#### Задолго до образования компании Taser int., которая сегодня является практически монополистом, лидирующей на рынке полицейского ЭШ оружия в США была фирма «NOVA», выпускавшая (и по сей день выпускающая) контактные эшу. Наиболее известной в то время была модель XR5000 — примерно так же, как Taser X26 сейчас. И естественно, NOVA, как и тазер в настоящее время, подвергалась различным нападкам правозащитников и СМИ, о якобы повышенной опасности шокеров и тяжелых последствиях для здоровья. Чтобы отбиться от этих нападок фирма заказывала и публиковала биомедицинские исследования, доказывающие безопасность ЭШУ. В них, в основном, для наглядности, приводится сравнение воздействия ЭШУ с ударом «от розетки», т.е. от бытовой электросети частотой 60гц и напряжением 110в.

Изучая эти материалы, можно почерпнуть массу полезной информации об измерении и оценке характеристик ЭШУ, о приведении импульсных токов к более «понятным» величинам. Ниже приводится исследование NOVA XR-5000, выполненное Т. Бернштейном в 1985г, в котором речь идет в основном о физических характеристиках ЭШУ. Материал приводится в полном и отформатированном виде, восстановлены формулы и таблицы. Взято когда-то давно с официального сайта новы.

#### EVALUATION OF THE ELECTRIC SHOCK HAZARD FOR THE NOVA XR 5000 STUN GUN

Theodore Bernstein, Ph.D. Professor of Electrical and Computer Engineering University of Wisconsin-Madison January 22, 1985

**INTRODUCTION**

The design of most electrical equipment ensures that an individual should rarely contact energized parts and be subjected to electric shock. For such equipment electrical safety is provided primarily by insulation or guarding to prevent contact and by suitable grounding. Any contact with energized parts is considered hazardous. There are other equipment where, even though it may not be intended, contact with energized parts is expected so that the electrical safety must be provided by ensuring that any possible electric shock will not be hazardous or lethal. Examples of such electrical devices are the electric fence, medical electrical nerve stimulators, welder, cattle prod, and fly electrocuter. The Nova XR 5000 stun gun is an example of a new device where individuals are deliberately subjected to electrical shock. The XR 5000 is a small, hand-held device powered by a 9V battery. There are two small probes extending from the front approximately 5 millimeters, 2 inches apart. The probes are intended to be pressed into an attacker’s body so that an electrical shock can be delivered to incapacitate the attacker. It is important that the attacker not be injured, as this is one of the major advantages of the device. This report evaluates the safety of the shock delivered by the XR 5000. This is done by analyzing the output current waveform and comparinq this shock to known safe and hazardous shocks. Safety criteria for the electric fence are used to compare the shock delivered to that delivered by the XR 5000.

**ABSTRACT**

The electric shock hazard for the XR 5000 is determined by comparing the shock delivered to the known effects of a 60 Hz shock. With 60 Hz shocks a current of 1 mA is at the threshold of perception, 5 mA is at the let-go current level where shocks are painful but not dangerous, and 50 mA is the level where ventricular fibrillation and death can occur. The XR 5000 output is a train of damped, sinusoidal pulses with an approximate 10 u s time constant. The true r.m.s. value of the output is not a valid indication of the hazard because the output contains frequency components well above the 1 kHz frequency above which the effect for a given frequency component is reduced. When these factors are considered, the output for the XR 5000 is in the 3 to 4 mA range of an equivalent 60 Hz shock and is not dangerous. The fact that the shock is delivered between two probes 2 inches apart adds to the safety because the current is concentrated in the region of the body between the two probes and only a negligible current can reach the heart.

**SINUSOIDAL, 60 Hz SHOCKS**

Electrical shocks involving alternating current have been investigated since before 1890 (Bernstein, 1975). Most of the recent studies have involved sinusoidal, 50 or 60 Hz currents, though the effects of other frequencies and waveforms have also been studied. This report compares the shock delivered by the XR 5000 to an equivalent 60 Hz shock. In order to do this, the effects of 60 Hz shocks are reviewed.

**Threshold of Perception**

For 60 Hz shocks, the lowest level of current that can be a problem is the threshold of perception level. This level, where some people may feel a slight tingle but should have no extreme startle reaction, Is usually con sidered to be 0.5 mA r.m.s. for 60 Hz currents and is the maximum allowa ble leakage current for appliances (ANSI, 1973). Dalziel and Mansfield (1950) have determined that the median threshold of perception current at 60 Hz was 1.067 mA for 28 men and 1.18 mA for four women. Shocks near but above the threshold of perception current may be a hazard because of injury caused by the startle reaction producing a dangerous body motion. **Ventricular Fibrillation** At the other extreme is the level of current where the heart may be thrown into ventricular fibrillation and death occurs. For shocks between any two limbs, Biegelmeier and Lee (1980) have re-evaluated experimental data on ventricular fibrillation induced by electrical shock in animals and related the results to the physiological response to electrical shocks. For short duration shocks shorter than a cardiac cycle, the electrical current to cause fibrillation must be large and occur during the vulnerable period, T wave. Shocks longer than a cardiac cycle can cause premature ventricular contractions that lower the shock threshold current to a minimum after four or five premature ventricular contractions. Using these concepts, a safe current limit has been established as 500 mA for shocks less than 0.2 seconds in duration and 50 mA for shocks longer than 2 seconds. For shocks between 0.2 and 2 seconds, the safe current is given by the expression

**I = 100/T mA r.m.s. (1)** where T is in seconds and 0.2 s < T < 2 s.

**Let-Go Current**

The let-go current level of shock is not immediately lethal as is the ventricular fibrillation level. At this level of shock, with a current path through the arm, the individual cannot let go of an energized conductor. This level is hazardous in that a person is receiving a very painful shock from electrical equipment that he cannot release. Such a long duration shock may eventually become hazardous because of evoked heart arrhythmias or a decrease in contact resistance because of perspiration or burns allows greater currents. Dalziel and Massoglia (1956) have determined that the 60 Hz let—go current level where 0.5% of the individuals cannot let-go is 9 mA for men and 6 mA for women. The median let-go level is 16 mA for men and 10.5 mA for women. The let-go level where 99.5% of the individuals cannot let-go is 23 mA for men and 15 mA for women. Underwriters Laboratories (1972) requires that the ground fault circuit interrupter trip with long duration shocks greater than 6 mA as most people can let-go at currents less than 6 mA. The electric fence controller (Underwriters Laboratories 1980) is designed so that any single controller failure will not produce a continuous current greater than 5 mA because of the let-go problem. Currents above an individual’s let-go current level could be hazardous and painful because the individual would be frozen to the circuit.

**EFFECT OF FREQUENCY**

The frequency of the electrical current is important in determining the effect on the human body of a given magnitude of current. When testing appliances or medical devices for leakage current, test loads have been devised which are supposed to simulate the response of the human body to the various frequency components in the leakage current. In order to do this, an electronic voltmeter is connected across the simulated load in such a fashion that a given reading of the voltmeter at any frequency is equivalent to the same effect shock. Underwriters Laboratories (1976) specifies a test load to measure leakage current such that the allowable leakage current is the same for all frequencies to 1 kHz. The allowable leakage current is increased directly proportional to the frequency for frequencies higher than 1 kHz up to 100 kHz. Above 100 kHz the allowable leakage current is the same as at 100 kHz——100 times the value at 1 kHz.The equivalent dc shock current for the same effect is taken as 40% larger than the 60 Hz current. The ANSI/AAMI (1978) test load is similar. There is a question as to whether the effect on the human body of a shock from a non-sinusoidal, periodic waveform can be considered the same as the effect of each individual frequency component effect summed appropriately. Until further data are available, there is no other way to analyze a non-sinusoidal, periodic waveform.

**THE ELECTRIC FENCE TRAIN OF PULSE SHOCKS**

The electric fence controller (Underwriters Laboratories, 1980) provides a basis for determining what is considered a safe electric shock for a train of pulses. The electric fence has been used for many years with the realization that humans will contact the fence but must not be injured. The controller delivers a pulse type output with the output during the «on time» being of the peak discharge-type output or of the 60 Hz sinusoidal-type output. All tests for the controller are performed with a 500 ohm load. The «off period» for the controller must be greater than 0.9 s for a sinusoidal type output or greater than 0.75 s for a peak discharge-type output. This «off period» is essential to allow an individual to get off the fence as the output during the «on period» is greater than the let-go current level. Continuous output is not permitted. Any single failure in the controller must not produce a continuous current greater than 5 mA. The «on period» for peak discharge-type controllers must be less than 0.2 seconds. For this peak discharge-type controller, the output delivered to a 500 ohm load during the «on time» is limited to a given value of milliampere-seconds, charge, depending on the length of the «on period.» The curve for the «on period» for peak discharge-type controllers provides allowable milliampere-second values for the time period from 0.03 s to 0.1 s. For «on periods» from 0.1 to 0.2 seconds the allowable output is 4 mA-s. The allowable output is reduced to 2 mA-s for a 0.03 second «on period.» For sinusoidal-type output the «on period» must be less than 0.2 s. For «on periods» between 0.025 s and 0.2 s, the allowable current must be less than

**1 = 75 — 350T mA r.m.s.**

where T is the «on period» in seconds. For «on period» between 0.025 s and 0.2 s, equation (2) allows sinusoidal type r.m.s. currents between 65 and 5 mA. These values are well below the 500 mA level considered dangerous for a single shock of such duration. It is important to note, however, that the fence controller produces a train of pulses rather than a single pulse. Noting that the pulse repetition frequency for the sinusoidal-type pulse is approximately 1 Hz, the true r.m.s. current can be calculated for different pulse «on periods» when the r.m.s. value of the current during the pulse is given by equation (2). The results for pulse width between 0.025 s and 0.2 s are given in Table 1

Pulse Width (T) | True r.m.s. Current (s) (mA) |

0.025 | 10.47 |

0.05 | 12.84 |

0.07 | 13.34 |

0.10 | 12.62 |

0.15 | 8.65 |

0.2 | 1.9 |

This indicates that the highest output current is about 13 mA which is above the 60 Hz let-go current for some individuals. The current should not electrocute a person at this level. There still is a question as to whether the true r.m.s. current given in Table 1 can be equated to the effect of 60 Hz currents. The pulse train will have frequency components above 1 kHz. To study the frequency components for the pulse train the Fourier spectrum (Cooper, 1967) for a single pulse is calculated. Because the pulses are periodic with a frequency of 1 Hz, the amplitudes for the individual harmonics are proportional to the value of the Fourier spectrum at discrete frequencies starting at 1 Hz and at all higher frequencies separated by 1 Hz. The peak discrete frequency component is 2/t times the Fourier spectrum value at that frequency where T is the period for the pulses in seconds. Above 1 kHz the effect of the frequency components on the human body decrease inversely proportional to the frequency. Using the Fourier spectrum and the decrease in effect of the shock for frequencies above 1 kHz, the effective r.m.s. current for the n’th harmonic is given in equation (3)

**I n = (75-350T) T ( [sin(n-60 π T / (n-60) π T] + [ sin(n+60) π T / (n+60) π T] ) x {1+(n/105)2}(1/2) / {1+(n/103)2}(1/2) mA r.m.s.**

where n is the harmonic and, in this case, its frequency (n = 1,2,3,—); T is the «on period» in seconds; and the frequency of the sinusoidal output during the pulse is 60 Hz. Above 1 kHz, equation (3) indicates that the harmonics are small and falling off rapidly so that the frequency components below 1 kHz are the most prominent. Thus, the true r.m.s. current values in Table 1 are equivalent to the 60 Hz values as far as effect on the human body is concerned.

**NOVA XR 5000 SHOCKS**

The Nova XR 5000 has an output consisting of a train of damped sinusoidal pulses. The current output depends on the electrical resistance between the probes. This will vary depending on the type of contact and whether the shock is delivered through clothes. In comparing current levels between the output of the XR 5000 and the previously discussed physiological effects it is important to take into account the path of the current. Ventricular fibrillation is caused by current traversing the heart. The XR 5000 has a very well defined path between the two closely spaced probes. The current delivered to the heart will be negligible. This makes discussing lethality using the total current a technique that provides an extra margin of safety. Medical inspection of volunteers undergoing XR 5000 shocks revealed no clinically significant changes to their E.K.G. The action of the XR 5000 in causing muscle contraction shows an action much like the let-go phenomenon. In the arm currents of 5 to 10 mA cause this effect. The XR 5000 is battery operated and ungrounded. Any electrical current will only travel between the two probes. A user holding the device and contacting ground with his other hand will receive no shock, as he is not in the current path between the probes.

**Output Voltage Waveform and Parameters**

The output voltage waveform for the XR 5000 consists of a train of damped sinusoidal pulses where each pulse is of the form

**v(t) = Vo (e )(-t/T) sin ωdt V**

the pulse repetition frequency is 16 Hz. From oscilloscope traces of the output voltage for various resistance loads, the parameters in equation (4) can be evaluated. The time constant T, and the frequency, ωd can be measured directly from the trace. V0 is calculated by finding the time, for the first voltage peak and the magnitude of the first voltage peak,Vp from the trace and then using **Vp =Vo e(-tp/T) sin ωd tp V**to find Vo. Using the output voltage traces for loads of 200, ‘160, and 1020 ohms the parameters shown in Table 2 were determined.

Load resistance (ohms) | Vp (V) | tp (µs) | Vo (V) | ω(d) (rad/s) |

200 | 1500 | ← 2.5 | 2000 | ← 7 * 105 → |

460 | 4000 | → 2 T (µs) | 5000 | 6.28 x 105 fd (kHz) |

1020 | 8000 | ← 10 | 10,000 | ← 111.4 |

1700 | 13,000 | → 8 | 17,600 | → 100 |

Using the values from Table 2, the r.m.s. output current for a pulse train of damped sinusoids with a repetition frequency of 16 Hz can be calcu lated and are shown in Table 3.

Load Resistance (ohms) | Effective current r.m.s. (mA) |

200 | 62.6 |

460 | 68.0 |

1020 | 61.4 |

1700 | 57.4 |

The effective current shown in Table 3 could be hazardous if they were at 60 Hz; however, the output pulses contain high frequency components which are much less lethal than 60 Hz currents. It is necessary to consider all the frequency components for the pulses using a suitable weighting factor.

**Frequency Components in XR 5000 Output**

The XR 5000 output is a train of damped sinusoidal pulses of the form** **

**v(t)=Voe-at sin ω dtV**

The Fourier series frequency components for the train of damped sinusoidal pulses are obtained from the Fourier spectrum (Cooper, 1967) for the single damped sinusoidal pulse of equation (6) and is:

**F(jw) = Vo ω d/{(jw)2 + 2a(j ω + (a2 + ω d2)}** where a = 1/T = 105s-1th

Equation (7) can be recognized as a second order system with the following parameters Undamped natural frequency

**(ωn) = ( a2 + ωd2 )1/2 = 7.07 x 105 rad/s**

or Undamped natural frequency **fn = 112.5 kHz** and Damping ratio **ζ = a/ ωn — 0.14**

Since the bandwidth for such a system is approximately 172 kHz, the spectrum has significant high frequency components within the bandwidth, but these are above the 1 kHz frequency so the effects of electric shock on the human body for a given magnitude current are reduced. Because the damped sinusoidal pulses are periodic with a frequency of 16 Hz, the r.m.s. values for the Fourier series harmonics are proportional to the value of the Fourier spectrum at the harmonic frequency. For this case the Fourier series has its fundamental frequency of 16 Hz with the higher harmonics all the multiples of 16 Hz. Using equation (7), the r.m.s. value for the harmonic at each discrete harmonic frequency, ω is

**I(j ω ) = [ √ 2f / r] [ Vo ωd / a2+ ωd2 ] [ 1/ {1-[ ω2/( a2 + ωd2)]} + j{ 2a ω / (a2 + ωd2)} ] A r.m.s.**

where f =16Hz a ; a = 1/T = 105s-1 wd = 7 X 105 rad/s and w has discrete values at w = 2π (16n) where n = 1,2,3, The true r.m.s. value for the current including the first n harmonics is the square root of the sum of the squares for the first n harmonic values from equation (8). The harmonics from equation (8) must be reduced by introducing the frequency response for the human body when the effects for shock currents are reduced proportional to frequency for frequencies between 1 kHz and 100 kHz. This can be accomplished by multiplying the magnitude for a given harmonic, n, found in equation (8) by the factor:

**G(jw) = [ 1 + ( f/105)2]1/2 / [1 + (f/103)2]1/2** **= (1 + 2.56 * 10-8n2)1/2 / (1 m + 2.56 * 10-4n2)1/2**

Combining equations (8) and (9) the r.m.s. values for the current to the 600th harmonic, 9600 Hz, have been calculated and are show in Table 4 Including higher harmonics would not increase the value significantly because of the attenuation at the higher frequencies.

Load Resistance (ohms) | I (mA) r.m.s. |

200 | 3.03 |

460 | 3.29 |

1020 | 2.97 |

1700 | 3.43 |

**PRIOR STUDIES RELATING TO XR-5OOO TYPE SHOCKS**

In a report prepared for the U.S. Consumer Product Safety Commission (Bernstein, 1976), another device intended to be used on people and to deliver a train of damped sinusoidal pulses at a frequency of 13 Hz was evaluated. This report indicates that the output was equivalent to an approximate 9 mA, 60 Hz shock. A later study where the effects of the different frequency components were more accurately calculated showed that the device output was equivalent to an approximate 3 mA, 60 Hz shock (BernsteIn, 1983). These techniques were used in this report. The XR5000 is certainly as safe as the device evaluated for the U.S. Consumer Product Safety Commission. In fact, it is safer because the well defined current path between the closely spaced probes of the XR5000 will significantly reduce the current delivered to the heart.

**CONCLUSIONS**

1. Table 4 shows that the output for the XR 5000 is about equivalent to a 3 mA, 60 Hz shock. Such a shock is not dangerous.

2. The 3 mA shock is at about the let-go current level. The shock may be more intense than that caused by such a 3 mA let-go current in the arm because the current density at the probes is greater and because of the sensation caused by the spark from the electrode to the skin.

3. Because the shocking current is only in the path between the electrodes about 2 inches apart, the current that might reach the heart is much less than in a limb-to-limb or an across-the-chest shock. This adds to the safety.

4. The units can be used in a damp or wet environment without hazard to the user. The unit may not work well because leakage between electrodes, but the operator should not be shocked if he keeps his hand in its usual position.

**REFERENCES**

- ANSI ClOl .1 (1973). American National Standard for Leakage Current for Appliances. American National Standards Institute, New York.
- ANSI/AAMI SCL 12/78(1978). American National Standard Safe Current Limits for Electromedical Apparatus. Association for the Advancement of Medical Instrumentation, Arlington, VA.
- Bernstein, T. (1975). Theories of the causes of death from electricity in the late nineteenth century. Medical Instrumentation, 9, 267-273.
- Bernstein, T. (1976) Letter report to Mr. Neil P. Zylich, U.S. Coonsumer Product Safety Commission. February 12, 1976. Revised February 7, 1977.
- Bernstein, T. (1983). Safety criteria for intended or expected non-lethal electrical shocks. Symposium on Electrical Shock Safety Criteria sponsored by The Electric Power Research Institute, The Canadian Electrical Association, and Ontario Hydro. Toronto, Canada. September, 1983.
- Biegelmeier, G. and W. R. Lee (1980). New Considerations on the Threshold of Ventricular Fibrillation for a.c. shocks at 50—60 Hz. Proc. lnstn Elec. Engrs., 127, 103—110.
- Cooper, G. R. and C. D. McGiIIem (1967). Methods of Signal and System Analysis. Holt, Rinehart and Winston, New or , pg. 121.
- Daiziel, C. F. and T. H. Mansfield (1950). Effect of Frequency on Perception Currents. Trans. Am. Inst. Elect. Engrs., 69, part 2, 1162-1168.
- Dalziel, C. F. and F. P. Massoglia (1956). Let—go Currents and Voltages. Trans. Am. Inst. Elect. Engrs., 75, part 2, 49—56.
- Underwriters Laboratories (1972). UL 943, Standard for Safety, Ground—Fault Circuit Interrupter, pg. 16B, revised January 7, 1977.
- Underwriters Laboratories (1976). UL 544, Standard for Safety, Medical and Dental Equipment, 2nd ed., pg. 30, revised January 17, 1977.
- Underwriters Laboratories (1980). UL 69, Standard for Safety, Electric Fence Controllers, 5th ed., pp. 12-13.