The dependence of weight training of figure skater''s hands and increase of multi-turn jumps Текст научной статьи по специальности «Медицинские технологии»

THE DEPENDENCE OF USING WEIGHTS IN FIGURE SKATER'S HAND TRAINING AND

INCREASE OF NUMBER OF TURNS IN MULTI-TURN JUMPS

V.I. Vinogradova, professor, Dr.Hab.

Moscow state engineering University (MAMI), Moscow

Key words: figure skating, hand weight training.

Introduction. Multi-turn jumps in figure skating are the main indicator of sports skills in single skating. A figure skater makes multi-turns by tucking when making an initial rotation in a jump. The influence of weight training of figure skater's hands can be estimated using the law of conservation of the principal moment of momentum of the mechanical system, if the system is not affected by external forces. For these purposes it is enough to model a figure skater by the anthropomorphic mechanism (AM), i.e. the mechanical system, made of absolutely rigid elements interconnected with joints without friction.

The purpose of the research was biomechanical modeling of jumps in figure skating using weights on athletes' hands and assessment of its effect on the increase of the number of turns in multi-turn jumps.

Results and discussion. The mutual arrangement of the elements of the AM can vary using internal forces (using skater's muscles). And the principal moment of momentum of the AM remains constant:

Jy CO = const,

where ^y - moment of inertia of the AM with respect to the axis ?, 01 - angular velocity of rotation of the AM about the axis y.

This implies that reducing the moment of inertia of the AM with respect to the axis ? leads to an increase in its angular velocity of rotation about this axis.

When a figure skater and therefore the AM tucks, his moment of inertia decreases, while angular velocity and, thus, the number of turns in a multi-turn jump increase.

The proposed approach to assessing the effect of the figure skater's hand weight training on the increase of the number of turns in multi-turn jumps is interesting since it is possible to construct the AM from elements with known or easily determined moments of inertia. In this case, the axial moment of inertia of the AM is the total of the moments of inertia of its elements. Using such an approach, the effect of hand weight training of figure skaters on the number of turns in multi-turn jumps can be assessed. Weights are introduced into the AM as concentrated masses that increase the weight of hands.

Hereby we are considering the case when the initial rotation in a jump is created by sliding along the arc [4]. We are using a three-element AM of a figure skater with a cylindrical shape of the body (Fig. 2.7 and Fig. 2.8 in [1]). The reason for choosing the AM with the cylindrical shape of the body is that, other conditions being equal, its parameters ensure reaching a higher rotation speed in a jump compared to the conical shape while creating the initial rotation by sliding along the arc [1].

The biomechanical process of jump execution is complex, ambiguous and depends on many factors such as: anthropometric parameters of figure skaters, their strength, psychological and other characteristics, which sometimes can not be controlled. In this case it is natural to exclude from the analysis the whole process and consider only those states of a skater (his AM) when jumping, which will explain the effect of weight training of hands on the number of turns in a multi-turn jump.

To achieve the set target let us consider the state of the AM in an untucked position, while sliding along the arc at the moment before the takeoff from the ice, and at the moment of its rotation around the axis of a figure skater after the tucking of the AM when being in the air during a jump. We will define the rotation speed of the figure skater during the jump with the help of his rotation speed while sliding along the arc, at the moment of takeoff from the ice. Then we will define the same rotation speed during the jump using hand weights. The influence of the weights on the rotation speed while in a jump and, consequently, the efficiency of increase of the number of turns in a multi-turn jump will be determined by comparing the obtained rotation speed of the figure skater with and without hand weights.

The biomechanics of creating the initial rotation by sliding along the arc was considered in [1]. We will use the results obtained in it. We will consider only the case when the elements of the AM do not cross

the axis ? while sliding along the arc before the takeoff from the ice. Let us denote the moment of inertia of

j*

the AM with respect to the axis ? of its rotation at the moment of takeoff from the ice as y. The moment of inertia for the calculation scheme on Fig. 2.8 in [1] is calculated using the formula below:

Jl = M(k A + 2k B + k C)5

where

A = 0,4r2 + [R-(L + r)sina]2, B = ^L2P +[R- (Lsina + Lp)f,

R - radius of the arc of sliding, r ~ radius of the head model, ^ radius of the cylindrical model of

the body, L ~ length of the body model, ^p ~ length of the arm model, 01 ~ angle between the axis of the

AM and the normal to the ice surface; hereinafter proportions by weight of head, arms and body

in the total weight of a figure skater.

After tucking arms of a figure skater are pressed to the body, increasing its weight, maintaining the shape and dimensions.

The moment of inertia of the AM of a figure skater - - with respect to the axis of its rotation in a jump after tucking under the assumptions made is determined by the following formula:

Jy = M(0,4£ r2 + 0,5(* + 2k )R ].

From the condition of the moment of momentum being constant

2

the speed of rotation 10 of a figure skater in a jump is calculated:

CO = —CD

J„

(4)

Let us assume that hand weights are modeled by lumped masses m located at the end of the rods -arms models. The moment of inertia of these masses with respect to the axis ^ is easily determined by the following formula:

J = m(R- Zsina -L )2 +m{R -Zsina +L )2,

or

Jy,m = 2mi(R - ¿sincx f + II ]

(5)

Therefore, at the moment a figure skater takes off from the ice his AM with hand weights is defined as follows:

(6)

Let us assume that hand weights do not change the weight of the figure skater. This assumption is

true if 2m«M> that is the mass of the weights is much smaller than the mass of the figure skater without the weights. The assumption is natural since it is hard to imagine the execution of jumps with weights the mass of which is comparable with the mass of the figure skater. On the other hand, the weights change the moment of inertia of the AM of the figure skater.

Thus, the moment of inertia of the AM of the skater before the takeoff from the ice is determined by the formula (6), and it does not change and remains the same after the takeoff from the ice and tucking.

Given the law of the main angular momentum being constant, we determine the speed of rotation of the figure skater in a jump:

or

(7)

Here ^y is calculated by the formula (1), ^y by the formula (2), and y'm - by the formula (5). Increase of the angular velocity of the figure skater in a jump by means of hand weights can be estimated as a percentage, taking the angular velocity of rotation without weights for the standard, co_ - co

A = -

-100%.

CO

Using (4) and (7), we get the following:

A = ^-100%.

For a quantitative estimate we take total body dimensions for speed skaters [3], as no other average values of anthropometric measurements of figure skaters could be found in relevant literature sources. Total dimensions are athlete's height of 172.2 cm and weight of 69.4 kg. Mass proportions and linear dimensions of arms, head and legs are defined according to recommendations [2]. With the help of Table 12 from [2] we obtain the following data for the calculation scheme in Fig. 2.8 of m 2kp = 0,09892, kr - 0,06940, ^=0,83168

The linear dimensions are defined by means of the regression equation and Table V of [2]:

Lp - 0,636 , ^-0,689 , T-1,45 • in a(j(jition, we assume that r '

Taking the radius of the arc of sliding before the takeoff from the ice equal to R=1 m, the angle

between the normal to the ice surface and the axis of the AM equal to a = 15 and the weights of each hand

equal to m = ^ kg, we get ^ m .

Obviously, the hand weights slightly increase the speed of his rotation in a jump. This result is expected since while sliding along the arc all parts of the figure skater's body and, consequently, elements of the AM are moved substantially away from the axis passing through the center of the arc of sliding. Since the mass of the weights is small compared with the mass of the figure skater, its contribution to the moment of inertia is negligible. The formulae confirm the physically intuitive result.

Salchow jump that is executed by sliding along the arc, is accompanied by an auxiliary method of creating the initial rotation by twisting the torso of a figure skater. According to the practical execution of this jump, the multi-turn nature is achieved by using the auxiliary method. Otherwise, the jump fail is frequent.

In order to determine the contribution of the auxiliary method in the increase of the number of turns in the Salchow jump, the effect of using weights on the hands of a figure skater when creating the initial rotation by twisting his torso is to be considered separately. It is also necessary for the reason that the method of creating the initial rotation by twisting the torso is the main one used when doing such jumps as loop, toe loop, flip, Lutz and Walley.

Fig. 1. Five-link anthropomorphic mechanism

We will use a five-link AM (see Fig. 1 [2]). The initial rotation is created by twisting the cylindrical body before the takeoff from the ice. During the flight muscle strength (internal forces for the AM) takes the body back to its untwisted state. The flight takes place with the rotation around its own axis with a speed 0)-

The value of the kinetic moment is determined on the assumption that the body is twisted in a linear fashion starting with its connection to the legs. It is assumed that the angular velocity of rotation of the

figure skater's shoulders 0)0 is known.

In [2] there is a formula for determining the kinetic moment for an untucked figure skater right before the takeoff from the ice into a jump:

Kx =MR2co0{0,4£ (j^f + 2k [^(^)2+l] + 0,25£ }.

Legs of a figure skater are modeled by means of homogeneous and absolutely rigid bodies. They are not twisted and therefore not involved in creating the moment of momentum of the figure skater before the takeoff from the ice.

The kinetic moment of using hand weights JC,m is determined by the following formula:

Kxm=2[m(R +L )2H-

We will describe the kinetic moment after tucking as ~ where w - rotation speed of the figure skater while in the flight.

The kinetic moment of the figure skater with hand weights is described as follows:

Therefore, the rotation speed while in the flight with hand weights co,n is defined via the rotation speed of the shoulders:

We are interested not in the value of the rotation speed of the figure skater while in the flight but in its increase. If we use the hand weights, then:

Otherwise A = ^-100%.

J

x,

For the anthropometric and weight measurements of a figure skater set above and the hand weights

m=lkg we find that A ~ 200%- If m = 2 , then A ~ 400%.

It is an expected result. The initial rotation is created by twisting the body around the axis of the figure skater. A light mass of the weight compared to all parts of the figure skater's body is moved substantially away from the axis of his rotation and, hence, significantly increases his kinetic moment and the rotation speed while in the flight.

Conclusion. While making jumps in figure skating, when body twisting is a primary or a secondary method of creating the initial rotation, weight training of hands should be used to increase their multi-turn nature.

References

1. Vinogradova, V.I. Fundamentals of biomechanics of jumps in figure skating / V.I. Vinogradova. - Moscow: Sovetsky sport, 2012. - 216 P. (In Russian)

2. Karpman, V.L. Sports medicine / V.L. Karpman. - Moscow: Fizkultura i sport, 1987. - 304 P.

3. Zatsiorsky, V.M. Biomechanics of human musculoskeletal system / V.M. Zatsiorsky, A.S. Aruin, V.N. Seluyanov. - Moscow: Fizkultura i sport, 1981. - 143 P. (In Russian)

4. Mishin, A.N. Biomechanics of figure skater's movements / A.N. Mishin. - Moscow: Fizkultura i sport, 1981. - 141 P. (In Russian)