当知道上一个和下一个潮汐时获取当前潮汐高度

Question

I'm trying to calculate the current tide height based on the height of the previous tide, the height of the next tide, and the time difference of the two.

I've tried to use this formula as a start but I think I either have something wrong in the formula or the formula won't work based on only having the previous and next tides (or both, and I'm way off):

Found here: https://www.dummies.com/article/academics-the-arts/math/trigonometry/measure-tidal-change-using-a-trigonometry-graph-187108/

I'm trying to solve this in Kotlin but can translate from any other language if given a working example.

My code looks like this:

val previousTideHeight = 5.3
val nextTideHeight = -.3
val timeBetweenTides = 60 * 60 * 6 // 6 hours in seconds
val timeSincePrevTide = 60 * 60 * 3 // 3 hours in seconds
val tideHeightDifference = previousTideHeight - nextTideHeight
val averageTideHeight = tideHeightDifference / 2
val tideAmplitude = Math.max(Math.abs(averageTideHeight - previousTideHeight), Math.abs(averageTideHeight - nextTideHeight))
val currentHeight = (tideAmplitude * Math.sin(Math.PI / timeBetweenTides) * timeSincePrevTide) + averageTideHeight

Answer 1

After messing with everything for a little I ended up with a formula that seems to be working but would love any feedback on it as I'm not totally certain how it all works.

val previousTideHeight = -1.3
val nextTideHeight = 5.2
val hoursBetweenTides = 6
val hoursSincePrevTide = 0

val timeBetweenTides = 60 * 60 * hoursBetweenTides
val timeSincePrevTide = 60 * 60 * hoursSincePrevTide

// We need to shift the graph horizontally based on the time since the previous tide
// and we need to produce a negative number so that we can get a value below the equilibrium
val timeShift = (timeSincePrevTide - (timeBetweenTides / 2)) * 2

// If the tide is going down we need to shift the graph the
// other direction to catch the down slope
val tideDirectionMultiplier = if (previousTideHeight > nextTideHeight) -1 else 1

val tideHeightDifference = previousTideHeight + nextTideHeight
val averageTideHeight = tideHeightDifference / 2

val tideAmplitude = Math.max(Math.abs(averageTideHeight - previousTideHeight), Math.abs(averageTideHeight - nextTideHeight))
val currentHeight = (tideAmplitude * Math.sin((Math.PI / (timeBetweenTides * 2)) * (timeShift * tideDirectionMultiplier))) + averageTideHeight

return currentHeight