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Starting order of the women's Olympic competition. The choice of the position was made in order of rank from 1st to last qualified.

First of all, it should be remembered that triathlon is a sport that requires a high degree of adaptation to contingent situations, not only in terms of environmental variables, which athletes must be able to manage and interpret with a good degree of adaptation, but even in

management. of the energies regarding the distance, which from race to race – with the same format – often vary by several hundred meters. In particular, in the case of the swimming fraction it is wrong to think that it is a mere transposition in open water of the pool dynamics, due to the never replicable competition field and the peculiarities of group swimming, with tacks at the buoys and more and more often the inclusion of Australian outings, not necessarily in the middle of the fraction (so much so that even in Tokyo the two splits in swimming were respectively 950 and 550 meters) or even usage of wet suit or not.

It would therefore be naïve to claim that the conditions of the competition field are the same for everyone at all times and it would be all the more naïve to compare the performance of the athletes (ie what they expressed in the race from a physiological and technical point of

view) with the results (ie with “the the result “of one’s own performance and that of others, in the contingent environmental context).

Nonetheless, through a simple but rational analysis, we have the opportunity to conclude whether in the Olympic race in question the start had a significant impact on the race, or rather, to understand if it is probable or unlikely that this has happened, even with all the limits. due to the scarcity of available data.

The start of the WTS of Leeds, swimming fraction with wetsuit unlike what happened in Tokyo

Instead of arbitrarily drawing data we have chosen to use only what we know of the Olympic test, thus comparing data that are certainly homogeneous, using Olympic access rank (robust athlete quality index, an input in our model), starting position from the pontoon ( the variable we want to control, another input of the model) and position and detachments of the first two splits and of the total fraction (which also contain the effect of the variable we want to control). Sorting by starting position and building the very useful heat map (Figure 3) we already visually notice three things:

1) The athletes with the best rank chose the right side of the pontoon (lower numbers)

2) The last 5 athletes (left end of the pontoon) obtained a much better performance than the athletes in the center, similar to those positioned in the “offending” part

3) It seems to be very difficult to separate the effect of the Olympic ranking from the effect of the pontoon

4) “At the bottom” of the pontoon Jeffcoat, Kingma and Barthelemy manage to enter the top 18

5) Lopes and Perriault in the middle of the group are 2nd and 12^{th}

Heat map start, split 1, split 2 and final positions swimming leg in Tokyo [1]

For further simplification we have created a matrix that counts the number of athletes in the three “input” blocks at the start (18 right – 18 center – 18 left) with the three “output” blocks in the two splits and with respect to the total fraction. For each group we then calculated the median rank.

In the first split (which should be most affected by the position effect at start) it appears that 13 out of 18 athletes have retained the starting “group”, 5 out of 18 in the middle group while 3 of the “left” group entered the top 18 already at the end of the first split.

Finally we reported the median position with respect to the starting group in the first split.

Observing this summary table (Figure 4) the difference in the athlete quality index along the pontoon is evident but also that those who started from the center and left managed to get ahead and at least on average there are no striking differences between the first split (different point starting point) and second split (same starting point)..

Summary of the values in the field and of the splits in the three macro groups right, center, left pontoon

Comparison of starting position and ranking in the two swimming splits and overall order of the fraction in Tokyo

A qualitative analysis respectful of the context and data therefore guided us towards at least two conclusions:

1) Those who started in the group of 18 athletes to the right of the pontoon did not enjoy any special advantages

2) It is difficult to separate the effect of the Olympic rank from the effect of the starting position

However, moving from qualitative analysis to quantitative analysis through Principal Component Analysis we are able to clarify the contribution of each variable to the phenomenon examined, so on the Main Component 1 we have the following contributions in descending order of importance: detachment of the second split and the second split (directly related to the total gap) substantially equal (weight 0.49), followed by Olympic ranking (weight 0.40) and last starting position (0.31), the latter two obviously inversely correlated to the total gap.

Therefore we cannot exclude some influence of the starting position on the result of the swimming fraction, but we can certainly say that this influence was residual.

Loading on Component 1

*I calcoli e i plot sono stati eseguiti con il software CAT, Chemometric Agile Tool (R-based) [6]

[2] [4] Kim H. Esbensen, Dominique Guyot, Frank Westad, Lars P. Houmoller, *Multivariate Data Analysis: In **Practice** : an **Introduction** to Multivariate Data Analysis and **Experimental** Desig*n, Multivariate Data Analysis, 2002. ISBN8299333032, 9788299333030

[3] R. Leardi, C. Melzi, G. Polotti, CAT (Chemometric Agile Tool), gratuitamente scaricabile al seguente link http://gruppochemiometria.it/index.php/software

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With this story we begin an in-depth study of the performance model of running to study the responses from a metabolic, mechanical, kinetic, kinematic point of view and to find the interactions between athletes and technical materials. In this first chapter we address the topic from a general point of view by reviewing the literature on the subject and looking at a first data set, collected in our laboratory, introductory and preparatory to answer the main question: which shoe maximizes the time gain in competition for this athlete? What are the choices to get the best result?

In recent years, the world of running has experienced an authentic technological revolution with the introduction of increasingly high-performance shoes, characterized by the use of “noble” materials such as carbon for the midsole. The rather intuitive principle is that a shoe capable of absorbing a greater level of energy in compression (in the phase of maximum loading) and of releasing the same in return (in the propulsion phase) reduces the metabolic cost of running, or at the same cost, increases the output, i.e. the speed [1] (Figure 1).

The condition to be respected is that the material used is able to bend and deform under load – so-called compliance -, returning to its original shape and conformation – so-called elasticity -, and to return most of the energy absorbed during deformation – so-called resilience -, being unloaded. Some materials offer a lot of compliance, for example plasticine, but very little resilience. This is the case of “protective” shoes, which reduce the force peaks in contact with the ground, with the intention of reducing the loads on the joints. Other materials, such as carbon fiber, bring these characteristics to the extreme, making it possible to create extremely reactive shoes.

The biomechanical model of running can be perfectly described according to the concepts of load and elastic deformation. In fact, in running, the body behaves like a spring or a ball, so the higher its rigidity the higher the rebound after touching the ground. Physiologically, the dynamics are the same, with the complex of muscles and tendons that store elastic energy (potential) upon impact with the ground. A reactive shoe is not only able to maximize the accumulation of energy but also to make its return extremely efficient, dissipating it (in the form of heat) less than traditional footwear. Formally this relationship is described by Hooke’s law for which the greater the elastic constant k (measure of the stiffness of the spring) the greater the force F necessary to produce the deformation x.

Similarly, if, at the same deformation, the constant k increases, then F will be larger … and then, potentially the bigger return of mechanical energy by the shoe, implicate a bigger “free” propulsion with consequent savings in muscle work and less consumption of resources internal.

Force-deformation curves, peak deformation, and energy return metrics for each shoe during vertical midsole loading with a peak force of *2000 N and contact time of *185 ms. As vertical force is applied, the shoe midsole deforms (upper trace in each graph). Then, as the shoe is unloaded, the force returns to zero as the midsole recoils (lower trace in each graph). The area between loading and unloading curves indicates the mechanical energy (J) lost as heat. The area below the lower traces represents the amount of elastic energy(J) that is returned” [1].

There are numerous scientific studies that have investigated the effects of shoe construction and an important review [2] concluded that “increasing the stiffness of the midsole within an optimal range of values can be beneficial in modifying the variables associated with performance “, to be precise, 5 of the 7 validated studies led to this conclusion.

Aside the equipment, when it comes to sports performance, an element that is anything but secondary must be taken into account, namely the athlete, and her/his unique characteristics, subject by subject, from an anthropometric, metabolic, mechanical and kinematic point of view. Especially when you are looking for maximum performance, you cannot limit yourself to knowing the “average” performance of your materials, but it is essential to know the type of the “tailor-made” interaction.

- 3 steps of 3 minutes each for each of the 2 models
- Step at 14.5, 16.5 and 18 km/h
- Gear: PNOE Metabolimeter, Motion Capture Optitrack with 6 cameras (full body 3D) at 120 Hz sampling rate (Figure 2), Stryd Power Meter [3], Polar H10 heart rate belt
- TOORX 9500 treadmill

The table shows the average values acquired in the single steps with the two shoe models of the main biomechanical variables. The last two columns show the athlete's subjective judgments on a scale of 1 to 5 (from worst to best).

Risti's lower kinetic chain reconstructed by the Motion Tracking system

We then carried out a Principal Component Analysis (a statistical technique that “unifies” all the variables making them comparable [4]) which led to the following conclusions:

- With this type of protocol the most evident factor is the variation in performance, as it is logical to expect using the three speeds
- Since the “performance” factor is constrained by choice, the second most important factor in the description of the behavior of the “athlete-shoe” duo emerges very clearly, namely stiffness, which is the real element responsible for the big difference between the two shoes

The choice to start investigating this issue with an indoor test was made for the guarantees of greater stability of the boundary conditions, starting with the behavior of the support surface, a crucial aspect for the purposes of the investigation. Obviously, it is not exhaustive in understanding the phenomenon and requires further tests in the “real environment”.

The "score" chart * of the PCA displays on the x axis the main component 1 (PC1) which explains the phenomenon analyzed in its entirety for a variance of 82.5%, in this case the correlation of the objects in the chart with the " performance level ”which shows a similar trend between the two shoes. The main component 2 (PC2) is represented on the y axis, which turns out to be the Leg Spring Stiffness, with an explained variance of 14.1%. On the PC2 the different behavior between the two Brooks models under test is highlighted, with greater Stiffness generated by the Hyperion Elite 2.

Calculations and plots were performed with CAT software, Chemometric Agile Tool (R-based) [6]

*Spring Stiffness* [5], increases, i.e. the overall effect of the compliance, elasticity and resilience characteristics that we have defined initially, resulting on the athlete’s body. The Hyperion Elite 2 are therefore really capable of returning greater elastic energy stored to Ivan and the difference is also statistically significant at 16.5 km/h but above all at 18 km/h. At 14.5 km/h the Ghost differs much less overall from the Elite 2. At that speed, therefore, the choice becomes neutral from an objective point of view, and depends heavily on the subjective athlete judgment (who was asked for a personal assessment of comfort and responsiveness at different running speeds) The greater stiffness triggers a reaction from the biomechanical point of view that includes greater width (the heel rises more drawing a circumference of greater radius, as well as confirmed by the optical detection system, Figure 4) and increases the flight phase, reducing conversely the ground contact time. All factors related to the increase in performance. Furthermore, from the point of view of stability, motion capture confirms one of the main features of the Elite 2 by observing the lateral-lateral aspect of the knees, ankles and hips.

The trajectory of the heels (rear view) confirms the quantitative data obtained from the accelerometer/gyroscope.

It must be emphasized that at the same speed this shoe, on the treadmill and in this specific protocol, seems to increase the share of metabolic cost destined for vertical movement, confirming the hypothesis that in order to gain the maximum benefit, the athlete must be able to reach high absolute speeds and above all that he should be equipped with an excellent running technique. In fact, the risk is to be literally launched up rather than forward, with the consequence therefore of having an inverse final result, i.e. using energy in the wrong direction!

The Elite 2 also seem to guarantee greater repeatability of performance, as seen by the much more compact red cloud (Figure 5), indicating that at each step the response is always very similar.

The HYPERION Elite 2 objects (red) are projected in the graph on the left in the mathematical space constructed from GHOST values only (in black). The ellipses represent the critical values of the probability of the inclusion of the samples in the same class, which at the speed of 18 km/h are statistically not attributable to the same category. In the right graph (influence plot) in the same way the HYPERION Elite 2 objects do not pass the diagnostic screen T^2 (distance of the points on the plane) and Q Index (distance of the points in space). We can therefore conclude that the two shoes under these conditions have a radically different behavior. Not the same happens at a speed of 14.5 km/h.

* Calculations and plots were performed with CAT software, Chemometric Agile Tool (R-based) [6]

Comfort

Reactivity

Comfort

Reactivity

This is what it was possible to observe and conclude in a consistent way from the indoor test but, since we are interested in knowing if this Risti-Elite 2 combination also works in the real world, we will ask Ivan for a further effort to go out and put the most performing Brooks model under pressure, on the road.

We intend to verify the behavior in a situation of constant energy cost and free speed (the opposite of what happens on the treadmill) and also the behavior over distance, both through the measurement of the metabolic cost with the exchange of O2/CO2 gas, and for as regards the performance of the Leg Spring Stiffness, which is an excellent proxy for muscle fatigue, certainly a fundamental variable in the performance model of long-distance triathlon, and more.

Furthermore, it remains to be understood both in general and for a specific individual which is the optimal level of compliance, elasticity and resilience to maximize performance, so a “horizontal” test between different brands/models offering the same type of product will be interesting.

[1] Hoogkamer, W., Kipp, S., Frank, J.H. et al. *A **Comparison** of the **Energetic** Cost of Running in Marathon Racing **Shoe*s. Sports Med 48, 1009–1019 (2018).

[2] Sun X, Lam WK, Zhang X, Wang J, Fu W.* **Systematic** Review of the **Role** of Footwear **Constructions** in Running **Biomechanics**: **Implications** for Running-**Related** **Injury** and Performance.* J Sports Sci Med. 2020;19(1):20-37. Published 2020 Feb 24.

[3] Imbach F, Candau R, Chailan R, Perrey S. *Validity** of the **Stryd** Power **Meter** in **Measuring** Running **Parameters** **at** **Submaximal** Speeds*. Sports (Basel). 2020 Jul 20;8(7):103. doi: 10.3390/sports8070103. PMID: 32698464; PMCID: PMC7404478.

[4] Kim H. Esbensen, Dominique Guyot, Frank Westad, Lars P. Houmoller, *Multivariate Data Analysis: In **Practice** : an **Introduction** to Multivariate Data Analysis and **Experimental** Desig*n, Multivariate Data Analysis, 2002. ISBN8299333032, 9788299333030

[5] Farley CT, González O. *Leg** **stiffness** and stride frequency in human running*. J Biomech. 1996 Feb;29(2):181-6. doi: 10.1016/0021-9290(95)00029-1. PMID: 8849811.

[6] R. Leardi, C. Melzi, G. Polotti, CAT (Chemometric Agile Tool), freely downloadable at the link http://gruppochemiometria.it/index.php/software

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