An attempt to analyze the trauma risk of blows to the head with a bare fist, compared to blows with a boxing glove.
Impact theory
A shock in mechanics is a short-term interaction of bodies, as a result of which their velocities change. The impact force depends, according to Newton's law, on the effective mass of the impacting body and its acceleration:
Rice. 1 Curve of development of impact force in time
F = m * a (1), where
F - strength, m - mass, a - acceleration.
If we consider the impact in time, then the interaction lasts a very short time - from ten-thousandths (instantaneous quasi-elastic impacts) to tenths of a second (inelastic impacts). The impact force at the beginning of the impact rapidly increases to the maximum value, and then drops to zero (Fig. 1). Its maximum value can be very large. However, the main measure of the shock interaction is not the force, but the shock impulse, numerically equal to the area under the curve F (t). It can be calculated as an integral:
where
E1 and E2 - kinetic energies of the first and second bodies before impact, E'1 and E'2 - kinetic energies after impact, E1p and E2p are the energy losses during impact in the first and second bodies.
In reality, all shocks are either absolutely or partially inelastic. Newton proposed to characterize the inelastic impact by the so-called coefficient of recovery. It is equal to the ratio of the velocities of interacting bodies after and before impact. The smaller this coefficient, the more energy is spent on the non-kinetic components E1p and E2p (heating, deformation). Theoretically, this coefficient cannot be obtained, it is determined empirically and can be calculated using the following formula:
With a mechanical impact, the speed of the body (for example, a ball) after the impact is the higher, the greater the speed of the striking link immediately before the impact. When hitting in sports, this dependence is not necessary. For example, when serving in tennis, an increase in the speed of the racket can lead to a decrease in the speed of the ball, since the impact mass during the strikes performed by the athlete is unstable: it depends on the coordination of his movements. If, for example, a blow is performed by bending the hand or with a relaxed hand, then only the mass of the racket and hand will interact with the ball. If, at the moment of impact, the striking link is fixed by the activity of the antagonistic muscles and is, as it were, a single solid body, then the mass of this entire link will take part in the impact interaction.
where
v is the speed of the bag, p is the impulse of the bag, m is the mass of the bag.
Using the formula for calculating the recovery factor (4) and assuming that the speed of the fist after the blow is zero, we obtain the value for a blow with a bare fist about 0, 12, i.e. k = 12%. For the case of a hit with a boxing glove, k = 14%. This is confirmed by our life experience - a blow on a punching bag is almost completely inelastic and almost all the energy of the blow goes to its deformation.
It should be noted separately that the fist in the karate glove had the highest speed. The momentum of the bag when hit with a karate glove was the smallest. Bare-fist strikes in this study were intermediate. This can be explained by the fact that the athletes were afraid to injure their arm and reflexively reduced the speed and power of the blow. When struck with a karate glove, such fear did not arise.
| Material | Young's modulus |
| Steel | 200 GPa |
| Concrete | 20 GPa |
| Bone | 10 GPa |
| Rubber | 0.001 GPa |
The above calculations were made on the basis of data on the rectilinear acceleration of the head after impact. But for all their relative complexity, they are very far from predicting the trauma of a blow. English physicist Holborn, who worked with gel models of the brain in 1943, was one of the first to put forward the rotational acceleration of the head as the main parameter of brain injury [4]. Ommai et al. [5] state that a rotational acceleration of 4500 rad / s2 results in concussion and severe axonal injury. An earlier work by the same author states that a rotational acceleration above 1800 rad / s2 creates a 50% chance of a concussion. In the article by Valilko, Viano and Bira [3], the parameters of 18 different strokes are given. If we take the same boxer and his blow with a hand speed of 9.5 m / s and a blow with a speed of 6.7 m / s, then in the first case the recovery factor is 32%, and in the second it is already 49%. According to all our calculations, it turns out that the second blow is more traumatic: a higher recovery factor (more energy was spent in the translational movement of the head), a large effective mass (2.1 kg and 4.4 kg), a slightly higher acceleration of the head (67 g and 68 g). However, if we compare the rotational acceleration of the head produced by these two blows, we will see that the first blow is more traumatic (7723 rad / s2 and 5209 rad / s2, respectively). Moreover, the difference in numbers is quite significant. This fact indicates that the trauma of a blow depends on a large number of variables and one cannot be guided by only one impulse p = mv when evaluating the effectiveness of a blow. The place of impact is also of great importance here, so as to induce the greatest rotation of the head. In connection with the above data, it turns out that the factor of the boxing glove in injuries and concussions does not play a major role.
Summing up our article, we note the following. The factors affecting the brain injury during a blow with and without a boxing glove do not differ significantly and can change in one direction or the other, depending on the boxer and the type of blow. Much more significant factors affecting a concussion lie outside the plane under consideration, such as the type and location of the blow to the head, which determine its rotational moment
At the same time, we must not forget that boxing gloves are designed primarily to protect the soft tissues of the face. Strikes without gloves cause damage to bones, joints and soft tissue in both the attacker and the attacked athlete. The most common and painful of these is a boxer's knuckle injury.
The boxer's knuckle is a term well-known in sports medicine used to describe a hand injury - damage to the joint capsule of the metacarpophalangeal joint (usually II or III), namely the fibers holding the extensor tendon of the fingers.
The danger of contracting various infections, including hepatitis C or HIV viruses and a host of other unpleasant consequences, including an unattractive appearance, in every possible way reject the thesis that fighting with bare hands is safer for health.
References:
1. Lamash B. E. Lectures on biomechanics.
2. Smith PK, Hamill J. The effect of punching glove type and skill level on momentum transfer. 1986, J. Hum. Mov. Stud. vol. 12, pp. 153-161.
3. Walilko T. J., Viano D. C. and Bir C. A. Biomechanics of the head for Olympic boxer punches to the face. 2005, Br J Sports Med. vol.39, pp.710-719 [PDF]
4. Holbourn A. H. S. Mechanics of head injury. 1943, Lancet. vol. 2, pp. 438-441.
5. Ommaya A. K., Goldsmith W., Thibault L. Biomechanics and neuropathology of adult and pediatric head injury. 2002, Br J Neurosurg. vol. 16, no. 3, pp. 220-242.
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