Valley Above Turquoise Lake, Lake Clark National Park, Alaska
A series of calculations performed for my own edification are included on this page. Are space blankets warmer than simple garbage bags as emergency shelters? Does 90% of the heat loss really come from your head? Is it better to have the thickest clothing layer on the inside or the outside?
Head loss occurs by conduction, convection, and radiation. Conduction is what happens when the heat travels along the length of a metal spoon. Convection is heat transfer by a moving fluid, usually wind blown air in our case. Sunlight is an example of radiation, although the invisible infrared radiation is also important.
Figure 1. Relative importance of convection and radiation to heat loss to the environment.
The amount of heat loss by each process depends upon circumstances. Conduction is important and usually dominant in heat transfer through clothing and may ultimately control the total heat loss. However the heat energy typically exits the body primarily by radiation and convection into the air and sky. Conduction loss is important, for example, when sitting on or touching a cold surface. For temperatures near freezing, Figure 1 illustrates the relative importance of radiation and convection on the heat exiting your outer clothing. During calm periods (<1 mph wind) radiation dominates and convection dominates in even a slight wind. Obtaining cover typically lowers the rate of loss from each.
Figure 1 only considers how the heat energy exits the outer clothing. The controls on the rate of heat loss depend both on how heat exits the outer clothing and how the heat energy reaches the outer clothing. The following graphs evaluate a two layer clothing system. It is assumed that the outer layer is windproof. Air temperature is at freezing (0) unless stated otherwise. The calculations consider conduction and radiation through the two layers coupled to radiation and convection loss from the outer fabric. Iteration is used to find the temperatures at each fabric interface as the solution to coupled nonlinear equations. The nominal thickness of the inner clothing layer is 6 mm (~Polartec 200) and the outer wind shell is 1 mm thick. A 5 mm air gap is assumed to exist between the inner and outer layers. This is near the optimal gap and seems plausible.
Figure 2. Importance of inner layer thickness on heat loss at two different wind speeds. The effect of removing the outer layer is also shown.
Figure 2 illustrates how heat loss responds to varying the thickness of the inner layer. The results are normalized by (i.e., divided by) the results for the base case of a 6 mm thick (Polartec 200) inner layer with a 2 m/s wind speed - notice that the graph crosses 1 at this point. Heat loss is significantly lower when there is no wind (orange line). Thicker layers are warmer, but there are diminishing returns, at least on a proportional basis. The wind speed is less important for thicker inner layers because the overall heat transfer is largely controlled by transport to the outer layer when the inner layer is thick (i.e., the temperature of the outer fabric is near ambient air temperature). A similar calculation can be performed for the thickness of the outer layer and shows similar results, although adding to the inner layer is more effective.
Having only a single windproof layer in the clothing system is shown as the red line for a wind speed of 2 m/s. In order to maintain a fair comparison the thickness of the outer layer (1 mm) was added to the thickness of the inner layer in the calculation (well, actually one just puts the air gap at zero thickness to force the two layers into one). For thin layers the single layer alternative with the same overall fabric thickness loses almost twice as much heat.The simple outer shell significantly increases warmth mostly because of the layer of stagnant air between the layers. This is why layering works and you can see that layering is most important with lighter clothing systems.
The situation where total insulation thickness is kept constant and varied between the inner and outer layers is very interesting and something I didn't fully anticipate. Is it better to have a very thin base layer with a thick
jacket outside or it is better to cover everything with a wind shell? This looks at the question of warmth for the weight efficiency.
Figure 3. Two layers of constant thickness with the thickness varied between the inner and outer layer. Results normalized by the nominal case of 6 mm inner layer and 1 mm outer layer. Wind speed is 2 m/s.
In Figure 3 the thickness is varied between the two layers while keeping the total thickness constant. This presumably simulates the situation where weight of the clothing is held constant. Given the options of: thick inner layer with wind shell, two equally thick layers, or light base layer with thick (Polartec-200) outer shell; which option provides the most warmth for the weight? At the left of Figure 3, we're wearing the (windproof) fleece on the outside with a thin base layer inside. In the middle of the figure we're wearing two equally thick (windproof) layers, on the right we're wearing the fleece on the inside with a wind shell outside. The interesting result is that putting the thick layer inside is warmest and the worst option is to wear the (windproof) fleece as the outer layer with a light inner layer. The reason for the surprising result is that the air gap between layers is a better insulator when it is in a relatively cold location in the clothing system. Radiation heat transfer is less efficient at lower temperatures. When the thin layer is on the outside the air gap between the layers is much colder than when the thick layer is on the outside and thus it is a better insulator. This is another reason why layers work, putting a fabric layer against the skin followed by an air gap to an outer fabric lowers the temperature in the air gap and makes the gap a better insulator. The air gap between layers has no weight - making for a very nice ultralight backpacking system.
A very light and loose outer shell is always a good idea even if the inner layers are windproof. The air gap being simulated is also more likely to exist with a thin, loosely fitting, outer layer, as there is nothing to compress the air gap between layers.
What if the surfaces between the two layers were coated with a low emissivity infrared coating (e.g., a space blanket or some of the new coatings the US military has developed, or Columbia Omni-Heat ® Thermal Reflective Technology)? Columbia and perhaps other manufacturers now market such materials. Alternatively, what if the outer layer were a space blanket versus a simple plastic garbage bag in an emergency situation?
Figure 4. Low emissivity coating (space blanket, aluminized) on surfaces between the two layers on either side of the air gap in the nominal clothing system (6 mm inner layer, 1 mm outer shell).
The emissivity of the surfaces between the two layers (i.e., on either side of the air gap between the clothing layers) is varied from 0.1 (aluminized space blanket material) to 0.95 (garbage bag, nylon, most other fabrics). The low infrared emissivity "space blanket" coating reduces heat loss by less than 10%. This is worth doing if there is no weight penalty, but for the most part, the space blanket with the aluminized layer pointing inward is not significantly warmer than a cheap heavy duty garbage "lawn and leaf" bag as an emergency shelter. Protection from the wind, and having an extra layer with stagnant air inside are much more important than the emissivity. As an interesting aside the emissivity would be more important in a thick outer layer, thin inner layer clothing system because the air gap is warmer in this situation. This is the case for some of the new jackets where the low emissivity coating is inside the insulating layer.
How does wind speed influence cooling?
Figure 5. Wind speed and heat loss for the nominal two layer system with aluminized fabric (space blanket) on the outside versus an ordinary fabric on the outside.
Figure 5 examines the influence of wind speed on the model two layer system and shows the effect of having an aluminized outer layer. The aluminized fabric makes about a 15% difference in heat loss for calm conditions but does very little in the wind. This is because radiation heat transfer only dominates at low wind speeds. This does show why aluminized outer fabrics can reduce condensation on tarps and tents because condensation is a greater problem at low wind speeds - where radiation is most important. In contrast, staying warm is a greater problem at high wind speeds. Notice the straight horizontal portions of the lines at low wind speeds. At low wind speed the convection currents caused by the body heating the air are more important than the wind in influencing heat loss.
What about heat loss from exposed skin? Do you really lose 90% of the heat from your head when not wearing a hat? Is it better to have a really, really thick coat, or should one have a moderate thickness coat with extra long johns, a good hat, and gloves?
Figure 6. Heat loss from exposed skin using the nominal clothing (Polartec 200 with a second windproof layer outside).
Figure 7. Heat loss from exposed skin assuming the clothing consists of the nominal Polartec 200 with a down coat and pants outside.
Figures 6 and 7 examine the fraction of total heat loss coming from exposed skin as the fraction of exposed skin is changed. Notice the slope of the curves which indicates that the first bits of skin exposed make a big difference in the heat loss.. For the nominal clothing system (Figure 6) , if 20% of the skin is exposed, half of the total heat loss will be caused by the skin exposure. With the warmer down clothing, exposing 10% of the skin (e.g., the head) causes 50% of the heat loss. The calculation indicates that is is best to entirely cover the skin, especially for very cold situations. A single thick jacket, in general, is not as effective as a thinner layer or layers covering the entire body. This calculation does not take into account that some portions of the body (the core, head, and neck) tend to lose more heat than others because they are not sacrificed by being allowed to cool below core body temperature. In these calculations it is assumed that exposed skin cools down 10 degrees below body temperature.
So what do all these calculations mean:
a) dress in layers
b) always have a loosely fitting outer wind shell in an ultralight backpacking or alpine climbing clothing system
c) a space blanket is no better in most emergency situations than an ordinary large plastic garbage bag, bivouac sack, or cagoule
d) have a clothing system that covers the entire body rather than relying on a single big jacket to stay warm
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Copyright 2014 John Walton