Can Iceberg Tugboats Beat Desalination? Modeling the Cost of Shipping Antarctic Ice

Background and Problem

The Persian Gulf suffers from severe water scarcity; desalination costs several pounds per cubic meter.

Experts propose towing icebergs from Antarctica, 9,600 km away, as an alternative to desalination.

The study investigates the economic feasibility of iceberg transport.

Model Preparation

Daily rental cost and maximum cargo capacity of the tugboat.

Fuel consumption (pounds per kilometer).

Melting rate (meters per day).

Model objective: choose vessel type and speed to minimize the cost per cubic meter of water delivered and compare it with desalination cost.

Model Assumptions

The vessel travels at a constant speed; total distance is 9,600 km.

The iceberg is spherical and melts uniformly over its surface.

Upon arrival, each cubic meter of ice can be melted into one cubic meter of water.

Model Analysis

Model Construction

Iceberg melting law: radius decreases linearly with time; melting rate is proportional to time and independent of other factors.

Travel distance after t days: d = 24 u t (u is ship speed in km/h).

Fuel consumption per kilometer is linear with distance.

Cost components include daily vessel rental, total fuel cost, iceberg initial volume, and volume delivered after melting.

Model Solution

The optimal vessel type and speed are searched by enumerating discrete combinations, using the derived formulas to compute total cost and cost per cubic meter of water.

Result Analysis

For a large tugboat of approximate size and a chosen speed, the cost per cubic meter of water delivered is about a few pounds, slightly lower than the desalination cost, but the model is highly simplified and ignores many adverse factors; the actual delivered volume would be significantly less.