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Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome, Italy

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Page 1: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Winter Alpine Physics

Alexey Abrikosov, jr.Institute of Theoretical and Experimental Physics, Moscow,

Russia

Andrei VarlamovCOHERENTIA, CNR-INFM, Rome, Italy

Page 2: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

0 50 100 150 200 250 km/h

Speed scales

Page 3: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Monte Rosa glacier under Matterhorn; Maximum gradient — 62°

Speed skiing

248.1 km/hr!Harry Egger, Austria, 1999.

Page 4: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Speed skiing tracks

Les Arcs, France

Page 5: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Harry EggerHarry Egger

Physics

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Page 6: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Object Time Speed (m/s) Speed (km/h)

Smooth sphere D=0.5 m 15.8 s ~106 m/s 381 km/hUpright body 16.4 s ~95 m/s 343 km/hHorizontal body 28.9 s ~37 m/s 135 km/hTuck body 23.0 s ~50 m/s 180 km/h

Free fall from 1000 m

Free Fall

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2;airF V

Page 7: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

airF

mg

V

FFV

2air pF C V mg

p

mgV

C

Wind tunnel

Page 8: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

1. Gravity and angle2. Air drag3. Friction

Physical factors in speed skiing

Page 9: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

The sport of bobsleigh began at the end of 19th century when the Swiss attached a steering mechanism to a toboggan. In 1897, the world's first bobsleigh club was founded in St. Moritz, Switzerland.

Eugenio Monti (Italy) won11 world championships(1957–1968 );

Bobsleigh & Luge

Page 10: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Track and speed

Sigulda bob & luge track

Nagano, 1998,4-man event

115 / ;averageV km h

max 230 / !V km h

Page 11: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Addends of victory

Push

Ride

Win!

Page 12: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Centripetal versus centrifugal

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Inertial frame Noninertial frame

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cpma

Page 13: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

1. Initial impulse2. Gravity3. Air drag4. Friction5. Optimal trajectory

Physical factors in bobsleigh

New!New!

New!New!

Page 14: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Luge speed record139.4 km/h

Tony Benshoof

Page 15: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

The problem of optimal trajectory

1. What is the fastest way from A to B?2. Is the straight way faster?

A

B

Page 16: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Brachistochrone

What is the path of quickest descent from A to B?

The minimal time problem

Galileo’s hypothesis — the circular arc?

Page 17: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Other minimum principlesBrachistochrone — minimal time problem

Mechanics —Maupertuis’ minimal action principle

Optics — Fermat's minimal time principle

Page 19: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Discipline Speed (km/h) Speed (m/s)

Downhill Racing ~130 km/h ~30 m/s

Super G ~105 km/h ~29 m/s

Giant Slalom ~75 km/h ~21 m/s

Special Slalom ~ 50 km/h ~14 m/s

Alpine Skiing

Page 20: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Special Slalom

Page 21: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

History of skiing

• Cave drawing from Eastern Russia. (between 7000 and 5000 B.C.)

Page 22: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Telemark skis.

• New skis were shorter (about 2 m 40 cm) than other skis used at that time.

Sondre Norheim (Telemark County, Norway, XIX century)

•The bindings were made of twisted willow from birch-roots.

Page 23: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Fridtjof NansenNorwegian arctic explorer, zoologist and statesman; Nobel Peace Prize 1922.

12 times national champion in skiing;World record for one-mile skating.

1890 — book On Skis Over Greenland

The first to cross the mid-Greenland ice cap on skis (1888).

Page 24: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Nansen Gallery

Page 25: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Telemark turn

Page 26: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Basics of alpine skiing

stem (faster)

wedge (slow)

parallel turn — Christiania

Page 27: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Ski robots

Shiro Shimizu

wedge

stem

Christiania

Page 28: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Skidding

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;F

fl

cos 0.A

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s

l

Work against friction A is proportional to swept area S

Page 29: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Hourglass contour

Carving revolution of 1990-ies

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•Easy to flex•Hard to twist•New geometry

No skidding

flared tail

wide tipnarrow waist

sidecut

Page 30: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

r

50;N 10 ;v m s

Optimal trajectory

0.5 !Lt sv

5 ;L N l m

10 ;l r cm

J.Heuga, USA

G.Perillat, France

Grenoble, 1968

K.Schranz, Austria

Page 31: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

With and without friction

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Skiing without friction

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center of massskis

Page 32: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Swing and parametric resonace

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Page 33: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Carving and acceleration

center of mass

skis

Page 34: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Center of mass in motion

Page 35: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Cross-country versus Alpine

center of massskis

Cross country

Alpine

Page 36: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Acceleration

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Alpine

Cross country

center of massskis

Alpine

Cross country

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Page 37: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

What it looks like

Ivica Kostelic, World Champion in slalom, 2003

Page 38: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Altitude loss and speed gain

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Page 39: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Speed control 1. Passive — skidding and carving;2. Active — flexion–extension.

Acceleration(extension)

Deceleration(flexion)

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Page 40: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Energy pumping

a

V

s

s

Bad (pastime) skier

–V

a

s

s

Good (sportive) skier

a — acceleration;V — velocity;s — distance;

V

a

s

s

=

Page 41: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Physical factors in alpine skiing1. Gravity 2. Air drag (downhill, GS, SuperG)3. Friction (skidding and carving)4. Optimal trajectory (slalom)5. Flexion-extension (slalom, GS) New!New!

winners;

loosers

Page 42: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Gallery of Alpine Glory - I

Anton SailerJean-Claude Killy

Page 43: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Gallery of Alpine Glory - IIGustavo Thoeni

Ingemar Stenmark

Page 44: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Gallery of Alpine Glory - III

Alexander Zhirov

Alberto Tomba

Page 45: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

AcknowledgementsYuriy Preobrajenskiy

1948 1972

Page 46: Winter Alpine Physics Alexey Abrikosov, jr. Institute of Theoretical and Experimental Physics, Moscow, Russia Andrei Varlamov COHERENTIA, CNR-INFM, Rome,

Skiing is not the bliss

but

a perfect substitute