Pop king Michael Jackson (MJ) died on June 25, 2009, at the age of 50. Its original special dance steps space steps (figure 1) and 45 degree forward (figure 2) are unforgettable.
In 1987, MJ shocked music fans around the world with an unbelievable supernatural gesture in his music video Master of Crime—his entire body tilted forward 45 degrees, but his feet were still firmly nailed to the ground, as if free from gravity.
Although many people believe that the dance king breaks the barrier between physiology and physics, the truth is that behind this strange dance step is a special dance shoe. MJ himself patented this special shoe in 1993 (Figure 3).
In 2018, several neuroscientists specifically studied MJ's performances around the world, analyzing the spinal biomechanics behind the stunt. The study was published in the academic journal Journal of Neurosurgery: Spine. According to the paper, MJ has set off an unparalleled 45-degree forward imitation boom, which the audience considers a miracle.
Many MJ fans, including the author, have tried to imitate this move, but most have failed (Figure 4) and often hurt themselves.
It's no secret that a nail pops up on the ground at the right moment and is wedged into a special sole (Figure 5). This gives the dancer extra grip or he will fall. However, neuroscientists point out that even with specially designed dancing shoes and the support of the connectors, this action is difficult to achieve. This requires strong spine, leg, and back muscles to provide strength that can resist gravity (Figure 6). The researchers found that MJ was subjected to considerable force on the Achilles tendon area when completing the action.
This article will build a simple mathematical model that uses the principle of mechanical equilibrium to calculate the amount of tension that MJ undergoes when performing a 45-degree forward tilt.
model
When the human foot is doing plantar flexion or dorsal flexion, the foot is basically rotating around the center of the ankle (Figure 7), and the center of rotation is almost the same (Figure 8).
When the standing body rotates forward around the center of the ankle joint by more than an angle, the position of the human center of gravity will exceed the tiptoe, the ground support force and the human weight force line will not be in the same straight line, the ground support force will not maintain the balance of the body, and the moment generated by gravity will cause the body to fall (Figure 9).
However, MJ did not tip over when performing a 45-degree forward tilt, mainly because the special dancing shoes fixed the foot to the ground, and the Achilles tendon muscles applied a reverse torque to the body, balancing with the gravitational moment (Figure 10).
The Achilles tendon is the most important anatomical structure of the calf muscle strength transmitted to the foot, and is an indispensable tissue for human standing, walking, running, climbing and other sports.
As shown in Figure 9, suppose the human body mass is , height is , and the center of gravity height is = , where is the ratio of the height of the center of gravity to height. When the body is tilted forward, the torque generated by gravity on the center of the ankle is as shown in Figure 10, assuming that the tension of the Achilles tendon muscle is, and the distance from the Achilles tendon muscle to the center of the ankle is, then the torque generated by the Achilles tendon muscle on the center of the ankle joint is the magnitude of the torque generated by the Achilles tendon muscle According to the previous analysis, in order to maintain balance, the torque generated by gravity must be balanced by the Achilles tendon muscle, that is, . So the tension of the Achilles tendon is that if we simply assume that the body mass is proportional to the cube of height, i.e. =. The distance from the Achilles tendon muscle to the center of the ankle is proportional to height, i.e. =, the above equation can be expressed as where sum is the proportional constant. The above equation shows that the tension of the Achilles tendon is a function of height and forward angle.
parameter
According to publicly available information, MJ has a height of =1.75 m and a weight of = 60 kg. The distance between the rotating center of the ankle joint and the plantar flexor muscle in adults is measured in the literature to be about = 0.05 m. To apply the model above to calculate the tensile strength of MJ's Achilles tendon muscle when leaning forward at 45 degrees, you also need to know the height of MJ's body center of gravity.
As shown in Figure 11, the position of the body's centroid can be measured by a simple experiment. In the experiment, the human body lies flat on a long plate, and the net weight measured at each end of the plate (minus the plate weight) is sum. The height of the human center of gravity can be calculated according to the principle of leverage, as well as the height of the center of gravity to the height ratio: the experimental measurement data of 16 men and women is given in the literature, and the corresponding statistical results of the height of the center of gravity to the height ratio are shown in Figure 12. The measurements show that the height-to-height ratio of the center of gravity of all people is not much different, almost between 0.5-0.6. On average, the height-to-height ratio for women is about = 0.543, compared to = 0.560 for men. Therefore, it can be considered that the height of the center of gravity of MJ is about 1.75 0.56 = 0.98 m.
If we take MJ as the standard body, and assume that the size of other heights in each dimension is only an equal scale of MJ. You can calculate the ratio factor of human body mass to height cube, and the ratio factor of the distance from the Achilles tendon to the center of the ankle to the height: result
First, let's apply the above model to calculate the force that MJ uses on the Achilles tendon when performing a 45-degree forward tilt. By substituting the parameters identified above into the model, the muscle tone of MJ's Achilles tendon is: This force is equivalent to 13.9 times MJ's own body weight, or equivalent to the gravity generated by 832 kg. Studies have shown that normal people can withstand about 12.5 times the strength of their body weight when running vigorously, and can withstand 6-8 times the strength of their body weight when jumping or cycling. Apparently, when MJ completed a 45-degree forward tilt, the Achilles tendon part was subjected to more force than usual strenuous exercise.
Next, we will discuss the effects of different heights and different forward angles on the tension of the Achilles tendon. By substituting the values of scale factors = 11.2 kg/m, = 0.0286, and = 0.56 (in male terms) into the model, we can obtain a height of A person with a forward tilt of Achilles tendon tension According to the above equation, we can plot a function image of the Achilles tendon tension of people of different heights at the same angle of 45 anterior leaning forward (Figure 13), and a function image of the Achilles tendon tension when people of the same height lean forward at different angles (Figure 14).
Figures 13 and 14 show that the lower the height and the smaller the forward angle, the less tension the Achilles tendon is subjected to, and vice versa. The Achilles tendon tension is proportional to the cubic of height and the sinusoidal value of the forward angle. If the cross-sectional area of the Achilles tendon is considered to be proportional to the square of height, the tensile force (tensile stress) on the cross-section of the Achilles tendon muscle unit is proportional to the height.
conclusion
Michael Jackson leans forward 45 degrees, as if free from gravity. In addition to special dancing shoes, the movement requires strong Achilles tendon strength. The Achilles tendon muscles exert a reverse torque on the body, in balance with the moment of gravity. Based on the principle of mechanical equilibrium, a mathematical model was established to calculate that the tension on MJ's Achilles tendon when performing this action is equivalent to 13.9 times MJ's own body weight, which is a considerable force, far exceeding the Achilles tendon tension during general strenuous exercise.
This article also generalizes the model to the situation where people of different heights lean forward at different angles. Studies have shown that the thinner the head, the easier it is to complete a 45-degree forward tilt, with the Achilles tendon tension proportional to the cubic of height when leaning forward, and the tensile force (tensile stress) on the cross-section of the Achilles tendon muscle unit proportional to height. The smaller the forward tilt angle, the smaller the tension on the Achilles tendon, and the tension of the Achilles tendon when leaning forward is proportional to the sinusoidal value of the angle. Jackson was able to complete this movement, on the one hand, thanks to the fact that he is a professional dancer, professionally trained, and the Achilles tendon muscles are thicker than the average person. On the other hand, it also benefits from its moderate height and low weight.
Michael Jackson's role as an unrepeatable icon is no accident. The 45-degree forward tilt action has a certain danger, and it is recommended that ordinary people do not try this action easily, and if you are not careful, it may cause injury or rupture of the Achilles tendon.
Resources
[1]
Manjul and Tripathi. How did michael jackson challenge our understanding of spine biomechanics? Journal of Neurosurgery. Spine, 2018.
[2]
Micheal jackson age, death, wife, family, biography and more:
[3]
J. R. Baxter and S. J. Piazza. Plantar flexor moment arm and muscle volume predict torque-generating capacity in young men. Journal of Applied Physiology, 116(5):538, 2014.
[4]
Stephanie Gambino. Center of mass of a human, 2009:
[5]
K. W. Barfod. Achilles tendon rupture; assessment of nonoperative treatment. Danish Medical Journal, 61(4):B4837, 2014.
The reproduced content represents the views of the author only
Does not represent the position of the Institute of Physics, Chinese Academy of Sciences
Source: HIMCM
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