Perigo sob seus pés: Um mergulho profundo no toque e na tensão de passo

Introdução

When we think of electrical hazards, muitas vezes imaginamos o contato direto com uma linha de energia de alta tensão ou uma peça de máquina que produz faíscas. Contudo, some of the most insidious dangers in electrical engineering occur without any direct contact with a live conductor. During a ground fault in an electrical substation or on a power line, large currents surge into the earth. This influx of electricity creates voltage gradients across the ground itself, turning the soil beneath a person’s feet into a potential death trap. This phenomenon is governed by two critical safety concepts: step voltage etouch voltage.

Understanding these concepts is not just an academic exercise; it is the cornerstone of substation design and utility safety. As noted by industry standards, the primary goal of a safe earthing system is to ensure that a person in the vicinity of earthed facilities is not exposed to the danger of critical electric shock[1][3]. This article explores the definitions of these voltages, the science behind how they affect the human body, the international standards that dictate safe limits, and the engineering methods used to mitigate these invisible threats.

Defining the Hazards: Step vs. Touch Voltage

To understand the risk, one must first understand the difference between the two types of potential differences a person might encounter during a fault.

Step Voltage is the difference in surface potential that could be experienced by a person bridging a distance of 1 meter (approximately one step) with their feet, without contacting any grounded [1][4] . Imagine a fault where current dissipates into the ground. The voltage is highest at the point where the current enters the earth (por exemplo, a downed conductor or a transmission tower) and decreases as the distance from that point increases[3] . If a person walks in the area, one foot might be at a point of higher voltage (closer to the fault) and the other foot at a lower voltage (further away). The voltage difference between those two points is the step voltage. If this voltage is high enough, it will drive a current through a person’s legs and lower body, potentially causing loss of muscle control or ventricular fibrillation[2][5]..

Touch Voltage, on the other hand, involves a path from hand to feet. It is defined as the potential difference between theGround Potential Rise (GPR) of a grounded structure (such as a substation fence or a metal enclosure) and the surface potential at the point where a person is standing while simultaneously touching that structure[1][4]. . Por exemplo, during a fault, a substation fence might rise to a dangerously high voltage relative to “true earth.” If a person standing a few feet away touches that fence, their body completes the circuit. The voltage trying to drive current through their chest (from hand to feet) is the touch voltage[2].

A third, related concept isTransferred Voltage, a special case of touch voltage. This occurs when a voltage is transferred into or out of a substation from or to a remote point via conductive paths like pipes, rails, or communication [1][3] . A person touching this “energized” remote object while standing on local ground could be exposed to the full force of the remote fault.

A Física de um Choque: Corrente Corporal e Fibrilação

Por que essas tensões são perigosas? O corpo humano é essencialmente um grande resistor. Quando uma diferença de tensão aparece através dele, fluxos atuais. A principal causa de morte por choque elétrico éfibrilação ventricular, uma condição em que a ação de bombeamento rítmico do coração cessa e ele começa a tremer caoticamente, tornando-o incapaz de bombear sangue[5][2].

A gravidade de um choque elétrico depende de três fatores principais: a magnitude da corrente, a duração da exposição, e o caminho que a corrente percorre pelo corpo (sendo a mão-pé a mais perigosa porque atravessa o coração) .

Padrões como o IEEE (Instituto de Engenheiros Elétricos e Eletrônicos) e IEC (Comissão Eletrotécnica Internacional) estabeleceram modelos matemáticos para determinar limites de tensão seguros com base nesses fatores. O padrão IEEE 80 uses a formula derived from studies by Dalziel, which assumes a body weight and a fixed body resistance of1000 Oh [1][5]. The allowable body current for a 50 kg (110 lb) person is calculated as:

${Eu}_{B} = \frac{0.116}{\sqrt{t_{s}}} Amperes$ EuB=ts0.116 Amperes

Onde $t_{s}$ ts is the duration of the shock in seconds. For a 70 kg person, the constant changes from 0.116 para 0.157[5] .

Using this, the tolerable touch and step voltages can be calculated. The formulas incorporate the body resistance (1000 Oh) and the resistance of the feet, which is modeled as a conducting disc. The foot resistance is dependent on the resistivity of the surface material ( $ρ_{s}$ ρs) on which the person stands. The standard equations are:

Step Voltage: ${Ele}_{s t e p} = (1000 + 6 C_{s} ρ_{s}) \frac{0.116}{\sqrt{t_{s}}}$ Elestep=(1000+6Csρs)ts0.116
Touch Voltage: ${Ele}_{t o e c h} = (1000 + 1.5 C_{s} ρ_{s}) \frac{0.116}{\sqrt{t_{s}}}$ Eletoech=(1000+1.5Csρs)ts0.116

The factor of “6” in the step equation accounts for two feet in series (the resistance of two foot contacts on the same surface), while the factor of “1.5” na equação de toque é responsável por dois pés em paralelo [1][3] .

O padrão IEC (IEC 60479-1) adota uma abordagem mais complexa, considerando a impedância corporal como uma variável dependente da tensão e do percentil da população, e introduzindo um “fator atual do coração” para diferentes caminhos atuais. Geralmente, o padrão IEC permite limites de segurança mais altos para durações de falta mais curtas do que 400 milissegundos, reconhecendo o momento da fase vulnerável da onda T do coração[2][5] .

Mitigação e Design de Engenharia

Porque não se pode confiar na própria terra para eliminar uma falha (uma haste de aterramento por si só não pode reduzir o potencial de toque a um nível seguro[3])), engenheiros devem projetar sistemas de aterramento para proteger ativamente o pessoal. O processo de projeto envolve medir a resistividade do solo, calculando a corrente máxima de falha, and then designing a grounding grid that ensures actual touch and step voltages remain below the calculated tolerable limits[1][3] .

Several key strategies are employed to achieve this:

1. The Grounding Grid: The primary defense is a well-designed grounding grid. This consists of a network of bare copper conductors buried in a grid pattern (often spaced 10 para 20 feet apart) and securely bonded to all above-ground metallic structures. This grid helps to keep the entire area at a more uniform potential and provides a low-impedance path for fault current[1][3][4].

2. High-Resistivity Surface Layers: This is one of the most visible and effective mitigation measures. In substations, a layer of crushed rock (gravel) is spread over the surface. This material has a very high resistivity ( $ρ_{s}$ ρs) compared to regular soil. Ao colocar esta camada entre os pés de uma pessoa e a terra subjacente, adiciona resistência em série significativa ao circuito de choque, reduzindo assim a corrente que pode fluir através do corpo[1][4]. A eficácia desta camada é contabilizada nas equações de segurança pelo fator de escala $C_{s}$ Cs[1].

3. Zonas equipotenciais: Para trabalhadores que devem estar em contato direto com equipamentos aterrados, criando umzona equipotencial é crítico. Isto é muitas vezes conseguido através de uma solução temporáriatapete de chão (uma malha metálica) que está ligado ao equipamento. Quando um trabalhador fica no tapete e toca o equipamento, ambos os pés e mãos estão no mesmo potencial, reduzindo efetivamente a tensão de toque para zero [4] . A ligação de todos os objetos condutores na área de trabalho imediata tem um propósito semelhante[3].

4. Limpeza de proteção mais rápida: The tolerable voltage limits are inversely proportional to the square root of the shock duration ( $\sqrt{t_{s}}$ ts). Portanto, the faster a protection relay can operate to clear a fault, the higher the voltage a person can theoretically survive. By reducing the fault clearing time, engineers can significantly increase the margin of safety .

Conclusão

Step and touch voltages represent a unique challenge in electrical safety: the hazard is invisible and exists on the ground we walk on. The danger is not the voltage of the power line itself, but the voltage gradient created by the earth acting as a conductor. Through decades of research into the effects of electricity on the human body, standards like IEEE Std 80 e IEC 60479 have provided engineers with the tools to quantify these risks and design systems to mitigate them[1][2]..

From the high-resistivity gravel beneath our feet in a substation to the complex computer models used to design grounding grids, every element works in concert to ensure that when a fault occurs, the invisible voltage gradient remains just that—invisible and, most importantly, harmless. As distributed energy resources and smart grids evolve, maintaining the integrity of these grounding systems remains paramount to protecting both the public and utility workers [3][4].

Referências

IEEE Standard 80,Guide for Safety in AC Substation Grounding .
IEC 60479-1, *Effects of current on human beings and livestock – Parte 1: General aspects*.
IEEE Standard 81,Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials of a Grounding System .
OSHA (Occupational Safety and Health Administration) guidance on electrical safety.
Dalziel, C. F., & Lee, Em. R. (1960s-1970s). Correntes elétricas letais.Transações IEEE na indústria e aplicações gerais .
CEI 62305,Proteção contra raios .

Conteúdo elaborado com assistência de IA e validado pelo autor com base em 30 anos de experiência na área de Qualidade de Energia.