# Objectives

The objective of this lab is to design and build a small vessel that floats on water. This is a competition lab that will be judged based on a ratio that uses cost and payload. In theory, the design should maximize the non-structural weight (payload) that the boat can lift and the time it can spend afloat, while minimizing the boat's structural weight and its cost. In practice, other design choices could also win the competition. Consider the components of the ratio and the rules before designing the boat.

# Overview

Boats are lighter-than-water vessels. They are widely used for recreation, military, touring, and commercial purposes. Boats range widely in size, shape, material, and design, ranging in size from a single person kayak to a shipping boat that can hold up to 25000 tons of cargo. Your goal is to design and optimize a boat to hold as much cargo as possible while still making the boat as lightweight as possible.

The Principle of Archimedes and Newton's Second Law of Motion explain how these vessels float.

## Principle of Archimedes and Newton's Second Law of Motion

The Principle of Archimedes states that when a body is immersed in a fluid (a liquid or a gas), an upward force is exerted on the body that is equal to the weight of the fluid the body displaces. This upward force is called buoyancy.

A boat will float if the weight of the water being displaced is equal to or greater than the weight of the boat.

The Principle of Archimedes can be expressed in an equation, which is more useful for engineering calculations.

From the definition of density (ρ = mass / volume = m / V), Newton's Second Law of Motion (F = ma), and for the acceleration due to gravity (a = g), the gravitational force on a volume of fluid is F = m*a = (ρV)(g). You can also calculate force using the definition of pressure, where pressure equals force divided by area (P=F/A), therefore force equals pressure times area (F=P*A). From here, pressure can be defined as hydrostatic pressure, which is equal to the gravitational force of acceleration (g) multiplied by the height (h) and density (ρ). There are a few ways that the buoyant force can be calculated; these equations can help you think of ways to optimize the design of your boat:

Fbuoyant = Fup - Fdown

Fbuoyant = (PA)up - (PA)down

Fbuoyant = pgAhbottom - pgAhtop

Fbuoyant =pgA(hbottom - htop)

## The Boat Competition Ratio

This lab is a competition. The boat competition ratio will be used to measure the performance of each design. $\displaystyle Competition\Ratio = \frac{Payload}{Cost*Weight of the Boat}\,$

Payload is the mass the design can lift before sinking a total of 2 inches. The weight of the boat is taken before it is placed in the water. The cost is the cost of the boat calculated from the materials price list.

The design will be allowed only ONE trial.

# Competition Rules

The following rules must be observed at all times during the competition. Violation of any of these rules will result in the disqualification of the balloon:

• The TA must approve the design before it can be entered in the competition
• All the materials used in the design must be purchased
• Unused materials may not be returned for credit
• The maximum boat size is 1 ft3
• The design is limited to ONE trial

# Design Considerations

• How is the boat volume maximized and weight minimized?
• Carefully consider weight, surface area, volume, material properties, and cost in the design process.

# Materials and Equipment

## Materials with Price List

• Drawing paper: $0.10/sheet • Aluminum foil:$0.15/foot
• Plastic wrap: $0.05/foot • Tissue wrap:$0.10/sheet
• 8.5" x 11" paper: $0.05/sheet • Kevlar string:$0.05/foot

• Scissors
• A glue stick
• A stop watch

# Procedure

Your goal is to construct a boat using the available materials. This lab is a competition. The design with the highest competition ratio wins.

Sketch a preliminary design. The maximum boat size is 1 ft3. Volume should be approximated and recorded in your lab notes. You or someone in your group will be in charge of adding weights. If you reach a point where no more weights can be added without them falling into the water, then that will be the end of the trial.

When finished, have the sketch approved and signed by a Lab TA. Construct the boat using the materials that were selected. For the competition phase, a payload will be placed in the boat after the boat has been placed in the water. A TA must be present for the trial, and the TA will weigh the boat before it is placed in the water.

The lab work is now complete. Please clean up the workstation. Return all unused materials to the Lab TA.

# Assignment

## Individual Lab Report

Follow the lab report guidelines laid out in the page Specifications for Writing Your Lab Reports in the Technical Communication section of this manual. The following discussion points should be addressed in the appropriate section of the lab report:

• Discuss the importance of boats today.
• Describe the rules of the competition in the Introduction. What consequences did the rules have on design decisions? In answering, use the appropriate equations.
• Describe the boat's design. Calculate the volume of the boat (i.e. dimensions and calculation) to show compliance with the rules. Explain the design choices. Include a discussion of the materials chosen and why. Explain the strategy for winning the competition.
• Describe how the design succeeded or failed. What choices could have improved the boat's final standing in the competition?
• Discuss and elaborate on how to improve the competition ratio for your design.
• Suggest possible improvements in conducting the lab.
• Include the spreadsheet with every boat's results. Describe the results and discuss the other designs in the class.

Remember: Lab notes must be taken. Experimental details are easily forgotten unless written down. EG1003 Lab Notes Paper can be downloaded and printed from the EG1003 Website. Use the lab notes to write the Procedure section of the lab report. At the end of each lab, a TA will scan the lab notes and upload them to the Lab Documents section of the EG1003 Website. One point of extra credit is awarded if the lab notes are attached at the end of the lab report. Keeping careful notes is an essential component of all scientific practice.

## Team PowerPoint Presentation

There is NO team PowerPoint for Lab 1.