# Objectives

The objective of this lab is to design and build a a small vessel that floats on water. This is a competition lab that will be judged by a ratio that uses cost and payload. In theory, the design should maximize the non-structural weight (payload) that the balloon can lift and the time it can spend aloft while minimizing the boats'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, materials, and design, ranging in everything 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 gravity 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 (&rho). There are a few ways that the buoyant force can be calculated, these equations can help you think of ways to optimize your boats design.

F_buoyant = F_up - F_down

F_buoyant = (PA)up - (PA)down

F_buoyant = pgAh_bottom - pgAh_top

F_buoyant =pgA(h_bottom-h_top)

## The Boat Competition Ratio

This lab is a competition. The boat competition ratio will be used to measure the performance of each design.

Competition Ration = Payload/(Cost*Weight of Boat)

Payload is the mass the design can lift before sinking to the bottom of the tank, a total of 2 inches. The weight of the boat is taken before it is placed in water, the cost is the cost of the boat.

The design will be allowed 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 1m^3
• Time aloft is the elapsed time from when the balloon rises from its initial height to when it sinks to that height
• If the balloon does not rise, the time aloft is zero
• The design is limited to three trials. Indicate the number of trials performed and the ratios in the Abstract of the lab report. The lab report should also show the results for each trial including dimensions, payload, estimated balloon volume, and competition results

# Design Considerations

• Which balloon shape best minimizes structural mass and effectively captures and retains warm air to fill and launch the balloon?
• How is balloon volume maximized and surface area 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 • Tissue wrap:$0.10/sheet
• 8 ½ x 11 paper sheets: $0.05/sheet • Kevlar string:$0.05/30cm
• Adhesive tape: $0.03/30cm • Plastic straws:$0

## Equipment Used

• Scissors
• A glue stick
• Paper clips
• A personal heater
• A stop watch
• A thermometer

# Procedure

Construct a hot air balloon using the available materials. This lab is a competition. The design with the highest ratio of payload divided by cost multiplied by time afloat will be the winner.

Sketch a preliminary design. The maximum balloon volume is 1 m3. Volume should be approximated and recorded on your lab notes.

The design must include an area near the bottom of the balloon where paperclips may be attached to add payload during the competition phase of the lab. In addition, there must be an opening that will allow hot air to enter the balloon when placed over the heater.

WARNING: Turn the heater off when not in use. Otherwise, it will become extremely hot and possibly melt the balloons.

When finished, have the sketch approved and signed by the lab TA. Construct the balloon using the materials that were selected. For the competition phase, a payload will be attached to the bottom of the balloon and it will be filled with hot air.

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

# Assignment

## Individual Lab Report

Follow the lab report guidelines laid out in the page called 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 hot air balloons 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
• Explain the Ideal Gas Law and the Principle of Archimedes. Include a definition and an example of each
• Describe the balloon's design. Calculate the volume of the balloon (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 balloon's final standing in the competition?
• Discuss and elaborate how to improve the competition ratio for this design.
• Suggest possible improvements in conducting the lab
• Include the spreadsheet with every balloon's results. Describe the results and discuss 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

The following discussion points must be addressed in the appropriate section of the presentation:

• Describe the rules of the competition. What consequences did the rules have on design decisions? Use the appropriate equations in the answer.
• Since one term in the competition ratio is cost, present the cost of the balloon. Use the page How to Show Cost Data in Presentations for instructions on how to do this.
• Explain the Ideal Gas Law and the Principle of Archimedes. Include a definition and an example of each.
• Were all materials purchased used?
• Describe the balloon's design. Show the volume of the balloon (i.e., dimensions and calculation) to show compliance with the rules. Explain the design choices. Discuss the materials chosen and why they were chosen. Explain the strategy for winning the competition.
• Describe how the design succeeded or failed. What choices could have improved the balloon's final standing in the competition?
• Discuss how to improve the competition ratio.

# Endnotes

1. National Aeronautics and Space Administration. 2017. “Scientific Balloons.” Accessed 20 August 2017 from https://www.nasa.gov/scientificballoons