When can you cross (time for a height)

How to think it through

1It is the reverse of height at a time: you know the water you need and look for when it is there.
2Work out the height of tide you need (draught + clearance − charted depth) and how many twelfths that is.
3Add the twelfths hour by hour until you reach it; in the last hour, take the proportion.

Worked example

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

When can you cross: time for a height

You must cross a bank charted at 0.2 m. Your draught is 1.8 m and you want 0.3 m under the keel. LW 08:35 (1.0 m), HW 14:50 (4.0 m). From what time can you cross?

Charted depth: 0.2 m
Draught · clearance: 1.8 m · 0.3 m
Low water: 08:35 · 1.0 m
High water: 14:50 · 4.0 m

What height of tide do you need to get across?
Why: You get across when the water covers draught plus a margin over the charted depth: the tide must make up the difference.
$h_{required} = Draught + Clearance - Charted depth$
Working: 1.8 + 0.3 − 0.2 = 1.9 m
Answer: 1.9 m
What is the range?
Why: Twelfths are fractions of the range: you need the total rise.
$Range = h_{HW} - h_{LW}$
Working: 4.0 − 1.0 = 3.0 m
Answer: 3.0 m
How many twelfths of the range must rise above low water?
Why: The rise you need, divided by the range and times 12, tells you how far into the tide you get.
$n = \frac{h _{required} - h _{LW}}{Range} \times 12$
Working: (1.9 − 1.0) ÷ 3.0 × 12 = 3.6/12
Answer: 3.6 /12
From what time is there enough water (rising tide)?
Why: Add the twelfths hour by hour (1, 2, 3, 3, 2, 1) until you reach what you need; inside the last hour, work out the proportion.
$T = T_{LW} + (k + \frac{n - n _{k}}{d _{k + 1}}) \times tidal hour$
Working: After 2 tidal hours: 3/12. You still need 0.6 of the 3 in the next hour, i.e. 0.20 of an hour. Time after LW: 2.20 × 63 min = 137 min → 10:53
Answer: 10:53

Now you try

With the examiner (even from a photo)