Near-Space Balloon Burst Altitude Calculator - Science

Perhaps you recognize this post's cover photo from a recent Late Show with Stephen Colbert skit: Astronaut Ice Cream is a Lie. Indeed, we at Launch with Us helped out to plan for, execute, and retrieve the space ice cream payload. To make sure that we reached our objective altitude, we had to ensure that we chose the proper launch configuration. How did we do it? More about predicting burst altitude is covered below, while more details on the story of the Colbert launch itself will be coming in the following blog posts!

A few months back, we introduced you to the Habhub Burst Calculator tool in our Space Camp #3 blog post about flight path predictions. Today, we will take a closer look at some of the science and assumptions behind this tool and we will break down some of the equations that go into making an accurate burst altitude prediction.

There is also an Excel version of the Burst Calculator available for download here, in case you need access to burst calculations without internet access or if you want to modify it for your own custom launch configuration.

Burst Altitude Basics

There are two primary factors that will influence how high your near-space High Altitude Balloon (HAB) can fly. They are:

  1. Balloon  Type (e.g. Kaymont 350, 800, 1200, or Hwoyee 600, 1600, etc.)
    1. Each balloon size and manufacturer will have a different Burst Diameter/Burst Altitude combination. These values are available from manufacturer data (available for Kaymont (Totex) and Hwoyee balloons - see Section 1 below)
  2. Initial Gas (i.e. Helium) Volume
    1. The lower the starting volume, the higher you will be able to go (and vice versa).

The explanation for this is the basic reason that HABs pop: they expand in diameter as they climb, until reaching a maximum diameter at which they burst.

When a balloon is initially filled with Helium, the starting diameter is determined by the point when the internal balloon pressure of the gas equals the external pressure from the atmosphere. Once released, the balloon diameter increases because the pressure on the outside is decreasing as the balloon rises.

According to the ideal gas law, PV = nRT, where:

  • P is the pressure of the gas
  • V is the volume of the gas
  • n is the amount of substance of gas (in moles)
  • R is the ideal, or universal, gas constant
  • T is the temperature of the gas
Re-arranging terms by dividing both sides by the Pressure "P", the volume of the gas can be expressed as: V=nRT/P. 

Assuming that the amount of the gas in the balloon is constant, the number of moles of gas "n" is constant, the Universal Gas Constant "R" remains the same, and assuming small changes in temperature "T", then the numerator "nRT" can be assumed to be a constant. Thus, as the Pressure "P" decreases, it will result in the Volume "V" getting larger (since P is in the denominator of the fraction), and thus the balloon expands as it climbs in the atmosphere.

At the maximum diameter for a given balloon size, the stresses in the balloon finally cause it to rupture (at a given burst diameter), and the HAB begins its voyage back to Earth.

1 - Balloon Type

The first piece of data that is needed is the Balloon Size and Manufacturer. This data will give you access to empirical burst diameter and burst altitude data from past launches, and is the primary predictor in estimating how high your balloon can go. The type of balloon will also impact some other launch parameters (such as Drag Coefficient, climb rate, etc.), but this blog post will be focusing on the impact on burst diameter and altitude only.

Published data for burst parameters of various Kaymont (Totex) and Hwoyee balloons is given below:

Kaymont (Totex) Burst Data:

 Kaymont (Totex) Balloon Burst Data. Source: https://ukhas.org.uk/guides:balloon_data The data above is based on the use of Hydrogen rather than Helium. Note: It is not recommended to use the Burst Altitude data published on Kaymont's website. Data for burst diameter is rounded to the nearest foot, resulting in large errors of estimated burst altitude for some cases.

Kaymont (Totex) Balloon Burst Data. Source: https://ukhas.org.uk/guides:balloon_data
The data above is based on the use of Hydrogen rather than Helium.
Note: It is not recommended to use the Burst Altitude data published on Kaymont's website. Data for burst diameter is rounded to the nearest foot, resulting in large errors of estimated burst altitude for some cases.

Hwoyee Burst Data:

 Hwoyee Balloon Burst Data. Source: https://ukhas.org.uk/guides:balloon_data

Hwoyee Balloon Burst Data. Source: https://ukhas.org.uk/guides:balloon_data

 

2 - Starting Gas Volume 

The second variable that will affect how high your balloon will reach is the volume of helium (or other gas) that you start with. The lower volume, the higher the maximum burst altitude for a given balloon (and vice versa - the more helium, the lower your burst altitude). Don't get too ambitious with a given balloon, though; too little helium to start, and your balloon may never burst! (this is called a "floater" in HAB vernacular) There is a time when it may be necessary to increase to a bigger balloon size to achieve higher altitudes. 

To illustrate the relationship of helium volume vs. burst altitude, a 350g Kaymont balloon with 1000g (2.2lb) payload exhibits the following altitude vs. helium volume relationship:

 A comparison of the effect on climb rate (orange) and burst altitude (blue) compared to initial Helium Volume.

A comparison of the effect on climb rate (orange) and burst altitude (blue) compared to initial Helium Volume.

Keep in mind that besides influencing the burst altitude, different helium volumes will also affect your climb rate, time of flight, and whether your balloon may be unsteady during climb. We recommend keeping the nominal climb rate between 4-5 m/s for optimal results (steady photography, reasonable flight times, etc.).

Assumptions in the HabHub Burst Estimator

There are several inherent assumptions in the HabHub Balloon Burst Calculator to be aware of. They are: 

  1. Balloon Burst Diameter and Altitude Data is based on published values for Kaymont (Totex) and Hwoyee balloons (See tables above)
  2. Standard Atmospheric Properties - hotter or colder atmospheric properties will lead to non-standard densities at altitude, and will have a minor impact on your balloon's performance.
  3. Initial launch altitude is at Sea Level for balloon measurements - keep in mind: 60 cubic feet of Helium from a Helium tank is a standard number that is measured at standard atmospheric conditions (ie a 60 cubic foot tank of Helium in Denver, CO and at Sea Level will be the same 60 cubic feet). However, if you are measuring the resulting balloon diameter due to the "60 cubic feet" of helium, just remember that the gas (and balloon diameter) expands as the atmospheric pressure decreases, and you may have to adjust your measurements if you are looking to "confirm" that you are starting with a given volume of Gas when filling at altitude (there is aa "Air Density" adjustment under Advanced Constants for the HabHub Calculator).

Note: Some advanced users can expand the "Constants (Advanced)" fields in the HabHub calculator to use non-standard air densities, adjust for using other Gases besides Helium, and even adjust Gravitational Acceleration (anyone looking to launch on the moon?!).

Secondary Altitude Effects

As previously mentioned, besides the Balloon Type and the amount of Helium used, there are several other factors that will impact how high your balloon will go. They are:

  1. Using other lifting gases (e.g. using Hydrogen, while not recommended due to safety, can result in higher burst altitudes due to a higher lift value for comparable balloon diameters, and thus requiring less total gas to achieve similar flight performance)
  2. Atmospheric Properties / Air Density - launching in a region of the world where the atmospheric air density is higher than standard assumptions will result in higher lift values for the same balloon diameter

Other conditions such as violent winds and weather at altitude, imperfections in the balloon surface due to contaminants that came in contact with the balloon during filling (e.g. oils from your hands, which is why you should always wear gloves), the method of payload attachment, and other secondary factors can affect the stresses in the balloon and can result in a balloon burst that varies from the published values.

Predicting the Burst Altitude

Having a solid understanding of the fundamentals, you now have all the tools at your disposal needed to predict how high your next HAB launch will go!

The steps for calculating the Burst Altitude are:

  1. Start with your HAB Initial Launch Volume
  2. Look up the published Burst Diameter for your balloon size and manufacturer (e.g. Kaymont 600 = 6.02 meter burst diameter)
  3. Calculate the Burst Volume of the balloon, assuming the volume of a sphere (Volume = 4/3*Pi*radius^3), where Radius = Diameter/2, Pi = 3.14
  4. Calculate the Burst Volume Ratio, which is equal to Burst Volume / Initial Launch Volume
  5. Finally, calculate the burst altitude by using the equation: Altitude (in meters) = -(7238.3*ln(1/(Burst Vol. Ratio).
    1. In this equation, ln is the "natural log" function, and 7238.3 is the Standard Air Density model "Scale Height" based on NRLMSISE, which is accurate to 80km.

There you have it! You hopefully now have a better idea of some of the assumptions and important parameters that impact how high your next HAB launch will go.