Theory: The effect of lateral foot displacement on overall energy expenditure in football



High level athletes, including the best soccer players in the world are surprisingly inefficient on their running mechanics disallowing them to reach their full fitness potentials. Soccer players are trained on fitness, kicking technique, headers and other specific technical skills needed for controlling and playing with the ball, but very few are taught about what takes up their majority of time on the field; running.
Sprinters all over the world dedicate countless hours of their training to polishing their running in search of “perfect” technique. The perfect movement synchronization and body biomechanics harmony. We have a lot to learn from these amazing athletes to then apply to other sports that include running. Making soccer athletes as fast and efficient as the fastest men on earth, if possible. 
A simple start on improving that technique could be to correct the most basic and common mistake that soccer players make when sprinting; something I like to call “skating technique”. What this name describes is a perpendicular motion of their non-propelling foot towards the midline of the body and then around the opposite leg to finally find the ground after a much longer trajectory than simple straight motion. This movement is extremely inefficient when trying to move forwards because it is just not moving in the same direction as the displacement of the body, creating conflicting vectors that have to be controlled by more effort.

A high level athlete can run in a 280 steps per minute cadence, but for the purpose of the analysis we will reduce that to an average of 240 steps per minute that is a slower more common cadence amongst running of soccer players. This means that every step takes about 0.5 seconds. Upon every step, if the athlete is “skating” the foot must move laterally towards the midline of the body and then back in those 0.5 seconds. Consequently, if that foot deviates only 10 cm the foot must travel that distance in less than 0.25s, needing a relatively high acceleration and deceleration to make that possible.

The foot must accelerate for 0.125s and then decelerate for 0.125s (considering a symmetric behaviour on the speed of the foot). This should happen then twice on each step in order to move away and back for the next step. Accordingly, the body has to create a 25.6 m/s2 acceleration and the same deceleration for the step. That aceleration is quite high, even for a light part of the body, so it does require a high amount of energy that could otherwise be spared. A foot weighs about 1.5% of an adults bodyweight. (Again, we will add a negative error on the energy used by the body by only using the foot of the athlete and not including the weight of the shins to provide a simpler analysis). For an 80kg athlete, the foot would weigh around 1.2kg. Now, using the acceleration provided earlier, every step would waste around 3.072 Joules of energy. But, human muscles are not 100% efficient, so, by applying the average efficiency of human muscle (23% movement vs 77% heat) that would mean the 3.072J would actually become 13.36J of energy use. Seems like a small amount, but it is multiplied by the amount of steps taken while sprinting on a game it becomes considerable and important. In a professional football match, an athlete travels around 10km, but only about 1500m are actually fast sprints to which we could apply our 240 steps/min cadence. So how many sprinting steps would a football player make on a game?

With 1.5km and an average of 1m per step according to (gpexe 2016) the sprints would add to 1500 steps, on  average. Which means: 13.36J * 1500 steps = 20.003 kJ.
20.003 kJ That the athlete would be wasting. This would be equivalent to a little more than running an extra of 1km at a 16km/hr pace on a flat surface for an 80kg adult (REF). Quite a lot of energy that you’re throwing out the door. Then, how much energy would that be compared to the total energy from a football game?

According to a study conducted by gpexe 2016, the total energy expended would be around 4,602kJ. That means that “Skating” would waste around 4.55% of the total energy from the game when skating exactly 10 cm every time. Theoretically then, if an athlete were to stop “skating” he would be able to run 4.55% more distance on a football match with the same fitness he immediately has. Something quite attractive for any coach and athlete in the world, without getting into how faster he could run and reduce the risk of injury of the muscles involved.

Additionally, putting that 4.55% into more clear words; it is the difference between the fittest athlete in the Premier league, that runs close to 11km and the average Premier league player which runs about 10-10.5km per match.

Evidently, when using energy as an effort measure on a football match, an athlete can benefit greatly by learning to stop “skating” when sprinting. On the other hand, ACL injuries (a common ocurrence on soccer players) could also be affected by this perpendicular unecessary movement of the foot, because it will give extra strain to the ligaments and tendons of the weight bearing knee to produce the forces we just observed.

If you are interested on seeing how “skating” technique varies depending on the distance away from the midline I have added a small table that shows the different amounts of energy wasted depending on the distance the foot travels.
If anyone finds an error on my calculations let me know! We all want to get correct information for our collective knowledge.

Crossing Foot Distance (cm) Work /step (kJ) Wasted Energy (J) Percentage to Total Energy
0.0 0.0 0.0 0.0%
1.0 0.1 200.3 0.0%
2.0 0.5 801.4 0.2%
3.0 1.2 1803.1 0.4%
4.0 2.1 3205.6 0.7%
5.0 3.3 5008.7 1.1%
6.0 4.8 7212.5 1.6%
7.0 6.5 9817.0 2.2%
8.0 8.5 12822.3 2.9%
9.0 10.8 16228.2 3.7%
10.0 13.4 20034.8 4.6%
11.0 16.2 24242.1 5.6%
12.0 19.2 28850.1 6.7%
13.0 22.6 33858.8 7.9%
14.0 26.2 39268.2 9.3%
15.0 30.1 45078.3 10.9%
16.0 34.2 51289.0 12.5%
17.0 38.6 57900.5 14.4%
18.0 43.3 64912.7 16.4%
19.0 48.2 72325.6 18.6%
20.0 53.4 80139.1 21.1%
21.0 58.9 88353.4 23.8%
22.0 64.6 96968.3 26.7%
23.0 70.7 105984.0 29.9%
24.0 76.9 115400.3 33.5%
25.0 83.5 125217.4 37.4%

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