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Martian Windchill in Terrestrial Terms Randall Osczevski

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Martian Windchill in Terrestrial Terms Randall Osczevski MARTIAN WINDCHILL IN TERRESTRIAL TERMS RANDALL OSCZEVSKI A two-planet model of windchill suggests that the weather on Mars is not nearly as cold as it sounds. he groundbreaking book The Case for Mars (Zubrin 1996) advocates human exploration and colonization of the red planet. One of its themes is that Mars is beset by dragons of the sort T that ancient mapmakers used to draw on maps in unexplored areas. The dragons of Mars are daunting logistical and safety challenges that deter human exploration. One such dragon must surely be its weather, for Mars sounds far too cold for human life. No place on Earth experiences the low temperatures that occur every night on Mars, where even in the tropics in summer the thermometer often reads close to –90°C and, in midlatitudes in winter, as low as –120°C. The mean annual temperature of Mars is –63°C (Tillman 2009) com- pared to +14°C on Earth (NASA 2010). We can only try to imagine how cold the abysmally low temperatures of Mars might feel, especially when combined with high speed winds Left: The High Arctic feels at least as cold as Mars, year round (Photo by R. Osczevski 1989). Right: Twin Peaks of Mars. (Photo by NASA, Pathfinder Mission 1997) AMERICAN METEOROLOGICAL SOCIETY APRIL 2014 | 533 Unauthenticated | Downloaded 09/30/21 08:37 PM UTC that sometimes scour the planet. This intensely bone- refer to the steady state heat transfer from the upwind chilling image of Mars could become a psychological sides of internally heated vertical cylinders having the barrier to potential colonists, as well as to public same diameter, internal thermal resistance, and core support for such ventures. Fortunately, it is an alien temperature as the human head. cold. Thermometer readings from Mars are highly misleading to terrestrials, who base their expecta- WINDCHILL. Air temperature alone is often a tions of thermal comfort on their experience with poor indicator of how cold the weather might feel. low temperatures in Earth’s much denser atmosphere. Wind, for example, makes a big difference to the A visitor to an educational National Aeronautics thermal sensation at any temperature. The original and Space Administration (NASA) website (NASA “windchill index,” invented by Siple and Passel (1946), 1997) noted that because the atmosphere of the planet combined the cooling effects of low temperatures and is so thin, “a –20°C temperature on Mars would not wind in a number that was proportional to the rate feel as cold as –20°C air on Earth.” They went on to of heat transfer from a small plastic cylinder. (Except wonder what a person on Mars would feel the tem- when referring to specific products, this paper will perature to be and suggested that “It might be more follow the originators, Siple and Passel, in spelling relevant to many people to see the values shown on windchill as one word, much as “rainfall,” “sunshine,” the website correlated to more human terms.” This and “frostbite” are each one word.) paper provides that missing perspective by expressing The windchill index was used successfully for the windchill on Mars as an Earth equivalent tem- decades until it was “improved” by expressing the perature (EET). EET is the air temperature on Earth, cooling power of the weather as an equivalent tem- in still air and without sunshine, that would result in perature (i.e., the air temperature that would cause the same heat transfer rate and surface temperature as the same heat transfer rate when there is no wind). the very cold but insubstantial winds of Mars. Although very popular, WCET is a deceptive simpli- The mathematical model used for this calculation fication that only seems to be easier to understand. was developed in 2001 to calculate the values in the Over the years, many authors have criticized the wind chill equivalent temperature (WCET) chart original WCET and the windchill index on which for North America (Osczevski and Bluestein 2005). it was based (Molnar 1960; Eagan 1964; Steadman In terms of heat loss rate, surface temperature, and 1971; Kessler 1993; Osczevski 1995, 2000; Bluestein cold sensation, EET is identical to the familiar WCET and Zecher 1999). In 2001, the calculation model was that is reported each winter across much of North updated (Bluestein and Osczevski 2002; Osczevski America. It therefore provides a familiar context for and Bluestein 2005) and a new WCET chart was assessing the rigors of weather on another planet, in produced for use in weather reports in Canada and this case Mars. the United States. While it is highly improbable that anyone would How cold it feels outside also depends on the ever directly experience the weather on Mars by physical properties of the medium in which one is exposing bare skin to the virtual vacuum that passes immersed. Many have experienced the shock of dis- as its atmosphere, it is also unlikely that anyone on covering that immersion in 20°C water feels much Earth would choose to face a WCET of –60°C without colder than being in air at the same temperature. proper protection. Both EET and WCET are indices Water carries the heat away from the body much of the potential cooling power of the weather, whether faster than air does at the same temperature. We or not anyone actually experiences it directly. They do not often experience this nuance of windchill on Earth because atmospheric properties do not vary greatly from place to place or from day to day, but AFFILIATIONS: OSCZEVSKI*—Defence Research and Development Canada, Toronto, Ontario, Canada they do from planet to planet. Earth’s atmosphere, *Retired being much denser than that of Mars, is analogous CORRESPONDING AUTHOR: Randall Osczevski, 246 Plymouth to the water in the above example. Trail, Newmarket, ON L3Y 6G7, Canada E-mail: [email protected] THE ATMOSPHERE OF MARS. Composition and The abstract for this article can be found in this issue, following the pressure. The air we breathe on Earth is mostly nitro- table of contents. gen, with significant oxygen, a bit of argon, and trace DOI:10.1175/BAMS-D-12-00158.1 amounts of other gases. The atmosphere of Mars is In final form 7 July 2013 almost entirely carbon dioxide (95%). The pressure at the surface is typically less than 1% of the sea level air 534 | APRIL 2014 Unauthenticated | Downloaded 09/30/21 08:37 PM UTC pressure on Earth. At the Viking 1 and 2 landing sites Bluestein’s (2005) windchill model, with the same of the 1970s the pressure averaged 8.5 mb (Tillman diameter, constant internal temperature, internal 2009). At the Viking 2 site it varied with season, being thermal resistance, and emissivity. Both cylinders about 10 mb in the Northern Hemisphere winter move into the wind at walking speed. Just what the and 7.5 mb in the late summer. On Earth, where the walking speed on Mars might be (Hawkey 2005) mean atmospheric pressure is 1,013 mb, pressures has yet to be determined, so an average terrestrial as low as those on Mars are only encountered in the walking speed of 1.34 m s–1 was used for both planets. stratosphere at an altitude of 32 km (110,000 ft) (ICAO Comparison of the Grashof number for free convec- 1993). This is two-and-a-half times the altitude at tion in still air or CO2 with the Reynolds number for which commercial airliners fly and more than three forced convection in the same gas confirms that on times the height of Mount Everest. both planets, free convection at this minimum rela- tive wind speed is only about a tenth of the forced Ambient temperatures on Mars. Viking 2, which landed convection and so may be neglected (Incropera and on Mars in 1976 at latitude 48°N, operated for over DeWitt 1996). On Mars, forced convection accounts 1,000 sols (Martian days) and provided the longest for only about a quarter of the total heat transfer at and the most nearly complete record of weather low wind speeds. Radiation is the dominant heat conditions on Mars (Tillman 2009). Martian sols are transfer mechanism on Mars at low to moderate wind 40 min longer than Earth days, and the solar year speeds. To calculate radiant heat transfer, the two- has 669 sols (Williams 2009). Wind and temperature planet model assumes that the ground temperature data for the first 1,000 sols that Viking 2 operated are on Mars is equal to the ambient temperature, which presented in Fig. 1. In summer, ambient temperatures, is approximately true when averaged over the whole measured at 1.5 m above the surface, ranged from a sol. The reference condition for calculating equivalent low of –80°C at night to a comparatively balmy high temperature is not still “air” (CO2) on Mars, but in of –30°C in during the day. In winter, they varied still air on Earth, at night. from roughly –120°C at night to –100°C during the Physical properties of CO . daylight hours. 2 The properties of CO2 gas at 8.5 mb, at the extremely low temperatures found Winds on Mars. Because of the physical size of robot on Mars, were extracted from an online calculator landers like Vikings 1 and 2, wind speeds on Mars (MegaWatSoft 2009) for a series of temperatures have never been measured 10 m above the ground, as down to –55°C, which was the low temperature they are by convention on Earth. The Viking landers limit of the calculator. Trend lines were fitted to the measured the wind at a height of 1.5 m, which is con- data to develop regression equations for thermal venient for modeling windchill as 1.5 m is about the conductivity, k; kinematic viscosity, n; and the height of the average adult’s nose.
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