The goal of umbilical boom is to guide the fuel pipes into the rocket and have enough support to withstand the exhaust from the rocket engine and to do this while using as little material as possible to optimize the construction process. We can tell if the boom will withstand this by finding the stress applied and comparing it to the stress required. To find the stress the total bending moment and the section modulus of the boom must be found first. To find the maximum velocity of exhaust.

DIA is the engine nozzle diameter, d is the distance D-L shown by this diagram:Isp is the specific impulse of the engine, and g is the acceleration of gravity. With this the pressure load can be found:

Where is the exhaust density of the engine, is the coefficient of drag, D is the distance between the tower and the center of the rocket, and x is some point between the center of the rocket and the tower. The boom is a cylinder because the coefficient of drag is the smallest for a cylinder and also the pipes are cylindrical so the material would be minimized. Next the total load can be found by finding the integral of the pressure load times the width of the width the boom.

With Total Load Plume Bending Moment can be found but first the point load of the centroid must be found.

In the equation A is the total load. Now the Plume Bending moment can be found.

The plume bending moment is found by subtracting the location of the centroid from the total distance between the center of the rocket and the tower and multiplying that by the total load on the boom. This gives the bending force of the exhaust on the boom but the weight of the boom must be accounted in order to find total bending moment which gives the total force that the boom will experience on rocket launch. To find Weight bending moment:

To find Weight Bending Moment Boom Weight is multiplied by half the length of the boom. Now Total Bending Moment can be found by adding the Plume Bending Moment and Weight Bending Moment.

Now the section of the boom must be found. For Cylinders it is:

The Section is the area of the boom. The section is found by finding the outside area and subtracting the inner area of the tube. Now we can find the stress applied to the boom.

The stress applied to the boom is found by dividing the total bending moment converted into inch-lbs by the section. In order to have a functioning boom: . The material of the boom is Aluminum T-5 which has a stress of 21,000 lbs-in2. With this material the boom can withstand the required amount of stress but use the minimum amount of material so construction is easy and quick.The cost of the boom is $16,280. The cost of welding is found this way:

The cost of Welding is $5600 where t is the thickness, L is the length, and n is the number of welds. The other part of the cost is the material cost which is $40 per pound of boom. The material cost is found by multiplying the volume of the boom by the specific weight ( ) of the material.

However these costs are for just one boom and therefore to find the total cost you must multiply these costs by the number of booms there are in the system which for this system is 2.

The umbilical boom is designed to withstand the required stress from the exhaust while using the minimum amount of material to maximize ease of construction. That is why the thickness is 0.25 of an inch the length is 10 feet and the boom is cylindrical.