## SHOE "à la carte"

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.

#### IN-DEPTH INFORMATION BOX

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.

###### Figura 1

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].

#### FROM SCIENTIFIC STUDIES TO AD HOC TEST

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.

#### THE TEST

Ivan has been using Brooks’ running shoes for years, so we have selected two models that are particularly appreciated by him, but also quite distant from each other in terms of type and use. On one hand, the Ghost, a cushioned and stable 294 gram shoe, on the other the brand new Hyperion Elite 2, classified as “fast”, weighing 215 grams and equipped with a carbon fiber plate in the midsole. Three intensity steps were performed for each shoe, replicating the speed of slow (around the Ironman race pace), medium and fast (almost to the anaerobic threshold) so as to fully explore the entire range of exercise.

Ivan has been using Brooks’ running shoes for years, so we have selected two models that are particularly appreciated by him, but also quite distant from each other in terms of type and use. On one hand, the Ghost, a cushioned and stable 294 gram shoe, on the other the brand new Hyperion Elite 2, classified as “fast”, weighing 215 grams and equipped with a carbon fiber plate in the midsole. Three intensity steps were performed for each shoe, replicating the speed of slow (around the Ironman race pace), medium and fast (almost to the anaerobic threshold) so as to fully explore the entire range of exercise.

#### TEST PROTOCOL

- 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

###### TABLE 1

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).

Since running is an extremely complex phenomenon, we used numerous variables for the analysis (Table 1), both measured directly and derived, also carrying out cross-checks of the same parameters acquired by different sensors. The results observed “one at a time” are difficult to interpret since it is essential to consider the interactions between them.

###### FIGURE 2

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 CARBON PLATE DOES WHAT IT PROMISES ... AND EVEN MORE

###### FIGURE 3

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]

In the graph in Figure 3, the three exercise intensity clusters are clearly highlighted and the two types of shoes also seem to clearly separate. Without even the need for a statistical validation, it is immediately instinctive to observe that we are dealing with “two different things”. In fact, as the performance level of the exercise rises (shift towards the right on the horizontal axis) the difference in the Leg *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.

###### FIGURE 4

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.

#### STATISTICAL IN-DEPTH

At the highest rate, the points acquired with the HYPERION are placed well outside the critical values for both T^2 and Q, indicating that at these speeds\powers (18 km/h with 4.75 W/kg expressed) the Elite 2 has a radically different behavior from the Ghost.

###### Figure 5

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]

#### THE ATHLETE’S FEELINGS

Numbers matter but, then in training and on the competition fields the athlete goes there, there are his feet and effort. What emerged from the acquisitions must necessarily be combined to the athlete’s feeling, so we spent a lot of time after the test chatting with Ivan: “The Ghost is a shoe that I really like at slow pace, it is soft but at the same time you can appreciate a good level reactivity – he said describing his sensations – It gives that feeling of a shock-absorbing shoe but at the same time is pretty dynamic. The Hyperion Elite 2 are radically different, they require a different ride, because you feel so much more thrust and by necessarily changing the width you have to adapt the rest “. Surprisingly, this increased reactivity does not seem to sacrifice comfort, which Ivan has given an identical rating to that of the Ghosts, 4 on a maximum scale of 5.

###### Brooks Ghost

###### Brooks Hyperion Elite

#### NEXT STEP

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.

#### REFERENCES

[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