While doing research for my new book “More Great Formulas Explained”, I came across a neat formula that can be used to calculate the surface area of a person. It goes by the name Mosteller formula and requires two inputs: the mass m (in kg) and the height h (in cm). The surface area S (in m²) is proportional to the square root of m times h:
S = sqrt (m * h / 3600)
For example, a person with the weight m = 75 kg and height h = 175 cm can be expected to have the body surface area S = 1.91 m². A note for American readers: you can use this table to easily convert the height in feet / inches to centimeters.
What’s the use of this? In my book I needed to know this quantity to compute heat loss. According to Newton’s law of cooling, the heat loss rate P (in Watt = Joules per second) is proportional to the surface area S and the temperature difference ΔT (in °C or K):
P = a * S *ΔT
with a being the so called heat transfer coefficient. For calm air it has the value a = 10 W/(m² * K). A person’s body temperature is around 37 °C. So the m = 75 kg and h = 175 cm person from above would lose this amount of heat every second at an air temperature of 20 °C:
P = 10 W/(m² * K) * 1.91 m² * 17 °C = 325 Watt
That is of course assuming the person is naked, clothing will reduce this value significantly. So the surface area formula indeed is useful.
According to the World Population Clock there are currently about 7.191 billion people alive. This year there have been 118 million births (or 264 per minute) and 49 million deaths (or 110 per minute), resulting in a net growth of 69 million people. Where will this end? Nobody can say for sure. But what we can be certain about is that the explosive growth has been slowing down for the past 40 years. I’ll let the graphs tell the story.
However, another graph reveals that there’s more to the story. I had the computer calculate the percentage changes from one decade to the next. From 1960 to 1970 the world population grew by 22 %. This was the peak so far. After that, the growth rate continuously declined. The percentage change from 2000 to 2010 was “only” 12 %.
Of course it’s too early to conclude that this is the end of mankind’s explosive growth. There have been longer periods of slowing growth before (see around 1750 and 1850). But the data does raise this question.
Talk to me again when it’s 2020 or 2030.
Just by the way: according to estimates, about 108 billion people have been born since the beginning of mankind (see here). This implies that about 101 billion people have died so far and that of all those born, 6.5 % percent are alive today.