Assessing skin thermal injury risk in exposure tests of heating until flight

TL;DR

The paper addresses skin thermal injury risk during high-power millimeter-wave exposure tests that continue until flight action. It builds a depth-penetration heat conduction model with uniform nociceptor activation, linking flight initiation to an unknown volume threshold via an observable flight time $t_F$, and quantifies damage with the Arrhenius metric $\Omega$. To cope with unmeasurable parameters $v_c$ and $P_d^{(0)}$, the authors develop a fully normalized, non-dimensional formulation, providing closed-form solutions for the temperature evolution and enabling simulations that map $t_F$ and beam geometry to burn risk. Sensitivity analyses reveal how $t_F$, beam radius, reaction time, baseline and activation temperatures, and material properties govern $\Omega$, yielding practical guidance for minimizing injury while achieving flight-triggered exposure. The framework offers a principled way to assess safety in exposure tests and to interpret observed flight times in terms of thermal damage potential.

Abstract

We assess the skin thermal injury risk in the situation where a test subject is exposed to an electromagnetic beam until the occurrence of flight action. The physical process is modeled as follows. The absorbed electromagnetic power increases the skin temperature. Wherever it is above a temperature threshold, thermal nociceptors are activated and transduce an electrical signal. When the activated skin volume reaches a threshold, the flight signal is initiated. After the delay of human reaction time, the flight action is materialized when the subject moves away or the beam power is turned off. The injury risk is quantified by the thermal damage parameter calculated in the Arrhenius equation. It depends on the beam power density absorbed into the skin, which is not measurable. In addition, the volume threshold for flight initiation is unknown. To circumference these difficulties, we normalize the formulation and write the thermal damage parameter in terms of the occurrence time of flight action, which is reliably observed in exposure tests. This thermal injury formulation provides a viable framework for investigating the effects of model parameters.

Figures (12)

• Figure 1: Results for $t_\text{F} = 1\text{s}$. Skin surface temperature vs $t$. (a) $r_b = r_s$; (b) $r_b = 1.25 r_s$.
• Figure 2: Results for $r_b =r_s$. (a) the thermal damage parameter $\Omega$ vs the observed flight action time $t_\text{F}$; (b) the absorbed beam power density$P_d^{(0)}$ vs $t_\text{F}$.
• Figure 3: $\Omega$ vs $t_\text{F}$ at $r_b = 0.5r_s$, $0.75r_s$, $r_s$, and $1.25 r_s$.
• Figure 4: $\Omega$ vs $t_\text{F}$ at $r_b = 1.5r_s$, $2 r_s$, $5 r_s$, and $20 r_s$.
• Figure 5: Curves of $\Omega$ vs $t_F$ for several values of beam radius $r_b$.