Engineering Log: The Timed Horological Epic

Alright, so the base Horological Epic has a line of verse for every minute or second in a twelve-hour period. The Timed Horological Epic goes by the second (not the minute) and has the end lines of every stanza determined by the second within which the three hands of a clock cross one another.

Sooo, this form takes a little math. And by a little I mean a lot. And by a lot I mean none at all because I’ve done it for you and will be sharing all the numbers over the next few months (and updating this post to link to them below) so that you can just concentrate on writing your very own 43,200-line epic.

But first I’m sharing the equations and such. Because I’m a nerd. Doing so is fun for me.

The Length of 43,200 Lines

A line of verse (V) for every second in a twelve-hour period gets you the equation of 12 hours multiplied by the 60 minutes per hour multiplied by the 60 seconds per minute or

V = 12 * 60 * 60 = 43,200

The 2 Equations Online Before I Showed Up

Background fact — no equation here — all hands cross/meet/start at 12 o’clock/zero hour. Also, in these equations S will represent the second, M the minute, H the hour, and T the time of a given crossing.

First equation, the second-hand crossed the minute-hand 59 times every hour for a total 708 crossings in twelve hours (because at every “minute zero” the second-hand gets a head start running the circle so it will take 1 and 1/59 trips for it to “see” the minute-hand again):

S = M * 60 / 59

Always multiple M by 60 to convert it to seconds and then divide by 59 to solve for S. Or, if you want to check my math using a spreadsheet, you can let the tech handle that for you to find the whole time using this equation:

T = H + M + (M / 59)

Second equation, the minute-hand crosses the hour-hand only 11 times (because the hour-hand is only going around the circle once while the minute-hand is going around once for every hour, but that very first hour starts with the minute-hand going “first” so that it will take 1 an 1/11 trips for it to cross the hour-hand):

M = H * 60 / 11

Here you get the minute plus decimal spaces, you can subtract the minute and multiply the remaining decimals by 60 to get the number of seconds or you can use a spreadsheet and this equation:

T = H * 12 / 11

If you do go the spreadsheet route for any of this, I highly recommend separate columns for hours and minutes (the basis of all the equations) and have all columns Formatted number-wise as [h] — doing so will save the trouble of having to write out every single hour-and-minute combo, plus it makes the work a little more straightforward for you. Though I should note, at the start/end of every hour you’re going to have to delete either the [h]:00:00.00 line or the [h]:59:00.00 line to keep from confusing yourself since they result in the same time.

The Equation Not Found Online That I Found Myself, Getting It Both Right and Wrong

The second-hand crosses the hour-hand 719 times over 12 hours (because the hour-hand goes around once while the second-hand goes around 720 with a “head start” on the first go-round so that it take 1 and 1/719 trips to cross the hour-hand every time).

T = ((H * 60) + M) * 60 / 719

This equation multiplies the hour by 60 to convert it to minutes, multiplies the minutes by 60 to convert to seconds, and divides by 719 to find how far along its journey the hour-hand has gone before it’s crossed.

This equation works when plugged into your spreadsheet.

Know where it doesn’t work? Calculating by hand.

Back in 2015 when I was falling in love and in the mood to write an epic romance about the hands of a clock, I did all of this work by hand. All 719 calculations of the second-hand crossing the hour-hand.

But if you’ve ever done Time math in a spreadsheet, you know the numbers do a funny thing. They are all divided by 86,400. A period of 24 hours when you change the format from [h] to standard 1234 numbers will equal 1. 24 = 1.

Doing the above calculation by hand without factoring in this factoid gave me the correct decimal but not the correct time.

Save Yourself the Time

It was in preparing this post and its math for you that got me making my own spreadsheet to double-check the numbers and realize my right and wrong calculation. And since I plan on ending each volume of my run at a timed horological epic on the lines where the minute-hand crosses the hour-hand, that’s how I’ve divied up all the calculations across eleven forthcoming posts.

Should you wish to write your own timed horological epic, that is.

I’ve also set up my spreadsheet to do the subtraction of how many seconds pass between crossings, multiply it by the 86,400 seconds of a given 24 hours, re-format to standard integers, and round it to the nearest whole number.

Just to keep things neat and tidy for all of us.

You’re welcome.

Schematics for the Timed Horological Epic