Wladimir Andreff
email: andreff@club-internet.fr

Economic development as major determinant of Olympic medal wins: predicting performances of Russian and Chinese teams at Sochi Games

Keywords: econometric modelling, forecasting, Olympics, medal wins, sports economics, winter sports

Starting from an econometric model successfully used to explain and then predict the distribution of medal wins across nations at the Beijing Summer Olympics, a similar model is elaborated on with some different explanatory variables for estimating the determinants of medals won per nation at Winter Games. A Tobit estimation of the model based on data from 1964 to 2010 shows that GDP per capita, population, the endowment in ski and winter sports resorts, and a host country dummy are significant determinants of medal wins at Winter Olympics. Then the estimated model is used for predicting the sporting outcomes at the 2014 Sochi Games with a focus on Russia and China. The Russian team is expected to perform better than in Vancouver 2010 and to be ranked fourth behind the USA, Germany and Canada while the Chinese team would be ranked ninth, a performance doomed to improve in the future given China's swift economic development.

Introduction

Soon after Russia had obtained the organisation of Winter Olympics in Sochi 2014, the official expectation of Russian government became that the Russian Federation will win the Games she is going to host. Such expectation may have been strengthened by the outstanding Olympic performance of China at 2008 Beijing Summer Games since the host country has won the greatest number of gold medals and the second overall number of medals. However, is hosting the Games enough to win? Sports economists are used to explain a nation's performance at mega-sporting events by more variables than a single host country effect. Their explanatory variables usually encompass at least economic development, GDP size or growth, and often the magnitude of a nation's population. Thus, a next question is to check whether economic development is a significant and possibly major determinant of Olympic medal wins.

This paper attempts to respond the above question with a focus on Russia and China. These two countries are of particular interest. China is now ranked the second country in the world as regard its GDP and has the biggest population compared to any other country. Moreover, its rate of economic growth has been one of the fastest in the world over the past two decades. Economists are not surprised that Olympic performances of the Chinese team have improved with such fast economic development, and the 2008 Games confirmed it.

The former USSR has been for decades one of the best two Olympic performers in the world, at both Summer and Winter Games, ahead of or right behind the USA depending on the year. Economic and political transition and the break-up of the former Soviet Union have interrupted the series of high Olympic achievements by the Russian team [START_REF] Poupaux | The institutional dimension of the sports economy in transition countries[END_REF]. With the transformational economic recession [START_REF] Kornaï | Transformational' recession. The main causes[END_REF] the former Soviet sport system fell apiece [START_REF] Andreff | Sport in Russia[END_REF]. Although Russia has recovered from recession after 1998, she did not get back to a number of Olympic medals comparable to the former times even when adding all other CIS countries to her medal count. Winning 72 medals at the 2008 Beijing Summer Games was considered as bad performance by Russian political and sporting authorities. With 15 medals won at the 2010 Vancouver Games, Russia ranked the sixth Winter Olympic country behind the USA, Germany, Canada, Norway and Austria; Russian authorities were disappointed again. The Russian performance at the 2012 London Games has improved up to 82 medals and new hope is that the Russian team would win the greatest number of medals at Sochi Olympics.

Consequently another question is to see whether Russia will be able to recover its former (Soviet) level of Olympic performance after nearly one decade of fast economic growth (1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006)(2007) and despite her muddling through the current global financial crisis since 2008. After a drop in her economic growth in 2008-2009, the Russian Federation returned to moderate growth in 2010 and recovered its pre-crisis output level in 2011. With a 142 million population and a $10,400 gross national income (GNI) per capita on average in 2007-2011 -according to World Bank data, Russia is still a big and rather developed country which should eventually come back again to better Olympic performance. In particular, if she is compared to China with a $4,930 GNI per capita and a 1,340 million population. Facing a lack of economic studies devoted to Winter Games in the sports economics literature so far, this paper attempts a breakthrough in this area. To the best of our knowledge nobody has elaborated on an economic model for predicting medal wins at Winter Olympics and this is [START_REF] Forrest | Explaining and forecasting national team medals totals at the Summer Olympic Games[END_REF] contention as well. This contrasts with Summer Olympics for which about thirty studies have estimated the economic determinants of medal wins. It has been empirically verified that the number of medals a nation can make at Summer Games significantly depends on its population and GDP per inhabitant [START_REF] Andreff | The correlation between economic underdevelopment and sport[END_REF]. In the past decade, various papers started providing economic predictions of medal distribution per nation at the next Olympic Games [START_REF] Bernard | Going for the Gold: Who Will Win the 2008 Olympic Games in Beijing[END_REF][START_REF] Bernard | Who wins the Olympic Games: economic resources and medal totals[END_REF]Johnson andAli, 2004, 2008;[START_REF] Maennig | Sozioökonomische Schätzungen olympischer Medaillengewinne. Analyse-, Prognose-und Benchmarkmöglichkeiten[END_REF][START_REF] Wang | Logarithm model prediction for 2008 Beijing Olympic Games[END_REF]. Our own model has exactly predicted 70%, and correctly (with a small error margin) 88% of medal win totals per nation at the 2008 Beijing Olympics [START_REF] Andreff | Les déterminants économiques de la performance olympique: Prévision des médailles qui seront gagnées aux Jeux de Pékin[END_REF][START_REF] Andreff | Economic modeling and prediction of Summer Olympic medal wins and FIFA World Cup semi-finalists[END_REF]. The dependent variable is the same for Winter and Summer Games -the number of medals won by each participating nation. Though some independent variables of the Summer Games model have to be kept for Winter Games, some new variables must be introduced to capture the specificity of Winter Olympic sports. Thus, we will take stake of good predictions achieved with our Summer Olympics model to adapt it in view of forecasting the distribution of medal wins per nation at the 2014 Sochi Winter Games.

The paper reads as follows.

1 It starts with briefly reminding the most interesting methodologies at work in estimating Summer Olympics medal win distribution.

2 Then it shows how our own model has resolved this issue.

3 The model was used to predict medal totals per nation at the 2008 Olympics and the prediction was compared to actual outcomes reached by different nations in Beijing, a comparison which is absolutely rare in the literature so far.

4 A brief discussion provides justifications for keeping some similar variables in a model attempting to estimate the determinants of medal win distribution at Winter Olympics and for introducing some new variables that fit better with explaining winter sports performance; the discussion comes out with a somewhat different model.

5 The latter is estimated with data gathered for Winter Games from 1964 to 2010.

6 The estimated model is then used to predict the medal win distribution across nations at the 2014 Sochi Winter Olympics with a focus on the performance of Russia and China.

7 A conclusion makes the reader aware that such predictions are to be taken with a pinch of salt.

Economic determinants of Olympic medals

An assumption is widespread among sports economists: a nation's Olympic performance must be determined by her endowment in economic and human resources and the development of these resources. Thus, the starting point of most studies about the economic determinants of Olympic medal wins consists in regressing medal win totals on the nations' level of GDP per capita and population. Note that the growth in the number of medals won by one nation logically is an equivalent decrease in medal wins for all other nations participating to the Olympics. Therefore, if one wants to understand the Olympic performance of one specific nation, account must be taken of all other participating nations within the overall constraint of the allocated medals total during one Olympics contest.

In the first papers about the economic determinants of Olympic performance, GDP per capita and population were combined as explanatory variables with weather, nutrition, and mortality in the athletes' home country. Later on, in various studies up to the 1970s, other variables were considered as possible determinants of Olympic medal wins: protein consumption, religion, colonial past, newspapers supply, urban population, life expectancy, geographical surface area, military expenditures, judicial system and those sport disciplines taught at school in a nation. However, with the cold war period another significant variable emerged: the nation's political regime. The first Western work attempting to explain medal wins by the political regime of nations [START_REF] Ball | Olympic Games competition: structural correlates of national success[END_REF] immediately triggered a Soviet rejoinder [START_REF] Novikov | The influence of selected socio-economic factors on the levels of sports achievements in the various countries[END_REF], both differentiating capitalist and communist regimes. The first two econometric analyses of Olympic Games [START_REF] Grimes | A socioeconomic model of national olympic performance[END_REF][START_REF] Levine | Why do countries win Olympic medals? Some structural correlates of Olympic Games success: 1972[END_REF] exhibited that communist countries were outliers in regressing medal wins on GDP per capita and population: they were winning more medals than their level of economic development and population were likely to predict. A last variable has been introduced, namely since [START_REF] Clarke | Home advantage in the Olympic Games[END_REF], which is the influence on medal wins of being the Olympics host country. The latter gains more medals than otherwise due to big crowds of national fans, a stronger motivation of national athletes competing on their home ground and being adapted to local weather, and not tired by a long pre-Games travel.

More sophisticated econometric methodology was used in recent articles predicting Olympic medal wins, such as an ordered Logit model [START_REF] Andreff | The correlation between economic underdevelopment and sport[END_REF], a Probit model [START_REF] Nevill | Statistical methods for analyzing discrete and categorial data recorded in performance analysis[END_REF] and an ordered Probit model [START_REF] Johnson | A tale of two seasons: participation and medal counts at the Summer and Winter Olympic Games[END_REF]. The most often quoted reference is [START_REF] Bernard | Who wins the Olympic Games: economic resources and medal totals[END_REF] whose Tobit model has been assessed as the most performing one and then used by [START_REF] Jiang | Medals in transition: explaining medal performance and inequality of Chinese provinces[END_REF], [START_REF] Pfau | Predicting the Medal Wins by Country at the 2006 Winter Olympic Games: An Econometric Approach[END_REF] and others. Bernard and Busse model is considered as the best one for estimating and predicting Olympic performance 2 ; its two major independent variables -GDP per capita and population -explain the great bulk of medal distribution across participating nations. Three dummy variables capture a host country effect, the influence of belonging to Soviet-type and other communist (and post-Soviet and post-communist after 1990) economies as against being a non-communist market economy. These dummies are supposed to capture the impact of political regime on medal wins.

Estimating the determinants of a nation sport performance at Summer Olympics

Starting from Bernard and Busse, we have elaborated on a more specified model [START_REF] Andreff | Les déterminants économiques de la performance olympique: Prévision des médailles qui seront gagnées aux Jeux de Pékin[END_REF] with a few improving emendations. The dependent variable is the number of medal wins 3 per nation: M i,t . Two primary explanatory variables are GDP per inhabitant in purchasing power parity dollars (PPP $) and population. Both variables are four-year lagged (t -4) under the assumption that four years are required to build up, train, prepare and make an Olympic team the most competitive in due time, four years later. That is, for explaining medal wins in 2008, 2004 GDP per capita and population were taken as estimators. A host dummy variable is used to capture a host country effect, i.e., the observed surplus of medals usually won by the national team of the host country. The first emendation to Bernard and Busse model regards the political regime variable: Bernard and Busse rather crudely divided the world into communist regimes and capitalist market economies which obviously fits with the cold war period. Since then, this is too crude when it comes to so-called post-communist transition economies [START_REF] Andreff | Would a second transition stage prolong the initial period of post-socialist economic transformation into market capitalism?[END_REF][START_REF] Andreff | Economie de la transition: La transformation des économies planifiées en économies de marché[END_REF] in particular as regard the sports economy sector which has differentiated a lot across former socialist countries during their institutional transformation [START_REF] Poupaux | The institutional dimension of the sports economy in transition countries[END_REF]. Such differentiation has translated into a scattered efficiency in winning Olympic medals after 1991 [START_REF] Rathke | Economics and the Summer Olympics: an efficiency analysis[END_REF].

The country classification which is retained here distinguishes first Central Eastern European countries (CEEC) which gave up a Soviet-type centrally planned economy in 1989 or 1990, and transformed into a democratic political regime running a market economy: Bulgaria, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia (and Czechoslovakia until its 1993 split), Slovenia, and the GDR (until German reunification in 1990). Another commonality to this group is that these countries have all joined the European Union in 2004 or 2007. A second country group (TRANS) gathers new independent states (former Soviet republics) and some former CMEA member states which have started up a transition similar to the one in CEECs but are lagging behind in terms of transformation into a democratic regime and some are stalling on the path toward a market economy: Armenia, Azerbaijan, Belarus, Georgia, Kazakhstan, Kyrgyzstan, Moldova, Mongolia, Russia, Tajikistan, Turkmenistan, Ukraine, Uzbekistan and Vietnam. None of them has joined the EU so far or has really an option to do so. The next two groups have not been Soviet regimes properly speaking in the past, although they were both communist regimes and planned economies. In the first one (NSCOM), we sample those countries which have started up a transition process in the 1990s: Albania, Bosnia-Herzegovina, China, Croatia, Laos, Macedonia, Montenegro, and Serbia (and the former FSR Yugoslavia before the 1991 break-up). Two countries have not yet engaged into a democratic transformation and a market economy: Cuba and North Korea, and must be considered as still communist regimes (COM). All other countries are considered as capitalist market economies (CAPME), the reference group in our econometric estimations.

Then a last variable is introduced that captures the influence on Olympic performance of a specific sporting culture in a region. For example, Afghan ladies are not used to have much sport participation or to attend sport shows, even less to be enrolled in the Olympic team. As a result of these cultural (sometimes institutional) disparities, some nations are more specialised in one specific sport discipline such as weight-lifting in Bulgaria, Turkey and Armenia, marathon and long distance runs in Ethiopia and Kenya, cycling in Belgium and the Netherlands, table tennis, judo and martial arts in Asia, sprint in Caribbean islands and the USA, etc. It is not easy to design a variable that would exactly capture such regional sporting culture differences 1 , but it is assumed here that regional dummies may reflect them. For model estimation, the world is divided into nine 'sporting culture' regions: AFS, sub-Sahara African countries; AFN: North African countries; NAM, North American countries; LSA, Latin and South American countries; EAST, Eastern European countries; WEU, Western European countries (taken as the reference region in our estimations); OCE, Oceania countries; MNE, Middle East countries; and ASI, (other) Asian countries.

A first model tested here is simply a specification à la Bernard and Busse, but with a differently defined political regime variable. Estimation is based on a censored Tobit model since a non-negligible number of countries that participate to the Olympics do not win any medal. Therefore, a zero value of the M i,t dependent variable does not mean that a country has not participated and we work out a simple Tobit, not a Tobit 2 (with a two stage Heckman procedure). Contrary to Bernard and Busse, it is not assumed that preparing an Olympic team is timeless and, then, independent variables are four-year lagged behind the dependent variable. Thus, GDP per inhabitant is noted (Y/N) i,t-4 , measured in 1995 PPP dollars, and N i,t-4 stands for population. Dummies are introduced to test whether the Olympics year is significant, taking 2004 as reference. These year dummies come out to be non-significant. In a second model, a data panel Tobit is adopted to take into account unobserved heterogeneity, whose test is significant 4 , and then estimation is with random effects. Sampled data 5 encompass all Summer Olympics from 1976Olympics from to 2004Olympics from , except 1980Olympics from and 1984 which are skipped out due to boycotts which have strongly distorted the medal distribution per country. The first specification (1) is:

* ,, 4 , ,4 ,, , ln ln it it it it pp i q q i i t pq Y Mc N γHost N Political Regime Year - - ⎛⎞ =+ + + ⎜⎟ ⎝⎠ ++ + ∑∑ αβ (1)
where 2) is an emended variant of Bernard and Busse model including our more specific political regime variable, but also above-described dummies standing for regions of sporting culture (Regions r,i ):

i,t ~ N (0, σ 2 ). M i,t observation is defined by ** ,, , * , if 0 0i f 0 it it it it MM M M > ⎧ = ⎨ ≤ ⎩ A second specification (
if 0 0i f 0 it it it it MM M M > ⎧ = ⎨ ≤ ⎩
In a third specification (3), an additional variable M i,t-4 is introduced on the right-hand side of model ( 2), just like Bernard and Busse did, though they did not comment why they proceeded in such a way. The justification here is that winning medals at the previous Olympics matters for an Olympic national team which usually expects and attempts to achieve at least as well as four years ago. Such inertial effect is all the more relevant that a nation is eager to win as many medals as possible from one Olympiad to the other (a sort of national 'Olympics cult' 6 ) and mobilise a lot of resources to succeed in. The resulting inertia differentiates those nations pulled by Olympics cult from those nations which are used to win zero or few medals. These two groups must be distinguished with using M i,t-4 , otherwise the prediction will be distorted. All econometric estimations deliver significant results (Table 1). In the first estimation, all coefficients are positive and significant at a 1% threshold, except for year dummies. Thus, it is once again confirmed that medal wins are determined by GDP per capita, population and a host country effect. Political regime is also an explanatory variable, in particular in the case of communist and post-communist transition countries. The second estimation (Tobit/panel) all in all exhibits the same results. The coefficients of regional sporting culture are significant except for Latin America, an area in which the North American sporting culture may have permeated namely through Caribbean countries and Mexico (classified in NAM).

Since Western Europe is the reference a significant coefficient with a positive sign means that a region performs relatively better than Western Europe in terms of winning Olympic medals (a negative sign means a lower relative performance than Western Europe). Sub-Sahara Africa, North America and Oceania perform better. It is a little bit surprising for Sub-Sahara African countries since they are among the least developed countries in the world (except South Africa), but such effect is due to a few African countries which are extremely specialised in one sport discipline where they are capable to win a non-negligible number of medals, such as Ethiopia and Kenya in long distance runs. With negative coefficients, North Africa, Asia, Eastern Europe and Middle East show a lower relative performance than Western Europe. It is not surprising for North Africa and the Middle East due to some restrictions to sporting culture in various countries. In the case of Asia, only few countries are really capable to win a significant number of medals (China, both Koreas, Mongolia). A surprise is the negative coefficient for Eastern European countries which are known as outliers or over-performers (given their GDP per capita and population). In fact, the negative coefficient results from the Political Regime variable which already captures their over-performance.

Predicting medal wins at Beijing Olympics: comparison with observed outcomes

Then model (3) was used to predict medal distribution at the 2008 Beijing Olympics:

if 0 0i f 0 it it it it MM M M > ⎧ = ⎨ ≤ ⎩
Since a pooling estimation 7 of model ( 3) is implemented, it may suffer from an endogeneity bias; the results may be biased by a correlation between the lagged endogenous variable and the error term. This issue is treated with a GMM dynamic panel [START_REF] Arellano | Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations[END_REF], a technique which provides estimated coefficients and predictions that are robust and close to those estimated with a Tobit model. Predictions have been first published [START_REF] Andreff | Les déterminants économiques de la performance olympique: Prévision des médailles qui seront gagnées aux Jeux de Pékin[END_REF] only for a sub-sample of countries gathered in Table 2.

The predicted first-rank winner was, as usual, the USA, followed by Russia and China, the latter benefitting from a host country effect at Beijing Games. Most developed and democratic market economies (CAPME) were forecast to be among the major medal winners together with some post-communist transition countries. The prediction for France was between 35 and 38 medals while the State Secretary for Sports was hoping that the French team would reach 40 medals (actually the achieved number was 41 medals). The publication of this article in France one month before the opening of Beijing Olympics rapidly became a hit in different French and European media and TV channels. First interviews focused on the predicted medal wins. In a second wave, after the Games end, interviewers became eager to know for which countries the model had provided correct or wrong prediction and, in the latter case, why were it so. This triggered the writing of a follow-up companion paper requested by the French National Institute for Sport and Physical Education (INSEP) to be included in its volume devoted to overall outcome for France at Beijing Olympics [START_REF] Andreff | Comparaison entre les prévisions et les médailles gagnées aux Jeux de Pékin, in INSEP[END_REF]. This paper systematically compared predictions and actual outcomes.

The above model (3) provided good predictions regarding those 189 countries for which data were available and computable: 70% of observed results belong to the predicted confidence interval. If one assesses a model prediction as acceptable when its error margin is not bigger than a two-medal difference between ex ante prevision and ex post reality, then model (3) correctly predicted 88% of all Beijing Olympics results. The remaining unexplained 12% (23 nations) account for sporting 'surprises' -unexpected results. Model (3) correctly predicted the first ten medal winners, except Japan (instead of Ukraine), missed only four out of the first twenty winners, although with a slightly different ranking. However, the most interesting results are witnessed when the model was clearly wrong in its prediction that basically happened for 23 countries, because this means that our five variables (plus the inertial variable) have not captured some core explanation of Olympics outcomes. Fortunately, economists are not capable to predict all the detailed Olympics results, otherwise why still convene the Games?

Which are the major 'surprises' delivered by ex post actual sporting results when compared with predictions? The first one is a quite bigger than expected number of medal wins by the Chinese team -all published predictions have been wrong in this respect. Model (3) has clearly underestimated the host country effect in China. Possibly, Chinese performance has also been boosted by some undetected doping 8 . A second surprise is the underperformance of the Russian Olympic team, the worst since the cold war. It was regarded so much 'catastrophic' that Vladimir Putin convened the highest decision makers of Russian sport to command a new Olympic policy likely to avoid a repeated disaster at the 2012 London Olympics. A policy which partly succeeded with 82 medals won in London. In the same vein, some other transition countries, namely Romania, have won fewer medals than expected in Beijing. The current state of reforming institutions and restructuring the whole sports sector in these countries has not been sufficiently captured in our model, despite our more refined political regime variable.

The last three significant surprises were Great Britain, Jamaica and Kenya, the latter being the only two developing countries ranked among the first twenty medal winners. Early preparation of a super-competitive team for the 2012 London Olympics may have been the cause for higher than expected outcomes of the British team, as it is suggested by [START_REF] Maennig | Sozioökonomische Schätzungen olympischer Medaillengewinne. Analyse-, Prognose-und Benchmarkmöglichkeiten[END_REF] who have introduced a 'next Olympics host country' variable in their prediction. However, such future host country effect slightly improves the authors' forecast: 38 predicted medals as against 47 won by Great Britain. Without such effect model (3) predicted between 32 and 35 medals for Great Britain. British medals concentration in cycling (12 medals) may trace back again to undetected doping and/or deep specialisation of a nation in one sport discipline. The latter is the most likely explanation for Jamaican medals 9 concentrated in sprint and Kenyan medals in long distance runs. Though such specialisation has been taken into account with the lagged M i,t-4 variable -Kenya had won seven medals and Jamaica five in the same disciplines at Athens Olympics -, the inertia captured by this variable reveals to be insufficient.

A model adapted to estimating the determinants of medal wins at Winter Olympics

The sporting context of Winter Olympics is rather different compared with the one of Summer Olympics. In 1976, 92 countries had participated to Summer Olympics with 6,084 athletes while they were only 37 countries participating to Winter Olympics the same year, with 1,123 athletes ( At first sight, the political regime seems to be less relevant as a variable that differentiates among the Winter Games medal winners; however it is kept in the model with some slight emendation compared to the Summer Olympics model. The reference country group remains CAPME for capitalist market economies; CEECs are those post-communist economies which have joined the EU in either 2004 or 2007; all the remaining post-communist economies are gathered in an EXCOM country group even though it would be sensible to consider Cuba and North Korea as still communist regimes (but their performance at Winter Games is negligible or nil).

A political regime variable might be a significant determinant (to be tested) of medal distribution per nation at Winter Olympics when looking at the data (Table 5). Being a centrally planned economy with some sort of communist regime was an advantage to win Winter Olympics medals until 1988. The average number of medal wins was higher in the EXCOM group than in the CEEC group and in the latter it was higher than in the CAPME reference group during this lapse of time, even though medals were concentrated on a small number of communist countries, namely the former USSR. The collapse of the communist regime seemingly had a significant impact on the number of medal wins which dramatically dropped in CEECs after 1990; it dropped much less significantly in other former communist countries, namely in the former Soviet Union, and recovered as soon as 1994 while the recovery in medal wins happened only in 2010 in CEECs. Such difference in momentum is probably due to a harsher shock of economic transition, a deeper and swifter transformation of the state-run sport system into a market sport economy in CEECs as compared with other post-communist countries, namely Russia. The distribution of medal wins across these four country groups from the 1964 to 2010 Winter Olympics (Table 6) suggests that snow coverage might well be a significant determinant of medal wins in winter sports. Countries with high snow coverage, followed by countries with polar-like climate and snow coverage, concentrate the great bulk of medal wins at Winter Olympics. The number of participating countries with high snow coverage increased from 14 in 1964 up to 19 in 2010 while their number of medals won grew from 39 to 134. During the same lapse of time, the number of countries with polar-like snow coverage augmented from 7 in 1964 to 13 in 2010 whereas their number of medal wins increased from 60 to 86. On the other hand, 13 countries with middle snow coverage had won only four medals in 1964; they were 33 participating at the 2010 Games where they won 37 medals. As regard countries with low (or no) snow coverage, the marked increase in their participation (from 2 to 17) did not translate into an impressive growth in medal wins (from 0 to 1 -with once four medals won in 1994 and once two medals in 2002). Snow coverage seems to be a differentiating factor among countries participating to Winter Olympics.

A second new dummy variable is introduced in the model to capture a country's endowment with winter sports resorts and facilities. Information is taken from data available on various websites describing ski resorts in different countries of the world, namely http://www.skiinfo.fr, http://www.sports-hiver.com, http://www.neigeski. com, http://www.levoyageur.net/stations, http://www.fr.snow-forecast.com, http://www. french-china.org. The RESORT dummy designed on the basis of such information consider a country as being endowed with many ski resorts and winter sports facilities when it has over 60 of them on its territory. A country with a number of skiing resorts between 5 and 60 is considered as having an average endowment by world standard. A country with a number of ski resorts and winter sports facilities below 5 is assessed and ranked as having few opportunities to win medals due to her short availability of resorts-facilities. The three country groups are comprised of:

• MANY winter sports resorts: Austria, Canada, former Czechoslovakia, France, Germany (GDR), Italy, Japan, Norway, Russia (CIS, USSR), Sweden, Switzerland, USA = 12 countries

• BETWEEN many and few winter sports resorts: Australia, Belgium, Bulgaria, Chile, China, Croatia, Czech Republic, Finland, Iran, Kyrgyzstan, Lebanon, Netherlands, New Zealand, Poland, Romania, Slovakia, Slovenia, South Korea, Spain, Turkey, Ukraine (former Yugoslavia) = 21 countries

• FEW/NO winter sports resorts: Albania, Algeria, American Samoa, Argentina, Armenia, Azerbaijan, Belarus, Bermuda, Bolivia, Bosnia-Herzegovina, Brazil, Cameroon, Colombia, Costa Rica, Cyprus, Denmark, Ethiopia, Estonia, Fiji, Georgia, Great Britain, Ghana, Greece, Guam, Guatemala, Honduras, Hungary, Iceland, India, Ireland, Israel, Jamaica, Kazakhstan, Kenya, Latvia, Lithuania, Luxembourg, Macedonia, Madagascar, Mexico, Moldova, Mongolia, Morocco, Nepal, Netherlands Antilles, North Korea, Pakistan, Philippines, Portugal, Peru, Senegal, Serbia, South Africa, Swaziland, Thailand, Taiwan, Tajikistan, Trinidad and Tobago, Uruguay, Uzbekistan, Venezuela, Virgin Islands = 62 countries. Participating countries with higher endowment in ski resorts and winter sports facilities are used to win an increasing number of Olympic medals from 89 in 1964 to 188 in 2010 (even 191 in 2006) while their number has always stood between and 14 (Table 7).

The number of participating countries with few or no resorts-facilities has grown from 9 in 1964 to 48 in 2010 whereas their number of medal wins has increased from 1 to 8. The number of countries with an average endowment stands in between as to their medal wins. It seems that a shortage of ski resorts and winter sports facilities is a hindrance to win medals at Winter Olympics whereas medal wins benefit to well-endowed countries in terms of winter sports facilities. Thus, the model is adapted to estimating the determinants of medal wins at Winter Olympics as follows:

if 0 0i f 0 it it it it MM M M > ⎧ = ⎨ ≤ ⎩
and N is a nation population, Y/N is its GDP per inhabitant, both variables being four-year lagged for the same reason as with the Summer Olympics model, Host is a dummy identifying the country that hosts the Games, Political Regime is a dummy which captures the impact of political regime on medal wins, Snow is a dummy variable differentiating countries as regard their degree of annual snow coverage, and Resort is a dummy capturing the impact of ski resorts and winter sports facilities located in a country on medal wins.

Economic determinants of medal win at Winter Olympic Games

Model ( 4) is now used for estimating whether the above-listed variables are significant determinants of medal wins at Winter Olympics. Econometric testing covers all Winter Olympics from 1964 up to 2010. Data for population and GDP per inhabitant are taken from CHELEM data base (which retrieves and proceeds to consistency checks between World Bank and OECD data). A first specification M1 resorts to a left-hand censored Tobit model since a non-negligible number of countries that participate to Winter Olympics do not win any medal. Therefore, a zero value of the M i,t dependent variable does not mean that a country has not participated; a simple Tobit is worked out, not a Tobit 2 (with a two stage Heckman procedure). This first specification takes on board five explanatory variables: population, GDP per inhabitant, three dummies Host, Snow and Resort. The MIDDLE country group which contains the biggest number of countries is taken as the reference for the Snow dummy. With the same rationale, the most numerous FEW/NO country group is taken as the reference for the Resort dummy. In a second specification M2, the censored Tobit model includes in addition a Political Regime dummy. A third specification M3 is the one which will be used later on for prediction; it encompasses one more explanatory variable, i.e., the inertial variable M i,t-4 .

In all three specifications (Table 8), GDP per inhabitant and population are very significant determinants of medal wins at Winter Olympics with a positive sign. Medals are basically shared across developed economies with rather important population. More interesting is that the endowment in ski and winter sports resorts is also a very significant determinant of medal wins. Belonging to the BETWEEN country group significantly increases a nation's probability to win medals at Winter Olympics and it is even more so for those countries with many winter sports resorts. The very existence of winter sports resorts reflects a high capacity of having a winter sports practice in a country and, consequently, selecting experienced athletes in the national squad.

Snow coverage surprisingly does not appear as a significant determinant of Winter Olympics medal wins. Compared with MIDDLE coverage country group, polar-like countries have a significant probability to win more medals, but this probability is not significant for high snow coverage countries; the probability to win fewer medals is not significant for low snow coverage countries. A same result shows up with the other two specifications M2 and M3. Indeed, some countries with high snow coverage do not perform that well at Winter Games such as Tajikistan and Kyrgyzstan. It is not enough ranks second with 28 medal wins while she has ranked first in 2006 (29 medals), 2002 (36 medals), 1998 (29 medals), 1992 (26 medals), and second in 2010 (30 medals). Canada takes over the third rank with 27 medals like in Vancouver 2010 (26 medals) and Turin 2006 (24 medals). France is expected to win 12 medals in Sochi (8th rank) as against 11 in Vancouver, 9 in Turin, 11 in Salt Lake City 2002, 8 in Nagano 1998, 5 in Lillehammer 1994, and 9 in Albertville 1992. Winning 24 medals, Russia would rank fourth at Sochi Games. It is not enough to host Winter Games to be the winner. However, it would be a quite better performance than the disastrous 15 medals won in Vancouver (6th rank) and 13 medals in Salt Lake City (6th rank). Sochi Olympics might materialise the end of the deep transformation in the Russian sports system undertaken during the 1990s and the 2000s. This would be a sign of Russian recovery as a Winter Olympics sporting power but without coming back to the 1976-1988 'golden age' when the Soviet team was usually winning between one fifth and one quarter of all distributed medals. Economic and sporting systems' transformation triggered a shock on Russian and CIS medal wins whose share fell below 10% of medals total since 2002. In particular, the transformational recession has seriously affected Russia's GDP per capita downwards until 1998; the same roughly applies to other CIS countries. In our model, a decreasing GDP per capita explains a lower number of medal wins. A decreasing number of medals for Russia is (only partly) compensated by the emergence of Belarus, Kazakhstan and Ukraine as more or less regular medal winners at Winter Games since 1994 (Table 10). 1964 1968 1972 1976 1980 1984 1988 1992 1994 1998 2002 2006 1998 (ranked 11th in 1998, 10th in 2002, 9th in 2006 and 8th in 2010) even though this cannot compare with the Chinese outstanding performance at the Summer Games hosted in Beijing. Thus, it is not surprising that the model predicts again 11 medal wins for China in 2014, but note that the upper bound of the confidence interval for China is 13 medals. If the Chinese team performs very well, it may even pretend to the 7th rank in terms of medal wins at Sochi Games. The swift economic development of China since the 1990s has obviously had an impact on the nation capacity to win more Olympics medals in general and including at Winter Olympics. However, China's performance at Winter Games is less outstanding than at Summer Games. This is probably due to a number of ski resorts and winter sports facilities which are not yet proportionate to the size of Chinese population and its increasing purchasing power. To the best of our knowledge, the number of winter sports participants and the number of ski resorts are both rapidly increasing these days in China. Probably, some time is still required to have a mass of winter sports participants huge enough to select a very performing national Chinese team of winter sports athletes. Hosting some future Winter Olympics in China may boost the expansion of ski resorts and winter sports practice throughout Chinese population. The candidature of a Chinese city close to a winter sports site would probably be in the prospects of some Chinese authorities in the medium term.

Conclusions: economic prediction and surprising sporting outcomes

All above predictions must be taken with a pinch of salt. This is namely due to surprising sporting outcomes. Indeed, there are many unexpected sporting outcomes observed ex post -i.e., achieved outcomes markedly different from the forecast -even though it happens more with the FIFA World Cup than Summer Olympics [START_REF] Andreff | Economic modeling and prediction of Summer Olympic medal wins and FIFA World Cup semi-finalists[END_REF]. Unexpected or surprising outcomes of a sport contest have not been analysed so far. They happen when opponents in a sport contest have clearly uneven sporting forces, and the underdog wins the favourite. Elaborating on a metrics to quantify surprising sporting outcomes should be a promising avenue for further research. It will be possible to check after the 2014 Sochi Games whether these Winter Olympics were characterised with many or few surprising outcomes.

As regard the host country, Russia is not likely to win the biggest number of medals at Sochi Winter Games. If she was to make it with more than 27 medals, then being ranked third with Canada, one would be allowed to conclude that she performed well, better than expected on the basis of the above economic model. Such a good performance should be due to exceptional efforts of Russian athletes and coaches before and during Sochi Games. If Russia would win less than 21 medals, we could join Prime Minister Medvedev and President Putin in complaining that the Russian winter sports team should really have done better -or that it was unexpectedly bad lucky. When it comes to the Chinese winter sports team, if it would be able to win a significantly higher number of medals than 11 in Sochi, this must be considered as an excellent outcome. If the number were to fall quite below 11, it should be considered as a counter-performance. Not to be expected so far! A test of maximum likelihood shows that the rho coefficient is significant (Pr = 0.00).

The data panel is not balanced since the number of existing countries in the world has increased between 1976 and 2004, namely due to the breakup of the former Soviet Union, former Yugoslavia and former Czechoslovakia (+20 countries), only partly compensated by the reunifications of Germany and Yemen (-2 countries). Which has been fuelled in particular by the cold war, but it has not vanished yet in a number of countries.

A test of maximum likelihood shows that the rho coefficient is not significant (Pr = 0.26) which allows to choose a pooling estimation. This issue is discussed in depth in [START_REF] Andreff | Les déterminants économiques de la performance olympique: Prévision des médailles qui seront gagnées aux Jeux de Pékin[END_REF] explaining why it was not possible to integrate doping among independent variables despite the fact that we wished to do so. Some Jamaican sprint finalists have been controlled positive in doping tests during the weeks after the Beijing Games, which may be another explanatory variable. Some exceptions are neglected here such as Dubai with its ski resort in a country without any natural snow coverage and without even a second winter sports facility in the country. Some countries which have participated to Winter Olympics are excluded from the sample since data about population and GDP cannot be traced back to 1964. They are: Andorra, Caiman Islands, Liechtenstein, Monaco, Montenegro, Porto Rico, and San Marino. No big medal winner.

A fourth specification has also been tested including the Regions dummy used in the Summer Olympics model. For three regions the test does not provide any result since these regions have never won a medal at Winter Games. For most regions, the variable is not significant even at a 10% threshold.

For more specific determinants of Olympics performances reached by the communist GDR: [START_REF] Dryden | For power and glory: state-sponsored doping and athletes' human rights[END_REF].

Table 1

 1 Tobit estimation of medal wins at Summer Olympics

	Independent variables	Tobit model (1)	Tobit (panel) model (2)	Tobit model (3) with lagged M
	Log population (t -4)	9.14***	4.15***	2.15***
	Log GDP per capita (t -4)	12.42***	5.44***	2.73***
	Host	24.37***	10.40***	10.04***
	Political regime (ref. CAPME)
	COM	24.34***	11.18***	5.76**
	TRANS	23.24***	20.97***	8.15***
	CEEC	21.43***	17.94***	6.71**
	NSCOM	11.98***	8.06***	5.22*
	Region (ref. WEU)
	AFN		-4.45*	-1.81
	AFS		3.67*	0.75
	NAM		7.93***	0.076
	LSA		0.57	-1.08
	ASI		-4.34***	-2.58*
	EAST		-5.53*	-3.5
	MNE		-5.00***	-2.47*
	OCE		6.277**	1.3
	Year dummy (ref. 2004)
	1976	4.63
	1988	-0.2
	1992	3.33
	1996	3.35
	2000	0.31
	Medals (t -4)			0.95***
	Constant	-138***	-51.30***	-31.57***
	Number of observations	941	941	831
	Log-likelihood value	-1,646.1	-1,551.5	-1,224.2
	Pseudo R 2	0.17	0.19	0.34

Table 2

 2 Prediction of medal wins at Beijing Olympics

		Medals won in 2004	Médial wins in 2008 predicted	Lower bound	Upper bound
	CEEC
	Bulgaria	12	12	10	13
	Hungary	17	19	17	21
	Poland	10	14	12	16
	Czech Republic	8	10	8	12
	Romania	19	21	19	23
	TRANS
	Belarus	15	17	14	20
	Kazakhstan	8	11	8	14
	Russia	92	96	93	100
	Ukraine	23	27	24	29
	NSCOM
	China	63	80	73	86
	Cuba	27	29	25	33
	CAPME
	Germany	49	52	50	54
	Australia	49	51	47	54
	Canada	12	15	13	18
	USA	102	106	103	110
	France	33	36	35	38
	Great Britain	30	47	32	35
	Italy	32	35	34	36
	Less developed countries
	Brazil	10	12	10	14
	South Korea	30	30	27	32
	Kenya	7	2	1	4
	Jamaica	5	3	0	4
	Turkey	10	9	7	11
	Source: Andreff et al. (2008)

  Table3). In 2004, 201 countries were participating to Athens Olympics with 10,658 athletes whereas 80 countries had participated to the 2006 Winter Games in Turin with 2,651 athletes. Winter Olympics is a quite smaller mega-sporting event compared to Summer Games. However, the former has grown a lot during the lapse of time covered in this paper. The number of participating countries has increased from 36 in 1964 up to 82 in 2010 while the number of participating athletes has augmented from 1,091 to 2,629. The number of medals to be won at Winter Olympics is smaller than the one observed at Summer Olympics (over 900 overall since 2000), but it has grown from 103 in 1964 up to 258 in 2010. The number of nations having won at least one Winter Olympic medal has increased from 14 in 1964 to 26 in 2010 (as against a maximum of 80 countries at the 2000 Summer Games).

Table 3

 3 Winter Olympic performances, 1964[START_REF] Andreff | Economic modeling and prediction of Summer Olympic medal wins and FIFA World Cup semi-finalists[END_REF]

	City	Year	Participating countries	Countries with M > 0	Overall number of medals	Participating athletes
	Innsbruck	1964	36	14	103	1091
	Grenoble	1968	37	15	106	1171
	Sapporo	1972	35	17	105	1008
	Innsbruck	1976	37	16	111	1123
	Lake Placid	1980	37	19	115	1072
	Sarajevo	1984	48	17	117	1279
	Calgary	1988	57	17	138	1424
	Albertville	1992	63	20	171	1772
	Lillehammer	1994	67	22	183	1747
	Nagano	1998	72	24	205	2176
	Salt Lake City 2002	77	24	234	2386
	Turin	2006	80	26	252	2651
	Vancouver	2010	82	26	258	2629
	Since population, GDP per inhabitant and the host country dummy variable have
	emerged as basic determinants of medal wins at Summer Olympics, they are kept in
	elaborating on a Winter Olympics model. Keeping GDP per capita in the model is
	particularly sensible because it is obvious from Table 4 that there is a relationship
	between the number of medal wins and the level of economic development. In Table 4,
	country groups are those defined by the World Bank. Developed market economies
	(DMEs) are countries with a GDP per inhabitant over $10,725 in 2006; (newly) emerging
	economies (NMEs) are countries whose GDP per inhabitant is between $3,466 and
	$10,725; intermediary income (developing) countries (IICs) are those with a GDP per
	inhabitant between $876 and $3,465; least developed countries (LDCs) are those with a
	GDP per inhabitant below $876. At Winter Olympics a concentration of medal wins on
	DMEs is witnessed whatever the number of participating DMEs. The average number of
	medal wins is always higher in DME and NME groups than in IICs and LDCs. Even with
	a growing number of participating countries -from 4 in 1964 to 20 in 2010 for IICs and
	from 3 to 13 for LDCs -these two country groups are not able to substantially increase
	their share in the medals total. In most Winter Games, LDCs have not won even a medal
	(except in 1992 and 1994 with just one medal win).

Table 4

 4 Uneven medal distribution at Winter Olympics by level of economic development

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
	1964	DME	77	3.67	1.27	21	12
		NEC	26	3.25	2.71	8
		IIC	0	0	0.00	4
		LDC	0	0	0.00	3
	1968	DME	83	3.95	1.13	21	11
		NEC	23	2.56	1.70	9
		IIC	0	0	0.00	5
		LDC	0	0	0.00	2
	1972	DME	71	3.38	1.12	21	13
		NEC	34	4.25	1.58	8
		IIC	0	0	0.00	4
		LDC	0	0	0.00	2
	1976	DME	64	2.67	1.26	24	13
		NEC	47	5.22	1.97	9
		IIC	0	0	0.00	4
		LDC	0	0	0.00	0
	1980	DME	67	2.91	1.24	23	14
		NEC	47	5.22	1.88	9
		IIC	1	0.25	2.00	4
		LDC	0	0	0.00	1
	1984	DME	61	2.26	1.54	27	13
		NEC	55	5	1.96	11
		IIC	1	0.17	2.41	6
		LDC	0	0	0.00	4
	1988	DME	78	2.44	1.56	32	13
		NEC	57	5.18	2.10	11
		IIC	3	0.3	3.17	10
		LDC	0	0	0.00	4
	1992	DME	141	4.41	1.58	32	16
		NEC	26	1.86	3.30	14
		IIC	3	0.25	3.48	12
		LDC	1	0.2	2.25	5
	1994	DME	149	4.52	1.58	33	16
		NEC	23	1.44	3.99	16
		IIC	10	1.67	0.76	12
		LDC	1	0.83	0.49	6
	Notes: σ: standard deviation; M: number of medals per country.

Table 4

 4 Uneven medal distribution at Winter Olympics by level of economic development (continued)

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
	1998	DME	170	5.15	1.50	33	17
		NEC	21	1.4	3.33	15	2
		IIC	14	0.67	3.03	16	5
		LDC	0	0	0.00	8	0
	2002	DME	197	5.97	1.64	33	16
		NEC	25	1.47	2.22	17	5
		IIC	12	0.67	2.94	18	3
		LDC	0	0	0.00	9	0
	2006	DME	201	5.74	1.54	35	15
		NEC	36	2.4	2.33	15	7
		IIC	15	0.83	3.13	18	4
		LDC	0	0	0.00	12	0
	2010	DME	207	6.09	1.60	34	16
		NEC	36	2.4	1.70	15	7
		IIC	15	0.75	3.35	20	3
		LDC	0	0	0.00	13	0

Notes: σ: standard deviation; M: number of medals per country.

Table 5

 5 Uneven medal distribution at Winter Olympics by political regime

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
	1964	CAPME	77	2.85	1.53	27	12
		CEEC	1	0.2	2.25	5	1
		EXCOM	25	6.25	2.00	4	1
	1968	CAPME	83	2.96	1.43	28	11
		CEEC	10	1.67	1.35	6	3
		EXCOM	13	4.33	1.73	3	1
	1972	CAPME	71	2.84	1.29	25	13
		CEEC	18	3	1.84	6	3
		EXCOM	16	4	2.00	4	1
	1976	CAPME	64	2.21	1.45	29	13
		CEEC	20	3.33	2.31	6	2
		EXCOM	27	13.5	1.41	2	1
	1980	CAPME	67	2.48	1.41	27	14
		CEEC	26	4.33	2.12	6	4
		EXCOM	22	5.5	2.00	4	1
	1984	CAPME	61	1.65	1.90	37	13
		CEEC	30	5	1.92	6	2
		EXCOM	26	5.2	2.13	5	2
	1988	CAPME	78	1.7	1.98	46	13
		CEEC	28	4.67	2.15	6	2
		EXCOM	32	6.4	1.98	5	2
	1992	CAPME	141	2.88	2.08	49	16
		CEEC	3	0.38	2.79	8	1
		EXCOM	27	4.5	2.03	6	3
	1994	CAPME	146	3.32	1.96	44	15
		CEEC	3	0.3	3.17	10	1
		EXCOM	34	2.62	2.38	13	6
	1998	CAPME	170	3.78	1.84	45	17
		CEEC	4	0.4	2.43	10	2
		EXCOM	31	1.82	2.53	17	5
	2002	CAPME	196	3.92	2.15	50	15
		CEEC	12	1.2	1.17	10	5
		EXCOM	26	1.53	2.37	17	4
	2006	CAPME	201	3.94	1.97	51	15
		CEEC	12	1.2	1.17	10	6
		EXCOM	39	2.05	2.67	19	5
	2010	CAPME	204	3.92	2.14	52	15
		CEEC	21	2.1	1.13	10	6
		EXCOM	33	1.65	2.45	20	5
	Notes: σ: standard deviation; M: number of medals per country.

Table 6

 6 Uneven medal distribution at Winter Olympics by level of snow coverage

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
	1964	POL	60	8.57	1.06	7
		HIGH	39	2.79	1,47	14
		MIDDLE	4	0.31	2.03	13
		LOW	0	0.00	0.00	2
	1968	POL	43	6.14	0.94	7
		HIGH	53	3.53	1.08	15
		MIDDLE	10	0.83	3.12	12
		LOW	0	0.00	0.00	3
	1972	POL	38	6.33	1.00	6
		HIGH	58	4.46	0.93	13	11
		MIDDLE	9	0.64	3.77	14
		LOW	0	0.00	0.00	2
	1976	POL	46	6.57	1.44	7
		HIGH	58	4.14	1.35	14
		MIDDLE	7	0.47	3.30	15
		LOW	0	0.00	0.00	1
	1980	POL	47	5.88	1.30	8
		HIGH	61	4.69	1.39	13	10
		MIDDLE	7	0.50	2.18	14
		LOW	0	0.00	0.00	2
	1984	POL	59	7.38	1.17	8
		HIGH	57	4.07	1.53	14	11
		MIDDLE	1	0.05	4.60	19
		LOW	0	0.00	0.00	7
	1988	POL	52	6.50	1.47	8
		HIGH	79	5.27	1.32	15	11
		MIDDLE	7	0.33	4.64	21
		LOW	0	0.00	0.00	13
	1992	POL	61	5.55	1.51	11
		HIGH	95	6.33	1.32	15
		MIDDLE	15	0.68	1.94	22
		LOW	0	0.00	0.00	15
	1994	POL	73	6.08	1.55	12
		HIGH	88	5.18	1.46	17
		MIDDLE	18	0.72	2.14	25
		LOW	4	0.31	2.74	13
	Notes: σ: standard deviation; M: number of medals per country.

Table

  Uneven medal distribution at Winter Olympics by level of snow coverage (continued)

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
		POL	75	6.25	1.42	12	6
		HIGH	98	5.44	1.47	18	9
		MIDDLE	30	1.03	2.56	29	8
		LOW	2	0.15	3.67	13	1
		POL	73	5.62	1.44	13	7
		HIGH	134	7.05	1.58	19	11
		MIDDLE	27	0.96	2.33	28	6
		LOW	0	0.00	0.00	17	0
		POL	93	7.15	1.30	13	8
		HIGH	122	6.78	1.43	18	11
		MIDDLE	37	1.12	2.70	33	7
		LOW	0	0.00	0.00	16	0
		POL	86	6.62	1.39	13	8
		HIGH	134	7.05	1.47	19	12
		MIDDLE	37	1.12	2.95	33	5
		LOW	1	0.59	0.41	17	1

Notes: σ: standard deviation; M: number of medals per country.

Table 7

 7 Medal distribution and winter sports resorts and winter sports facilities

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
	1964	MANY	89	7.42	0.97	12	10
		BETWEEN	13	0.87	2.98	15	3
		FEW/NO	1	0.11	3.00	9	1
	1968	MANY	91	7.00	0.57	13	12
		BETWEEN	15	1.00	2.56	15	3
		FEW/NO	0	0.00	0.00	9	0
	1972	MANY	89	6.85	0.69	13	13
		BETWEEN	16	1.14	2.31	14	4
		FEW/NO	0	0.00	0.00	8	0
	1976	MANY	95	6.79	1.15	14	12
		BETWEEN	15	0.94	2.38	16	3
		FEW/NO	1	0.14	2.71	7	1
	1980	MANY	95	6.79	1.11	14	13
		BETWEEN	18	1.28	2.06	14	4
		FEW/NO	2	0.22	2.00	9	2
	1984	MANY	100	7.14	1.10	14	13
		BETWEEN	16	1.00	3.25	16	3
		FEW/NO	1	0.56	0.43	18	1
	Notes: σ: standard deviation; M: number of medals per country.

Table 7

 7 Medal distribution and winter sports resorts and winter sports facilities (continued)

	Year	Country group	Number of medals	Mean: m	Coefficient of variation: σ/m	Number of countries	Countries with M > 0
	1988	MANY	120	8.57	1.02		13
		BETWEEN	18	1.13	2.14		4
		FEW/NO	0	0.00	0.00		0
	1992	MANY	148	11.38	0.76		12
		BETWEEN	20	1.18	1.75		6
		FEW/NO	3	0.09	4.22		2
	1994	MANY	150	12.5	0.71		11
		BETWEEN	25	1.25	1.64		7
		FEW/NO	8	0.23	3.00		4
	1998	MANY	155	12.92	0.66		11
		BETWEEN	44	2.00	1.86		9
		FEW/NO	6	0.16	3.06		4
	2002	MANY	186	15.5	0.73		11
		BETWEEN	42	1.83	1.47		10
		FEW/NO	6	0.14	4.07		3
	2006	MANY	191	15.92	0.59		11
		BETWEEN	55	2.50	1.52		11
		FEW/NO	6	0.13	3.85		4
	2010	MANY	188	15.67	0.72		11
		BETWEEN	62	2.82	1.43		10
		FEW/NO	8	0.17	3.29		5

Notes: σ: standard deviation; M: number of medals per country.

Table 9

 9 Prediction of medal wins at Sochi Winter Olympics

	Countries	Medals won in 2010	Medal wins predicted in 2014	Lower bound	Upper bound
	USA	37	36	33	38
	Germany	30	28	26	30
	Canada	26	27	25	28
	Russia	15	24	21	27
	Norway	23	24	22	25
	Austria	16	15	14	16
	Sweden	11	13	12	14
	France	11	12	11	13
	China	11	11	9	13
	South Korea	14	11	10	13
	Switzerland	9	9	8	10
	Japan	5	7	6	9
	Italy	5	7	6	8
	Netherlands	8	6	5	7
	Poland	6	6	4	8
	Czech Republic	6	6	4	7
	Finland	5	5	3	6
	Australia	3	3	1	4
	Slovenia	3	2	1	4
	Croatia	3	2	0	4
	Slovakia	3	2	0	3
	Belarus	3	1	0	3

  The confidence interval for Russian medal wins is between 21 and 27 (Table9). So that, in the worst case, Russia may win less medals in 2014 than at the 1994 and 2006 Winter Games, which would not be considered as very rewarding by Russian sports authorities. Moreover, the model predicts no medal win for Kazakhstan and Ukraine at 2014 Sochi Games and only one for Belarus.The transformational recession lasted a shorter lapse of time in CEECs than in CIS countries. Nevertheless, the transition shock has triggered a dramatic drop in CEEC medal wins at Winter Games. The recovery in medal wins was quite slower than economic recovery since the sports sector was not a top priority in the transition strategy backed by Washington organisations (the IMF and World Bank). The most spectacular shock on medal wins in CEECs derives from German unification in 1990. The former GDR also enjoyed a sort of 'golden age' from 1972 to 1988 with between 14 and 25 medal wins at Winter Olympics 13 . At the 1992 Winter Games, the unified German team, taking stake of East German athletes, outperformed (with 26 medals) all participating countries including the CIS unified team (23medals). Since then Germany became top performer at Winter Olympics with the biggest number of medals won from Albertville 1992 to Turin 2006 (except Lillehammer 1994, 2nd rank behind Norway, and Vancouver 2010, 2nd rank behind the USA). At the 2014 Sochi Games, model (4) forecasts only 16 medal wins for CEECs taken altogether, which would be a step back compared to the 2010 recovery with 21 medals though better than 12 medal wins in 2002 and 2006. China would rank 9th at Sochi Games according to the model prediction. In fact, China has appeared as a new Winter Olympics winner since 1992, and more basically since

										2010
	CEECs
	Bulgaria					1				1	3	1
	Czech Republic									3	3	4	6
	Estonia									3	3	1
	Hungary					1
	L a t v i a									1	2
	Poland			1						2	2	6
	R o m a n i a		1
	Slovakia									1	3
	Slovenia									3	1	3
	Former Czechoslovakia	1	4	3	1	1	6	3	3
	Former GDR		5	14	19	23	24	25
	Former Yugoslavia						1	3
	CEECs/medals total %	1.0 9.4 17.1 18.0 22.7 26.5 22.5 1.7 1.6 1.9 5.4 4.8 8.1
	CIS countries
	Belarus									2	2	1	1	3
	Kazakhstan									3	2	1
	Russia									23	18	13	22	15
	Ukraine									2	1	2
	U z b e k i s t a n									1
	Former USSR	25	13	16	27	22	25	29 23*
	CIS/medals total (%)	24.3 12.3 15.2 24.3 19.1 21.4 21.0 13.4 16.9 11.2 6.0 9.9 7.4
	Other EXCOM
	China								3	3	8	8	11	11
	Croatia									4	3	3
	N o r t h K o r e a								1
	Note: *CIS unified squad

W. Andreff

With regards to the Regions dummy variable supposed to capture differences in sporting culture, it is not expected to be as much significant for Winter Olympics as it appeared to be for Summer Olympics. The reason is very simple: all those countries which participate to Winter Games have in common a sporting culture geared towards the practice of winter sports wherever they are located and whatever their overall sporting culture. This is confirmed by the fact that, contrary to Summer Olympics, many countries in the world do not participate to Winter Olympics. Thus, the regional dummy is skipped out from the Winter Olympics model.

If a country would like to develop a wide range of winter sports on its territory, making it able to train and select performing athletes, it could not significantly achieve it without some proper weather conditions, in particular enough snow coverage per year, and more than a minimal endowment in winter sports resorts and facilities 10 . These two new variables are to be introduced in the model. The first one is coined SNOW; it is a dummy differentiating countries as regard their average degree of annual snow coverage. Indeed, among those countries which have participated at least once to Winter Olympics, the degree of snow coverage is quite variable, but it is not easy to obtain a precise measure of snow coverage back to 1964. Thus, data and information provided by Maps of the World and the World Meteorological Organisation have been gathered regarding main climates, snow precipitations and temperature in order to build up the Snow dummy. The outcome in the sample of participating countries 11 is as follows:

• POL (a so-called 'polar' coverage in countries with a long duration of annual snow coverage): Belarus, Canada, Estonia, Finland, Iceland, Latvia, Lithuania, Mongolia, Nepal, Norway, Russia (by extension CIS and the former USSR), Sweden = 12 countries Introducing a Political regime dummy in the second specification improves the estimation overall (Pseudo-R 2 increases). The host country dummy is significant (though at 10%). Being a Central and Eastern European post-communist nation increases her probability to win medals at Winter Olympics and it is even more so for the EXCOM country group (CIS countries and all other non-Soviet former communist countries).

The third specification M3 is by far the best one with a marked improvement of Pseudo-R2. Moreover, all explanatory variables are significant except snow coverage with regards to high and low snow coverage countries. The inertial variable -medal wins at previous Winter Olympics -is significant as well and the host country dummy becomes significant at 1% 12 . This model fits well for predicting medal wins at Sochi Winter Games.

Economic prediction of medal wins at the 2014 Sochi Winter Olympics: Russia and China

The prediction exercise based on model M3 takes CHELEM preliminary data for 2010 as regard population and GDP per inhabitant and then calculates the Sochi Games outcome in terms of medal wins (Table 9). The expected winner (first ranked country) is the USA with 36 medal wins, just like it happened in Vancouver 2010 with 37 medals. Germany Notes 1 [START_REF] Hoffmann | Public policy and olympic success[END_REF] consider that an important determinant of Olympic successes lies in the degree to which sport and sporting activities are embedded in a nation's culture. The proxy used to capture such determinant is the total number of times a country has hosted Olympic Summer Games between 1946 and 1998. Our regional variable does not intend to capture only a nation's sporting culture but how much it is specific (different from the one of nations located in a different geographical area). 2

It was certainly so until the most recent publication by [START_REF] Forrest | Explaining and forecasting national team medals totals at the Summer Olympic Games[END_REF]. 3

Bernard and Busse use the percentage of medal wins per country i for M i,t instead. Our regressions are calculated with both the absolute number of medals (Table 1) and the percentage of medals per country, and the results are not significantly different.


Learningfrom Critical Analysis ofHazard Studies andfrom Accidents in France

According to

the European Directive (l) related to the prevention of major technological hazards, a lot of individual hazards investigations wore performed for oil, liquefled gas, chemicals, grain, fertilizers plants and storages.

Individual hazards investigation are generally carried out for each individual facility and, according to French regulations (2), three different reports might be issued :

-a survey of thc hazards (Etüde des dangers) to emphasize the main hazards in the facility and preventive and protective measures, -an Infernal Operation Programme (Plan d'Operation Interne -POI -) with the aim of organizing fire fighting and other safety measures, -in some cases, administrative authorities may ask a third party for a critical survey (etude de sdrete ou analyse critique de l'etude de dangers) of the hazards and related infernal Operation Programme issued under the responsibility of the plant's owner.

In addition, general survey of an industrial estate is sometimes required by the administrative authorities.

The authors were personnally involved in some of these individual and general actions äs well äs in accident investigations.

In the first part of this. gaper, acceptable pressure and heat radiation thresholds and-energy thresholds for missile effect have been choosen for the scenarios of major technological hazards such äs fires and explosions, The effects on the Population and on the facilities are critically analysed and emphasis on energy thresholds-for fragment dispersion will be given when presenting means of assessing the effects.

The three following parts will be devoted respectively to caiculatlon means used for evaluation of the effects Of pool fires, bleve and explosions (both confined and unconfined). Observations drawn from the Investigations of accidents will be critically reviewed.

International Conference and Workshop on Modeling and Mitigating

II.l.l. Effects on individuais.

After a dose examination of existing dafa the followino threshold values for human being were accepted : '••-' 170 mbar, threshold for a significant lethality, -50 mbar, under this threshold, pressure effects on man are reversible.

The levels are consistent with the values fixed In French regulation related to safety distances In pyrotechnic plants (3) when using the pressure versus the scaled distance curves determined with trinitrotoluene detonations äs exemplified in table l. These thresholds values are defined in terras of Incident pressure. We do know this is an over-estimation for small explosions (for instance 100 kg TNT equivalent).

In fact, time has to be considered : the Impulse effects have an important influence on men and facilities. For men, two types of effects are in fact to be examined :

-injuries to eardrums and lungs -people set in motlon by the shock wave.

It is well known that eardrums do not withstand a rapid rise in pressure. Time is a parameter to be taken into account by the means of Impulse. Transient effects may appear when surpression exceeds 0.015 bar, if positive Impulse -I-is over 0.02 bar. ms. Eardrums may be ruptured with a surpression up to 0.35 bar and an Impulse over 0.5 bar.ms. A sudden overpressure on the thorax may easily cause pulmonary injuries. Importance of the disease is an increasing function of the ratio P/Patm (overpressure/atmopheric pressure)-and of the ratio I/M 1 /^ Patm 1 /^ äs exemplified on figure l 'where I is the positive Impulse and M the weight of the individual.

But people may also be set in motion by the shock wave. The initial speed is function of the overpressure P, and of I/M^/3. When this speed is less than 3 m/s, there is no particular risk. By collision of the head against a pari of a fixed Installation, a fracture of the skull may happen when this speed is 4 m/s ; it will happen quite surely when the speed is 7 m/s and with 50 % probability when speed is 5.5 m/s. By collision of an other part of the body than the head the corresponding values for speed are 6.4, 42 and 16.5 m/S.

Effects on structures.

Data are available about the behaviour of walls structural equipment and window panes [START_REF] Winter -G | Comportement des vitrages aux effets d' une onde de choc -Doc CERCHAR SMM[END_REF]. Structural equipment design may include layout and devices to limit explosion damage.

Nevertheless the analyst has to bear in mind the synergetic effects a blast wave may produce on the surrounding equipments-Only few informations is avalable for instance in an existing plant, the main difficulty lying in the lack of data for previous designs.

As regards the pressure effect on facilities, TNT curves (4) glve the incident peak overpressures versus scaled distances . But the effects of reflections are to be considered ; these curves are consistent for explosives and mainly in the far fields. For detonation of gases [START_REF] Lannoy | Estimation des consequences d'un rejet accidentel dans l'atmosphere d'un produit toxique ou inflammable[END_REF], evaluation tests are summarized on figure 2.

), X. _JÂ »rnr.-.i.>-i"i" E'"] i «<.v:(««' * i<i«/».<w. nnu>.-.ri-i.

["] . l.l 10-i' ntirAi'r ruMH • htmir^" . ...HO---' t") -unconfined explosions are mostly deflagrations the flame speeds of which are mainly variable in relationship with ignitlon sources [START_REF] Winter | Explosions de melanges gazeux ä l'air libre -Inflammation par une source d'amorcage faible" -Internal report CERCHAR[END_REF] and geometry of the confinement. However, in some cases, transition from deflagration to detonation may occur (7) (B),

-bursting of vessels in relationship with production of missiles.

Currently, only scattered results are known [START_REF] Lannoy | Estimation des consequences d'un rejet accidentel dans l'atmosphere d'un produit toxique ou inflammable[END_REF] and experimental investigations to validate physical modeis are needed.

Heat radiation thresholds from fires and bleve.

Effect on individuais.

For the survey of hazards the following thresholds are generally considered when the duration of the fire is quite high (more than 60 s). :

-0.52 W/cm 2 , for severe casualties and lethality, -0.29 W/cm 2 , under this threshold, the radiation eftect on man is reversible.

These thresholds are to be used only when men are unable to escape and run away from heat effects.

Nevertheless, when people is properly drilled, higher values could be accepted (for instance : 0.8 W/cm 2 for firemen with suitable equipment and a quite short stay).

For long duration effects, it is possible to quote correlations giving the threshold value of injury (at a low probability) and lethality äs a function of time [START_REF] Mudan | Thermal radiation hazards from hydrocarbon pool fires[END_REF].

In the case of Bleve, the phenomenon is very quick and higher threshold values, function of time, are thus to be used. For l % fatality level, the threshold flux : 0 = 190.81 t-0.771 (0 kW/m 2 and t s) is given on figure 3 according to EISENBERG values quoted by MUDAN [START_REF] Mudan | Thermal radiation hazards from hydrocarbon pool fires[END_REF]. Currently, one may assess that the duration of a Bleve is in the order of 20-30s for spheres containing 500 m3 to 1500 m3 of liquefied gas.

Sometimes, this threshold is presented in term of dose (joules). It must be said, that in this case, this flux 0 and time t are connected by the following formula (0 * t = constant) but this relation is no mors valid when t is higher than 10 s.

Figure 3 [From MUDAN (9)] 11.2.2. Effects on facilities.

As regards the heat radiation effects on facilities, various cases are to be taken into account. Thus, threshold values cannot be easily and univocally given. Many caiculations are possible when the behaviour of the material in presence of fire is known. For example LANNOY (10) deals with heat conduction in concrete. But spacing distances derived from thermal radiation modeis are also needed. They are for instance given by CROCKER and NAPIER [START_REF] Crocker | Thermal radiation hazards of liquid pool fires and tank fires" -I[END_REF] For individuais, tlic only importoni: energy thrcshold for missiles cfJEcct is thc onc corrcsponding to Icthality. It is no worth worrying about dcfining a rcversibility thrcshold for wlicn o missile pcnotrates any pari of thc body.

The frcnch pyrotcciinic rcgulation givcs this lethality thrcshold os equal to 20 Joules. This valuc is connected to thc boundary botwcen zonc Z^ (dcfined by "serious and may be lothai injuries") and zonc 23 (dcfined by "injurics") (sco fable l).

' ' "^ "' f Whon an explosion occurs, thc impulsc J pdt which sets the fragmcnts in motion is of paramount influcnce.

One has to bear in mind two diffcrcnt approaches :

-the first one related to "small fragments". In -fchis case, the spatial distribution is of first importance and the question to deal with is about possible penetration in the human body, -the second pertalning to "important f^agments" where the Penetration does not matter, but wher'e the iroportance is -given to injuries by percussion of the skull. The skull may be fractured (at a low probability level) when hit by a missile the speed of which is greater than 4 m/s.

The first of these approaches is valid for some anununitions.

In industry, for the vast majority of accidental explosions experience proved that the mean weight of a fragment is of the order of 30 to 100 kg. When the fragment has a 10-15 kg weight and a 4 m/s speed, its cinetic energy is 80-120 Joules. Thus we have choosen an energy threshold equal to 100 Joules.

Missile effects.

For the prediction of the missile effect during accidental explosions, simple caiculation methods were defined in TNO yellow book (18). They were completed in the UCSIP (Union des Chainbres Syndicales de l'Industrie du petrole) guide for hazard .evaluation in the petroleum industry [START_REF] France | Direction Industrielle -"Methodologie de determination univoque du niveau de risque afferent ä tout Systeme ou equipement de rafflnerie[END_REF].

This approach can be summarized in the three following Steps :

-energetic caiculation of the initial speed of a fragment, -ballistic caiculation with possible consideration of a drag coefficient, -comparison of the ballistic results to lethal energy thresholds for individuais and to impact Perforation speeds for pieces of equipment.

Even though, complex softwares have been developped ; until now the mechanisms of bursting for different types of material and vessel shapes was only validated for simple configurations and mainly metallic materials under dynamic loading frorn an explosion.

Therefore the first main difficulty is to define the bursting pressure of the vessel, the location where the initial breaking occurs and the number and shapes of the missiles. Then during the projection, the direction i s strongly dependent on the shape and mass of the missiles.

Keeping in mind all these remarks, the following formulas are applled to the missile :

-for the initial speed VMIS (m/s) with a fragile rupture of a vessel of volume V (m3) and mass M under a pressure P (pascal), VMIS = 0.97 f^Pyl 0 -5 L "J -for the maximum height Z^ (m) Z i = VMIS^in^/Zg (with « • ( , angle for the projection) -for the landing distance from the vessel (m) X2 = VMIsZsin 2 °< /g These last two formulas do not consider the drag coefficients and some results for different vessel volumes under 3 x 10 4 pascal pressure with the assumption of °< = 45 are given for a mass of the niissile of 100 kg in table 3.

The influence of the drag coefficient DRAG «= k a/nl/3 on landing distance X2 (k : empirical constant : 0.0014 m~l kg1 /3 for a subsonic missile with a between 1.5 and 2) is emphasized on last colunin of table 3 for x^ Drag. X2 is caiculated assuming the missile is ejected from ground levei * KZ drag is caiculated assuming the missile is ejected from the top of the vessel Such assumptions are consistent with observatlons made for example in San Jüan Ixhuatepec accident [START_REF] Pietersen | Analysis of the LPG Incident in San Jüan Ixhuatepec[END_REF].

But, for apparatus of complex shapes and buildings, directional'ieffects and the exact location of the weakest part of the System combined with the propagation mechanism of the explosion imply great uncertaintles about the maximum landing distance for the missile and its random distribution.

Therefore, we have more confidence about the results gained by investigating accidental explosions and simple caiculations are sufficient for prevision purposes in hazard studies (see V.2).

in./ POOL FIRES.

The main purpose is to assess the For this, three parameters are burning rate, flame height, amount fire. radius of the effect (r). Then, the burning rate m (kg/m 2 .s) may be written : m = y/> with (kg/m3) specific mass of the fuel.

Äccording to Mudan (9) this way of assessing the mass burning rate underestimates the value for liquefied gases by almost a factor of two. In this case, the correlation for the mass burning rate may be preferably written : For LPG, we have considered an emissive power of 60 kW/m 2 according to MIZNER and EYRE (22) to be compared to 30 kW/m 2 for liquid hydrocarbons).

From this thermal radiated flux one can caiculate the flux received considering view factor and attenuation through air. The table 4 gives caiculations of the radil for different heat radiation thresholds with 20 and 30 m long square pools.

As previously mentioned these first type caiculations are conservative and other parameters such äs the geometry of the dyke, screen effect of construction, view factors are to be taken into account if more accuracy is needed.

Table 4

Radius from the edge of the pool at different heat radiation thresholds -L -(m) The influence of the wind could be also of paramount importance leading to the tilt and the drag of the flame.

Then, the radiative effect may be caiculated from a tllted cylinder in the wind direction. The area involved takes an elllptical shape. Even, the longest dimenslon is only 25 % higher than the previously caiculated radius. But, the convective effect may become predominant.

Nevertheless, the tilting angle and the flame length are usefui to determine the pieces of equipment engulfed in fires.

IV./ BLEVE.

This phenomenon, by its thermal effects, . can trigger the most important major technological hazards. Comparisons between thermal and pressure effects are given.

For examples, for propane or butane spheres (the volume of which ränge from 500 to 1500 m3) the following caiculations can be made.

IV.l. Thermal effects of Bleve.

We have considered the existing empirical correlations giving the radius and the duration of the fire ball and its radiation and compared these caiculations.

According to NAZARIO ( 14) the duration of the fire ball in seconds is caiculated by : t = 0.45.MO-333

Where M (kg) is the quantity of LPG in the fire ball typically taken äs the maximum content of the vessel.

The radiation from the fire ball can be estimated by : qf = (0.176.R. LHV. M 2 / 3 ) / L 2 where : : qf is in W/m 2 : R is the radiative fraction of combustion energy taken äs 0.3 if the bursting pressure is less than the set pressure of the pressure relief valve or 0.4 if the bursting pressure is greater than the pressure relief valve set point : LHV is the net heat of combustion for the materlal (J/kg) : L (m) is the distance from the center of the fireball ' : M (kg) is the content of the vessel TNO (18) proposes to caiculate the duration of the fire ball and its radius using the formula : duration (seconds) t = 0.852 MO•26 radius (m) = 3.24 nO-325

M (kg) äs previously defined

Assuming the heat radiation on the surface of the ball 1s 200 kW/m2, and using the threshold curves reported by K. S MUDAN (9) about-fatality levels for thermal radiation, it is possible to caiculate : radius (m) for l % lethallty =3.12 M 0 -425 radius (m) for significant burns =4.71 M 0 -407 These radii are caiculated at ground level, without attenuation by air. 11 would be possible to consider the height the ball reaches in the atmosphere. According to LIHOU and MAUND [START_REF] Liiiou | Thcrmal radiation hazards from fireballs" -I[END_REF] this height 1s equal to 10t*. In fact, the correction it introduces is included in these oversimplified hypotheses, the main unknown data being the heat radiation on the surface of the ball.

According to UCSIP [START_REF] France | Direction Industrielle -"Methodologie de determination univoque du niveau de risque afferent ä tout Systeme ou equipement de rafflnerie[END_REF], the radius of the fireball may be caiculated by : radius (m) of the fire ball = 2 M 1 / 3 radius (m) for lethality = 7.182 M 1 / 3 radius (m) for significant burns = 10.157 M 1 / 3 BAKER, COX, WESTINE, KULESZ and STREHLOW (4) have developped a means of assessing the diameter and the duratlon of the fireball, using adimensional numbers : diameter (in) of the fireball = 3.86 x 1.387 x MO-32 (where 1.387 = (1350/3600)-1 / 3 is due to the influence of temperature) When comparing these results, it is evident that there are large discrepancles (mainly related to the values of emissive powers, the position of the fireball, the attenuation by air). Very likely, these evaluations by STREHLOW on one hand and by others on the otlier hand cannot be compared. Nevertheless, the use of adimensional groupation is interesting.

Until now we propose the use of TNO formula (18).

IV. 2. Pressure effects of -the Bleve.

According to TNO Yellow book (18) the peak overpressure of a shock wave with adiabatic flash for hydrocarbons is related to the scaled distance r/(2M)0.33 with the parameter "superheating" (liquid temperature of the contents of the vessel just before bursting open -the atmospheric boiling points of the liquid).

Assuming an overheating of 150 K, it is possible to caiculate the radii for pressure thresholds of 170 mbar and 50 mbar. radius (m) for lethality (at a tew % probability pressure threshold = 170 mbar) = 3.84 (M) 1 / 3 radius (m) for reversible wounds (pressure threshold = 50 mbar) » 8.70 (M) 1 / 3 For example for a 1500 m 3 butane sphere, the radius for significant burns, given in the above mentioned table, is 1162 m while the radius for reversible injuries (pressure threshold 50 mbar), caiculated by the above formula is 792 m.

It can be concluded that the pressure effects radli are lower than those for heat radiation. Consequently, for the protection of •the population, (if we do not consider the missile effect), one need to consider mainly the radiation effects. But it might be pointed out that, until now, the delay of occurrence of a BLEVE is quite unpredictable.

V./ CONFINED AND UNCONFINED EXPLOSIONS.

Accidental explosions may be either confined or unconfined with hazardous substances äs diverse äs explosives, propellants, fertilizers, combustible gases and vapors and flammable dusts. With gases and vapors, DAVEMPORT (19) pointed out that only a small part of the released gas 1s generally involved in the explosion.

Such an explosion occurred sonie years ago in France in a chemical plant after the accidental release from a vessel under 40 bar pressure ; 160 kg of a-'Tntxture on H^-CH^ (H2/CH4 3) were relaased, after the breakage of a connecting duct äs a guillotine opening. In this particular case, froni the effect given by the blast wave and the mechanical damages it may be concluded that only l kg of H2-CH4 mixture (out of an amount of 160 kg released) was Involved in the explosion. After dose examination of the mechanical damages, the TNT equivalent could be assumed äs 5 kg. In these particular conditions, only the turbulence was responsible of the mixing process before this explosion. The ignition source was unknown but the ignition occurred a few seconds after the release.

In the survey of the hazards for assuming the maximum effects of the explosion, the time lag at which'the Initiation of the explosion occurred is äs important äs the source location in order to define the safety distances. Unfortunately, a few Codes can describe the generation of a cloud, particularly when it results from the discharge in air of a vessel pressurized by a flanunable gas. We established a code describing the Variation with time of the dimenslons of the flammable cloud and validated it by testing the horizontal discharge in air of a 120 dffl3 vessel pressurized by 10 MPa of H2 or CH4 through a hole of dianieter d(6<d<24 mm). Finally it was concluded that the volume of the zone, where the air-gas mixture is flammable, is characterized by an increasing phase followed by a decreasing phase ; the proflle of the concentration versus distance curve (fig. 4) is hyperbolic äs in a stationary jet . Caiculated (JET l code) and experimental values for the distance at which the lower flanunabllity limit -xLFL-is obtained 1s given in fable 6 (20). An example of the caiculated xLFL contour can be seen on figure 5. The JET l code is able to caiculate the volume of the flammable mixture in the decreasing phase in the choosen operating conditions. At the moment, tests with higher values of the vessel volume and of the hole diameter would be necessary to have longer increasing phases and to predict the instant of the transition between the two phases when the flammable volume is a t its maximum. Nevertheless this volume remains very low (5 to 10 % of the initial amount of flammable gas).

But explosions are also possible in confined spaces.

V.2. Confined explosions.

For example, in 1986 in a casting line, a very violent aluminum explosion occurred causing the-death of 4 people, injuring 25 others and with extensive material damage. Lightning was recognized äs the initial factor of the explosion. A modest amount of the lightning energy was involved in the Vaporisation and atomisation process of liquid aluminum. The resulting vapors and droplets, mixed with air ignited by the lightning, gave an explosion of and above the casting line (ground level). Then, a second explosion, not äs powerfui äs the first one was initiated in the casting pit by the action of liquid aluminum on water. By examination of the damages to the casting pit and to the surrounding buildings, evidence was gained that the TNT equivalent was about 200 kg and 100 kg respectively for the first and second explosions. Pieces of equipment of the casting line were thrown up to 700 m äs examplified on figure 6. This figure shows the asymetrical projection of debris with some screening effects given by the foundry equipment located westwards from the center of the explosion. This projection field is hardly caiculable.

Aluminum explosion : projection field of 52 missiles (x) (mean weight : 62 kg, maximum landing distance : 600 m) Every year, a lot of accidental dust explosions occurred in elevator buildings and silos. Damages can be more or less extensive but in some cases, when the confinement 1s important, with rather resistant concrete buldings, concrete missiles must be thrown. In 1982 a barley and malt dust explosion occurred in Metz, France and induced the collapse of nine out of 14 concrete cells (äs a consequence of the fact that there was quite no links between the cells -independent cells-). A violent explosion in the work tower resulted in a shock wave with the projection of lightweight panels blown in a verydirectional area (no more than 100 m). The disperslon of very important concrete blocks was not larger than 80 m corresponding to the maximal height of the elevator.

The same year, another explosion was initiated in the upper part of a sugar storage plant (2 x 20 000 t cells and l x 40 000 t cell).

The two 20 000 t cells were covered •with an expanded concrete roof and during the explosion,, guite small pieces were thrown' up to a distance of 500 m, but the vertical walls remalned Standing even though "some crevices appeared. For the largest cell (40 000 t) the reinforced concrete roof first was raised up with some dismantH.ng In large pleces but then feil agnin into the silo cell.

With these examples of explosions, 1t became evident that there is a lack of validated methods to predict the effects of such accidents. Efforts must be devoted to validating the existing modeis or to improving them.

VI./ CONCHJSION. •••-.•'--•

The critical' analysis of hazards studies and accident connected to pool fires, BLEVES and confined and unconflned explosions pointed out many lacks of Information to evaluate the pressure, heat and missile effects.

The acceptable pressure and heat radiation thresholds and the energy thresholds for missile effects are generally based on experience gained after accident investigation or intentional explosions.

The effects on individuais and facilities are both to be considered separately.

For pressure thresholds, the effects on human beings are quite well understood ; but for facilities, only scattered data are avallable. Validations by experiments with existing physical modeis are needed with dose examination of the effect of reflected pressures and of small TNT charges (less than 100 kg).

-15 -Heat radiation thresholds are to be choosen differently whether Bleves or large pool fires are involved.

As an energy threshold for missile effect, values between 20 joules (used in pyrotechnic plants) and 100 joules (related to observations after accidental explosions) are likely.

For the maximum landing distances of missiles energetic and simple ballistic caiculations gave an order of magnitude for bursting of vessels. In other cases only results galned from accident investigatlons are useful.

As regards pool fires, caiculation means are consistent to evaluate the heat radiated from LPG and liquid hydrocarbona fires. The effect of convection needs more consideration.

For Eleve, current caiculations are sufficient for predictive purposes but the delay of occurrence is strongly influenced by the type of equipment and preventive means (insulation, external water, steam or foam spraying) and rather unpredictable.

More experimental investigations for both confined and unconfined explosions are needed to get a better understanding of the mechanisms of the explosion, and of the behavior of eguipment and buildings under dynamic loads glven by these explosions.

]

  . P. Pineau, J. Chaineaux, Y. Lefln, and G. Mawothalassitis Chechar-B.P. 2-60550 Vemeuil en Halatte-France l./ INTRODUCTION.

  Consequences of Accident Release of Hazardous Materials, Hartford, 20-24 mal 1991, pp. 563-84. II./ PRESSURE ftNP HEAT RflDIRTION THRESHOLDS flND ENERGY THRESHOLDS FOR MISSILE EFFECT. 11.1. Pressure effects.

  ) : radius from the center of the explosion m(kg) : welght of TNT involved

Figure 2 :

 2 Figure 2 : Detonation peak overpressure of unconfined air-hydrocarbon mixtures (spherical geoinetry) [from A. Lannoy (5)]

  successively caiculated : of heat radiated from the III.l. Burning rate. The burning rate values are either published in the literature (22) or caiculated using correlations. The first of them is given by Burgess and Zabetakis : Ymax = 1-27 x 10-6 A^c ("/s) A Hv where Ymax is ^e rate at which the liquid pool level decreases with time in the absence of external supply. & Hn and & Hy are respectively the net heat of combustion and the heat of vaporization (in J/kg) at the bolling point of the liquid fuel. For usual liquid hydrocarbons ymax ^ l" the ränge 2-4 mm/min.

  if the boiling temperature is under the ambient, one has to consider A ny* -AHy.For LPG, theorical assumptions and experiments led to the value m" = 0.11 kg/m 2 .s.'111.2. Flami^Jleight.The flame height -h -1s caiculated using Thomas's formula with equivalent diameter or the correlation given by HESKESTAD[START_REF] Heskestad | Luminous heights of turbulent diffusion flames" -Fire safety[END_REF] for a C*t Hß 0^ molecule. THOMAS gives : specific mass of air (kg/m3) D : equivalent diameter (m) g : acceleration of gravity (m/s 2 ) m" : äs previously defined (kg/m 2 .s) 111.3. Heat radiated from the fire.

:

  Jlll^;l"'llH':U L,,'^,! l.y<;;-oc.'irltoii;;

  bal l .-»ccor-.llnii by 'JLrcIttnw (1 -3.flGxl.J07 H 0 ;R urntlon of tlie rire ball .iccor-<llnK t.u .-tr.il.low L « 7.W ." 0 --^,) Ilndlus for unlic.-irablc pnln ncror-UlnB l-o Sl.i-chlnw 1 -0 --> ' ) ' 1 Em)

Figurc- 5 y

 5 Figurc-5

Figure 4

 4 Figure 4

BIBLIOGRÄPHY ( 1 )

 1 Councii Directive of 24th june 1982 on the major accident hazards of certain industrial activities [82/501/EEC] Official Journal of the European Communitles, n L230 of 5th August 1982 (2) Lol du 19 juillet 1976 relative aux installations classees et decret d'application du 21 septembre 1977 (3) "Securite pyrotechnique" -Edition des Journaux officiels de la Republique Francaise, 1988, n 1196

  in table 2.Tlicso considerakions arc global and do not: involvc probicnis to which thc analycl: lias to pay atkcnfcion. For instance, the iiivcstigoL-ton of accidcnts lcd to concludc that synergetlc eJEfeds have to bc considorcd. In a givcn casc study, a small open firc in a drain cu l : o.Cf a nunibcr of proccss scnsors with major conscqucnccs for thc plant.

				Tohle_2
	llcrirci'c r"i!nl ine	KRCOliiincndccI tank Epi-iciiiQ;:; (S) basod 011 37.0 ItWin"" in 11 10.1 11 l'J 32 •W •U l.O'l ?n 3G • 13.'; U.13	1.1 1.0	-0.1 -0.1
	Ih.'x.liic r.iii.ioni	• i.C n.';	11 l'i.J	\(, .-1. f.	;1 :'7.'i	;G 33	ü.'i'l 0.7'1	0.6 0.')	-0.5 -0.7
	r<]ll l v.l I rut	n.Mli.itnr	Modri (Vr	rt.ic.ll	l.n-.)rl) (;;)
	Hciizruc r"»ol ine llcx.inc mii.inoi	• ). 5 H..l • 1.0 r,	in 15.; 1 . r , K)	;'.;.•) ?1.3 l».r, rJ	3?.'1 ?/ 13.'; l B	31 .1; 11-, 111	o.nri 0.73 0.31; 0.17	1.0 0.0 0.'! o.r,	-0.0 -0.6 -0.3 -3.Z

7

-incidcnk rodiaU.on (Tliomaa (5) L/D corrclotion) nia_ ______r Am: niAiir.ir.H (ni)

;oli<l ri.mic llodpi (l Hnir),in/ll.imiH.on V.r.) "('"./m" Avn-.ir)i-HAlir.r-OF ;/" r.-Uio l: n n k .';p,ic inn/rliamc fccr 11.3. Explosion energy thresholds for missile effect. 11.3.1. Energy throsholds.

Table 3

 3

	V (m 3 )	VMIS (m/s)	Zi (m)	X2 (m)	X2* (m)
	1630	35.6	32	129	138
	2900	36.5	34	136	144
	3650	38.2	37	149	156
	4500	38.8	38	154	161
	6530	39.7	40	161	166
	11600	40.5	42	167	173
	14570	40.6	42	168	174
	57600	43.5	48	192	198,6