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.

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.

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.

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.

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

- As the boat speeds up, its bow and stern waves become longer
- The bow wave and the stern wave constructively and destructively interact. The produces peaks and valleys in the curve of resistance vs. speed.
- When the bow wave is as long as the boat, there will be a crest at the bow, a trough amidships, and a crest at the stern.
- To travel faster than this, the boat must climb it own bow wave
- This is hull speed

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

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.

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.

- Archimedes' Principle
- The Technology Process Model
- Hydrostatics, principles of ship stability
- Hydrodynamics, principles of ship resistance and powering
- Required Freight Rate, the cost of shipping

Obtain the following materials:

- Styrofoam sheets. Get them at your cafeteria. Buy the largest size. Estimate 2 to 3 sheets per student.
- One set of weights to use for the towing force. Have enough weights to produce up to 5 ounces of force in 1 ounce increments (
*e.g.*4, 2, and 1 oz. weights). - Hot wire cutter
- Craft Knives
- Hot glue guns and plenty of glue sticks
- Straight edges, scales, rulers

Make:

- 150, 1" X 1" X 4" blocks of wood to use as cargo "containers". Decorate as desired. The density of wood has an important effect on the stability of the barges. The lighter the wood,the more difficult the design. Don't use weights or anything heavier than water.
- 20 to 30, 1" X 1" X 2" blocks of wood. Each of these will count as a half container.

Setup:

- The towing rig on a tow tank, fill the tank to 5".
- The smart pulley on the tow line (or mark off 6 feet on the tank side.
- A computer to record data using the ULI Data Timer for the smart pulley (or use a stop watch to time the barges travelling 6 feet).

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.

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..

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:

Where:

- 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.

- Prior to commencing production , show your instructor
- A set of drawings of the proposed barge.
- A completed Ready to Start Building sheet that includes the calculated volume, displacement, and KM of the proposed barge and
- The estimated KG and GM of the loaded barge
- Manufacture the barge, mark the side with the design draft.
- Produce and present and oral report on your design
- Provide a performance demonstration, record the amount of cargo carried, the towing force used and maximum speed attained. Calculate R.
- 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.

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:

- L/B ratio. Longer thinner barges tend to go faster, but carry less cargo.
- B/T ratio. Barges with more draft carry more cargo, but might be slower and are probably less stable.
- Length. Longer barges can go faster with the same pulling force.
- Hull shape. Barges that have pointed ends and rounded bilges go faster but can carry less cargo
- Pulling force. More pulling force results in a faster barge. Will twice the pulling force result in enough speed increase to cover the increased cost?
- Structures. The barge must be strong enough to carry the cargo without breaking. But excess structural material is weight carried at your expense.