Luge track safety
Mont Hubbard
Department of
Mechanical & Aerospace Engineering
University of California, Davis
mhubbard@ucdavis.edu
biosport.ucdavis.edu
Luge Track Safety
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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
• Blades very thin and nearly flat
cross-sectional radius rC~ 0.002 m
longitudinal radius: rL~14 m
• 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
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 corners
Allows 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 to
make 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.
Track modifications
1. Higher walls added
2. 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.”
If FIL cause of accident sounds like “black magic”
what could offer a more cogent explanation?
How about Newton’s laws?
Can derive and integrate ode’s for sled motion
Assume particle model for sled.
Equations of motion
on ice surface
Fillet surface adequately approximated by torus
Fillet (torus) surface shape
Two parameters (angles) characterize location on ice surface
u = “longitude”
v = “latitude”
First and second fundamental matrices
of the toroidal surface
Normal curvature – instantaneous curvature
of 3-D path on ice surface
Gaussian curvature K
is product of maximum
and minimum (principal)
curvatures at a point
Sign shows principal curvatures on fillet are of opposite sign!
Equations of motion
2 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 go
between velocity and tangent to fillet toe.
Qualitative character of results depends strongly on entry angle go
0
0.1
z (m)
0.5
0.05
1
0
1.5
−0.15
−0.1
−0.05
0
0.05
0.1
y (m)
(Note: x axis not to scale)
x (m)
Fillet variables at contact loss vs entry angle
vmax (rad)
2
1
0
−1
0
2
4
velocity (m/s)
10
6
8
10
vertical
lateral
5
0
0
2
4
6
8
10
2
4
6
8
10
2
4
6
entry angle (deg)
8
10
zenith h (m)
2
1
0
−1
0
tc (s)
0.1
0.05
0
0
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 wall
4. Ejection occurs if vertical velocity sufficient to clear exterior wall.
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.
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 interest
Cost = 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