Hot Air Balloon Competition

Objectives

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

Overview

At Versailles on September 19, 1783, two 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 were inspired by watching hot embers rise and float above a fire. Later, in November 1783, they launched the first manned balloon flight.

Hot air balloons are examples of lighter-than-air aircraft. They are widely used for recreation and advertising. Another example of this type of aircraft is the dirigible, which consists of a rigid steel frame with bags of light gas inside it, causing it to lift. Because of the weight of the frame in early dirigibles, an extremely light though flammable gas, such as hydrogen, was used. This led to safety problems, so dirigibles are no longer in service. A blimp is a lighter-than-air aircraft that is essentially a big helium balloon with engines attached. It does not have a structural frame like a dirigible and took its name from the sound it makes when hit with something. An aerostat is a blimp that does not have engines, but is attached by a tether (rope) to the ground. Aerostats are frequently used for advertising or finding a location. The person trying to find the location just looks for the aerostat in the sky attached to the location and travels to it. Aerostats are also used as weather stations and radar platforms since they can reach altitudes of up to 15,000 feet. Building a structure that tall would probably be impossible.

The fundamental concepts in this lab are the Ideal Gas Law, gas density, the Principle of Archimedes, and Newton's Second Law of Motion.

Ideal Gas Law and Gas Density

Usually, when a gas is heated, it expands so the same mass has a larger volume and the density decreases. The expansion can be quite pronounced and a mass of warm air is considerably less dense than an equal mass of cold air. This can be expressed quantitatively by using the Ideal Gas Law to describe the behavior of a gas. 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.
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 [ambient] air and one filled with an equal amount of warm air), the Ideal Gas Law predicts that the warmer balloon will contain fewer moles of gas, so the warmer balloon will be lighter because the air inside it will be less dense.

It is most convenient to rewrite the Ideal Gas Law in terms of density (ρ), ρ = ^P/_RT, and for a constant pressure and gas composition, even more simply

$\rho ={\frac {C}{T}}\,$

where ρ is the air density in ^kg/_m³, at temperature T in Kelvin. For a pressure constant at 1 atm, C is 347 ^{K · kg}/_m³. (Obtained from dry air density of 1.164 ^kg/_m³ at 20 °C and 1 atm pressure: i.e., 293 K x 1.164 ^kg/_m³.)

Principle of Archimedes and Newton's Second Law of Motion

But why does this difference in temperature and gas density 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. If the air is heated, it expands. It pushes out and so displaces the cooler, denser air. Because of this displacement, a net upward force is produced on the warm air mass, causing a tendency to rise. In a 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.

The Principle of Archimedes can be expressed in a more useful form for engineering calculations (an equation).

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).

Due to Archimedes' Principle and the hotter fluid being at a lower density (ρ_hot), the net buoyant force can be obtained from the difference F_net = (m_amb g – m_hot g), where m_amb is the mass of the displaced ambient air and m_hot is the mass of the air inside the hot air balloon. If this net buoyant force goes entirely to lift a payload (m_ideal) it is,

$F_{net}=m_{ideal}g=\left(\rho _{amb}-\rho _{hot}\right)Vg\,$,

Combining the above equation with ρ = C / T and convenient approximations, the maximum payload of an ideal hot air balloon is

$m_{ideal}=\left(4.0{\tfrac {g}{m^{3}K}}\right)V\left(T_{hot}-T_{amb}\right)\,$

If the actual hot air balloon mass is determined by m_balloon — by weighing it before it is filled with hot air — then the maximum possible payload can be determined. i.e., payload_real < m_ideal – m_balloon.

The Balloon Competition Ratio

This lab is a competition. The design's performance will be judged against the other designs in the section. The balloon competition ratio will be used to measure the performance of each design.

${\frac {TimeAfloat[s]}{Cost[\$]}}\times Payload\,$

where Payload is the number of paperclips the design can lift.

The design will be allowed three trials.

Design Considerations

• What 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.

Assignment

Individual Lab Report

For Sections A, B, C, D/H, E, and G, this report is optional and will count as a Bonus Lab Report if submitted. Extra Credit will be applied to the PowerPoint presentation since report is optional.

For Sections HS, this report is required and will count as a regular 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.
• Discuss minimal design. Were all the materials purchased used? Describe the importance of minimal design and explain how it was employed in the design.
• 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. 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 how to improve the competition ratio.

Team PowerPoint Presentation

The following discussion points are to 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.
• Discuss minimal design. Were all materials purchased used? Describe the importance of minimal design and explain how it was employed in the design.
• 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.

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 balloon volume is 1 m³.
• 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 in the Abstract of the lab report. The lab report should also show the results for each trial including dimensions, payload, and competition ratio results.

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/foot
• Adhesive tape: $0.03/foot
• Plastic straws: $0

Equipment Used

• Scissors
• Glue stick
• Paper clips
• Personal heater
• Stop watch
• Thermometer

Procedure

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

Sketch a preliminary design. The maximum balloon volume is 1 m³.

The design must include an area near the bottom of the balloon where paper clips may be attached in order to 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.

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, weight 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.