Posted by: Andrew | February 16, 2010

Luge Safety at the Vancouver Winter Olympics: Physics and Technical Solutions

During practice on the Luge run at the Vancouver Winter Olympics, the Georgian athlete Nodar Kumaritashvili was tragically killed when he apparently lost control on curve 16 of the run, slid off the track and collided with a steel support pillar. The author would like to offer his sincere condolences to his family, friends, and fellow athletes.

The official line, after a hasty investigation, was that the athlete was responsible, and that the track design was not at fault.  I am a little sceptical of having the officiating body (the Fédération Internationale de Luge de Course, FIL), conduct an investigation; for instance, when an airliner crashes, it is not the airline that conducts the official investigation. The course was designed according to FIL guidelines, so is the investigation going to be truly impartial? They are being asked to investigate their own guidelines! The investigation by the Coroner in British Columbia will hopefully be thorough and conclusive.

Nevertheless, the competition for the men was allowed to run, but using the starting position for the women’s competition, further down the track, to reduce the speed of the racers. Similarly, the women’s event will be run from an even lower starting point. Changes were also made to the ice profile on the run.  This strongly suggests to me that this is a de facto admission that the design of the run could be changed to help prevent the accident. The design should include the possibility that an athlete might make a mistake. The consequences of that mistake should not be fatal.

Now, I personally think that the press release blaming the athlete was grossly insensitive at best, and avoiding the issue in hand at worst.  Luge is a dangerous sport which is run in an entirely artificial environment.  The luge run is a man-made construct, not a natural artefact. The designers and engineers responsible for the run should have allowed for the possibility of human error and the possibility of a rider being ejected from the run at high speed.  Modern training methods and new advanced materials have also produced stronger athletes and more slippery luges, which makes the speeds down the runs faster than they used to be.  It appears that the sport has not kept pace with this increase in performance, with a commensurate increase in safety precautions.  As Ladkin [1] has commented,” It doesn’t seem to me that organised sports activities of this nature apply similar standards of safety engineering as in aviation or nuclear power. Why not? ”  A very good question.

Let’s apply a little physics [2] to see what could be done to prevent such a tragedy.

We start with Newton’s second law of motion, stated in its original form: “the force applied to an object to change its motion is proportional to the rate of change of momentum.”  The momentum of an object is, in classical physics, the mass multiplied by the velocity.  The velocity is a vector quantity, with both magnitude (the speed) and a specified direction [3].  This bit of physics is often stated as the “Momentum-Impulse Theorem” in physics textbooks.

The equation below shows the momentum-impulse theorem for an object of mass m, moving initially at speed v and finally at vfinal.  If the time for the change in velocity is t, then the average force which has to be applied to the object to do this is F.

Momentum Impuse Theorem

In the case of an object in a collision, the final velocity is zero, because the object comes to a complete halt after collision. The second line in the equation accounts for this, and rearranges the equation in terms of the average force applied [4].  Thus someone flying through the air with an initial speed of v will experience an average force F, when colliding with a fixed object and coming to a complete halt.  The time t is the collision time taken to bring the person to a halt from that speed, not the total time spent in the air.

If you are used to visualizing consequences of algebraic expressions, you can see that increasing the collision time, t, (i.e. increasing the time taken for the athlete to stop) decreases the average force.  The same thing can be shown by putting a few numbers into the equations. Suppose the mass of the person is 60 kg, and the initial speed is 145 km/h (40 m/s, about 90 mph). If the collision time is 0.010 seconds (10 milliseconds), then the average force exerted during the collision is 240,000 newtons [5].  If the collision time is increased to 100 milliseconds, the average force is reduced by a factor of 10, to 24,000 newtons. A slower collision can occur if there is some padding or cushioning between the moving and stationary objects. This is exactly what the airbag in your car does in the event of a collision. It should be stressed that the average force is less than the maximum instantaneous force, so that you need to allow an extra safety margin. It is also desirable to make sure that the force is distributed over a wide area of the human body, and not applied to highly localized parts, especially the head.

The survivability of high impact collisions is not an exact science, but many semi-quantitative approximations can be used to determine if a collision will be survivable or not [6]. Reducing the magnitude of acceleration (v/t) below 1750-2000 m/s2 is essential for survivability, possibly with severe injury.

In this case, if we assume an initial speed of 145 km/h (40 m/s), then to get below 1750 m/s2 acceleration, we would need to have a collision time of greater than 0.023 seconds (23 milliseconds).  Ideally we would like a collision time several times greater than that, to try and prevent serious injury as well.

Now consider some possible safety measures that could be taken:

1                     Change the design and shape of the existing luge runs. This could be expensive.

2                     Change the rules on luge/sled construction to make the luge slower by increasing the friction force on it as it goes down the run.  This would be analogous to the redesign of the javelin in the athletics competition.  Athlete performance had increased so dramatically that with the old style javelin, they were in danger of throwing it into the crowd.  The solution was to change the aerodynamic characteristics of the javelin so that it just couldn’t fly as far.

3                     Apply passive safety measures to the zone around the luge run.  Options which might be feasible include enclosing the run with a transparent top to prevent the rider being thrown off, and padding or webbing around the fixed structural supports. At Whistler, the steel support girders were not protected at all. This would be the simplest option.

4                     Apply active safety measures such as air bags around the luge run which are only activated when an athlete comes off the track.  This might be technically demanding, as they would have to deploy very rapidly, and only deploy where they were needed.  On the other hand, these could presumably be retrofitted to the existing runs, a much less expensive option than rebuilding the entire run. Airbag technology in cars is a mature technology and can deploy airbags into their operating positions 60-80 milliseconds after the start of a crash. With this level of performance, an athlete flying through the air at 40 m/s would travel about 3 metres while the airbag was deploying.  This might not be adequate, but a faster operating system could certainly be developed. One could imagine having sensors attached to the athlete or the luge itself, which would send an emergency signal to the safety system in the event of the athlete being thrown off the track.  Some form of position monitoring would then allow the appropriate sections of the active safety system to deploy.  It would also be possible to put the sensors in the luge run itself.  However access to the sensors (under the ice) would be more limited and difficult.

A little imagination and a lot of technical effort and money would be required to implement these safety measures. But what price is a human life?

[1] http://www.abnormaldistribution.org/2010/02/13/thoughts-on-the-luge-crash-in-vancouver/ accessed 14th Feb 2010

[2] I have deliberately kept this analysis to the level of first year university or college level in the US/Canada or A-level Physics in the UK.  Much more sophisticated analysis is possible, but doesn’t add much to the conclusions.

[3] In physics the terms velocity and speed have distinct meanings. Velocity is a vector quantity and has magnitude and direction. Speed is a scalar quantity and has magnitude only.

[4] The negative sign indicates that the direction of the applied force is in the opposite direction to the initial velocity.  The magnitude of the force is indicated by the symbol |F|.

[5] The newton is the unit of force in the metric system.  You exert a force of approximately 1 newton when you push a button to ring a doorbell.

[6] “Physics of the human body”, Irving P. Herman, Springer; Corr. 3rd printing edition (Jan 9 2007), ISBN-13: 978-3540296034, page 159

Copyright Andrew Robinson February 15th 2010.

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