Optimal load calculation in iron sports

Choose optimal training weight weights are not easy for athletes. It is known that the most effective method in developing strength is the method of repeated efforts with weights from 6 to 10 RM (RM - repeated maximum), which achieves a rational ratio between the growth of strength and muscle mass. In this case, the weight of the burden should be approximately 80%. However, determining the maximum weight not always possible or desirable because it may cause injury. Sometimes the student does not have the necessary equipment. Moreover, in some exercises - hanging pull-ups on a bar with a weight (or counterweight), squats with a barbell - the working weight of the barbell, weights or counterweight cannot be calculated as a percentage at all. Therefore, in most cases, the training weight is set conditionally.

But “conventions” alone won’t get you far, and high-quality control of training loads is the dream of any bodybuilder. But how to achieve it? After all, as we said above, it is often difficult to determine the desired weight of weights for an impressive number of exercises. How to get “optimally” instead of “conditionally”? - it turns out that this is not so difficult to achieve... The proposed article discusses a number of methods that make it possible to make fairly accurate calculations of the required working scales, and thereby significantly improve control of training loads your training.

^{*The only inconvenience is that this article was published a very long time ago (in post-Soviet times), and the main proposed calculations in it are performed on some kind of domestic “micro-calculator”, which has lost its relevance in our turbulent age of computerization and technological progress. However, the proposed calculation algorithms and ideas have not lost their relevance to this day. And having correctly understood the calculation method, you can easily and successfully use it for your calculations.}

^{**The proposed algorithms are extremely difficult to understand, so we advise you to focus your attention on the attached examples - they will help you accurately understand complex formulas, grasp the essence and not go into too much programming of the calculator...}

Algorithms for calculating optimal loads in bodybuilding and fitness

It has become widespread in professional bodybuilding. method for determining burden, based on the fact that an athlete can perform eight repetitions with a barbell of a specific weight (without breaking technique). In this case, it is possible to increase the load by 2.5 kg, and the weight of the weight remains unchanged until eight repetitions are again freely performed in all approaches. Then the weight of the projectile is increased again, and the whole cycle is repeated.

The problem under consideration can be successfully solved by mathematical calculation according to the methodology proposed by the authors, based on the results of a single testing of athletes. The weight of the weight during testing is chosen arbitrarily, and the working weight can be calculated for any given number of repetitions by calculating all the options available for a given level of fitness for combining the weight of the weight and the number of repetitions in one approach.

It has been experimentally established that in the range from 1 to 50 repetitions, the relationship between the possible number of repetitions in one approach and the ratio of the maximum force to that actually developed at a given load is a linear value. The calculation of the coefficients of the direct and inverse regression equations gave the following values: a = -31.93, b = 33.16 - for the direct and c = 0.965, d = 0.03 - for the inverse.

Without going into details of mathematical operations, we will use several examples to show the effectiveness of the methodology for calculating the most important parameters of the training load (weight of weights and number of repetitions) depending on the level of physical fitness of the trainees. This operation can be conveniently performed using a programmable microcalculator (for example, MK-61) according to the programs we have compiled. The calculation is performed according to the instructions, and program statements are entered line by line from left to right.

Barbell weight calculation, with which you can perform the required number of repetitions for the case when its movement is not accompanied by the movement of significant parts of the body (bench press, sitting, biceps curl, etc.).

Let's say the student has produced barbell bench press weighing 40 kg 12 times. It is required to determine the weight of the barbell with which he will perform this exercise 10 times.

To do this, use the following program to calculate loads:

Program 1

B^ ПхС - ПхА + ПхВ  F1/x <-> FxУ С/П  В/О

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program I);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter regression coefficients (0.965, x PS, 0.03, xPD);
6. Enter the value of the number of repetitions during testing into register O (12, xPO), and then the value of the weight of the barbell with which testing was carried out into register I (40, xPI);
7. Enter the number of required repetitions of barbell lifts and run the calculator to count (10, C/P). After completing the calculation, the weight of the barbell we are interested in (42 kg) will appear on the calculator indicator;
8. To calculate new values, proceed to step No. 6.

Calculation of the possible number of lifts of the barbell.

Suppose for the same student it is necessary to calculate the maximum possible number of lifts of a barbell of a certain weight, for example 35 kg.

Program 2

B^ ПхВ <-> FхУ ПхА х ПхС + С/П   В/О

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 2);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter regression coefficients (0.965, xPS, 0.03, xPD);
6. Enter the digital value of the number of repetitions during testing into register O (12, xPO), and then the value of the weight of the barbell with which testing was carried out into register 1 (40, x P1);
7. Enter the weight of the bar you intend to work with and run the calculator to count (35, C/P). At the end of the calculation, “will appear” on the calculator indicator. a value corresponding to the number of possible repetitions of lifting a barbell weighing 35 kg (18 times);
8. To calculate the number of lifts of a barbell of a different weight, you should proceed to step No. 7, and to perform the calculation for a new student, go to step 6. When doing pull-ups on the bar without weights, with weights or with a counterweight, when bending/extending your arms in support (push-ups from floor / on parallel bars) in similar conditions, it is difficult to select the required optimal weight of the weight or counterweight, as well as to calculate the number of pull-ups with a given weight or counterweight (number of times).

For example, it is necessary to determine what the weight of the counterweight should be so that someone who exercises with a weight of 60 kg, and is able to do 7 pull-ups with his own weight, can do 10 pull-ups in one approach.

Program 3

хПО хП7 О хПЗ хП4 хП5 хП6 хП7 ПхО – I + С/П хП1 F1n х ПВ ПхЗ + хПЗ ПхВ Fx2 Пх4 + хП4 Пх7 С/П хП2 F1n хП9 Пх5 + хП5 ПxВ Пх9 х Пх6 + хП6 FLO 07 ПхЗ Пх5 х Пх7 Пхб х - ПхЗ Fx2 Пх7 Пх4 х - + хПВ Пх5 ПхЗ ПхВх - П*7 + Fex хПА С/П ПхВ С/П

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 3);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter regression coefficients (0.965, x PS, 0.03, xPD);
6. Enter the value of the number of pull-ups with your own weight in register O (7, xPO), and then the weight of the student in register I (60, xP1);
7. Enter the required number of weighted or counterweighted pull-ups (10, C/P). At the end of the calculation, the value of the counterweight mass (-4 kg) will appear on the calculator indicator;
8. To calculate the mass of the counterweight for a new number of pull-ups for the same student, proceed to step No. 7;
9. For a similar calculation of the counterweight mass for another student, proceed to step No. 6.

Thus, the mass of the counterweight should be -4 kg (the minus sign indicates that in order to successfully solve the motor task, conditions are necessary that facilitate the performance of pull-ups).

Definition possible number of pull-ups. Let's say that we are interested in the number of pull-ups that the same person can do with a weight of 5 kg.

Program 4

х П6 Пх3 Пх1 FxУ хП5 Пхб + хП4 ПхО ПхД х ПхС + Пх2 Пх5 + ПхВ х х Пх4 + Пх А + С/П БП 00

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 4);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter regression coefficients (-31.93, xPA, 33.16, xPT, 0.965, xPS, 0.03, xPD)1;
6. Enter the true number of pull-ups with your own weight in register O (7, xPO), the value of the weight of the student in register I (60, xP1);
7. Enter the weight of the burden or counterweight (5, S/P). At the end of the count, the calculator indicator will show the required number of pull-ups (4);
8. With a new amount of weights, proceed to step No. 7;
9. When changing the student, proceed to step No. 6.

If it is necessary to select the weight of the counterweight for a beginner who has never been able to do a pull-up on the bar or perform flexion/extension of the arms in support (from the floor/on the uneven bars), a test is carried out to determine the minimum mass of the counterweight with which it is possible to perform the exercise once.

Calculation of required mass counterweight. What should be the weight of the counterweight with which an 80 kg student can do 10 pull-ups in one approach, if with a counterweight of 10 kg he can do 1 pull-up?

Program 5

ПхА - х П4 ПхО  ПхД х ПхС + ПхВ х хП6 Пх 3 Пх 1 FxУ х П5 Пх2 + Пхб х Пх4 + Пх5 - С/П БП  ОО

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 5);
3. Switch to automatic operation mode (F, AVT);
4. Clear program counter (V/O);
5. Enter regression coefficients (0.965, xPS, 0.03, xPD);
6. Enter the value of the counterweight weight with which the student was able to perform one pull-up in register 0 (-10, xPO), the weight of the student in register I (80, xP1);
7. Enter the desired number of pull-ups (10, S/P). At the end of the calculation, the desired value of the counterweight mass (-25) will appear on the calculator indicator;
8. To calculate the mass of the counterweight for a new number of pull-ups for the same student, proceed to step No. 7;
9. To carry out the calculation for another student, return to point 6.

Calculation of the possible number of pull-ups. How many times can this student do pull-ups using a counterweight of -20 kg?

Program 6

ПхI + ПхО  ПхI + ПхВх <-> + ПхА + С/П  БП  ОО

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 6);
3. Switch to automatic operation mode (F, AVT);
4. Clear program counter (V/O);
5. Enter the regression coefficients (-31.93, x PA, 33.16, x PV);
6. Enter the weight of the counterweight, with which the student was able to do one pull-up, into register O (-10, x PO), the weight of the student into register I (80, x P1);
7. Enter the weight of the counterweight with which you can perform the required number of pull-ups (-20, S/P). At the end of the counting, the required number of pull-ups (7) will appear on the calculator indicator;
8. With a new value of the counterweight mass, proceed to step No. 7;
9. When making calculations with another student, return to point 6.

Program 7

ПхД х ПхС + ПхО Пх1 + <-> + Пх1 - С/П   БП  ОО

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 7);
3. Switch to automatic operation mode (F, AVT);
4. Clear program counter (V/O);
5. Enter the regression coefficients (-31.93, xPA, 33.16, xPT, 0.965, x PS, 0.03, xPD);
6. Enter the number of squats performed during testing in register O (5, xPO), the weight of the student - in register I (80, xW), the weight of the barbell with which testing was carried out - in register 2 (60, xP2), the constant 0.667 - in register 3 ( 0.667, xPZ);
7. Enter the planned number of squats (10) and run the calculator to count (S/P). At the end of the calculation, the desired weight of the barbell (51) will appear on the calculator indicator;
8. With a new number of squats, proceed to step No. 7.
9. When making calculations with another student, return to point 6.

Calculation of the possible number of barbell squats. How to find out how many repetitions of squats a person can perform in one approach with a barbell weighing 65 kg?

Program 8

Пх1 + ПхО ПхД х ПхС + Пх1 х ПхВ  х <-> + ПхА + С/П   БП   ОО

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 8);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter the regression coefficients (-33.93, xPA, 33.16, xPT, 0.965, xPS, 0.03, xPD).
6. Enter the number of squats performed by the student during testing in register O (5, xPO), the weight of the student in register I (80, xGN), the weight of the barbell with which testing was carried out in register 2 (60, xP2), constant 0.667 - to register 3 (0.667, xPZ);
7. Enter the specified weight of the barbell and run the calculator to count (65, C/P). At the end of the count, the number of possible squats with a given weight (3) will appear on the calculator indicator;
8. With a new value of the weight of the bar, proceed to step No. 7;
9. When changing the student, return to point 6.

Methodology for calculating the number of sessions required to achieve the desired level of strength fitness.

The increase in strength during targeted strength training has a pronounced exponential dependence on the number of training sessions performed and can be described by the formula:

Y = ah^b + s

where Y is the magnitude of the force: X is the number of training sessions; a, b, c - empirical parameters (coefficients).

Empirical parameters a, b, c depend on a number of factors: individual characteristics of the trainees (age, body constitution, morphological characteristics, health, mental state, etc.), organization and methodology of the training process.

If you find the values ​​of coefficients a, b, c for a specific person (or group of exercisers), then you can calculate with a high degree of reliability the number of training sessions required to achieve the desired level of strength development.

It should be remembered that establishing an empirical formula makes sense provided that only one method (training system) is constantly used to develop strength, classes are conducted without long breaks, a normal diet and rest regime is organized for the trainees, constant exercise is carried out (at least once every week) control over the development of strength, and the total number of sessions conducted is at least 30.

Let's look at a specific example of the methodology for constructing a mathematical model of the training process. Let's assume that student B trained 4 times a week and at every fifth workout, a 10 RM was determined in the bench press. As a result of regular testing, a time series was obtained that reflects the empirical dependence of strength (in our example, this is 10 RM) on the number of training sessions performed.

where X is the number of the training session at which testing was carried out, and Y is the result shown in the bench press.

Using the values ​​of this time series, we will construct a graph of the dependence Y (see figure):

Using this graph, we will determine the value of coefficient C. To do this, we will find three points on the graph with abscissas X1, X2, and X3 «= √(X1*X2) and ordinates, respectively, Y1, Y2 AND Y3 (points X1 and X2 are chosen arbitrarily).

Let's say in our example X1 = 7, X2 = 37, X3 = √(7*37) = 16, then we get Y1=40, Y2=6O, Y3=48.

Coefficient C is calculated according to the following formula:

C = (Y1*Y2 - Y3*Y3)/(Y1 + Y2 - 2*Y3) = (40*60-48*48)/(40+60-96) = 24

To calculate the coefficients a and b, we turn to the help of a programmable microcalculator (for example, MK-61), for which, based on mathematical formulas, we have compiled program 9.

Since this program finds the values ​​of the coefficients a and b for the relationship Y - aX^b, and the exponential dependence of strength growth on the number of training sessions performed is described by the expression Y - аХ^b + C, then, naturally, aX^b must be equal to Y-C, i.e. it is necessary to first transform the time series by subtracting from each Y value the value of the resulting coefficient C:

X

2

7

12

17

22

27

32

37

42

Y-C

11

16

21

26

26

31

33,5

36

36

Program 9

B^ ПхД х ПхС + хП4 <-> ПхО <-> - ПхД х Пх1 х Пх4 + С/П   БП  ОО

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 9);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter the data in the following order: N, S/P, X1, S/P, Y1, S/P, X2, S/P, Y2, S/P, ... Xn, S/P, Yn, S/P. For our example, the following occurs: 9, S/P, 2, S/P, 11, S/P, 7,. S/P, 16, S/P, etc.; N is the number of pairs of X, Y values;
6. After entering all the X and Y values, the value of coefficient a will appear on the calculator indicator. To obtain coefficient b, you must press the keys Px, B.

In our example, a=7.808; b=0.411.

Then the mathematical model of the training process under study will take the form:

Y = 7.808 * X^0,411*+24, from where

X = ^0,411√((Y-24)/7.808)

Using the above mathematical model of the training process for student B, you can find answers to the following questions:

1. What will be the level of 10 RM in this exercise for this practitioner after n training sessions?
2. How many training sessions do you need to carry out in order for his 10 RM value in this exercise to reach the planned value?

For example, what value will 10 RM be for exerciser B after 50, 60 and 70 workouts?

Substituting the formula Y = 7.808 * X^0,411+24 corresponding values ​​of X, we obtain at X=50 Y=63 kg, at X=60 Y=66 kg, at X=70 Y=68.8 kg.

If you need to find out how many training sessions you need to do to achieve a level of 10 RM (let's say 65, 70 or 75 kg), you need to use the formula:

X = ^0,411√((Y-24)/7.808)

1. at Y = 65 kg X = 56.6 ~ 57 workouts
2. at Y = 70 kg X = 74.8 ~ 75;
3. at Y = 75 kg X = 96.2 ~ 96.

By using a programmable microcalculator, you can significantly simplify the calculation process using the formula: Y = aX^b +Cusing program 10.

Program 10

B^ ПхД х хП4 <-> ПхС х ПхО ПхД х ПхС + Пх1   х <-> Пх4 + С/П    БП   00

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 10);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter parameter a into register “A” (xPA), parameter b into register “B” (xPV), parameter c into register “C” (xPS).
6. Enter the value X on the keyboard. Press the S/P key. At the end of the count, the indicator will display the Y value expected at the X workout.
7. To find the Y value for other X values, proceed to step No. 6.
8. When carrying out calculations for another student, proceed to step No. 5.

For calculations using the formula: X = ^IN√((Y-C)/a) a program for calculating loads No. 11 is required

Program 11

ПхД х ПхС + ПхО ПхД х ПхС + Пх1    X <-> + С/П БП ОО

Instructions:

1. Enter programming mode (F, PRG);
2. Enter the program (according to the text of program 11);
3. Switch to automatic operation mode (F, AVT);
4. Clear command counter (C/O);
5. Enter parameters a into register “A” (xPA), parameter b into register “B” (xPV), parameter c into register “C” (x PS);
6. Enter the value Y on the keyboard. Press the S/P key. At the end of the count, the X value will appear on the indicator, at which the required Y value will probably be achieved;
7. To find the X values ​​at which other Y values ​​will be achieved, proceed to step No. 6;
8. When carrying out calculations for another student, proceed to step No. 5.

The correlation analysis between the actual values ​​of 10 PM and the values ​​obtained analytically revealed a high correlation (0.992). In this case, the coefficient of determination (D = 0.992² * 100% = 98.4) indicates that the mathematical model we found is 98.4% correctly describes the relationship between 10 RM and the number of training sessions using this method. If testing is carried out regularly under the same conditions and there are no errors in the calculations, the derived mathematical formula quite accurately reflects the course of the training process. In our practical work coefficient of determination did not fall below 90%.

Thus, using the empirical formula Y = aX^b + C, it is possible to extrapolate, i.e. predict strength growth when choosing new training methods, perform calculations of the required number of training sessions using the applied method to achieve the planned result, carry out an individual approach to each student, more effectively solve the problems of managing the educational and training process, based on scientific based on planning, setting long-term goals and objectives for strength training.