Rule of Twelfths Spreadsheet

A

ancientsailor

Well-Known Member
Joined
19 Feb 2005
Messages
218
Location
Somerset
www.sailskills.co.uk
I had a query about interpolation from South Africa.

Apparently the rule of twelfths is used there over the full interval between HW and LW :eek: and to an accuracy of 0.01 m (1cm) :eek: :eek: – not the six hours and 0.1 m I’m used to.

When I recovered from the shock and answered the questions :confused: I spent some time on the problem and developed a spreadsheet.

Anyhow, if anyone wants it I’ve put it on my website where it can be downloaded free.

http://www.sailskills.co.uk/Webdemo_Tides/rule of 12s note.html

If anyone wants to comment on the sheet, I have put links into it.

Enjoy!
 
I'm sure that's correct and probably accurate but I've always thought that the beauty of rule of twelfths is it's simplicity and that it can be done in your head.
 
DanTribe said:
I'm sure that's correct and probably accurate but I've always thought that the beauty of rule of twelfths is it's simplicity and that it can be done in your head.
Click to expand...

That was exactly my reaction (and the way I use it) ... but it seems not always elsewhere. Perhaps it's something to do with less widely-available tidal data in some parts - or just the way it's taught?
 
DanTribe said:
I'm sure that's correct and probably accurate but I've always thought that the beauty of rule of twelfths is it's simplicity and that it can be done in your head.
Click to expand...

There's a rule of tenths, which should be easier.


Rule of tenths.
The rule of twelfths works well enough for anyone used to working with feet, fathoms, etc.

For anyone more at home working in decimal the rule of tenths might be easier to use.

So, instead of using twelfths uses percentages.
•10% for the 1st hour of range


•15% for the 2nd hour of range


•25% for the 3rd hour of range


•25% for the 4th hour of range


•15% for the 5th hour of range


•and 10% for the 6th hour of range


Read more: Rule of Twelfths for quick tidal estimates http://www.diy-wood-boat.com/Rule_of_twelfths.html#ixzz12j5QqBNi
Under Creative Commons License: Attribution
 
Last edited:
The rule-of-twelfths loses a lot of its elegance when applied to metric data. In the days of feet and inches, if you knew the tidal range was x feet then one twelfth of that was x inches.
 
If you are using a spreadsheet, you could put the local coefficients in.
Rule of twelfths only works very vaguely on much of the UK south coast. It might well work better in SA, where the tide is much less diverted by land masses.
Anyone doing tide calcs to 1cm around here is wasting their time, except to show the method is right and they can do the maths properly.
A look at a few tide gauges will show the weather influence is often >10cm without any 'big' weather events. Not rare for it to be >30cm, especially around the 20% or 80% areas of the curves.
Why not use the spreadsheet to compare the different rules with the curve in the almanac for a few local ports?
 
Rules

I dug this out from my YM Theory course notes, may be relevant.

TIDAL HEIGHT CORRECTIONS RELATED TO PRESSURE

963 mb +0.5m
973 mb +0.4m
983 mb +0.3m
993 mb +0.2m
1003 mb +0.1m
1013 mb 0
1023 mb -0.1m
1033 mb -0.2m
1043 mb -0.3m

Sticky
 
Inadvertently started another hare running here!

My own experience of the rule of twelfths is that it's a simple, rough way of quickly making an informed approximation of tidal ht - normally by mental arithmetic.

But ... I was asked to help someone in interpolating to 1 cm over (say) 72 mins

The spreadsheet is only to allow a quick verification of the interpolation ... I became interested in the problem and thought others might find the spreadheet helpful

Atmospheric pressure was discussed earlier this year at

http://www.ybw.com/forums/showthread.php?t=236960&highlight=average+pressure
 
Not sure why you would want to take this route but it is late and my brain isn't working - not that it works well at any time.

The rule of twelfths is an approximation of the movement you might see on a typical tide but then every tide is a bit different and so the accuracy of approximation will vary. Add into that atmospheric pressure effects and wind effects, and whilst you might mathematically be calculating a number to 1 cm or whatever you have set your spreadsheet to do, the actual tide height you get wont be to anything like that accuracy. It's spurious accuracy - kiddology if you like.

But in any case the sailor who relies on a tidal height calculated to 1cm is a plonker - it would be rare that the sea is flat to within 1 cm.

Am I missing something obvious here - got to be!

P.S. There is a similar accuracy error that some of my students have made - plotting a GPS position on a chart and believing it is within the 7 metres accuracy sometimes quoted for the GPS system . Leaving aside that interpretation of the GPS accuracy stats, they are ignoring the tolerances in the charts themselves and even the thickness of the pencil line
 
OK my darlings, it's late but I couldn't resist some quick hackery in C and GnuPlot...

twelfths.jpg


This shows a sinusoidal rise and fall compared to a straightforward rule of twelfths (round to the nearest hour) and an interpolated rule of twelfths (interpolate between the hour before and the hour after).

The maximum error with the simple rule is 10.4% or range, rms error 5.3% and the maximum error with the interpolated version is 2.5% of range, rms error 1.5%.
 
Ubergeekian said:
OK my darlings, it's late but I couldn't resist some quick hackery in C and GnuPlot...

twelfths.jpg


This shows a sinusoidal rise and fall compared to a straightforward rule of twelfths (round to the nearest hour) and an interpolated rule of twelfths (interpolate between the hour before and the hour after).

The maximum error with the simple rule is 10.4% or range, rms error 5.3% and the maximum error with the interpolated version is 2.5% of range, rms error 1.5%.
Click to expand...

Which I think shows how useful the rule of twelfths can be much of the time.
 
Tides

I appreciated the chart on Barometric pressure versus height. I always knew it were so but have not seen this chart. Around here we mostly have very small Astronomical Tides so although predictions are given they can't account for Baro Pressure. Then of course the winds make a difference. In summer we always get a wind off the sea. This always raises the water level.
My guess then is that here Baro Pressure Wind and moon can all have equal amount of effect. (that is generalised and not necessarily accurate of course). I realise in UK Astronomical tides are so huge that they dominate all other effects. olewill
 
oldfatgit said:
Which I think shows how useful the rule of twelfths can be much of the time.
Click to expand...

Use it all the time as a rough bit of mental arithmetic when anchoring.

But Geeky's calculations rely on a base assumption - the sinusoidal curve. How many tidal curves really are a true sine wave? very few I suspect since many arent even symetrical about HW. But even taking the calx at face vale a max error of 2.5% on a range of (say) 5 metres is 125cm

Sorry but I dont see the point of using a lappy and a spreadsheet to apply the rule of twelfths given the ready availability of full tidal curves to do the job right.
 
sticky said:
I dug this out from my YM Theory course notes, may be relevant.

TIDAL HEIGHT CORRECTIONS RELATED TO PRESSURE

963 mb +0.5m
973 mb +0.4m
983 mb +0.3m
993 mb +0.2m
1003 mb +0.1m
1013 mb 0
1023 mb -0.1m
1033 mb -0.2m
1043 mb -0.3m

Sticky
Click to expand...

It might be amusing to compare this with observations locally.
My feeling is that tides are not so simply influenced by local pressure, you have to look at the distribution of pressure around the English Channel, and how it has changed over the last couple of days.
http://www.pol.ac.uk/ntslf/networks.html
This site will give some real measurements.

But, care is always required, I once dried my boat against the wall here in Portsmouth and found the high tide was a good foot above predicted. I would have been in trouble if I'd relied on predicted and beach it at the peak of tide!

When I was first let out on a cruising boat, I tried anchoring in Studland, reasoning that the tide would have already fallen by 3/12ths. You learn from experience, and what I learned from that was how to read local tide curves! (And Bilge keelers have their uses!).
 
Bosun Higgs said:
Use it all the time as a rough bit of mental arithmetic when anchoring.

Sorry but I dont see the point of using a lappy and a spreadsheet to apply the rule of twelfths given the ready availability of full tidal curves to do the job right.
Click to expand...

Yup...that's my approach as well. Rule of twelfths in my head for anchoring purposes, otherwise use a published curve if the shape is likely to be unusual.

But this discussion on the theory is nevertheless interesting and reminds us all that accuracy is meaningless unless one can take account of barometric pressure, surge, swell, etc. So even for general navigation the Rof12ths (or 10ths?) plus a sensible safety margin is surely all we need in reality?
 
Bosun Higgs said:
Sorry but I dont see the point of using a lappy and a spreadsheet to apply the rule of twelfths given the ready availability of full tidal curves to do the job right.
Click to expand...

To be honest, I've never really seen the point of using full tidal curves to make calculations to high precision, when other effects - pressure, storm surges and so on - mean that the basic curves are often inaccurate to start with. Perhaps if I sailed on the east coast I'd feel differently ...
 
An interesting theoretical discussion indeed.

Why Did I Do It?

I queried with my South African Correspondent why he was being asked to interpolate to 1 cm over the full period, when as far as we are concerned (in the UK) rule of 12ths is usually rough and ready over 6 hrs. Yes, I did point 1 cm is pretty insignificant compared with likely weather effects ...

His response was to the effect that they were required to do it this way and followed up with a couple of questions he was working on for his certificate (to 1 cm, 1 minute, over the full period of the tide)!

After demonstrating graphical and mathematic methods of interpolating for him, I felt a spreadsheet would be a useful back-up in checking the accuracy of the calculations - I quite liked the challenge(!):o

I do not advocate use for accuracy - I use the curves!

Pressure Variation

However, I just make a comment about pressure variations and effect on tide which was discussed fully in the thread http://www.ybw.com/forums/showthread.php?t=236960&highlight=average+pressure

Admiralty tidal predictions are based on the average pressure for an area, which changes over the year. So the tables of pressure effects in this thread have to be used with some care. They may be based on a different average to that used by the Admiralty.

This was the subject of considerable debate before any consensus was reached, so here's the current quote from the Admirality Easytide website

"Q: Predictions are referred to being computed for average barometric pressure. What is average, and how do tides react to differences from this average?

A: Tidal predictions are computed for average barometric pressure at the particular place concerned. The average barometric pressure for certain places is given in Admiralty Sailing Directions and information is also given in some instances concerning the changes in level which can be expected under different conditions.

A difference from the average of 34 millibars can cause a difference in height of about 0.3m. A low barometer will tend to raise sea level and a high barometer will tend to depress it. The water level does not, however, adjust itself immediately to a change of pressure and it responds, moreover, to the average change in pressure over a considerable area. Changes in level due to barometric pressure seldom exceed 0.3m but, when mean sea level is raised or lowered by strong winds or by Storm Surges (wind-induced long period waves causing higher and lower-than-predicted levels to occur), this effect can be important." http://easytide.ukho.gov.uk/EASYTIDE/EasyTide/Support/faq.aspx
 
You must log in or register to reply here.

Share this page

Top