Time and Tide Wait For No Woman: The Rule of Twelfths
From The Panama Cruising Guide, Fifth Edition, by Eric Bauhaus. Depths shown in meters. Not to be used for navigation.
I don’t want to panic anybody, but I’m nervous.
See that anchor symbol on the chart, between Isla Casaya and Isla Ampon?
That’s SV Hanalei.
See that large reef growing around us?
Take a closer look.
Those ++ signs on yellow signify rocks; the yellow scallops are reef.
NOW do you see it?
Looking southeast from Isla Casaya toward Isla La Mina, low tide.
It isn’t coral, it’s hard rock. Not like the cafe. More like holing the boat.
As I watch the tide fall, I’ve been pondering the musical question, how will we get out of here?
Now you don’t see the entrance…
… now you do.
About Charts
The chart makes it look easy enough to plot my way out, but there are caveats.
Chart depths shown are approximate, not absolute. Their contours are extrapolations based on old surveys and new soundings. They can’t account for every rock on an uneven seabed, let alone changes since the data were collected. The more remote the area, the less reliable the chart.
That’s why the disclaimer, “not to be used for navigation.”
Neither is our chart plotter, according to the fine print I just read, and it's not nearly as detailed. According to their lawyers, I am on my own.
Go figure.
What we all agree on is to use multiple sources when navigating.
Or any time.
Low, Rising Tide
I need help.
The cruising guide advises me to leave on a “low, rising tide.” No further explanation.
How low is too low? Rising how much?
The idea is that if we “touch”–the sailor’s euphemism for bottoming out–a rising tide will float us off. Eventually. Unless water is pouring through the hole I just made.
And if we hit bottom on a high tide, it’s a bad day.
So, yes, I’m nervous. Nervous enough to resort to numbers.
Tidal Arithmetic
The Chief Engineer shoots me a look. He thinks I don’t do numbers.
This is untrue.
I don’t do math numbers–math puts me to sleep–but I do excellent arithmetic. If classroom word problems used coral reefs and limestone rocks instead of trains and stations, I would have progressed far beyond math not-genius.
I’m sorry to do this to a perfectly nice blog, but I’m dropping in a word problem.
Christine is nervous about crossing the reef. She wants to do it with 1.5 meters more water than the chart says, so there’s room to make mistakes. How soon after low tide should she leave? Calculate the tidal range and flow based on tide table (or boating app with tides).
Show your work.
Tides
From her boating app, Christine learns high tide is 4.24m (13.78’) at 6:38 pm. Low tide is -.39m (-15.2” or 1.26’) at 12:22 pm. High and low are 6 hours and 16 minutes apart.
It’s a few days past the full moon so tides are higher and lower than normal–.39m (15”) LOWER than the chart, to be exact.
There’s also the matter of the tide times being approximate. These are for Isla del Rey, twelve miles away. No offsets are available to calculate time differences in anchorages, another reason to use caution.
U.S. Cheat Sheet
1 METER = 39 INCHES (3.3 FEET)
.1 METER = 3.9 INCHES
Tidal Range
Now that Christine knows the tides, she can figure out the day’s tidal range, the height difference between low and high tides. She knows to SUBTRACT low tide from high tide, but this low tide is negative. Fortunately, she remembers that subtracting a negative number is the same as ADDING it, avoiding a rookie trap.
Tide Meters Feet
High 4.24 13.78’
Low + .39 + 1.26’
Range 4.63 15.04’
If low tide is -.39 m and high tide is 4.24 m (-1.26’ and 13.8’), the day’s tidal range is 4.63m (15’). That’s why, although she anchored in eight meters at high tide, she has less than four at low.
Correct. So, two hours after low tide , how much depth do you have over what's charted?
No problem. Christine knows the amounts are cumulative. High and low are 6 hours and 16 minutes apart.
15-ish feet divided by 6-ish hours is 2-ish feet per hour, right?
She shows her work to the Chief Engineer.
“Partial credit. Be more precise.”
Easy peasy.
.77 m (2.4 feet) per hour. Two hours after low tide, I’ll have 1.54m (4.8 feet) of extra water.
The Chief Engineer shakes his head in not-amazement.
Rookie mistake.
Rule* of Twelfths
To calculate the depth correctly, Christine needs to use The Rule of Twelfths.
Tides aren’t static. They take a while to get rolling, then peak and slow down. The Rule provides a rough estimate of what’s happening.
The Rule says the first hour after low tide, 1/12 of the tide comes in; second hour, 2/12; third hour, 3/12; fourth hour, 3/12; fifth hour, 2/12; sixth hour 1/12.
Hour 1 1/12
Hour 2 2/12 (1/6)
Hour 3 3/12 (1/4)
Hour 4 3/12 (1/4)
Hour 5 2/12 (1/6)
Hour 6 1/12
*It’s a rule, not a law. Like the Pirate Code, it’s more what you’d call ‘guidelines’ than actual rules.
How To Apply It
1. Divide the tidal range by twelve to find the base rate (or what 1/12 is today).
4.63m /12 = .385
or
15’ /12 = 1.25’.
2. Multiply the base rate hourly according to the Rule.
Example
Here’s a table. It shows the suggested base rate of tidal movement, cumulative added depth and how much actual depth there is over datum (OD).
Hr. Rate. Cumul. OD
1 .385 or 15” or 1.25’ same 0
2 .77m (.385 x 2) 1.15m .77m (2.5’)
3 1.15m (.385 x 3) 2.3m 1.15m (6.25’)
On a chart that shows two meters of depth, there won’t be two meters until almost three hours after low tide.
4 1.15m (.385 x 3) 3.4m 3.0m (10’)
5 .77m (.385 x 2) 4.3m 3.7m (12.5’)
6 .385m 4.6 m 4.24m (13.78’)
What It Shows Us
Hour 1 The tide is NEGATIVE; -39 (-15”) under mean low tide. That’s about the same as 1/12 of the range. The amount that comes in the first hour will only bring the depth up to the chart datum. An hour after low tide, you’ll still see tidepools on the reef. There’s virtually no extra water
Hour 2 After two hours, there’ll be an extra meter of water, not the 1.5 meters Christine thought she’d have.
Hours 3 - 4 Fully half the total comes in during peak flood the third and fourth hours.
After three hours, half the tide has come in or gone out. After four hours, it’s three-quarters.
Hour 5 The flood covers the reef; ebb reveals tidepools. You still have 1/4 of the water left to go. You’re almost at high or low tide an hour beforehand.
Hour 6 Reef? What reef? Nothing to see. Or you see nothing but.
Pelican working hard at Isla Casaya.
Got it.
Two-and-a-half hours after low tide, there’ll be enough water to make it past the reef.
Toolkit:
Tide table
Tidal range
Rule of Twelfths
All these numbers make me sleepy. I’m going to hit the hammock and supervise the pelicans. The Chief Engineer can wake me when it’s time to go.
Fair winds,
Christine
P.S. Not to be used for actual navigation.
Do Tell
Do you have a rule of thumb–or guidelines–when you navigate a reef?
