Thermal balance of livestock: 2. Applications of a parsimonious model

Abstract

A mathematical model developed from heat transfer principles to predict the thermal status of a homeotherm was applied to sheep and cattle outdoors and pigs and broiler chickens indoors. The climatological variables considered in the model include air temperature, wind speed, vapour pressure and solar radiation. For sheep, the fleece depth varied seasonally and thermal balance was achieved by a metabolic response, vasodilation and panting. For cattle, the thermal responses included sweating and piloerection of the coat. The insulation provided by the pig’s sparse hair coat was neglected, but the increase in its body insulation with age and environmental conditions was included as a major determinant of heat loss. For chickens, the insulation provided by the body tissue and feathers was described by a single thermal resistance. Their thermal responses included feather fluffing, vasomotor action in the combs and feet, and changes in respiration rate and body temperature. The models were tested successfully for each species by simulating the experimental conditions used by previous workers and comparing the predictions with measured values of heat loss, skin and body temperature. The interception of solar radiation by animals outdoors was also tested successfully for solar elevations up to 45°. For sheep, the predicted heat loss agreed with measurements to within 10%. The onset of vasodilation for a shorn sheep on maintenance food intake was predicted successfully to occur at an air temperature of 25°C, and the variation of skin temperature on the legs with air temperature was predicted to within the uncertainty of the measurements. The model predicted the heat loss from cattle in the cold with acceptable accuracy when the wind speed was low, but overestimated heat loss from calves by up to 30% in wind. In warm conditions, the evaporative heat loss from cattle as a consequence of sweating was predicted with acceptable accuracy. The errors incurred by ignoring solar radiation penetration into the coat were acceptably small, given the associated reduction in model complexity. Sensitivity analysis showed that the predictions of heat loss from sheep and cattle were sensitive to wind speed and coat length, especially when the coat is short. For both species, the level of stress was sensitive to ambient vapour pressure at high air temperatures. For a single new-born pig, the model underestimated heat loss at 30°C with an overall error of −9% over the range of wind speeds likely to be experienced indoors. The model over-predicted heat loss by an average of 20% at 20°C, probably due to the absence in the model of a temperature-dependent huddling response. However, for a 25 kg pig exposed to air temperatures from −5 to 35°C, the model predicted the skin temperature on the trunk — a good indication of its thermal status — to within the limits of the experimental uncertainty. The total heat loss from chickens exposed to temperatures in the range 0–38°C was predicted with an overall error of 6%. In a separate test, the body core temperature of hens was predicted to within 0.3°C on average for the same range of air temperature, again within the limits of experimental uncertainty. Sensitivity analysis showed that the prediction of body temperature for chickens was most sensitive to ambient humidity at high air temperatures, and to body resistance. The paper discusses the limitations of the models and the need for more measurements of heat losses from current breeds of livestock.