Welcome back to Sports & Building Aerodynamics, in the week on the 100 meter sprint aerodynamics. In this module we're going to focus on wind effects, and we start again with the module question. And actually this module question is also the same one that was asked in the introductory module and in the introductory movie of this MOOC. So it's about a runner that runs a 400 meter lap on a circuit. And he first runs this lap without wind, and then he runs it, actually the first 200 meter, with a head wind and then the next 200 meter with a tail wind of the same magnitude. And the question is, which of these laps is the fastest? Is that the lap without the wind, or the lap with head wind first, and then the same tail wind next? 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 wind effects can be implemented in mathematical-physical models of the 100 meter sprint. You will understand the effects of head winds versus tail winds. And you will understand what the effects are in terms of 100 meter sprint performance. There has been a statistical study, actually a very detailed, very valuable statistical study on the effect of wind on the 100 meter sprint times, and this was a study by Linthorne in 1994. So this was a study that focused on finalists at the US Olympic Trials and at TAC Championships for a period of 11 years, and multiple performances by individual athletes at recent Olympic Games, recent being at the time of publication, and World Championships. And actually quite consistent results were found for both studies. And a very remarkable finding was that the rate of improvement in race time due to wind, decreases with increasing wind speed. So this means that the disadvantage by head wind is greater than the advantage by a tail wind of the same magnitude. And then the advantage of such a 2 meter per second tail wind is about 0.10 seconds for male sprinters and 0.12 seconds for female sprinters. So all for the 100 meter sprint. Then we can actually implement the effects of wind in the mathematical-physical model and we're going to follow the model again by Mureika and also the implementation by Mureika and this actually is his model. So with the two equations and then with the different terms and symbols in it explained on the right-hand side, so Newton's second law, which can then be solved by numerical integration. And actually the wind effects are implemented in the drag term. So, this is a drag term as we had it in the previous module. With the running speed squared, appearing here and highlighted in red, and if we want to implement the wind speed together with that, then this is actually the resulting drag term. So it's the running speed minus the wind speed. And you can present that in a graph. And this is a graph actually that shows the drag force divided by mass as a function of time for different head winds and tail winds going up to five meters per second tail wind and minus five meter per second, that means the head wind. And also here it's clear, that the head wind is more important, has a larger effect, or this component this drag force component is larger than with the tail wind. Then there is actually also a simplified version of this mathematical-physical model that is a simple algebraic expression, so no need for numerical integration there, which is actually a very convenient tool to very quickly correct 100 meter sprint times. And, this is actually this model, where t naught is the corrected time. So actually that is the still-air equivalent, so without wind, then tw is the official race time, so including the wind effects, and uw is the so-called along-track component of the wind velocity, which can be the head wind or the tail wind. And if you plot this curve for the case, where the official race time is 10 seconds. Then you can get this graph, that shows the time advantage on the vertical axis, versus the along-track wind speed. On the left side the head wind, and on the right side of the zero meters per second, you see the tail wind. And also here it is clear indeed that a head wind for a given absolute value of this wind speed is larger, or the effect of the head wind is larger than the effect of the tail wind. And this is quite an important finding. So it's important to measure wind speed during races. So how is this done? Well actually, these days this is done according to the IAAF rules, and is done with a two-dimensional ultrasonic anemometer, indicated here. You also see some other ultrasonic anemometers indicated on this slide. Here you see it actually mounted alongside the track, at a Diamond League meeting actually in Brussels, this was in 2013, where we actually took some shots of the races. So this mounting height should not be more than 1.22 meters. Then it's positioned actually at 50 meters from the finish line, as indicated here in this graph. It should also be placed within 2 meters from the first lane, so on the infield position. Then actually wind speed is sampled for 10 seconds, so 10 seconds starting from the beginning of the race. The measurement resolution is 0.01 second, but unfortunately, this is rounded off. So they are only reported up to 0.1 seconds. And this is the rounding-up procedure. If you have a wind speed of 1 meters per second, 1.00, it's rounded up, or it's rounded, to 1.0. If you have 1.01, it's rounded up to 1.1 meters per second. But if you have 1.09, it's also rounded up to 1.1 meters per second. So this is actually showing some accuracy that is lost by rounding up. The wind effects, and also the IAAF rules on wind assistance can have some consequences. One of these consequences is that head wind can hamper exceptional performances. Another one is that you will see that the top legal performances are often achieved with a tail wind just below 2 meters per second. And that equipment malfunctioning, which can really happen, can contaminate record tables for a very, very long time to come. So let's look at a few examples of these consequences. The first about head wind that can hamper exceptional performances. This is a table that shows for different top athletes, Maurice Green, Tyson Gay, Usain Bolt, and so on, their mark, so their time, on a 100 meter sprint in the presence of wind. Then the wind speed. So these were all achievements with a substantial head wind. And then the venue. And if we use the simple algebraic expression, the back of the envelope equation by Mureika, then we can correct those times. And you will see indeed that those times are substantially better of course, if you correct them to the zero wind condition. Let's have a look at a second example, how top legal performances are often achieved with a tail wind just below two meters per second. What you see here is the all time top of the ranking on the 100 meter sprint for male athletes, for different competitors. You'll also see the time that was run in the windy conditions. You also see the wind speed, where a positive wind speed indicates a tail wind. And you see that these are all tail winds, except, actually, the third time of Usain Bolt, that was achieved with a zero meters per second wind speed. And the time of Yohan Blake, that was achieved, actually, with a slight head wind. If you would correct those times with the simplified algebraic expressions, or the back of the envelope expression by Mureika, you see these corrections. So in most cases, indeed due to the tail wind, you will see that the corrected time is substantially higher than the official race time. And if you then make a new ranking, you will see that Usain Bolt is still the number one, but that the second best time is not a time by Usain Bolt, but is actually the time by Yohan Blake, who did this exceptional performance with, as mentioned before, a slight head wind. So actually the ranking on the right side is the correct ranking, but unfortunately the IAAF uses the ranking on the left side, so not using actually state of the art scientific knowledge, which is a bit a pity. Let's then look at the third example. How equipment malfunctioning can contaminate record tables and we're going to look now at the all-time ranking, the top of the all-time ranking, with the female competitors on the 100 meter sprint. And then you see that the first three positions are held by the late Florence Griffith-Joyner, which was really a fantastic athlete, but at some point during a race in Indianapolis, she ran actually a very remarkable 10.49 seconds. And the wind speed measured at that time was zero meters per second. And this actually, this surprisingly good result, much better than all her other performances raised some suspicion. If you correct that ranking with the given wind speed, then you'll see that of course the zero wind speed doesn't change, so the record of Florence Griffith-Joyner, remains. But you see quite some substantial changes in the other records. And as mentioned before, very remarkable is the fact that, her first time is much better than the two other times, which were actually very close to each other. So what's going on here? Well, there's a common belief that this current world record by Florence Griffith-Joyner was strongly wind-assisted, even though the measurement gave zero meters per second. And that is believed to be caused by equipment malfunctioning. So let's have a look at that particular race, which was actually a US Olympic trial in Indianapolis, where Florence Griffith-Joyner in the heats ran 10.6 seconds, wind-assisted. Then in the quarter finals, this remarkable 10.49, where the zero wind speed was measured. Then 10.7 in the semifinals, wind-assisted. And then finally, a good performance, 10.61 in the final. There were some concerns as mentioned before. That zero meters per second reading was actually very suspicious because this day was a very windy day. Many people present in the stadium actually couldn't believe this measurement of zero meters per second. And then the triple jump, which was actually held in the same stadium, had suffered a lot from high wind speeds, because only three of the 46 measurable jumps were wind-legal. So with a wind speed below the two meters per second, or equal to two meters per second. And then the triple jump wind-indicator just before the first of the three 100 meter quarter finals, which was the one where Florence Griffith-Joyner put this world record on the table, had a tail wind of 4.3 meters per second. Then the second quarter final also had a measured zero meters per second. And then suddenly in the third quarter final there was this 5.0 meters per second. And actually there was a very interesting study by Nick Linthorne, who demonstrated that the actual wind assistance, during this first quarterfinal should have been 5.5 meters per second tail wind, which is a very very large value, and which could explain this exceptional performance. So let's have a look at this record table again, so the top of the all-time ranking with the female athletes, now with a 5.5 tail wind. So then if we correct those times using the simplified algebraic expression, you'll see that we get a much more credible result for this particular quarterfinal by Florence Griffith-Joyner. It's higher than her other performances, a longer time, but that's also logical because in the quarterfinals athletes that are much better than their competition in this particular race often do not give their best, because they want to save strength, so they slow down at the end of the race, and so this longer time is quite logical. But if you compare that with other performances in this table, you see that actually the corrected rank is fifth. You will see that she also had another very good performance with a rank 3, and another one that is actually her third ranked performance, official ranking 3, that would be ranked second now. What is actually very remarkable here and also quite important is that with the corrected ranking and assuming indeed that there was this 5.5 meters per second tail wind, the world-record holder would not be Florence Griffith-Joyner. The world-record holder would be Carmelita Jeter. And that's quite a remarkable conclusion. So let's go back to the module question now. What is fastest? A 400 meter lap without wind? Or a 400 meter lap where we have the first 200 meters a head wind and then the next 200 meters a tail wind with the same magnitude? And the answer is, it's a 400 meter lap without wind. And the reason is, as we saw in this graph before, that the effect of a head wind is larger, so the negative effect of a head wind is larger than the positive effect of a tail wind of the same magnitude. And the reason for that in turn is actually that the effects of wind are non-linear effects on the drag force, as shown by this equation. In this module, we have learned about how wind effects can be implemented in mathematical-physical models of the 100 meter sprint. We've looked at the effects of head winds versus tail winds and how the head wind and the tail wind can affect the 100 meter sprint performance. In the next module, we're going to focus on altitude effects and how these can be implemented in mathematical-physical models for the sprint. And we are also going to look at the effects of altitude differences on records in the 100 meter sprint. Thank you for watching again, and we hope to see you again in the next module.