Height of tide at a given time

How to think it through

1You have the times and heights of LW and HW; you want the height at a given time.
2Split the tide into six tidal hours: the first rises 1/12 of the range, then 2, 3, 3, 2, 1.
3Height = LW + twelfths risen × range. Then add the charted depth to get the depth of water.

Every step says why you do it, which formula you use, the working and the answer.

Height of tide by the rule of twelfths

Low water 10:25 (1.0 m), high water 16:45 (5.5 m). What is the height of tide at 11:28?

What is the range of the tide?
Why: Twelfths are fractions of the range: first you need the total rise.
$Range = h_{HW} - h_{LW}$
Working: 5.5 − 1.0 = 4.5 m
Answer: 4.5 m
How many minutes is one tidal hour?
Why: The tide rarely takes exactly six hours: split the real duration into six tidal hours.
$Tidal hour = \frac{T _{HW} - T _{LW}}{6}$
Working: 6 h 20 min = 380 min ÷ 6 = 63 min
Answer: 63 min
By 11:28, how many twelfths of the range have risen?
Why: The tide rises slowly, then fast, then slowly: 1, 2, 3, 3, 2, 1 twelfths hour by hour.
$n = 1 + 2 + 3 + 3 + 2 + 1 (up to the hour you need)$
Working: 1 = 1/12
Answer: 1 /12
What is the height of tide at 11:28?
Why: Add to low water the part of the range already risen.
$h = h_{LW} + \frac{n}{12} \times Range$
Working: 1.0 + 4.5 × 1/12 = 1.38 m
Answer: 1.38 m
A bank dries 0.8 m (underlined on the chart). How much water is over it at that time?
Why: Drying ground is above chart datum, so its height is subtracted.
$Depth = h - drying height$
Working: 1.38 − 0.8 = 0.57 m
Answer: 0.57 m