seconds and hours and days

SECONDS

Any given calendar system for humans must have a smallest unit of around the second, because the second is partially based around the average resting Heartbeat rate for an adult human (between 60 and 100 bpm). This should be no lower than 0.8 seconds and no higher than 1.6 seconds. That's fine for humans in some alternate world, but if you happen to be building a mod for a video game, you need to much more closely match the seconds of a human who already knows how long a second should be. Thus, for a human who already knows of seconds and has a decent perception of time, the basic unit shouldn't deviate from between 0.9 and 1.2 seconds long.

MINUTES AND HOURS

For planets with rotational periods greater than around 3 or 4 hours (which would be pretty extreme anyway) there must be at least two more scales of measurement. At the 3 hour point it's reasonable to just make a day fulfill the purpose of an hour. For the moment let's assume we're dealing with planets that have reasonable rotational periods.

In the human/earth time system, there are as many seconds in a minute as there are minutes in an hour. This is a helpful mnemonic, but not necessary. For the video game mod, the time span just above a second must remain 60x, but for a calendar that requires no interaction, other measures of seconds/minute and minutes/hour are fine. For our system, minutes must remain 60x a second, and thus hours should be either exactly half that, twice that, or equal to that in minutes. (30 or 120 is kind of similar to 60 in terms of memorability)

HOURS AND DAYS

Hours MUST have an integer ratio with the solar rotational period of the planet, and the Day MUST be equal to exactly 1 solar rotational period. You can NOT have a time system where your days have 16.53 "hours" in them.

THE PROBLEM

So what we have is this problem:

SEC per second * 3600 * HOR per Day = Day Length.

Since we know SEC must be a certain range of possibilities, we need to solve for HOR per Day.

HOR = Solar Day / (SEC times 3600)

Note that this assumes MIN = 60 SEC and that MIN/SEC and HOR/MIN are equal.

THE SOLUTION

Let's say we have a planet with 65.243 real world hours in its rotation period. We need to find an hour length that will satisfy the limit on seconds. So all we need is 65.243/65, and we get a second value of 1.0037384615384615. More tantilizingly, an hour length of 60 might be used, with a second length at 1.087383333333...

If we wanted more reasonable hour count, we would have to either give up the hour=min trick or give up the restrictions on seconds. The lowest hour count would be a 54 hour day, while the highest is 72 hours.

DUNA

In Kerbal Space Program, the planet Duna has a solar rotational period of 65766.707 seconds, or 18.2685297222 hours. The nearest integer is 18, which makes for an 18 hour day with second length of 1.0149183179, which is not bad. (Boundary of 15 hours to 20 hours per day)