A Proposal
As our goal of sending humans to Mars edges closer, it becomes more and more imperative to develop a colendar to be used to monitor Martian time.
A Martian year, or the time it takes for the planet to make one complete trip around the sun, is comprised of approximately 668.5991 sols. Remember, a Sol is roughly 24 hours, 39 minutes, and 35 seconds of Earth time. Because a Martian year is so much longer than an Earth year, it wouldn't be beneficial to monitor its time with a typical calendar used on Earth.
Following a typical year/leap year system, the Martian calendar could sport two versions, one with 668 sols and one with 669 sols (the leap year). Because the remainder sol is greater than 0.5 sols at 0.5991, most years would be the leap year with 669 sols per calendar year instead of the less common 668. The way to measure this is simple.
As you may already know, a year on Earth is a leap year if it's divisible by 4. However, it's not a leap year if it's divisible by 100. However yet again, it'll still be a leap year if it's divisible by 400. This is commonly practiced, and will keep the calendar in sync with the Earth's revolutionary period for thousands of years. By the time this becomes an issue (to the point where we're off a day), we'd adjust accordingly, and have several more thousands of years in check.
The Martian leap year calculation works very similarly to Earth's. If the year ends in an odd number or a 0, it's a leap year. Thus, generally, 6 out of 10 years are leap years (and have 669 sols). If the year is divisible by 100, it's not a leap year. However, if the year is divisible by 500, it's still a leap year. This adjusting will keep the Martian calendar in sync with the martian revolution cycle for some twelve thousand martian years.
So now that we have 668 or 669 sols per martian calendar year, how do we arrange them?
My main idea here is to divide them simply into quarters. Thus, in a 668 sol year, each quarter would have 167 sols. Observe the following image.
The final quarter has the potential leap sol at the end. One thing to immediately note here are that each quarter is shy of one sol to finish out its final (24th) 7 sol week. If the calendar stays as portrayed, you would simply go from Saturday to Monday to transition between quarters (with an exception to leap year final quarters moving to a new calendar year). If you do this, the calendar would forever have its sols line up consistently with the sol of the week, as shown in the image. This calendar is ideal for business tracking, as the quarters are evenly divided.
As a side note, please be aware that though the quarters may roughly coincide with the seasons on Mars, they do not line up as neatly as on Earth. Due to Mars's more eliptical orbit, its seasons are quite uneven. However, I would line Mars's northern hemisphere's winter solstice up with the beginning of this calendar. This is a personal preference, but seems as good a place as any to start. (Another variation uses the Spring Equinox.)
Finally, the idea of 167 sols per quarter may seem daunting to people. Thus, according to the Darian Calendar, the quarters are broken up into 6 months each. The first 5 months of the set would contain 4 full weeks, resulting in 28 sols. The final week of the 6th month would only have 6 sols, and thus result in a 27 sol month (except for the final month of a leap year). In this way, you can have 'pay sol' more regularly, and perhaps maintain daily schedules easier for the average person. The divisions for these months are displayed in the above image, colored in blue and white.
As a personal note, it might be hard to convince people to work every 24th week and only get one sol off before starting a new week. Who'd travel months in a tin can to work that kind of schedule? A friend of mine came up with an idea for that final 6-sol week would be to have 4 sols of work, and still have a full weekend! Now that sounds much better!
Want to see a real Martian clock and calendar in action? Be sure to check out my inner planets page!