Maths Sailing Question

[Ottiebow]

You are approaching a harbour which has a bar with a charted height 0.6 metres below chart datum. Your Boat draws 1.4 metres and owing to the fairly calm conditions, you judge that a clearance of 0.5 metres will be enough for safety.

What height of tide do you need to cross the bar? Assuming a perfectly sinusoidal tide pattern, if LW is at 1500hrs with a height of 1 metre and HW is at 2100hrs with a height of 4 metres,

What is the height at 1800hrs?

Your help would be much appreciated

[mike11111]

You need Molly for this one. She's the expert on boats.

[mollykins]

And maths hang on a mo while I work it out . . .

[mollykins]

the answer to the second part is 2metres, still working on the first bit.

[mollykins]

If you draw a graph of it for the second bit, the line crosses the 6pm line at exactly 2metres . . . if you wanted to know how that was done that it.

[mollykins]

No it's not, scrap that, as it starts at 1 metre hang on . . .

[mollykins]

i'm confused . . .:( sorry.

[mollykins]

The second bit is 2.5 metres at 6pm.

[Ottiebow]

thanks so much do you know the first bit - What height of tide do you need to cross the bar?

[mrs_overall]

The height of the tide at 1800hrs is 1.9 metres
With a clearance of 0.5m, this is the earliest time you can cross the bar

[mrs_overall]

Mollykins has worked it out wrong becaue she has not taken into account that the bar is 0.6m BELOW chart datum

[mike11111]

God, I'm impressed! There's more to you than just an overall!

[mrs_overall]

Thanks mike! There is more to me than my supermodel looks!

[mollykins]

true mrs-o.

[Ottiebow]

thanks to all of you - especially Mrs O

[nightmare]

If LW corresponds to a height of 1m and HW to 4m, then the height at 1800hrs (i.e. midway between LW and HW) must be 2.5m.
Thus there is 2.5 + 0.6 = 3.1m of water over the bar at 1800hrs
The height of tide (above datum) necessary to cross the bar is 1.4 + 0.5 - 0.6 = 1.3m.
i.e. 1.3m height of tide plus the 0.6m below datum of the bar to give 1.9m clearance.
....or have I got it completely wrong ?