A.4.1.2.3: Balloon Design
The following is a detailed outline of the design process that was used in order to develop the model for our balloon design.
The first balloon design procedure begins with a simple Newtonian model to approximate the system. Looking at the free body diagram, we determine that the two forces acting on the balloon are weight and buoyancy. The weightis initially calculated from Ginzinski and Wanagas’ feasibility model.1With this model, initial weight estimates for the gondola and the rocket are made and used in the first model. These values are shown in Tables 1 and 2.
Table 1: Mass of Gondola ElementsGondola Elements / Gondola
Cardboard Sections / 100
ACS / 100
Telemetry System / 30
Flight Support Computer / 50
Batteries / 100
Steel Cables / 70
Framework, Mechanisms / 1050
Chute System / 150
Electrical Cables / 100
Swivel / 50
Table 2: Mass of Rocket Elements
Rocket Elements / Rocket
Engine Tankage Structure / 650
Avionics / 100
Payload / 250
Payload Fairing / 100
Cabling / 50
Propellant / 6800
Attitude Control / 50
Total / 8000
Knowing the payload that is to be carried would be far smaller than the estimated 250 pound payload that the model presents, our initial model scales the mass elements by creating a payload ratio between the desired payload and the payload given in table two. The next part of the weight calculated is the weight of the lifting gas used in the balloon. The two gases that are first considered are hydrogen and helium. The densities for the two gases are 0.08988 grams per liter and 0.1786 grams per liter respectively. However, in order to calculate the needed volume of the gas to be used, the buoyancy force must be calculated.
The buoyancy force is found using the method outlined in the document by Tangren.2 Using Archimedes’ principle, the static lift of the balloon can be determined byconsidering the volume of air that is displaced by the lifting gas. Following the derivation, a lift coefficient is introduced and defined in equation A.4.1.2.3.2.#1.
/ (A.4.1.2.3.2.#1)where Clis the lift coefficient of the lifting gas, ρa is the density of air and ρg is the density of the lifting gas. All of these variables are kg/m3. To determine the lift coefficient of the lifting gas as a function of altitude, we calculate density using a form of the combined Boyle and Gay Sac gas laws. The equation is shown below
/ (A.4.1.2.3.2.#2)Where P, ρ, and T are the pressure, density, and temperature. The subscript indicates the values are at sea level. The other values are at the desired altitude.
Assuming that the ratio of densities applies to all gases, the lift coefficient will change as follows.
/ (A.4.1.2.3.2.#3)To account for the diffusion of air into the balloon and gas out of the balloon, it is customary to assume 95% gas purity.2 Furthermore, for stable flight of the balloon,Tangren states the gross static lift should exceed the load of the balloon by 15%.2 The actual lift coefficient is thus calculates
/ (A.4.1.2.3.2.#4)With the final lift coefficient, the balloon size and the amount of lifting gas can be determined by the following equation.
/ (A.4.1.2.3.2.#5)Where V is the volume and Mtotal is the total mass of the launch vehicle. Dimensions of the balloon are then derived using spherical balloon assumption.
The next step in our design was refinement of our preliminary design. We began to consider alternative designs for both the balloon. We initially assume the balloon is a perfect sphere. At this stage, we began to consider alternative to a single balloon that would allow for a vertical launch. Two such conceptsare shown below in Figures 1 and 2.
Fig.A.4.1.2.3.1: Concept sketch of Balloon apparatus
Fig.A.4.1.2.3.2: Concept sketch of Balloon apparatus
This design provides for a vertical launch platform without having to launch through the balloon or getting caught in the balloon tether to the gondola. However, the design is rejected due to the large amount of stress put on the cross beams. Similar multi-balloon concepts are considered. However, due to complexity and problems with supports such as those in figure 1, we chose to use the single balloon design. This requires the rocket to launch from a gondola, not interfere with the tether, and actually penetrate the balloon.
The second aspect in our design that we refined is the gondola. During brainstorming sessions, two gondola concepts came out. The first involves hooks being latched onto the rocket to secure it to the balloon. The other involves holding the rocket in some kind of basket. This basket serves as the launch platform for the rocket. To provide a launch rail for the rocket, we chose the basket concept.
Reference:
1 Gizinski, Stephen J. and Wanagas, John D., “Feasibility of a Balloon-Based Launch System,” AIAA International Balloon Technology Conference, Albuquerque, NM, 1991
2 Tangren, C.D., "Air Calculating Payload for a Tethered Balloon System," Forest ServiceResearch Note SE-298, U.S. Department of Agriculture - Southeastern Forest Experiment Station,Asheville, North Carolina, August 1980.