Hot Air Balloon Competition

EG1004 Lab 8: Hot Air Balloon

8.1 Objectives

The objective of this lab is to design and build a hot-air balloon. This is a competition lab. Your design should maximize the amount of non-structural weight (the payload) that your balloon can lift and the time it can spend aloft, while minimizing the balloon’s structural weight and its cost. In designing your balloon you may wish to make use of several concepts from physics, including the Ideal Gas Law, and the Principle of Archimedes.

8.2 Overview

At Versailles on September 19, 1783, the French brothers, Joseph-Michel and Jacques-Étienne Montgolfier, loaded a sheep, a rooster, and a duck into the basket of their hot-air balloon and untethered the ship for the entertainment of the King of France, Louis XVI. They'd gotten the idea from watching hot embers rise and float above a fire. Later, in November 1783, they launched the first manned balloon flight.¹

Background Concepts

Usually, when an object is heated it expands. The same amount of mass occupies a larger volume and therefore the density of the object decreases. For gases, this is especially important because the expansion can be quite pronounced, and a mass of warm air is considerably less dense than an equal mass of cold air.

This idea can be expressed quantitatively by using the Ideal Gas Law to describe the behavior of air. This law states that

PV = nRT

where P is the gas pressure, V is the volume of gas being considered, T is its absolute temperature and n is the number of moles of gas.

If pressure is measured in atmospheres, volume in liters, and temperature in Kelvin, the universal gas constant R has a value of 0.0821 L atm/mol K.

Comparing two equal volumes of air at the same pressure (say a balloon filled with cold air and one filled with an equal amount of warm air), the Ideal Gas Law predicts that the warmer one will contain fewer moles of gas, so the warmer balloon will be lighter because the air inside it will be less dense.

But why does this difference lead to a tendency for warm air (and hot-air balloons) to rise? The Principle of Archimedes provides an explanation. The Principle states that when a body is immersed in a fluid (a liquid or a gas), an upward force is exerted on the body equal to the weight of the fluid the body displaces. This upward force is called buoyancy.

For a balloon containing air at the same temperature as its surroundings, the buoyancy force is balanced by the weight of the air in the balloon and there is no net force or effect. However, if the air is heated, it expands. It pushes out and so displaces the colder ambient air. Because of the displacement of the colder, denser air, a net upward force is produced on the warm air mass, causing it to tend to rise. In our hot-air balloon, the mass of warm air is trapped by the balloon’s skin, allowing the difference between its buoyancy force and its weight to be harnessed if it exceeds the structural weight of the balloon and its payload.

With this background, think carefully about your design. What balloon shape will you use to minimize structural mass and to effectively capture and retain warm air as you try to fill and launch your balloon? Think about how you will maximize balloon volume and minimize surface area. Cost is also an important concern. Carefully consider weight,surface area, volume, material properties, and expense in your design process.

This lab is a competition. Your team's performance will be judged against the other teams in your section. The Balloon Competition Ratio will be used to measure the performance of each team

${\frac {TimeAfloat}{Cost}}*Payload$

You will be allowed three trials.

8.3 Your Assignment

PowerPoint Presentation and Individual Lab Report (one report per student)

The following discussion points are to be addressed in the appropriate section of your lab report and presentation:

• Describe the rules of the competition in your introduction. What consequences did the rules have for your design decisions? Use the appropriate equations in your answer. You may do this in a numbered list, but use full sentences please.
• Explain the Ideal Gas Law and The Principle of Archimedes. Make sure you include a definition and an example of each.
• Discuss minimal design. Did you use all the materials you purchased? Describe the importance of minimal design and explain how you employed it in your design.
• Describe your balloon's design. Explain the choices you made. Make sure you include a discussion of the materials you chose and why. Explain your team’s strategy for winning the competition.
• Describe how your design succeeded or failed. What choices could you have made to improve your final standing in the competition?
• Discuss how you would improve the ratio.

8.4 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 your balloon:

• The TA must approve your design before it can be entered in the competition.
• All the materials you use in your design must be purchased.
• You may not return unused materials for credit.
• The Maximum Balloon volume is 1m³.
• You are limited to three trials.

8.5 Materials and Equipment

• Garbage Bags (60 cents)
• Tissue Wrap (10 cents/sheet)
• 8 ½ x 11 Paper Sheets (5 cents/sheet)
• Kevlar String (5 cents/foot)
• Adhesive Tape
• Plastic Straws
• Scissors
• Glue Stick
• Paper Clips
• Personal Heater
• Stop Watch

8.6 Procedure

Construct a hot air balloon using household materials. This lab is a competition. The team with the highest ratio of payload divided by cost multiplied by time aloft will be declared the winner.

First, sketch your preliminary design. The maximum Balloon Volume is 1m³.

Note: Your design must include an area near the bottom of the balloon where paper clips may be attached in order add weight during the competition phase of the lab. In addition, there must be an opening that will allow the balloon to be placed over the heater.

When you are finished, have your sketch approved and signed by the lab TA. Construct your balloon using the materials you have selected. For the competition phase, your team will attach weight to the bottom of your balloon and hot air will be added. The winners are determined by the Balloon Competition Ratio.

_{${\frac {TimeAfloat}{Cost}}*Payload$}

Note: An extra 10 points will be awarded to the team with a first place finish. The second place team will receive 5 points. These points will be added to your TA lab report grade.

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

¹ "Montgolfier, Joseph-Michel and Jacques-Étienne" Britannica Student Encyclopedia from Encyclopædia Britannica Online. http://www.search.eb.com.databases.poly.edu/ebi/article?tocId=9275924 [Accessed November 3, 2004].

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