Amateur Athlete iPhone apps
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When we run we generate heat. If we cannot dissipate that heat fast enough, then our core body temperature rises. A rising core temperature leads to fatigue and possibly heatstroke and even death. So we need to stay within our limits.
"Running in the heat" helps us have a sane idea of what those limits are. Given our body weight and running speed, it calculates the rate of heat generation. Given the air temperature and relative humidity and an estimate of body surface area from the body weight and height combination, it calculates the rates of heat dissipation due to conduction/convection, thermal radiation and evaporation of sweat. If the ratio of the rate of generation to dissipation is less than 100% then we are probably OK. If it is over 100% then we need to change our environment or slow down.
Here is a sample combination of runner weight, height, air temperature, relative humidity and pace that will result a rising core temperature.
The first step to using "Running in the heat" is selecting your:
Relative humidity is shown on every weather channel along with the air temperature. It is a measure of how saturated with water vapor the air is at a given temperature. So, when it is raining the relative humidity is at 100% in between the water droplets. A relative humidity of 50% or below is common in the dessert during the day time.
Once the above components are selected, hit the "Watts" button and the following is calculated:
As long as the "Generation/Dissipation" is below 100%, you should be OK. The details are explained below.
I had never run competitively but had jogged for personal recreaton during my twenties. At the age of 50, I started to run again. Initially I found it to be a very unnatural activity but was glad to still be able to do it. Soon after I began run training, I overdid it and developed Achilles tendonitis. Around this time, my wife revived her interest in running and then motivated us to run a marathon. We decided to do the Disney marathon so it could also be part of a family vacation. I trained inside a climate-controlled gym on a treadmill because I didn't want to be stranded out in the countryside if my tendonitis really flared up. So I was not prepared for running outside in the elements. Half way through the Disney marathon I was sweating profusely and I knew that I was in trouble. By the time I finished, the humidex was well above 30 degrees C. It had taken me over 5 hours. Our teenage daughter semed to sail through the race in Boston-qualifying time and my wife was in between us. This was my first lesson in how hot, humid weather can be a deal-breaker in racing.
The thermal balance of our bodies can be modelled from an engineer's point of view, given certain assumptions and simplifications. Our bodies are kind of like chemical reactors. We convert food energy into metabolic work, external work and heat. As long as we can dissipate heat faster than we generate it, then our core body temperature will reach a steady state and not continue to rise. Normally, our core temperature is about 37 oC. If it gets above about 40 oC, we become at risk of getting heatstroke or even an untimely end to our lives. Fatigue usually motivates us to change our environment and exertion intensity before these processes occur. So, runners would benefit from a sane estimate of the pace they could sustain in specific conditions. The assumptions and methods of calculating these rates followed closely what was described by Dennis and Noakes.1
At least half of the energy we use during running results in heat generation rather than moving our body. The rate of heat generation depends on our body mass and speed. So, the heavier we are and the faster we go, the more heat is generated. With body mass in kg and speed in meters/second, the proportionality factor is about 4 J/kg-1m-1 to get power in watts (J/s).
We dissipate heat mainly through three mechanisms:
All three depend on our body surface area, which depends on our body mass (in kg) and body height (in cm).
All three of the dissipation processes also depend on our skin temperature, Tskin. This was assumed to be a constant of 35 oC (the same as what Dennis and Noakes did).
Heat dissipation by conduction and convection depends on the temperature difference between our skin and the surrounding air, the rate of air flow and our body surface area. These processes are fairly complicated, even for simple geometries and air flow patterns. Dennis and Noakes used an expression developed and modified by others for humans.
The temperatures are in degrees Celsius, the air flow speed (Greek v) in meters/second and body area, A, in m2. The resulting heat rate is in watts. The air flow speed is the net air speed that the body experiences after accounting for running speed and wind. So, our net air flow is higher when we are running into the wind and lower when the wind is at our backs. Under warm, humid conditions the effect of wind speed is usually small compared to the other factors and so was omitted in this model (as Dennis and Noakes did). So, the model mimics the situation of running through still air.
We also dissipate heat by thermally radiating to our surroundings. This process is even more complicated than that for conduction and convection. Our skin interacts radiatively with every object in its field of view in a non-linear fashion with respect to surface temperatures. Thankfully for modelling purposes, it is usually less influential, in terms of heat dissipation, than conduction or evaporation. It was modelled by Dennis and Noakes (and others before them) by:
where A is body area (m2) and Tambient is the ambient temperature. One of the assumptions behind this is that heat input by radiation from the sun is not accounted for. Therefore, it is only valid for cloudy conditions. Under sunny conditions, the heat dissipation rate from radiation could easily be reversed and be a net heat input.
Under warm, humid conditions, our main way of dissipating heat is by evaporation of sweat. The energy required to evaporate water is substantial, which is why evaporation is effective. The rate of evaporation depend on the concentration difference of water vapor between the air just above your moistened skin and the ambient air. The concentration of water vapor is measured as a partial pressure. The evaporation rate is also influenced by the air flow rate. So, the rate of heat dissipation by evaporation was modelled by:
This assumes that the entire body surface has a thin layer of sweat that can evaporate. Another key assumption is that the sweat rate is not limited by inadequate fluids intake. This is not to say that the fluids intake must match fluids loss becasue a certain amount of imbalance is OK.
The final item calculated is a measure of the balance between heat generation and dissipation. It is shown as the ratio of these two, expressed as a percent. So, at 100%, the rate of heat generation matches heat dissipation. Above 100%, the heat generation rate exceeds the heat dissipation rates and core temperature will climb. Below 100%, the cooling rates exceed the generation rate and your core temperature should remain stable.
Hopefully, the use of this app will prevent some heatstroke (and worse) incidents by runners who go too fast in the heat. Two key assumptions and limitations in it are that it is for cloudy and windless conditions. Given our body weight and height, the air temperature and relative humidity, we can use it to see if the running pace we want to do is possible without overheating.
1Steven C. Dennis and Timothy D. Noakes, "Advantages of a smaller bodymass in humans when distance-running in warm, humid conditions", Eur. J. Appl Physiology, vol. 79, p. 280--284, 1999.