# Specifications

The rocket was designed with the following design requirements in consideration. These are in compliance with Federal Aviation Administration (FAA) clearance.

Specification Value
Minimum Average Thrust of Propellant 90 N (20 lb)
Minimum Total Impulse of Propellant 1280 N*s (288 lb*s)
Maximum Total Impulse of Propellant 5120 N*s (1150 lb*s)
Minimum Altitude of Rocket 3000 ft
Minimum Velocity of Rocket 500 ft/s
Minimum Number of Launches for the Rocket before minor repairs 5
Minimum Number of Launches for the Rocket 20
Stability Coefficient for the Rocket 1-2

As per the problem statement, the project is to build a rocket with an electronics bay capable of measuring altitude, velocity, and acceleration of the rocket while being propelled by experimental solid rocket propellant. For a test flight to be considered a success the rocket must fly over 2500 feet, and reach a velocity greater than 500 feet per second. The reason for the minimum altitude and velocity is due to this is the typical performance of a commercial off-the-shelf rocket motor which the experimental propellant would be replacing. This would ensure that our propellant is meeting industry standard for its performance. The rocket motor must also generate an average thrust of over 20 pounds at all times. As the name implies, average thrust is the average force the motor outputs during the burning of the motor. In order for a motor to be used in a rocket, its average thrust must be greater than three times the weight of the rocket. Given the estimated total weight of our rocket to be approximately 6.5 pounds. The average thrust of the motor must be 19.5 lb or greater. This will be predetermined by testing the propellant and casing to be used in a static fire in the test stand before launch.

The rocket and motor casing must also be reusable to keep costs down and allow for repeatable testing. The rocket should be fully reusable for multiple launches. It should be able to go through multiple launch and recover scenarios and require little to no maintenance between flights. Due to the unpredictable nature of rocket launches, this required life cycle for our rocket has been set to five launches without requiring repair. This was chosen because five was estimated to be the maximum number of launches able to be done in one day. At the end of five launches it is expected that some minor repairs may be required. The rocket should also be able to fly at least twenty times, including the required minor required repairs, before it sustains any damage to great for the rocket to fly without major repairs being done. These life cycle requirements will be met by using quality materials for fabrications and assembly.

A specification not related to the performance, but still just as crucial, is the stability of the rocket. A rocket is defined as stable if the center of gravity it between one and two lengths of the body tube above the center of pressure. The equation for the stability coefficient is shown below.

$Stability Coefficient=\left(x$CoP - xCoG)/(Outer Diameter of Rocket)

where xCoG is the location of the center of gravity from the tip of the nosecone of the rocket, xCoP is the location of the center of pressure of the rocket from the nose cone.

For a stable rocket the center of pressure must always be behind the center of gravity. To make this process simpler, the distance between the two points is normalized by the diameter of the tube. The reason for a coefficient between 1 and 2 is the nature of the rocket. The center of pressure is where the resultant lift and drag forces on the rocket. If the rocket it knocked off course due to environmental or design issues, then the length between the center of gravity and center of pressure will allow for the rocket to self-correct itself. A stability less than one results in an insufficient moment arm while greater than two isn’t an issue in most cases it can lead to over correcting of the rocket leading to more issues. For the most part the center of gravity remains fixed based on placement of rocket components, as well as chosen lengths of the body tube. Therefore, the changing of the center o pressure is most effective which is done through the shape of the fins.

As per the problem statement, the rocket will be launched using multiple motor sizes, and so it must be designed to be stable for different center of gravities. Therefore, the rocket needs to be stable for any type of motor configuration to ensure a safe flight. This would be done through the use of the stability coefficient once finding the location of the center of gravity and pressure.