A.5.0 Structures1

A.5.2.6.2 Stress Analysis on Balloon Launch Configurations

When we decided we were going to do a balloon launch, we needed to figure out how to carry the launch vehicle. There were two design configurations that were considered. The first was a simple basket type gondola that would simply hold the launch vehicle and we would launch out of the basket. The other design was a hook system, where brackets would be attached to the launch vehicle. From the balloon would be some type of hook system that would fall off when the launch vehicle was lifting off. After looking from the structural point of view and at the stresses that would be put on the launch vehicle, we decided to go with the basket type gondola system. The launch vehicle simply sits in the gondola and launches straight up.

In performing a balloon launch, there are several stresses that need to be considered in order to make the launch successful. However, given the time frame of the project not all the stresses were taken into account. The main stress that was analyzed is the stress on the gondola from the sitting launch vehicle. This stress is used in designing the size and shape of the gondola.

The stress of the gondola is calculated using the area of the gondola base, the mass of the support rails and support rings of the gondola, the mass of the launch vehicle, the mass of the avionics support piece, and the mass of the avionics. All the masses are added up and multiplied by the acceleration to get the force exerted on the area of the gondola base. The area of the gondola base is found with the properties tool in CATIA. This area is used to find the stress the gondola base is experiencing. This stress is then compared to the ultimate stress of the material used for the base and if the stress on the base is less than the stress of the material than the gondola is able to hold itself and the launch vehicle. The equation used for the force exerted on the gondola base can be described by Eq. (A.5.6.2.1).

(A.5.6.2.1)

where F is the force exerted on the area of the base of the gondola, mrr is the mass of the support rails and support rings of the gondola, mr is the mass of the launch vehicle, mas is the mass of the avionics support piece, ma is the mass of the avionics and g is the gravitational acceleration 9.80665.

The stress the gondola base is experiencing can be described by Eq. (A.5.6.2.2).

(A.5.6.2.2)

where σ is the stress the base of the gondola experiences, F is the force exerted on the gondola base, and A is the area of the gondola base. The strengths of the gondolas are shown in Table A.5.6.2.1.

Table A.5.6.2.1 Strength of the Gondolas
Variable / Value / Units
200g Strength / 56,301 / Pa
1kg Strength / 32,704 / Pa
5kg Strength / 75,479 / Pa

The material being used for the gondola is aluminum. Aluminum was chosen because it is a material that is cheap and light weight as well as easy to work with when it comes to welding and riveting. Figure A.5.6.2.2 is the final gondola design drawn in CATIA.

Fig. A.5.6.2.2: CAD drawing of the balloon gondola (Sarah Shoemaker)

The sizing of each of the gondolas for each of the payloads can be found in Table A.5.6.2.2 through A.5.6.2.4.

Table A.5.6.2.2 Sizing of the Gondolas-200g Payload
Variable / Value / Units
Mass / 177.188 / kg
Length
Width
Ring Diam. / 3.346
0.876
1.3015 / m
m
m
Footnotes: All thicknesses of the beams and rails are 0.04 m.
Table A.5.6.2.3 Sizing of the Gondolas-1kg Payload
Variable / Value / Units
Mass / 227.114 / kg
Length
Width
Ring Diam. / 3.849
1.000
1.1264 / m
m
m
Footnotes: All thicknesses of the beams and rails are 0.04 m.
Table A.5.6.2.2 Sizing of the Gondolas-200g Payload
Variable / Value / Units
Mass / 338.320 / kg
Length
Width
Ring Diam. / 5.133
1.380
1.8386 / m
m
m
Footnotes: All thicknesses of the beams and rails are 0.04 m.

Originally the gondola was going to be in the shape of a triangle because triangles are one of the strongest shapes. However, because of the nozzle of the launch vehicle needing to fit through the base of the gondola, the shape had to be changed to fit the nozzle.A circular base was also considered but because the launch vehicle needed to rest on the base a circle would not have worked.

The final design of the gondola has four rails used in supporting the launch vehicle on its initial assent. The reason for these rails is to help guide the launch vehicle so that it may launch in the direction we decided. The gondola also has support rings riveted around the support rails. These rings are needed to help support the rails from the stresses the rails will experience when the launch vehicle takes off.

At the top of the gondola is a solid square with a hole cut out to fit the launch vehicle. The platform is riveted to the support rails and is used for holding the avionics needed for controlling and keeping track of the entire balloon-launch vehicle-gondola configuration. The avionics are riveted to the platform. The base of the gondola is a square consisting of four beams welded together. The support rails are welded to the four corners of the base. The shape of a square was chosen because of its simplicity.

The gondola attaches to the balloon by its tethers. The tethers will be made out of a steel cable. This cable has not had a stress analysis done on it. If an analysis were to be done, the tension in the cable will need to be analyzed to make sure the cable will not snap under the pressure of the tension.

There are several stresses that are left out of this analysis due to the time constraint. One of these is the stress on the connections from the gondola to the balloon. The connections were assumed to be able to handle both the gondola and the stress from buoyancy of the balloon. If this analysis was to be done there may have been some added mass to the top of the gondola to help with the stress from the tension in the tethers from the balloon. Another stress that is not being analyzed is the stress the balloon material experiences with the inflating of the balloon and the stress on the material from the assent and the pressure changes along the way.

Since we are assuming the launch vehicle could possibly launch through the balloon, there are stresses involved in that as well. However, this stress analysis was not done again because of the time constraint. If it were to be done, the stresses on the launch vehicle from bursting a balloon would cause the launch vehicle to possibly go off course and therefore it would cause more stress on the launch vehicle to control the course of the launch vehicle. Also there would be an added stress on the nose cone when the launch vehicle was trying to bust the balloon. Another thing not taken into account is the amount of stress needed to burst the balloon.

Another stress analysis that is not being done is that of the swinging and rotating of the launch vehicle-gondola combination. When something is attached to the bottom of a balloon it tends to swing back and forth like a pendulum and sometimes the object will rotate while swinging. This swinging and rotating will put added stress on the gondola joints where the tethers are attached. It will also put added stress on the gondola support rails holding the launch vehicle which will then put stress on the support rings. The swinging and rotating will also put stress on the tether attachment to the balloon, adding stress to the balloon material. This stress analysis was also not done because of the time constraint.

When the launch vehicle takes off from the gondola, there will also be stresses on the gondola which were not taken into account. The gondola was designed to minimize the stress on the sides by making the support rails flush with the launch vehicle. This helps with when the launch vehicle takes off, it is already touching the support rails and therefore not adding stresses to the support rails. However what is not being taken into account is the stress on the support rails if the launch vehicle were to take off at an angle due to the swinging and rotating. If the gondola were to swing out to the side and the launch vehicle were to lift off at that point, the stresses on the support rails the launch vehicle would be “resting on” would need to be analyzed. This analysis would cause the mass of the gondola structure to increases in able to handle these stresses.

The final stress on the gondola structure that is not being considered is the impact stress when the gondola lands. We are assuming that after the launch vehicle lifts off and bursts the balloon, the gondola will fall back to the ground. We have not done any analysis on how the impact of this landing will affect the gondola structure because we are not planning on reusing the gondola.

A.5.2.6.2.1 Math Models

The code that was used for the construction of the gondola is very simple. The code takes in the gross lift off weight of the launch vehicle and adds it to the mass of the guide rails, support rings and avionics bay. The code also takes in the area of the base of the gondola. Then the code uses the masses added up and multiplies them by the acceleration of gravity to obtain the force exerted on the area of the gondola base. After the code generates the force, it then divides the force by the area to get the stress exerted on the base of the gondola. This stress is compared to the maximum strength of aluminum and if it is less than the aluminum strength then the gondola is good.

Author: Sarah Shoemaker