Welcome back to Sports & Building Aerodynamics, in the week on the 100 meter sprint aerodynamics. In this module, we're going to focus on altitude effects and we start again with a module question. If an athlete wants to establish a new record on the 100 meter sprint, which location should she or he choose? Is it A) Eindhoven in the Netherlands at 35 meters above mean sea level. Is it B) Hogvalen in Sweden, at 835 meters above mean sea level. Is it C) Mexico City, 2,250 meters above mean sea level. Or finally, D) La Paz in Bolivia, at 3,640 meters above mean sea level. Please hang on to your answer and we'll come back to this question later in this module. At the end of this module you will understand how altitude effects can be implemented in mathematical-physical models of the 100 meter sprint, and you will understand the effects of altitude differences on the 100 meter sprint records. There has also been a statistical study on altitude effects just like wind effects, as explained in the previous module. This was again the study by Linthorne in 1994, and he found that running at an altitude of Mexico City provides an advantage for top athletes of about 0.07 seconds. So it's not a very large effect. But considering the fact that records are often achieved by very small incremental improvements, this is certainly substantial. Let's look again at the mathematical-physical model, and how we implement altitude effects in this model. This is again the model by Mureika. As mentioned before, we have these equations, so Newton's second law here with the four propulsive and counter-propulsive terms, and this is the drag term, and it's also in the drag term that you implement the altitude effects. And that we do by actually changing the density, because it's density that changes with altitude. And then actually this is the improved drag term, where rho naught is 1.18 kilogram per cubic meter, which is the density at sea level at 25 degrees C, and H is the altitude in meters above mean sea level. And then we can plot this drag force divided by mass as a function of the running time, And that's what you see here in this graph. So it's clear that the drag force decreases substantially with increasing altitude, so with decreasing density. So we can also implement these altitude effects in the mathematical-physical model. But also in its simplification, in the simplified algebraic expression that allows us to correct the 100 meter sprint times. And this yields this equation here, where t naught naught is the corrected time, so at zero wind speed, but also at mean sea level, t wH is the official race time at the wind speed uw and at the given height. So this is the height above the mean sea level in meters and then uw is the along-track component of the wind velocity and we can plot this curve here and then you can see indeed that there's a substantial improvement in the race time, with an increase in height. What does the IAAF say about altitude? Well, actually, it does not place a restriction on the maximum altitude for acceptance of records. And this is to some extent surprising, because it does this for wind speed, but not for altitude, although performances achieved at sites above 1000 meters are called altitude assisted. But they can appear in record tables, so they are indeed still ratified. So let's look at some examples, where it's shown that altitude can give rise to exceptional sprint times. This is the first example, Jim Hines from the US, who was the first to run under 10 seconds, but he achieved this in Mexico City, at 2,250 meters above mean sea level. And you can see his mark there, 9.95. But if you correct that, we get a much more realistic time, which is also quite similar to the time that he achieved at Sacramento at about zero meters above mean sea level. The second example is Obadele Thompson from Barbados, who ran a very impressive 9.69 seconds at El Paso in Texas, but this was achieved with a tail wind of 5.7 meters per second and at quite a high altitude. And if you correct that result we get a much more realistic time, but still it is substantially better than his other achievement, which was, however, achieved with a certain head wind. But what can also play a role here is the effect of variable winds. Variable winds have a different effect than a constant uniform wind that does not change throughout the race. So let's turn back to the module question: If an athlete wants to establish a new record in the 100 meter sprint, which location should she or he choose? And as opposed to what we saw in the first week with cycling, where Mexico City was the best location, here it is La Paz in Bolivia. Because the 100 meter sprint in terms of biophysics, biomechanical issues, is quite different from the cycling performance in the world hour record in cycling. And let's have a look at the table here, what the records could be when we would try to achieve them at these different altitudes. So this is the record time of Usain Bolt achieved with a tail wind of 0.9 meters per second in Berlin. If we assume that this record would have been achieved at a wind speed of zero meters per second, then the correction, of course, is zero, so it remains as 9.63 seconds. And if then Usain Bolt would do this attempt in Eindhoven, which has about the same height of Berlin, it doesn't change that much but if you would run the 100 meter sprint in Hogvalen you see that the record time decreases quite substantially, and it keeps decreasing when we move to higher altitudes. So the question is maybe could Usain Bolt's World Record be improved? And certainly yes, it can be improved by himself. Just allow him to run the 100 meter sprint at La Paz in Bolivia. In this module, we've learned about how altitude effects can be implemented in mathematical-physical models for the 100 meter sprint. And we've looked at the effects of altitude differences on 100 meter sprint records. In the next module, we're going to focus on the complexity of wind-flow patterns inside a stadium. We're going to see how these wind-flow patterns can influence the 100 meter sprint times. And how the IAAF should adjust its wind speed measurement in stadiums. Thank you for watching and we hope to see you again in the next module.