# Method of measuring speed of motion of pedestrian before run-over of transportation vehicle

FIELD: measurement technology.

SUBSTANCE: method can be used for criminal and official inquires of road accidents. Method is based upon measurement of speed of pedestrian and calculation its arithmetical mean. Method differs from known ones, as speed of motion is measured experimentally 10 to 30 times with three different pedestrians having like age and physical condition as victim of run-over. Results are processed as small sample by using central deviations and those deviations are used to determine average meaning of speed of motion, standard deviation, error and truth of the average mean. Upon finding truth of average mean the necessary number of trials is calculated which number has to be compared with real number of trials. Additional trials are conducted if necessary. Factor of truth of experimental data is calculated from speeds of motion of pedestrians taking part in experiment. Probability and factor of confidence is determined accordingly to speed of motion of injured person and speeds of motion of pedestrians involved into experiment, as well as according to truth of preset limit values of this parameter. If values of preset factors correspond to legitimate values or limits admitted for investigation of road accidents, statistically true minimal and maximal values of speed of motion of injured pedestrian are calculated on the base of normal distribution law by means of subtraction the speed from its average value and addition of product of factor of confidence with standard deviation. Limit values of speed of motion of injured pedestrian are presented for forensic examination to make calculations determining availability or lack of availability of prevention of run-over. For this purpose the statistically truthful minimal and maximal values of speed of motion of injured pedestrian should be calculated in relation to accessible values or limits of probability which is higher than 0,95 and if confidence with speed of motion of injured pedestrian and pedestrians involved into experiment correspond to each other. Preset precision of pedestrian's speed of motion should be within limits of +-0,5 km/hour.

EFFECT: improved precision of measurement; higher probability of prevention of road accident.

2cl, 2 tbl

The invention relates to medicine, namely to psychophysiology, and can be used to determine the speed of movement of pedestrian collisions before him the vehicle in criminal and internal investigation of road traffic accidents (RTA). Criminal investigation accident investigation is MIA and Prosecutor's office and investigation - motor transportation enterprises, organizations and other

The speed of pedestrian collisions before him the vehicle is crucial in the investigation of an accident to establish the presence or absence of the possibility of preventing the driver of the accident. Sometimes the change in the value of this parameter even by 0.5 km/h can lead to the opposite conclusion about the presence or absence of the possibility of preventing a collision of the vehicle with a pedestrian. And this in turn will lead to conviction of the innocent driver or to excuse the guilty.

The results of the patent search showed that the determination of the speed of pedestrian collisions before him the vehicle at the invention level is still not considered. Therefore aligning and description of prototype or analogue is not possible.

To address this question at the present time, it is recommended to use speed peshehoda the data, established by the research, for example, the Leningrad NILSA in 1966, speed children - according to the Central forensic laboratory in Moscow, established in 1960, it is Recommended to use the data about the speed of movement of pedestrians and children are listed in other technical literature, for example the book Illarionova VA Examination of road accidents. - M.:Transport,1989. - 254 S., and others

Practiced also view the result on the judicial technical expertise to the speed of the pedestrian established experimentally with another pedestrian the same age as the victims. For this investigation is an experiment in the same conditions, with a threefold repetition and is determined by the arithmetic mean value of the speed of the pedestrian, which is represented on the judicial technical expertise.

Is obvious and does not require proof of a fact that cannot be applied in the expert calculations to establish the presence or absence of the possibility of preventing a collision of a vehicle-pedestrian accident data on its speed, taken from the technical literature, for example, installed in Leningrad and Moscow 33-39 years ago, because no one, including the investigator, will not be able to prove that the injured pedestrian motor is the very precisely with such speed. Therefore, the investigator is not entitled to submit such data on the speed of the pedestrian in the judicial technical expertise, and exports may not perform calculations to determine the possibility or impossibility of preventing a collision of the vehicle with a pedestrian with these data, and taking them at the discretion of the technical literature.

As we can see from the proposed method, without mathematical treatment received by experimental values of the speed of the pedestrian is also not apply to expert estimates its average value. This is due to the fact that experimental determination of the speed of the pedestrian, we are dealing with random variables, because the involved experiments pedestrians can't accurately reproduce the actual value of the speed of movement of the affected foot. Therefore, in the expert calculations can be used only statistically significant limit values - minimum and maximum values of speed of movement covered by the experiments of pedestrians within which likely will be the actual speed of motion of the injured pedestrian.

The aim of the invention is to improve the accuracy of determining the speed of movement of pedestrian collisions before him transport among the STV to establish the presence or absence of the possibility of preventing the accident.

This goal is achieved by the proposed method, which is carried out as follows. The consequence conducts investigatory experiment 10-30 times with three pedestrians of the same age and the same physical development with the victim, by definition, its speed, the rate of which is established by the testimony of the driver and witnesses or witnesses. The results of the experiments are treated as a small selection using Central deviations by which to determine the average speed, standard deviation, coefficient of variation, or variation, the average error, the accuracy of the experience or the percentage of error of the experiments and the reliability of the average value. When revealed the reliability of the average value calculate the required number of experiments that compared with them actually carried out and if necessary, conduct additional experiments. Then calculate the coefficient of reliability of the experimental data on the speed of movement covered by the experiments pedestrians, determine the probability and the percentage of confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the credibility of the established limit values for this parameter. If the values specified probability is of pokazateli accepted for criminal and internal investigation of traffic accidents their valid values or limits calculated on the basis of the law of normal distribution, which controls the speed of the pedestrian, a statistically significant minimum and maximum values of the velocity of motion of the injured pedestrians by subtracting its mean value and adding to it the product of coefficient of reliability by the standard deviation. Set the limiting value of the velocity of motion of the injured pedestrians present at the judicial technical expertise to produce calculations to determine the presence or absence of the possibility of preventing a collision of the vehicle with a pedestrian.

To obtain these statistical and probabilistic indicators used books: Butler M. Handbook on variational statistics. - Yoshkar-Ola: PLTI, 1961. - 99 si, Garman VE, probability Theory and mathematical statistics. - M.: Higher school, 1977. -479 C. Can be used also any other books that outline mathematical statistics and probability theory, for example, Urbach VY Statistical analysis in biological and medical research. - M.: Medicine, 1975. - 295 S. and hares I.A. Higher mathematics. - M.: Higher school, 1991. - 399 S. and others

The proposed method and the establishment of subordination to the speed of the pedestrian in a normal distribution of frequencies is based on the author of numerous experts the mental research this option from pedestrians of different age groups, in various road conditions and rate of speed. Was conducted 4585 experimental determinations of the speed of movement of pedestrians. For Providence studies were designed and manufactured photoelectric sensor device and an electric savesee device that worked with svetlucavi oscilloscope To-5-22. The results of these experimental studies were published in two monographs author “Organization of safe traffic at road junctions and pedestrian crossings”. - Kazan: Publishing house of Kazans. University, 1991. - 135 C., “Organization and traffic safety”. - Kazan: Publishing house of Kazans. University, 1993. - 127 S., dissertation and thesis for the degree of doctor of technical Sciences (1998).

Data of the pilot study were subjected to mathematical processing on the computer. Submission to the speed of the pedestrian in a normal distribution of frequencies established using criteria consent of Pearson and V. Romanovsky known in mathematical statistics methods.

Obeying the speed of movement of pedestrians in a normal distribution of frequencies allows to determine the results of experimental studies of statistically valid minimum and maximum values of this parameter.

Example. Held on 25 definitions karasti movement three pedestrians and obtained the following data: 9,5; 8,8; 10,2;9,5; 9,1; 7,9; 8,8; 9,7; 9,5; 9,2; 9,0; 8,1; 9,5; 8,9; 10,3; 9,6; 9,8; 10,0; 9,2; 9,4; 8,7; 8,8; 9,5; 9,8; 10,2 km/h Given the data in table 1, we find the sum of the set values, the Central problems and their squares.

Defined statistics:

The average value

where ΣX_{i}- the sum of the speeds of movement of pedestrian, km/h;

n is the number of experiments;

To determine the Central variance use the expression

for example, the first speed it will be α=9,5-to 9.32=0.18 km/h standard deviation

The coefficient of variation or variations

With up to 5% variation is considered to be weak, 6-10% - moderate, 11-20% is significant, 21-50% - large, greater than 50% is very large.

Error of the mean0,136 km/h

The percentage of error experiments

Reliability medium

if t_{c}equal to or greater than three, then the parameter value is a reliable, accurate and can be used for various comparisons and conclusions. In this example, t_{c}=68,5>3, therefore the average value reliably.

The required number is the number of experiments to obtain statistically reliable values of the speed of the pedestrian is determined only when the reliability of the average value, using the formula

where t is the coefficient or confidence score; with probability, for example, to 0.68; 0.95 and 0,997 t respectively equal to 1; 2 and 3;

m_{3}- specified accuracy km/h

Given, for example, a probability of 0.95 and an accuracy of 0.3 km/h determined the required number of experiments

which is less than the number. Therefore, a sufficient number of experiments. It should be stated that the greater the accuracy will be specified in the calculations, the more experiments need to spend. So, if m_{3}in this example, is equal to 0,2 km/h, then N will be 46 when m_{3}=0,1 km/h 185 experiments. If you ask less accuracy, the number of experiments will require less, for example, in this example, when m_{3}=0,4 km/h - 12, m_{3}=0.5 km/h - 7.

Here we can note that, for the criminal and internal investigations of accidents, you must accept the possibility of not less than 0.95 and given the precision of the experimental data when determining the speed of the pedestrian is not more than ±0,5 km/H. This means that the values of the majority (more than half) experimentally certain speeds, pedestrians should not differ from their mean by more than the specified accuracy of ±0.5 km/H. If this condition is e runs you need to increase the number of experiments. This method is recommended as a criterion for a preliminary assessment of the required number of experiments.

If we apply this criterion to our example above, it turns out that only in 9 cases out of 25 average speed of pedestrians (to 9.32 km/h) differs from the experimentally derived velocities on the value of ±0.5 km/h (for example, to 9.32-10,2=-0,88 km/h; to 9.32-7,9=1,42 km/h and so on). This suggests that the probability of matching the speeds of the victim and covered by the experiments pedestrians will be more of 0.95, which, as will be seen, is confirmed by our subsequent studies and is 0,9997.

Next, determine the coefficient of reliability of the experimental data, for which formula N is solvable relative to t, replacing it N actually conducted a number of experiments N_{f}i.e.

Substituting in this formula the corresponding value: N_{f}=25; m_{3}=±0.5 km/h, σ=0,68 km/h, installed that

The obtained value of t corresponds to the probability 0,9997 (smfbl). Therefore, confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability of installed prodelin the x value of this parameter is of 99.97%.

Thus, a statistically significant minimum and maximum values of the velocity of motion of the injured pedestrians were

i.e. with the confidence of 99.97% can be argued that the speed of movement of the injured pedestrian was within 6,82...11,82 km/h

Note for use in table 2 given probability values and percent assurance that the velocities are affected and covered by the experiments of pedestrians, as well as the correctness of the limit values of this parameter for different values of the coefficient or index of reliability of the experimental data t. Are given in table 2 probability values at the respective reliability coefficients taken from the book of Garman VE, probability Theory and mathematical statistics. - M.: Higher school, 1977. - S. 479,

and the percent assurance that the velocities are affected and covered by the experiments of pedestrians, as well as the reliability of the established limit values for this parameter recalculated by us.

Now we will show an example of solving the issue in triplicate experiments to determine the speed of the pedestrian. Suppose that you have the following values when Oreste pedestrian movement: 7,9;
of 9.4 and 8.9 km/H. Treating the above method, set the following statistics: average=8.7 km/h; standard deviation σ=±0,75 km/h; the coefficient of variation or variations From=8,62%; average errorthe percentage errors of the experiments P=4,98%; reliability medium t_{c}=20,1; 20,1>3, therefore the average value reliably.

With probability of 0.95 and the specified accuracy±0,5 km/h, using the above formula N, we establish that the required number of experiments will be

and there were just 3 of the experiment.

The fact that not a sufficient number of experiments can be set also by applying the above criteria for preliminary evaluation. As can be seen from the set of experimental data, two of the three speeds of pedestrians to 7.9 and 9.4 km/h differ from their mean by 8.7 to 7.9=0,8 km/h and 8.7-9,4=a-0.7 km/h, which is greater than the specified accuracy ±0,5 km/h, i.e. fails the criterion of the preliminary assessment of the required number of experiments. This, as pointed out above, suggests that the probability of matching the speeds of the victim and covered by the experiments of pedestrians is less than 0,95. Looking ahead, we should specify that this probability is the outer coat will be only 0,754, which will be established below.

The value of the coefficient or index of reliability of the experimental data, calculated by the formula t, is

The obtained value of t corresponds to the probability 0,754 (smfbl). Therefore, confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability limit for this parameter is 75.4%.

Thus, a statistically significant minimum and maximum values of the velocity of motion of the injured pedestrian in this case are

that is, with the confidence only 75.4% can be argued that the speed of movement of the injured pedestrian was within 7,83...9.75 km/h

We will show another example of solving the issue at tenfold repetition of experiments to determine the speed of the pedestrian. Set the following values speed two pedestrians: 8,5; 8,8; 9,2; 9,5; 8,1; 7,9; 7,8; 9,7; 8,5; 9,2 km/h Obtained the following statistics: averagestandard deviation σ=±0,67 km/h; the coefficient of variation or variations From=7.68 per cent; the average errorthe percent error of the experimental is tov P=2,43%;
the reliability of the average t_{c}=41,1; 41',1>3, therefore, the average value reliably. With probability of 0.95 and the specified accuracy ±0.5 km/h the required number of experiments N=7. Conducted 10 experiments, hence their number is sufficient.

This conclusion could not be done after mathematical processing of experimental data, applying the above criteria the preliminary assessment of the required number of experiments. As you can see, only half of the experimental data differ from their mean by more than ±0,5 km/h: 8,72-8,5=0,22; 8,72-8,8=-0,08; 8,72-9,2=-0,48; 8,72-9,5=-0,78; 8,72-8,1=0,62; 8,72-7.9=0,82; 8,72-7,8=0,92; 8,72-9,7=-0,98; 8,72-8,5=0,22; 8,72-9,2=-0,48 (smodern values). This shows that a sufficient number of experiments.

The value of the coefficient or index of reliability of the experimental data, calculated by the formula t, in this case, is

which corresponds to the probability 0,982 (smfbl). Therefore, confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability limit for this parameter is to 98.2%.

Thus, a statistically significant minimum and maximum values of the velocity of motion of the injured pedestrian in this case with the U.S

i.e. confidence level 98.2% can be argued that the speed of movement of the injured pedestrian was within 7,14...10,30 km/h

Based on the above, we conclude that to avoid the investigative and judicial errors must be taken in the expert calculations to establish the presence or absence of the possibility of preventing a collision of the vehicle to the pedestrian, not the data from the technical literature and the average speed of the pedestrian is determined as the arithmetical mean value in triplicate, and statistically valid minimum and maximum values obtained by mathematical processing of the experimental data with valid values or limits the likelihood of not less than 0.95 and confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability of the established limit values for this parameter, not less than 95% and given accuracy for the experiments the speed of the pedestrian, not more than ±0,5 km/h

The judicial technical expert must make calculations for establishing the presence or absence of the possibility of preventing a collision of the vehicle with a pedestrian in two versions - with a statistically significant minimum is Oh and maximum values of the speed of the pedestrian. A definitive conclusion about the presence or absence of the possibility of preventing the incident may be made only if the minimum and maximum values of the velocity of motion of the injured pedestrian obtained the same conclusions.

The investigator is obliged, first, to provide expert installed above-proposed method statistically significant minimum and maximum speed not less than three pedestrians on the results of 10-30 measurements indicating the probability and percent assurance that the velocities are affected and covered by the experiments of pedestrians, as well as the reliability of the established limit values for this parameter; the rate of speed of the injured pedestrian is established by the testimony of the driver, witnesses or witnesses; second, to require the expert opinion in two variants; and third, to make a definitive conclusion about the direct cause of the accident only with the same conclusions expert on the presence or absence of the possibility of preventing a collision of the vehicle with a pedestrian in both variants of calculation.

If the investigator is not able to establish a statistically valid minimum and maximum values of the speed of the pedestrian according to the investigative judge is of riment proposed above, for the calculations it can formally invite the engineer or mathematician, who should participate in the experiments, since the required number of experiments should be designed immediately after this proceeding, if necessary, can be repeated experiments with the same pedestrians.

The calculation of a statistically valid minimum and maximum values of the speed of the pedestrian according to the investigative experiment can be charged and also the expert, giving him the question and presenting the measurement results obtained during the experiments. In this case, you should check the required number of experiments, using recommended above criteria preliminary assessment of this indicator, according to which value more than half of the experimentally derived velocities pedestrians should not differ from their mean by more than the specified accuracy of ±0.5 km/H. If you do not complete this requirement, it may happen that the expert will not be able to draw conclusions about the presence or absence of the possibility of preventing accidents with a probability of at least 0.95 and confidence in accordance velocities are affected and covered by the experiments pedestrians, and reliability set the certain limiting values of this parameter will be less 95%. As we saw in the above second example, the three-time repetition of determining the speed of the pedestrian specified probabilistic indicator was 0,754 and 75.4%.

In conclusion, we can note that, as in the conclusions of the expert about the presence or absence of the possibility of preventing the incident and the findings of the investigator about the guilt or innocence of the driver committing a traffic accident must be specified probability and the percentage of confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability limit the value of this parameter. In the conclusions of the expert must be specified, for example, that with a probability of at least 0.95 and confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability limit the value of this parameter is not less than 95% to be approved, which in this case had or did not have the possibility of preventing a collision of the vehicle with a pedestrian. Or here is another variant of the example with a probability of only 0,65 and confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability of the established limiting values of this parameter, only 65% stated that in this case there was or not they are the moose is possible to prevent a collision of the vehicle with a pedestrian. In its conclusions on the establishment of the guilt or innocence of the driver of the vehicle, the investigator must also specify the above probabilistic indices.

As can be seen from the above, depending on presents the result data of the judicial technical expertise, these probabilistic metric can be significantly less than their valid values or range - 0.95 and 95%, which should be taken into account when assessing the consequence of the reliability and credibility of forensic technical examination and justification of conclusions about causality and direct cause of the accident, as well as in assessing their judicial authorities.

1. The method of determining the speed of movement of pedestrian collisions before him the vehicle, including the measurement of the speed of the pedestrian and the establishment of its average value, characterized in that conduct experimental determination of the speed 10-30 times with three pedestrians of the same age and the same physical development with the victim, treat the results as a small selection using Central deviations by which to determine the average speed, standard deviation, error, and accuracy of the average value, the detection reliability of the mean of the races is cityway the required number of experiments, that could be compared with them actually carried out and if necessary, conduct additional experiments, calculate the coefficient of reliability of the experimental data on the speed of movement covered by the experiments pedestrians, determine the probability and the percentage of confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability of the established limit values for this parameter, if the values of these probability rates adopted for criminal and internal investigations of traffic accidents their valid values or limits calculated on the basis of the law of normal distribution statistically valid minimum and maximum values of the velocity of motion of the injured pedestrians by subtracting its mean value and addition works with him the reliability coefficient by the standard deviation and represent the judicial technical expertise limit value of the speed of movement of the injured pedestrian to produce calculations to determine the presence or absence of the possibility of preventing a collision of the vehicle with a pedestrian.

2. The method of determining the speed of movement of pedestrian collisions before him transport is the means by p. 1, wherein to establish the presence or absence of the possibility of preventing a collision of the vehicle with a pedestrian in criminal and internal investigation of traffic accidents to determine a statistically valid minimum and maximum values of the velocity of motion of the injured pedestrians with valid values or limits the likelihood of not less than 0.95 and confidence in accordance velocities are affected and covered by the experiments of pedestrians, as well as the reliability limit for this parameter is not less than 95% and the given accuracy for the experiments to determine the speed of the pedestrian is not more than ±0,5 km/h

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