Sensitivity Analysis for Ascending Zero Pressure Balloons Carl Olsson Rymdteknik, master 2019 Luleå tekniska universitet Institutionen för system- och rymdteknik Abstract This work analysed the sensitivity in ascending velocity for three different zero pressure bal- loons of different sizes. A program that considers the atmospheric and thermodynamic con- ditions was written to try and simulate the balloons ascent throughout the atmosphere. The sensitivity for ascending velocity was determined with the Monte-Carlo method and measur- ing the mean vertical velocity throughout the atmosphere. The performance of the simulated flight when compared to its real flight, was accurate in the troposphere and then started to deviate in the stratosphere. Whether the drag is underestimated or overestimated during the stratosphere would depend on the size of the balloon and when it is released. Changing the free lift for the balloons showed that small balloons have almost the same sensitivity in the troposphere as in the stratosphere, while a larger balloon could be more sensitive in either part, depending on the time it is launched. With a changing ground temperature, the balloons with less cloud cover would be more sensitive in the stratosphere. Balloons flying during hours with sunlight are less sensitive to a changing cloud cover than balloons that fly with little to no sunlight, but some more data should be analysed for a proper conclusion. Larger balloons are more sensitive with a changing ground albedo value compared to smaller balloons. Contents 1 Introduction 3 1.1 Previous work . .4 1.2 Outline of thesis work . .4 2 Governing equations in balloon flight 4 2.1 Dynamic model . .6 2.1.1 Forces . .6 2.1.2 The drag coefficient . .7 2.1.3 Equations of motion . .8 2.2 Geometric model . .8 2.3 Thermal model . .9 2.3.1 Heat transfer to the balloon film . .9 2.3.1.1 Optical properties . 10 2.3.1.2 Solar elevation angle . 10 2.3.1.3 Solar radiation . 11 2.3.1.4 IR radiation . 12 2.3.1.5 Heat convection . 13 2.3.2 Heat transfer to lifting gas . 15 2.4 Atmospheric model . 15 3 Sensitivity analysis 15 3.1 Balloon launch information . 17 3.2 Free lift analysis . 18 3.3 Ground temperature analysis . 18 3.4 Cloud factor analysis . 18 3.5 Ground albedo analysis . 18 4 Results 19 4.1 Simulation performance . 19 4.2 Sensitivity with an abundance/excess of buoyant gas . 20 4.3 Sensitivity for a changing ground temperature . 21 4.4 Sensitivity for a changing cloud cover . 22 4.5 Sensitivity for a changing ground albedo . 23 5 Discussion 24 6 Conclusions 25 7 References 27 Lule˚a University of Technology January 7, 2019 1 Introduction A scientific balloon is an aerial vehicle that is used for scientific and engineering purposes. There are different kinds of scientific balloons, such as the zero-pressure balloon and the super- pressure balloon. This work will be looking at the zero-pressure balloon, where the pressure difference between the inner lifting gas and atmosphere are zero. Depending on its size, the balloon can carry payloads weighing several tons at altitudes over 30 km. The contents of the payload are usually expensive equipment such as radars and scientific data collectors that would be retrieved after the flight is done. Due to the temperature differences that occur between day and night, some operational procedures will be made during the balloon flight. During daytime, the buoyant gas will expand and the balloon will rise. If the volume of the buoyant gas exceed the designed volume of the balloon, some excessive gas will be vented out. When the sun sets over the horizon and night arrives the buoyant gas will cool down and shrink. This will cause the balloon to lose some of its lifting force and it will sink. In order to regain its altitude, the balloon will have to drop some ballasting weights. With this procedure the balloon can stay in the stratosphere for several hours or even days before it is time to terminate the balloon and drop its payload. Where it will land depends on when and where the balloon is released. To avoid diplomatic problems with neighbouring countries or having to retrieve the payload from the ocean, a trajectory prediction tool can be very useful. Figure 1: Balloon launch in Kiruna, Sweden 3 Lule˚a University of Technology January 7, 2019 1.1 Previous work There are existing simulation tools that will predict a balloon's trajectory, such as NASA's Scientific Balloon Analysis Model (SINBAD). Although they give a reasonable accuracy, the prediction will hardly be the same as the real flight due to computational instabilities and existing uncertainties for the balloon flight. This work will focus on how such uncertainties affect the ascension of a balloon. The use of balloons or buoyant vehicles are not that common for space exploration, however there is a community that are exploring this kind of technology. Farley [1] wrote a manual on how to build a tool, that can describe the vertical and horizontal motions of a balloon. Van Dossalaer [2] wrote the Buoyant Aerobot Design and Simulation tool BADS, that can be used for exploration on other planets. Sensitivity studies on how uncertainties influence the balloon trajectory have been made in the past. Lee et al. [3] classifies these uncertainties into four categories: operational uncertainty, uncertainty in the prediction model, environmental uncertainty, and uncertainty by the manufacturer. They used a Monte-Carlo analysis on each uncertainty separately to identify the most dominant uncertainty parameter in the distribution of landing points. Although they did show the landing point for each uncertainty, they only tried on one type of balloon with the same mass and size. Saleh et al. [4] studied the difference in ascension speed of the balloon in the troposphere and stratosphere with different launch dates and launch sites. Their conclusion to that was that there is no significant effect on ascending velocity at troposphere, but rather in the stratosphere. Dai et al. [5] discussed the film radiation properties and clouds have on the balloon's thermal behaviour but missed out on how the ascent of the balloon varied. 1.2 Outline of thesis work The work done for this thesis is: (1) Building a tool that simulates the balloon's ascent and rate of climb, (2) Investigate how much of an influence different parameters have on the rate of climb. In other words, this work aims to study the sensitivities of balloons of different sizes and launch times in different parts of the atmosphere. 2 Governing equations in balloon flight To know the balloon's trajectory during its flight, it is important to know what forces that acts on the balloon. The balloon as a vehicle works because of Archimedes principle where the buoyant force is equal to the weight of the displaced medium. The ascending velocity is determined by the buoyant force and the drag, which means that it is necessary to calculate these correctly during the balloon flight. In order to calculate the buoyant and drag forces, the surface area and volume for the balloon needs to be known. Another force that acts on the balloon is the weight from the balloon and its payload. The volume and weight of the balloon varies depending on the flight and are usually given by the manufacturers of the balloon. The forces that act on the balloon is determined by a dynamical model.A geometric model and a thermal model needs to be introduced in order to give information that is necessary for the dynamical model. Reference areas, incidence areas etc. will be given by the geometric model while the balloon film temperature, lifting gas temperature etc. will be given by the temperature model. An atmospheric model will also be needed to supply information about the surrounding air temperature, pressure and density. 4 Lule˚a University of Technology January 7, 2019 Figure 2: A block diagram describing the simulation tool Figure 2 is a brief description on the simulation tool used for this work. Before describing it in detail, some assumptions will be made. • The balloon is considered a 3 degree-of-freedom point mass. • The variation of g (acceleration of gravity) is ignored. • Lifting gas and air assumed to follow the ideal gas law. • Effects of humidity on atmospheric pressure are neglected. • The density and pressure of the lifting gas inside the balloon is considered uniform. • Lifting gas is transparent, so it does not absorb nor emits. • The temperature inside of the balloon is uniform. • The temperature along the surface of the balloon is uniform. • The shape of the balloon is constant. • There are no winds pushing the balloon. 5 Lule˚a University of Technology January 7, 2019 2.1 Dynamic model 2.1.1 Forces To write the differential equations that describe the balloon dynamics, it's important to know the forces that act on the balloon. A simple analysis will give the forces of greatest importance • net buoyancy • weight • aerodynamic drag Figure 3: The forces that acts on the balloon during flight The net buoyancy, usually defined as the gross inflation, GI is given by GI = g · (ρair − ρgas) · V olume (1) The volume of the balloon is determined by the ideal gas law Tgas V olume = Mgas · Rgas · (2) pgas The temperature, Tgas, pressure, pgas and densities, ρair and ρgas, will be discussed in a later section. Rgas is the specific gas constant for the lifting gas, which in this work is helium and the mass of the helium inside of the balloon is Mgas = 0:1602 · Mgross · (1 + F reeLift) (3) with Mgross as the gross mass and F reeLift as the desired extra lift for the balloon.