Monohull, catamaran, trimaran . . . so many choices. Which hullform to pick? Can we draw upon any science to guide our choices, or shall we beg Lady Luck to guide us? Although hullform selection does involve some experience and artistic preference, naval architects definitely utilize a scientific framework when selecting hullforms. This achieves the best hull for each mission and gives us a rationale to justify the final decision. Today we expose the basic science of hullform selection.

# 1.0 The Candidates

Time to meet the contenders. Table 1‑1 shows the five major types of hullforms. Each hullform has its place and application; several overlap in their capabilities.

**Table 1‑1: Major Hullform Types**

MonohullOne of the most versatile ship types available. Excellent high weight capacity. | |

Catamaran
| |

Trimaran [1]
| |

SWATH
| |

Planing Hull [2]Delivers high speed capabilities in a very small package. |

# 2.0 A Little Math

What separates the different applications for these hullforms? Speed and cargo capacity. Speed matters because different physical forces become dominant as we go faster. Assume we start with some fixed amount of displacement. The speed determines the shape of the hull that achieves that displacement. Then deadweight (cargo capacity) enters the picture. Deadweight dictates how much of the displacement we devote to cargo versus propulsion and accommodations. The trick is identifying which hullforms work best at different ranges of these two requirements.

Of course, everything depends on size. “Fast” speeds for a small speedboat evoke entirely different physics then the same speed on a giant oil tanker. Sorry, I must resort to math now. Naval architects utilize non-dimensional coefficients to compare all ships on the same level playing field. These coefficients factor out the ship size and ensure that two ships with the same coefficient are governed by the same major physics. Naval architects have a whole field of non-dimensional coefficients to compare all aspects of ship design. For today, the two we care about are Froude number and deadweight coefficient.

## 2.1 Froude Number

William Froude (Figure 2‑1) developed the Froude number. Many consider him as the father of modern naval architecture. This grants us a way to compare ship speed on vessels of different length. (Equation 2‑1)

Where:

Fn = Froude number

U = vessel speed (m/s)

g = Acceleration from gravity (m/s2) = 9.81 m/s2

L = Ship length (m)

## 2.2 Deadweight Coefficient

The deadweight coefficient compares the deadweight of the ship (cargo weight capacity) to the total ship displacement. (Equation 2‑2) For this equation, the deadweight includes cargo weights, fuel weights, provisions for the crew, etc. Basically, anything that isn’t bolted down as a permanent part of the ship.

Where:

C_{dw} = Deadweight coefficient

W_{L} = Light ship weight (tonne). Basically anything not bolted down.

W_{S} = Ship weight (tonne)

# 3.0 Design Space

## 3.1 Froude Number

Those equations only provide half the story. They are useless unless we frame those numbers with the context of typical values. Table 3‑1 shows typical ranges for the Froude number. This dictates the shape of the hulls. As the Froude number increase, the hulls get more skinny and rounded. Eventually, that leads to problems with ship stability; this drives designers to solutions with catamarans or trimarans. The selection of hullform strongly depends on the speed, measured as Froude number.

**Table 3‑1: Typical Ranges for Froude Number [3]**

Froude
| Dominant Physics | Typical Vessels |

0.0 – 0.1 | Almost entirely friction resistance | |

0.10 – 0.20 | Mostly viscous resistance, minor wavemaking | Crude oil carrier |

0.20 – 0.30 | Balance of viscous resistance and wavemaking | Container ships, freighters |

0.30 – 0.50 | Wavemaking increases over viscous resistance | Ocean tugs, offshore supply vessels |

0.50 – 0.70 | Hydrodynamic lift starts to affect the hull. Vessel hull shaped to minimize wave resistance. | Ferries. Patrol vessels. |

0.70 – 1.0 | Hydrodynamic lift begins supporting ship. Vessels with chines have less drag than round bilge hulls. | Planing boats. Military patrol vessels. Sports craft. |

1.0 – 4.0 | Vessel weight almost entirely supported by hydrodynamic lift | Seaplane. Extremely fast planing boats. |

## 3.2 Deadweight Coefficient

The deadweight coefficient informs how we get to use the space on the ship. Higher coefficients devote more weight to cargo and fuel. But lower coefficients may also mean that we require a design focused on volume, not weight. Table 3‑2 shows a typical breakdown. Notice when the designs switch to being driven by weight towards driven by volume.

**Table 3‑2: Typical Deadweight Coefficients [4]**

Deadweight Coefficient (Cd) | Typical Ship | Design Driver |

0.65 – 0.75 | Cargo ships | Weight driven design |

0.79 – 0.85 | Large tankers / bulk carriers | |

0.82 | Ore carriers | |

0.60 | Container ship | |

0.55 – 0.60 | Refrigerated cargo | Volume driven design |

0.35 | Passenger vessels | |

0.20 – 0.30 | High speed ships [5] |

## 3.3 Combining for Hullform Selection

Combining all the lessons learned thus far, we begin to see a map for hullform selection. (Figure 3‑1). Notice the overlap between all the different types of hullforms. Sometimes either solution fits a mission profile well. Or we may combine technologies. For example: a planing boat can also be a monohull, or maybe a catamaran. This map refuses to dictate a hullform. Instead, it guides our selection and encourages out of the box thinking. That is the critical skill for hullform selection. See past the limitations of past examples and consider new alternatives.

# 4.0 Specialized Hullforms

I didn’t forget the SWATH hullforms. Short for Small Waterplane Area Twin Hull (SWATH), these hulls are really a specialized form of catamaran. Within each hullform category, we start to see specialty hulls which serve a single and specific mission. These hulls have their place as well; their designs excel at achieving singular goals and specific mission profiles. Don’t forget to consider them. They may serve your purpose far better than anything else.

# 5.0 Conclusion

Selecting the best hullform does not yield to simple algorithms and pure rational science. Neither do we stumble blindly through trial and error. We utilize past experience, non dimensional coefficients, and simplified physics to discriminate between the utility of various hullforms. No option works for every case. The talented naval architect considers the entire field of options. We begin with a rational basis, and we adjust for mission requirement, owner preferences, and a little artistic preference. This results in a hullform best suited to the task and well justified through careful consideration.

# 6.0 References

[1] | M. Hanlon, “U.S. Navy Orders a Second Trimaran Littoral Combat Ship,” New Atlas, 21 December 2006. [Online]. Available: https://newatlas.com/go/6651/. [Accessed 4 Apr 2018]. |

[2] | R. Cogswell, “Speedboat on Lake Michigan In Chicago,” Wikimedia Commons, 24 Dec 2015. [Online]. Available: https://commons.wikimedia.org/wiki/File:Speedboat_on_Lake_Michigan_in_Chicago.jpg. [Accessed 21 Apr 2018]. |

[3] | S. Turnock, Writer, Lecture Notes: Recreational and High Speed Craft. [Performance]. University of Southampton, Southampton, U.K., 2008. |

[4] | A. Molland, Writer, Lecture Notes: Ship Design and Economics. [Performance]. University of Southampton, 2006. |

[5] | C. McKesson, Writer, Lecture Notes: Advanced Marine Vehicles. [Performance]. University of new Orleans, 2008. |

It is incorrect relationship, if to use it as recommendation or guidance. It should be dependent on Volumetric Froude number.