0.2 Module 3 - query/answer/significance: body ambient bondgraph  (Page 2/3)

System equations

The system equations layer of the model forms the basis for mathematical evaluation of system energy transfer. The equations presented below are empirically derived based on experimental field data.

• For approximate heat generated during running,

HFbc = (body mass[kg])*(running speed[m/s])[4J*s/m/kg]

• For heat loss due to evaporation,

HFeva = .312(Teva) + 25.2 [W/m²]@ Tamb = 35ºC; 3.0m/s wind speed

• For heat transfer due to conduction and radiation,

HFrad = .5833(Trad) + 30.96 [W/m²]@ Tamb = 35ºC; 3.0m/s wind speed

HFcon = .169(Tcon) + 21 [W/m²]@ Tamb = 35ºC; 3.0m/s wind speed

• An ideal transducer,

HFamb*Tamb = HFsk*Tsk

• For a more realistic model,

HFamb = (Tsk/Tamb) * HFsk * (1 + D)

D = sensor introduced deviance

• Overall system equation,

HFbc = (.312(Teva) + 25.2 + .169(Tcon) + 21 + .5833(Trad) + 30.96 – .312(Teva) + 25.2)·(Tsk/Tamb)·(1+.03)

• For our measuring device,

Vout = HF* 125µV·W-¹·m² ± 3.0%

Results

Solving the equations, we arrive at the following results:

HFeva = -35.5 W/m²;HFrad = 50.2 W/m²; HFcon = 26.6 W/m²

HFbc = 440 W/m²

Vout = 55 ± 5.5 mV

This readout holds for when the ambient, heat production from work, and body thermoregulatory responses are in steady-state.

If we take the heat flux chart readout from a similar study, we see heat flux measurements from four different locations on the body, as well as characteristic response typical of an athlete in an aerobic exercise under constant environmental conditions.

Figure 2: Heat flux transducer chart recorder readout; W/m² with respect to time

This above data can be described in terms of several distinct periods,

• An initial period where the heat flux spikes to high value due to the onset of physical work and generation of heat.
• A dampening of heat flux as the body’s thermoregulatory responses compensate for the increased heat flow (at which we see 50mV readout, correlating to 399.5 W/m² heat flux).
• Some variation in heat flux during a steady-state activity, that can be accounted for several factors detailed in the model, such as
• A change in ambient temperature or relative humidity
• A change in wind speed
• A change in level of exertion
• Changes in sensor functionality, such as contact w/ the skin
• As physical exertion is completed, the heat flux from body to ambient gradually decreases to zero as

For this type of exertion, prior to the onset of heat illness, one would expect to see a consistent, gradual decrease in heat flux as thermoregulatory responses begin to decline (such as when the runner has expended their supply of body water for sweat, and no longer dissipate heat by sweat evaporation). It is at this point safety monitoring personnel should query the runner to gauge the onset of heat illness, and consider removing the athlete from the competition.

Changes in environmental conditions, such as temperature, humidity, and wind speed, can be accounted for by comparing changes in steady-state heat flux to characteristic equations for those components in the model.

Errors in the heat flux transducer can be shown to be small compared to the peak heat flux measured, and as such can be filtered from a change in heat flux evaluation used to predict heat illness.