Hydrodynamics deals with water in motion (e.g. a boat moves through the water). The Canal Barge Challenge, Cargo Ship Challenge, and Comet Cup all deal with hydrodynamics.

Ship Geometry

How fast will it go?

In the age of sail, the total sail area in a design was based on rules of thumb and centuries of experience. These rules of thumb were passed from father to son, until Samuel Pepys the famous diarist traded his families knowledge for a position in the admiralty.

In the 1800's steam replaced sail, but no one was sure how big a motor was required to power a boat. William Froude solved this problem by developing a method of predicting ship resistance (and hence powering requirements) from model tests. In doing so, he divided resistance into three parts. Based on Froude's work, Total Resistance consists of frictional resistance, wavemaking resistance, and other minor factors.

Frictional Resistance

results from the friction between the skin of the boat and the surrounding water. For a smooth hull, this resistance depends only on the wetted surface area of the hull. The frictional resistance increases as the square of boat speed.

Wave Making Resistance

A boat underway produces a characteristic wave pattern consisting of transverse and divergent waves. The wave pattern travels at the speed of the boat. Since the group velocity of the waves is on half of the wave velocity (celerity), energy must be continuously supplied to produce the wave pattern.

Longer waves travel faster, faster waves are longer

The speed of a wave in deep water is

c (ft/sec) = 2.26 times the square root of the length of the wave in feet
Hull speed (ft/sec) = 2.26 times the square root of boat length in feet
Hull speed (knots) = 1.34 times the square root of boat length in feet.

Other Stuff

there are other minor factors in resistance, such as form resistance.

Basic model tests do not account for the resistance of appendage (such as the rudder). These must be accounted for separately.

Canal Barge

Students design and build small barges out of styrofoam (or other materials if they desire). These barges will then be loaded with cargo (wood blocks) and towed in the tow tank. Towing force is provided by a weight and pulley system. The speed of the barge is recorded. The object is to design the barge that will carry cargo the most efficiently. This is the barge that will carry the most cargo the fastest with the least towing force.

Principles taught

Instructor Guide


Obtain the following materials:



Required Freight Rate

The shipping business is very competitive. Coustomers will usually choose the company that charges the least amount of money. The amount of money charged is usually expressed as dollars per ton-mile, know as the Freight Rate. The minimum freight rate that a company must charge to make an acceptable profit is called the Required Freight Rate. The shipping system with the lowest Required Freight Rate will generally get most of the customers, or make the most money, or both.

In our model, we relate the towing force (F) to the cost of fuel, the major contributor to freight rate. If we can move the most cargo (W), at the fastest speed (V), with the least F, we will have the lowest Required Freight Rate (R). In our model, we use a simplified calculation for R where in R = (3 + F ) / (V W). The "3" in the formula represents the costs of operating the barge (crew, capital, etc.) that are independent of speed.

Student handout

The need

Since before recorded history, people have used boats as a means of transportation. Until the middle of the last century, boats were the only way to carry large amounts of cargo. It is no accident that most major cities, have grown up on the seacoast or navigable rivers. In the 1800's large systems of canals were built to connect inland cities. Barges on rivers and canals are still one of the most important ways of moving cargo at relatively inexpensive cost. Barges may also be part of a larger intermodal transportation system using shipping containers to move cargo from origin to destination while still packed in the same container..

The Technology Problem

Construct a barge to be towed in a canal system. The barge must be able to navigate the canal systems both loaded and unloaded. Cargo consists of shipping containers that come in full-sized (1" X 1" X 4") and half-sized (1" X 1" X 2"). The canal system has these characteristics.
Controlling depth of water 5 inches
Smallest locks 11 inches long and 8 inches wide
Clearance under lowest bridge 6 inches

The barge should be constructed to carry cargo in the most economical manner, as determined by the following formula:

R = (3 + F) / (V x W)


R is the Required Freight Rate. This factor is to be minimized.
W is the number of full container equivalents
V is the highest speed of the barge
F is the force required to tow the barge

The barges will be tested by towing them in the tow tank while fully loaded. The amount of towing force will be chosen by the student, but cannot exceed 5 ounces. Any barge that ships water or capsized at any time during a run will be disqualified for that run. A minimum GM of 0.5 inches is required.

The Output

  1. Prior to commencing production , show your instructor
  2. Manufacture the barge, mark the side with the design draft.
  3. Produce and present and oral report on your design
  4. Provide a performance demonstration, record the amount of cargo carried, the towing force used and maximum speed attained. Calculate R.
  5. At the conclusion of this activity, prepare and submit a written report. The report must include a set of drawings of the completed barge, the results of the performance demonstration, and the cost of resources used.

Factors to Consider

Technology design problems, unlike other kinds of problems that you may have solved, have no one best solution. Every solution to a design problem involves a series of tradeoffs between competing parameters. The goal is often to optimize a certain result. Some of the tradeoffs associated with this design are:


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