daily life.” − Natalie Wolchover

Physics of Everyday Life

“Physicists have figured out some extremely fine details of the universe, from the radius of black holes to the behavior of subatomic particles - neither of which we can even see. It may surprise you to learn, then, that they lack explanations (or have

• nly recently stumbled upon them) for many common phenomena

we observe in daily life.” − Natalie Wolchover

The Cheerios Effect

Why your breakfast cereal tends to clump together or cling to the sides of a bowl of milk? - See Vella and Mahadevan, The ’Cheerios effect’.

Getting a Kick From Water

Getting a Kick From Water

A Simple Model 1

Reaction Force

◮ Re = aV

ν ∼ 105 ⇒ Inertial regime.

◮ We = ρV 2z

σ

∼ 100 ⇒ Neglect surface tension.

◮ Fr = V 2

zg ≫ 1 ⇒ Neglect buoyancy.

F = 1 2ClρwV 2Simf (θ, β)n

• Lift

+1 2CdρwV 2Simf (θ, β)t

• Drag

1Based on: Rosellini et al, 2005 e Boqcuet L, 2002.

A Simple Model 1

Reaction Force

◮ Re = aV

ν ∼ 105 ⇒ Inertial regime.

◮ We = ρV 2z

σ

∼ 100 ⇒ Neglect surface tension.

◮ Fr = V 2

zg ≫ 1 ⇒ Neglect buoyancy.

F = 1 2ClρwV 2Simf (θ, β)n

• Lift

+1 2CdρwV 2Simf (θ, β)t

• Drag

Stone Shape: Immersed Surface

Sim = R2

• arccos
• 1 − s

R

• −
• 1 − s

R 1 −

• 1 − s

R 2

• , s = |z|

sin θ

A Simple Model

Spin?:

What is the effect of spinning?

A Simple Model

Spin?:

What is the effect of spinning?

• 1. Lift force is applied in the

immersed surface - destabilizing torque;

• 2. Only a specific range of θ is

favourable to skipping;

• 3. Gyroscopic effect - Stabilizing

torque;

¨ θ + In − It It ˙ φ 2 (θ − θ0) = Mθ It (θ − θ0) ∼ MθIt ˙ φ2(In − It)2 To work ˙ φ 20Hz.

A Simple Model

To address the problem of the angle we need to go deeper in the model

• M¨

x = − 1

2ρ(˙

x2 + ˙ z2)Sim(z) sin(θ + β)(Cl sin θ + Cd cos θ) M¨ z = −Mg + 1

2ρ(˙

x2 + ˙ z2)Sim(z) sin(θ + β)(Cl cos θ − Cd sin θ) Notice that: β = arctan −˙

z ˙ x

• and θ ∼ Cte.

A Simple Model

To address the problem of the angle we need to go deeper in the model

• M¨

x = − 1

2ρ(˙

x2 + ˙ z2)Sim(z) sin(θ + β)(Cl sin θ + Cd cos θ) M¨ z = −Mg + 1

2ρ(˙

x2 + ˙ z2)Sim(z) sin(θ + β)(Cl cos θ − Cd sin θ) Notice that: β = arctan −˙

z ˙ x

• and θ ∼ Cte.

Model expansion and simulation

Cd ≪ Cl ≃ 1

On water: (z < 0)

• M¨

x = − 1

2ρ(˙

x2 + ˙ z2)Sim(z) sin(θ + β) sin θ M¨ z = −Mg + 1

2ρ(˙

x2 + ˙ z2)Sim(z) sin(θ + β) cos θ

On air: (z > 0)

• M¨

x = 0 M¨ z = −Mg

Immersed Area

Sim =        R2

• arccos
• 1 − s

R

• −
• 1 − s

R

1 −

• 1 − s

R

2

• , z < 0 & |z| < 2R sin θ

πR2 z < 0 & |z| > 2R sin θ 0, z > 0

M = 0.1 kg ρ = 1 g/cm3 g = 9.8 m/s2 R = 0.025 m

Simulation: Stone Position

Simulation: Stone Position

Simulation: Energy Loss

◮ We can try a little analytical trick:

∆E ≃ 1

2M ˙

x2

f − 1 2M ˙

x2

0 =

tcoll Fx ˙ xdt ≃ −1.4NMg2π

• M sin θ

CρR

≃ −1.928 J But in the end the most precise result come from the model:

Simulation: Best Angle

Angle With Water:

◮ ’Magic angle’

≃ 20o

◮ Best angle

≃ 15o

Experiment 1 - Rosellini

Set up: Results:

Experiment 1 - Rosellini

Set up: Results:

Experiment 2 - Hewitt

Contests and curiosities

A little bit of history

◮ Record of stone skipping as a sport goes back at least to 1583. ◮ Tradition holds that the sport was begun by an English king

who skipped stones across the Thames.

◮ Nowadays there are tens of tournaments and championships

• n stone skipping.

Stones manufactured for skipping

The current record for stone skipping is Russ Byars with a throw of 51 skips.

Feeling Lucky?

51 skips

Simulation: Mass

Simulation: Radius