Tide Calculations for Rescue and Ship Refloating

Posted on May 4, 2024 in Mathematics

RESCUE AND SHIP REFLOATING

CALCULATION OF TIDES for refloating

This guide explains how to calculate tides for rescue and ship refloating operations.

DEFINITIONS:

  • DM: Duration of the trip (time between high and low tide)
  • HP: Height of high tide
  • HB: Height of low tide
  • A: Amplitude of the tide (difference between high and low tide)
  • Sc: Probe letter (depth measured from the water surface to the seabed)
  • PRF.REAL: Real depth (actual depth of the water, considering the tide)

REAL DEPTH CALCULATION:

Example: Calculate the actual depth on March 24, 2006, at 18:46, with a probe letter (Sc) of 9.27m.

  1. Using tide tables, find the high tide height at the given time (18:46). In this case, it is 3.19m.
  2. Add the high tide height to the probe letter to get the real depth.

PRF.REAL = Sc + hp = 9.27m + 3.19m = 12.46m

PROBE LETTER CALCULATION:

Example: Calculate the probe letter on April 26, 2006, at 17:45, knowing that the real depth (Prf.real) is 21m.

  1. Using tide tables, find the low tide height at the given time (17:45). In this case, it is 1.35m.
  2. Subtract the low tide height from the real depth to get the probe letter.

Sc = Prf.real – hb = 21m – 1.35m = 19.65m

CALCULATING THE HEIGHT OF THE TIDE AT A PARTICULAR TIME:

Example: Calculate the height of the tide at 4:30 am on August 2, 2006.

  1. Using tide tables, find the high and low tide times and heights before and after the given time (4:30 am).
    • Low tide: 00:01 – 0.97m
    • High tide: 06:14 – 3.11m
  2. Calculate the duration of the trip (DM) between high and low tide.

DM = 06:14 – 00:01 = 06:13 hours

  1. Calculate the amplitude of the tide (A).

A = HP – HB = 3.11m – 0.97m = 2.14m

  1. Use the universal tide table to find the closest DM and A values to the calculated ones. In this case, DM = 06:15 and A = 2.2m.
  2. Calculate the time interval (I) between the given time and the previous low tide.

I = 04:30 – 00:01 = 04:29 hours

  1. Use the universal tide table with the closest DM and A values to find the additive correction for the given time interval (I). In this case, the correction is 1.8m.
  2. Add the correction to the low tide height to get the tide height at the given time.

HM = HB + Correction = 0.97m + 1.8m = 2.77m

CALCULATING REAL DEPTH AT A SPECIFIC TIME:

Example: Calculate the real depth on March 5, 2006, at 13:00 with a probe letter (Sc) of 10m.

  1. Follow the steps above to calculate the tide height at the given time (13:00). In this case, the tide height is 1.4m.
  2. Add the probe letter, the low tide height, and the tide height to get the real depth.

PRF.REAL = Sc + HB + Tide Height = 10m + 0.51m + 1.4m = 11.91m

CALCULATING THE TIME FOR A SPECIFIC DEPTH:

Example: Calculate the time when the depth will be 12m on August 8, 2006, with a probe letter (Sc) of 10m. The tide must be young and growing.

  1. Calculate the difference between the desired depth and the probe letter.

Depth Difference = 12m – 10m = 2m

  1. Using tide tables, find the low and high tide times and heights that are closest to the depth difference, ensuring the tide is young and growing.
    • Low tide: 04:33 – 1.31m
    • High tide: 10:57 – 2.85m
  2. Calculate the DM and A values as before.

DM = 06:24, A = 1.54m

  1. Calculate the time interval (IA) between the desired depth and the previous low tide height.

IA = 2.0m – 1.31m = 0.69m

  1. Use the universal tide table to find the time interval corresponding to the calculated IA and DM values. In this case, the time interval is 03:02.
  2. Add the time interval to the previous low tide time to get the time when the desired depth will occur.

Time = 04:33 + 03:02 = 07:35

CALCULATION FOR RESCUING A STRANDED SHIP:

Example: We want to refloat a stranded ship on January 11, 2006, at 15:00 with a high tide height (HM) of 7.32m. The ship needs 8.9m of water to refloat. When can we refloat the ship?

  1. Calculate the tide height at the given time (15:00) as before. In this case, the tide height is 1.43m.
  2. Subtract the tide height from the high tide height to get the probe letter (Sc).

Sc = HM – Tide Height = 7.32m – 1.43m = 5.89m

  1. Subtract the probe letter from the depth needed to refloat the ship.

Depth Needed – Sc = 8.9m – 5.89m = 3.01m

  1. Using tide tables, find the next date and time when the tide height will be greater than 3.01m. In this case, it will be on January 17, 2006.

Therefore, the ship can be refloated on January 17, 2006, when the tide height is sufficient.