Beach Tide Calculator

Beach Tide Calculator estimates tide height at a specific time using high tide height, low tide height, their respective times, and the target time, based on a simplified sinusoidal model for semi-diurnal tides.

Enter values (times in HH:MM, 24h format):

High Tide Height (m):

Low Tide Height (m):

High Tide Time (HH:MM):

Low Tide Time (HH:MM):

Target Time (HH:MM):

Methodology Used in Beach Tide Calculator

The calculator estimates tide height using a sinusoidal model:

1. Tide Height: \( h(t) = \frac{h_{\text{high}} + h_{\text{low}}}{2} + \frac{h_{\text{high}} – h_{\text{low}}}{2} \cdot \cos\left(\frac{2\pi (t – t_{\text{high}})}{T}\right) \)

Where:

\( h(t) \): Tide height at time \( t \) (m)
\( h_{\text{high}}, h_{\text{low}} \): High and low tide heights (m)
\( t, t_{\text{high}} \): Target time and high tide time (hours)
\( T \): Tidal period, ~12.42 hours (semi-diurnal)

Assumes a simplified semi-diurnal tide cycle.

Example Calculation

Sample Input

High Tide Height = 3.5 m, Low Tide Height = 0.5 m, High Tide Time = 06:00, Low Tide Time = 12:30, Target Time = 09:00

Step 1: Mean height: \( \frac{3.5 + 0.5}{2} = 2 \, \text{m} \)

Step 2: Amplitude: \( \frac{3.5 – 0.5}{2} = 1.5 \, \text{m} \)

Step 3: Time difference: \( t – t_{\text{high}} = 9 – 6 = 3 \, \text{hours} \)

Step 4: Phase: \( \frac{2\pi \cdot 3}{12.42} \approx 1.52 \, \text{radians} \)

Step 5: Cosine term: \( \cos(1.52) \approx 0.058 \)

Step 6: Tide height: \( h(9) = 2 + 1.5 \cdot 0.058 \approx 2.09 \, \text{m} \)

Result: Tide Height ≈ 2.09 m at 09:00.