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Transportation and Ship Design

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The content and activities in this topic will work towards building an understanding of buoyancy and gravity, as forces influencing ship design and water transportation.

Boats come in many different shapes and sizes (Fig. 8.32). Larger boats are generally referred to as ships. The main feature of a successful boat design is the ability to stay afloat in water. The physical force that keeps boats and other objects floating in fluids is called buoyancy.


Fig. 8.32. (A) A rowboat is used to travel on a river.

Image courtesy of Silje L. Bakke, Wikimedia Commons

Fig. 8.32. (B) A trimaran is a boat with three hulls.

Image courtesy of WPPilot, Wikimedia Commons


Fig. 8.32. (C) A tugboat is pulling a flat-bottomed cargo barge.

Image courtesy of DAVID ILIFF, Wikimedia Commons

Fig. 8.32. (D) A submarine breaches the surface of the ocean.

Image courtesy of US Navy


Buoyancy and Flotation

Buoyancy is the force that supports things in a liquid or gas. When a ship is floating in still water, the pressure of water on the boat below the waterline pushes upward, creating a buoyant force. Net buoyant force on an object is the difference between the ability of the liquid to support that object and the gravitational force working to sink it.

  • When the net buoyant force on the object is zero, the object floats and is stationary.
  • When the net buoyant force is positive (+), the object rises.
  • When the net buoyant force is negative (–), the object sinks.


The equation for the net buoyant force of a boat is

Net buoyant force = buoyant force – mass of boat


The buoyant force is equal to the mass of the water displaced by a boat. Force is the amount of push or pull on an object. Force can be measured in a number of ways and is often expressed as Newtons, a unit that is proportional to an object’s mass and acceleration. Another unit often used to measure force is the gram force (gf), defined as the force of gravity on 1 g of mass at sea level. A kilogram force (kgf) is 1,000 times as large as a gram force.


Ships can float, even though the material they are made of is denser than water. The principle of flotation explains how ships float. The principle of flotation states that a floating object displaces a weight of liquid equal to its own weight.




Fig. 8.33. A 204 kgf iron block sinks, whereas a 204 kgf iron bowl floats.

Image by Byron Inouye

Consider a one cubic foot (1 ft3) solid block of iron shown in Fig. 8.33. It weighs 204 kgf (450 lb). Placed in water, the iron block rapidly sinks, displacing its own volume of water, which is 1 ft3. (A cubic foot of water weighs 28.3 kgf or 62.4 lb.) This is evidence of a downward force on this block of 204 kgf and an upward force of 28.3 kgf. The greater downward force causes the block to sink.


Suppose the same iron block were reshaped into the iron bowl shown in Fig. 8.33. The iron bowl displaces a much greater volume of water than the iron block, but the bowl’s weight remains the same at 204 kgf. If we place the bowl gently onto the surface of the water, it settles and floats. The floating bowl has displaced its own weight of water. The iron bowl floats because it has an upward force of 204 kgf equaling the downward force of 204 kgf.


The principle of flotation, first discovered in 250 BC by Archimedes, can be easily demonstrated. However, iron ship advocates were still being called fools in the late eighteenth and early nineteenth centuries. “Wood can swim; iron can’t,” sailors would say. John Wilkinson built the first floating metal boat in 1787, a 70 ft barge constructed of iron plates. This vessel was the forerunner of the steel ships sailing the ocean today. Modern building materials such as fiberglass and high-quality plastics provide both strength and low-density materials for smaller vessels like racing boats, canoes, and kayaks. However, larger transport vessels such as cargo container ships and naval warships are still built primarily of metal (Fig. 8.32).


Ship Tonnage

Ship tonnage is a measure of what a ship can carry. The two major categories of ship tonnage are tonnage by weight and tonnage by volume (Fig. 8.34). Tonnage by weight, or displacement, is the weight of water displaced by a loaded vessel. This weight is expressed in metric tons. A metric ton is the weight of 1 m3 of fresh water. Tonnage by volume is based on the English system of the measure of cubic capacity. In this system, 100 ft3 is called a ton. It is equal to 2.83 m3. For example, a ship that has a tonnage by volume of 1,000 tons can hold 100,000 ft3 of cargo.


Image caption

Fig. 8.34. Two categories of ship tonnage are (A) tonnage by weight and (B) tonnage by volume.

Image copyright and source

Image by Fan Yang


Ship Displacement

To gauge a ship’s weight, or its displacement, at any time during the loading or unloading of cargo, the ship’s officers take the average of the bow (forward part of the ship) and stern (back part of the ship) drafts, the vertical distance from the waterline to the keel (lowest structural point on ship). The heavier a ship is, the lower it sits in the water, and the greater the weight of displaced water. Draft marks on a vessel’s bow show the distance in feet (ft) from the keel to the waterline. An enlargement of the bow draft of the ship in Fig. 8.35 shows that the bow draft is 30 ft (approximately 9.1 m). Look at the displacement curve shown in Fig. 8.35 for the ship in Fig. 8.35. Different ships have different displacement curves. If this ship were loaded to its 25-foot draft mark, it would have a displacement of approximately 18,000 metric tons.


Image caption

Fig. 8.35. Draft marks on a ship’s hull are to estimate displacement.

Image copyright and source

Image by Byron Inouye


Load lines, or Plimsoll marks, show the maximum depth to which a ship can be legally loaded in different zones and seasons. They are used for ship safety. Fig. 8.35 shows the placement of Plimsoll marks and draft marks on a ship. In the enlarged view of the Plimsoll marks shown in Fig. 8.36, the following abbreviations are used to show load lines under different environmental conditions:

TF = tropical fresh water
F = fresh water
T = tropical
S = summer
W = winter
WNA = winter North Atlantic


Image caption

Fig. 8.36. A displacement curve is shown for the ship in Fig. 8.35. The more cargo a ship is carrying, the greater its displacement, and the lower it sits in the water (as indicated by a higher draft mark).

Image copyright and source

Image by Byron Inouye




Fig. 8.37. Plimsoll marks, also called load lines, of a boat help to gauge how much cargo should be loaded onto a ship.

Image by Byron Inouye

Because the majority of shipping occurs in marine (saltwater) conditions, freshwater conditions receive special notation. Ships that are sailed in fresh water will float deeper than in salt water, because fresh water has a lower density than salt water. Ships sailing through the North Atlantic ocean basin are also given special attention (Plimsoll code “WNA”) because cold water is denser than warm water and affects a ship’s buoyancy. AB, in Fig. 8.37, stands for American Bureau of Shipping, the agency that validated the ship’s Plimsoll marks.


Ship Stability

Stability is the tendency of a floating object rolling from side to side to return to an upright position. A rocking chair on a floor is an example of a non-floating object that rolls from side to side but still has stability. Stability is vital in the design of a ship. Stability can be achieved in two ways—leverage stability and weight stability. Leverage stability is achieved where there is a wide stance at the base. Examples of leverage stability can be seen in the construction of barges or catamarans (Fig. 8.38). Weight stability is achieved by anchoring the base (Fig. 8.39). A portable tetherball stand with its pipe cemented in a tire has weight stability. A hull with weight distributed toward its base has weight stability.


Image caption

Fig. 8.38. Leverage stability is demonstrated using the front view of (A) a barge and (B) a catamaran.

Image copyright and source

Image by Byron Inouye


Image caption

Fig. 8.39. Weight stability is demonstrated using (A) a tether ball pole with weighted base, (B) a sailing ship hull with weighted base, and (C) a cargo container where cargo creates a weighted base.

Image copyright and source

Image by Byron Inouye


Gravitational force and buoyant force operate in opposite directions and affect the stability of every ship. Gravitational force (G) is the sum of the entire weight of a ship acting straight downward on its center of gravity (CG). The center of gravity of an object of uniform density is at the geometric center of the object. Fig. 8.40 shows the center of gravity as a dot. The arrow represents the gravitational force. The center of gravity of an object not uniformly dense, however, tends to be close to the densest portion of the object. Notice the location of the center of gravity (the dot) in Fig. 8.41 as compared to the one in Fig. 8.40. Most ships are objects with unevenly distributed density.


Fig. 8.40. The center of gravity (CG) in objects of uniform density is shown. The center of gravity is represented as a dot, and the arrow represents the gravitational force.

Image by Byron Inouye

Fig. 8.41. The center of gravity is shown in a ship hull of uneven density that uses a weighted base for stability.

Image by Byron Inouye



Fig. 8.42. The center of buoyancy and center of gravity is shown in a ship hull of uneven density that uses a weighted base for stability.

Image by Byron Inouye

Buoyant force is the force of a liquid acting straight upward at the center of buoyancy (CB) of the submerged part of an object. Fig. 8.42 shows the center of buoyancy as a yellow dot. As with the center of gravity, the center of buoyancy is at the geometric center of the submerged part of an object of uniform density. The center of buoyancy shifts as downward force is exerted on the ship. The ship floats at a level where the density of the submerged portion is less than the density of the water it displaces. Recall from Unit 2 that an object that is less dense than the liquid around it will float on that liquid. In Fig. 8.42, the stable ship shows a center of buoyancy in the middle of the ship. However, in Fig 8.43 B and D, the ships have become unstable. The displacement of water has changed and the center of buoyancy has also shifted.


For a review on buoyant force see Density, Temperature, and Salinity.



Fig. 8.43. The forces of buoyancy and gravity affect stable and unstable ships. (A) A stable ship in calm water with its center of gravity (CG) and center of buoyancy (CB) positions marked. (B) An unstable ship with unevenly distributed density cannot tilt itself back upright. (C) A ship with a weighted hull (uneven density) in calm water. (D) An unstable ship with a weighted hull (uneven density) that cannot right itself from a tilted position.

Image by Byron Inouye

Ship stability is determined by the balance between the forces of gravity and buoyancy. For a vessel in a calm harbor, the two forces of gravity and buoyancy are in a line and are balanced, as shown in Fig. 8.43 A. A stable ship rights itself when tilted. In Fig. 8.43 B, the ship is stable. The center of buoyancy of the tilted ship is shifted to the right because the area submerged has been shifted. The opposing forces acting at the CB and CG will twist the ship back to an upright position. An unstable ship will not right itself; it will continue to fall over because the buoyant and gravitational forces act on the ship to keep it moving in the direction of the tilt (Fig. 8.43 C and D).




Fig. 8.44. A cross-sectional diagram of a ship (A) with cargo and (B) without cargo, but with added ballast.

Images by Byron Inouye

Cargo ships often travel with a load of cargo to their destination and then return to their home ports with empty or partially empty holds. The amount of fuel in the fuel tanks also changes in a ship as it progresses on its journey and burns fuel. The change in weight of both the cargo and the fuel can dramatically change the stability of a ship. To compensate for this, ships have ballast systems (Fig. 8.44). Early sailing ships used large stones for ballast. Some of the roads in American colonial towns were paved with ballast stones from cargo ships arriving from Europe. Modern ships rely on a ballast system in which water is pumped into and out of holding tanks.



Fig. 8.45. The zebra mussel (Dreissena polymorpha), an invasive freshwater species, was introduced to the North American Great Lakes through ballast water.

Image courtesy of US Geological Survey (USGS)

One of the unexpected impacts of the switch from ballast stones to ballast water has been the unintentional transport of marine and freshwater organisms around the world. Planktonic larvae travel from one port to another in ballast water, where they can become established as an invasive species. Invasive species are organisms that are non-native to the area, and when established, can cause harm to the ecosystem. For example, the zebra mussel (Fig. 8.45) arrived in the North American Great Lakes in ballast water carried from Europe in the ballast tanks of cargo ships. Birds that are found in Europe, but not found in North America, prey upon the mussel. Without any predation from these birds in North America, the mussel outcompetes native species, leading to death of native species and an ecosystem made up of only a single species when there should be many. Many marine species have become established as a result of ship transportation including sponges, algae, corallimorphs, and barnacles. Though many ecosystems have been overrun with invasive species, little has been done to address the problem of larval movement in ballast water, and it is an ongoing concern.




Size of Transport Conveyances

Ships convey enormous amounts of goods and people around the world. According to the U.S. Department of Transportation Maritime Administration, more than 2.1 billion metric tons of goods were transported to, from, and within the United States by ship in 2011. Thousands of passengers embark on cruise ships and transport ferries every year.


The size of the vessels needed to convey such a volume of goods and people is immense. Although we can readily visualize the dimensions of a vehicle, most of us cannot easily picture the size of a supertanker. A sedan automobile, for example, is almost 5 m long and weighs about 1590 kg (3505 lbs). By comparison, some oil tankers are 350 m long (almost four football fields) and weigh 500 million kg (500,000 metric tons). Fig. 8.52 shows profiles of a supertanker and a vehicle along with other modes of conveyance and their statistics.


Fig 8.52. (A) Sedan automobile

Image by Byron Inouye

Fig. 8.52. (B) Supertanker

Image by Byron Inouye


Fig. 8.52. (C) Airplane

Image by Byron Inouye

Fig. 8.52. (D) Container ship

Image by Byron Inouye


Fig. 8.52. (E) Nuclear submarine

Image by Byron Inouye

Fig. 8.52. (F) Fishing boat

Image by Byron Inouye


Ship Hull Design and Construction


Fig. 8.53. This primitive animal-hide boat with skin stretched over wooden ribs (Tibetan design) was among the first type of boat used by humans.

Image by Byron Inouye

A ship architect must design a ship so that it has the strength to withstand a combination of forces: the upward force of buoyancy, the downward force of gravity, and the powerful force of ocean waves. The ship must also be streamlined for speed. For thousands of years, ships have been designed much like the bodies of vertebrate animals. The ships' ribs have been covered with a skin or hide, bark, planks, or metal plates. The skin not only made the ships watertight and buoyant; it also provided the necessary strength for their hulls (Fig. 8.53).


Ship hulls were traditionally designed as small-scale models. The models were approved, and then sawed into sections. Blueprint measurements were made of each section. These were mathematically enlarged when the ship was built to full scale. From the full-scale measurements, parts were constructed and assembled to build the full-sized hull. Today, computers are used to design ship models and draw blueprints.


Ship Dynamics

Speed and fuel efficiency are extremely important when considering transporting materials by ship and are important in ship design to increase efficiency. Speed is distance per unit of time. Most of us are familiar with car speeds expressed in miles per hour:


Efficiency is a measure of work done per unit of energy used. The less energy used to do a given amount of work, the higher the efficiency. Imagine a captain of a cargo ship carrying redwood from Oakland, California, to Honolulu, Hawai‘i. The captain has no arrival deadline, so he is not concerned about whether the voyage takes 5 or 10 days. But the captain does want to complete the voyage (the work to be done) using the least amount of fuel (the energy used) possible. To get the best efficiency, the captain must determine what speed will require the least fuel to complete the voyage. Remember that work is equal to force and weight, and it is needed to calculate efficiency as seen in the equation below.



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Exploring Our Fluid Earth, a product of the Curriculum Research & Development Group (CRDG), College of Education. University of Hawaii, 2011. This document may be freely reproduced and distributed for non-profit educational purposes.