Luge track safety

Mont Hubbard

Department of Mechanical & Aerospace Engineering

University of California, Davis

mhubbard@ucdavis.edubiosport.ucdavis.edu

Luge Track Safety

• Introduction and motivation• Luge/bobsled track design• Kumaritashvili accident• Sled motion differential equations• Numerical solutions• Safe practices and track design flaws

Olympic Bobsled, Luge Skeleton Tracks

• Olympic and World Cup competitions• FIL and FIBT closely regulate tracks & competitions• All track designs require certification• Precise specifications and rules• Committees for design, running competitions, etc.• Natural tracks exist

Luge event

• Luge-rider is feet first and supine• Sled surface shape conforms to body• Minimum time performance

Bridge connects runners to sled

Luge sled steering

• Blade-ice contact region L~ 12 cm• Blade planes tilted inward from vertical

• Sled and blade planes deformable about lateral horizontal axis so steerable with opposite shoulder/leg pressure• Sleds go where they are steered

• Blades very thin and nearly flat

cross-sectional radius rC~ 0.002 m longitudinal radius: rL~14 m

Track design

• Every 4 years like clockwork• Highly banked curves linked by straight flat sloping sections• Udo Gurgel (Leipszig) has designed last 8 tracks• Designs “look” same

Whistler track

Straight section design

Both walls roughly vertical Flat bottom contains rounded inner cornersAllows gentle alignment and return to center

Banked curve cross-section design

Outside surface smoothly curved (5 g’s possible) Inside vertical wall roughly cylindrical Bottom flat but also has rounded inner corner !

The Accident

Accident location

Looking up track

Conclusion of FIL Official Report

The sled “appears to have hit the wall at an exceptional angle that caused the sled to compress … result[ing] in the sled serving as a catapult when it decompressed launching … the sled into the air”

FIL Official Report

Suggested that circumstances of accident were so complex and exceptional as tomake it “unknown and unpredictable”1.

1. International Luge Federation, Official Report to the IOC on accident of Georgian athlete Nodar Kumaritashvili, at the Whistler Sliding Center, Canada on February 12, 2010 during official luge training for the XXI Olympic Winter Games, 2010. accessed December 2011.

1. Higher walls added2. Fillet was removed from ice track corners even in sections where it is specified by the rules (curious)

Track modifications

FIL report mentioned “Squaring off the curve of the ice between the base of the track and the sidewalls of the outrun.”

Track modifications

Can derive and integrate ode’s for sled motion

Assume particle model for sled.

If FIL cause of accident sounds like “black magic” what could offer a more cogent explanation?

How about Newton’s laws?

Equations of motion on ice surface

Fillet surface adequately approximated by torus

u = “longitude”v = “latitude”

Fillet (torus) surface shape

Two parameters (angles) characterize location on ice surface

First and second fundamental matrices of the toroidal surface

Normal curvature – instantaneous curvature of 3-D path on ice surface

Gaussian curvature Kis product of maximum and minimum (principal) curvatures at a point

Sign shows principal curvatures on fillet are of opposite sign!

Equations of motion2 second order ode’s for u and v

Neglects aerodynamic and friction forces but includes gravity and large track normal force

Simulation results

Parameters

Hold speed vo constant, vary angle o between velocity and tangent to fillet toe.

Qualitative character of results depends strongly on entry angle o

(Note: x axis not to scale)

Track design flaw is presence of inner fillet. A fillet at the base of an inside wall can launch a

slider into flight across the track.

Importance of negative Gaussian curvature

1. Positive lateral curvature (v) turns lateral velocity to vertical 2. Negative longitudinal curvature (u) means contact is eventually lost

3. Thereafter flight path lies in vertical tangent plane to inner wall4. Ejection occurs if vertical velocity sufficient to clear exterior wall.

Speed exacerbates ejection

• Top speeds 13% larger than design values• 13% larger vo => 13% larger lateral speed• 13% larger vo => 27% larger zenith height

Quotes

Georgian President Mikahail Saakshvili (2010) “ No sports mistake is supposed to lead to a human death.”

Richard Feynman (1986 during space shuttle Challenger investigation)“ For a successful technology, reality must take precedence over public relations for nature cannot be fooled.”

Design and review process

Much potential for financial conflicts of interestCost = C$105M

I year effort to get 4 numbers for this study failed

Design and review process

• Track cost = C$105M• Much potential for financial conflict of interest

• My one-year effort (emails and telephone calls to Udo Gurgel and Whistler Sports Legacy Society ) to get 4(!) numbers for this study failed

• No independent review process exists

Conclusions• Ice track ejection can be explained with a simple analytic model of fillet surface shape and Newton’s laws. • Interaction of the right runner with the fillet resulted in vertical velocity necessary for, and was the cause

of, ejection in the Whistler accident.• Bending of the bridge was caused by the normal force but was not the cause of ejection.• A more open review and investigation process is desirable and could only increase resulting safety of

athletes using the tracks.

Thanks for listening

BEAT NAVY!

EXTRA