Appendix 1: Customer/Market Requirements

Table 5: shows the developed customer requirements

Appendix 2: Governing Equations to predict Apogee

See Numerical Analysis

Appendix 3: Parachute area calculations and results

Table 6: shows parachute areas calculated across a range of weights and descent velocities

Appendix 4:

-Rourk’s Formulas for Stress and Strain, 7th E 12.2 P.534 (based on calculations from last year’s digitation)

E ⋅ ≔106 * 6.9 psi - SGlass Rourk’s Formulas C.1 P.830

υ ≔ 0.27 Poisson’s Ratio

R ≔ 4 in Airframe radius (may vary in future reports)

t ≔ 0.03 in Airframe thickness (may vary in future reports)

FT ≔ 4500 N

Assumptions:

- Neglect sonotube strength

- Isolated tube

- Static Load

Solution:

The critical stress according to Rourk for a tube is:

According to Roark, Theory is generally off by 40-60% therefore a correction factor of .4 is included

The maximum von Mises stress predicted by SolidWorks for rocket flight is:

The maximum von Mises stress predicted by classical equations for rocket flight is:

The airframe buckling FOS is then:

Engineering Calculations

When engineering a rocket, the calculations involved (2) (4) can be quite complex and the accuracy of the calculations depends on the assumptions established to analyze the rocket. Overall system calculations can be developed that are independent of several of the specifications involved in rocket design. A first step in conceptualizing engineering requirements is to understand the relationship between the energy stored in a rocket motor and how it can be utilized to estimate rocket flight parameters. In the Nomenclature & Governing Equations subsection of this report included in Appendix 3, the equations required for such estimation are defined and explained. It is important to realize that these equations make assumptions that inherently induce differences between a theorized model’s performance and an actual performance of the fully developed concept. Other factors will affect a rocket’s performance, and the calculations associated with these factors are still being investigated. The most basic factors involved in a successful performance regard to buckling of the airframe, the fin area and subsequent flutter, and as mentioned, the various parameters predicted by the a motors impulse and average thrust ratings. Further sources have only recently been procured into which a more in-depth analysis can be investigated. This draft of the final report does only include the equations required for the calculation of various in-flight parameters as they are calculated from the rocket motor specifications. All motor’s investigated had the same cross-sectional area and were assumed to be used in the same four inch diameter rocket.

Parachute Area Equations

See Appendix 3

Buckling Equations

See Appendix 4

Importance of Stability

Stability

Stability is the ability of a rocket to resist displacement, and if displaced, to develop forces to restore the original condition. The difference between a stable and unstable rocket can be the difference between a safe and unsafe rocket. There are two properties rockets that determine their stability: the location of its center-of-gravity (CG) and its center-of-pressure (CP). The relationship of between these two entities determines if the rocket will be stable or unstable. For a rocket to fly in a stable manner, the location of the rocket’s center-of-gravity must be forward of the location of the rocket’s center-of-pressure (4).

Center of Gravity – the point at where the rocket will balance when on a fulcrum with respect along the axis from the rocket’s nose to the rocket’s tail. Modeling the rocket may provide a better estimate of the CG’s location.

Center of Pressure – the location upon the rocket where all the aerodynamic forces are in balance; thus the forces acting on the front part of the rocket equal the forces acting at the back. It can be difficult to determine location of the CP, but the most accurate method is testing the rocket in a wind tunnel and examining the forces trying to rotate it. By observing pivot points along the rocket and measuring the reaction forces, it is possible to find the location where the forces acting upon the pivot become zero. Another method is the Barrowman method, which is quite intensive and will be used to help confirm the results of a wind tunnel test. An old method is to make a 2D outline of the rocket and balance it on the edge of a ruler. The location of the fulcrum can be considered an approximation of the CP and is not exact but rather classified as overly conservative. The problem is that it locates the CP too far forward so a lot of weight is added to the nose cone thus making the airframe heavier than necessary.

Again, it is important that the rocket’s CP is behind its CG for the rocket to be stable. If the CG is at least one body tube diameter in front of the rocket’s CP, then it is called one-caliber stability. If the rocket’s CG is two body tube diameters in front of the rocket’s CP, then it is called two-caliber stability, and if the rocket’s CG is more than two body tube diameters in front of the rockets CP, the it is considered overly stable. A swing test can be done to the model while it is in its liftoff condition prior to flight. A swing test is done affixing a string to the location of the rocket’s already located CG. Swinging the rocket horizontally, if it flies straight, it should be stable and safe to launch, but if the tail flies first or in some other position than nose first, then it is unstable or the CG is too near the CP despite being forward of it on the rocket.

Correcting Rocket Instability

There are three ways to correct instability:

Moving the CG forward, which can be accomplished by a couple of methods:

• Removing mass from the rear of the rocket
• Add mass to the front of the rocket as close to the tip of the nose cone as possible
• Lengthening the body tube
• Recessing the engine into the body, though no more than one body tube diameter into the rocket

Moving the CP rearward by:

• Moving the fins rearward on the body tube or sweeping them toward the rear
• Increase the size of the fins

*As a rule of thumb, the fin size should be at least 1.5 body tube diameters wide and long, but if more area is needed, it is more effective to increase the span than the length (4).

An alternative to moving the CG or the CP is to induce spin on the rocket causing it to gain angular momentum, which will assist in canceling out any unbalanced forces acting on the rocket. A drawback to increasing spin is the increased amount of drag it produces on the face of the fins.

Rockets with small fins have a harder time producing the necessary forces to restore the model to the correct flight path. By increasing the velocity of the rocket, the fins will produce larger restoring forces because more air is flowing over them.

*Interestingly enough, if a rocket is generally cone-shaped, it may not need any stabilizing fins at all. Cones have inherent stability and the CP is located 2/3 of the way back from the tip toward the base of the cone. So if the CG is forward of this location, the rocket will be stable. This is accomplished by adding mass to the nose in front of the recovery device and/or recessing the engine into the base of the cone.

Societal and Environmental Impact

Rockets are exciting to people of all ages and abilities.  This excitement can be a great way to motive younger students to take an interest in science and engineering.  The Experimental Sounding Rocket Association recognizes this as great motivator to advance K-12 S.T.E.M. learning.  This is why the association has created an opportunity for addition points to be given to payloads that are evolved in K-12 outreach.  It is possible that this may motivate a child to one day pursue an education that leads to a S.T.E.M. based career.  Any increased interest from younger generations in science and engineering can only be a seen a benefit to society.

Rockets are generally fired in areas with low population density and few people are even aware that rocket launches are even occurring mere miles away. However, there is a chance of someone objecting to the launch (5). Special permissions are need from the relevant parties (FAA, landowners, neighbors etc.) prior to launches or tests to ensure no one objects to a rocket test in the area.

Rockets themselves are inherently dangerous objects, combining highly combustible, sometimes toxic propellants, with a large, high velocity, usually unguided airframe. Without proper care and caution rockets can be very dangerous. To mitigate these potential risks, steps need to be taken to understand how they might interact negatively with the environment and society.

The risks to the environment are the result of a failure at any stage of a rocket flight. These risks are to be mitigated in the following ways:

1. To reduce risk of fire, we will adhere to the safety rules outlined in the rules and any rocketry best practices. Failsafe’s and multiple safeties will be built into the rocket to prevent premature ignition.
2. By using non-toxic propellant (as per rules), we will not be producing undue harm to the environment, nor be posing excess risk to ourselves, competition staff or spectators.
3. By implementing a redundant recovery system, we will minimize the risk of a terminal rocket impacting at high speed.

Standards and Regulations

Besides the competition, there are other sources of standards and regulations for high-powered rockets. One source is the National Fire Protection Agency under article 1127 that deals with high-powered rocketry. Chapter 4 of this article deals with the requirements for construction and operation of a rocket. The most important standard is making sure that the rocket is safe for not only the user but also for anyone watching the launch of the product. Some of the safety requirements stated make sure that only certified personnel work and launch (4.2), the rocket must withstand the stresses that will be acting upon during the launch and ascent while still maintaining its structure (4.6), and that the rocket must have been proven to be stable before the launch (4.8). The standards for the stability of the rocket are especially strict because instability in the rocket will cause it to fly off course ad become a potential danger to the surrounding areas. Under this chapter the rocket is also supposed to fire at angle lower than 200(4.12.3) as well as not be fired towards an audience in order to keep participants safe and out of the recovery landing zone. It also warns people not to try and catch a rocket that is about to land. Lastly it also mentions building the ignition so that the rocket won’t have a misfire while a participant is working on it (4.13). A good portion of the standards that deal with the launch will be handled by the competition of the officials as long as our rocket uses their launch pad instead of one that we would have created. A general safety code has been developed to address important areas, but may be updated as issues are realized.

Safety Code

Materials: The high-powered rocket will be made of lightweight suitable for the power used and the performance required from a high-powered rocket. The use of metals will be minimized.

Engines: Motors will be constructed under the direct supervision of EEE certified personnel. Solid fuel motors will be utilized to minimize the possibility of failure.

Recovery: A recovery system will be utilized to safely return the rocket to the ground so that it may be flown again. Precautions will be made to prevent damage due to launch and deployment.

Stability: Stability tests will be performed before launching the rocket.

Payload: This rocket will not contain live animals or payloads that are intended to be flammable, explosive, or harmful.

Launch Site: The rocket will only be launched outdoors in a cleared area, free of tall trees, power lines, building, and dry brush and grass. People in the launch are will be aware of the pending model rocket launch and can see the model rocket’s liftoff before lift-off count down is initiated.

Launcher: The launching device will be stable, providing rigid guidance until the rocket reaches speeds adequate to ensure a safe flight path. The launcher will be equipped with a locking mechanism when not in use. The launcher will have a device to prevent the engine exhaust from hitting the ground directly and will only be launched in area cleared of easy-to-burn materials.

Ignition System: The system used to launch the rocket will be remotely controlled and electrically operated. It will contain a launching switch that will return to “off” when released. The system will contain a removable safety interlock in series with the launch switch.

Launch Safety: No one will be allowed to approach the rocket on the launcher until it has been made certain that the safety interlock has been removed or that the battery has been disconnected from the ignition system. In the event of a misfire, five minutes must pass before anyone is permitted to approach the launcher.

Flying Conditions: The rocket will only be launched when the wind is less than 20 miles an hour and it will not be launched into clouds, near aircraft in flight, or in a manner that is hazardous to people or property.

Launch Angle: The launch device will be pointed within 30 degrees from vertical. The rocket engines will never be used to propel any device horizontally.

Recovery Hazards:  If the rocket lands in a dangerous place, no attempts will be made to retrieve it.

*To launch rockets weighing over three pounds including propellant, or rockets containing more than 2.2 ounces of propellant, must obtain a waiver from the Federal Aviation Administration (FAA) (4).

The Basic category of the 10th IREC requires the competing team to wholly design and construct a rocket. Due to these specifications, as well as the payload and apogee requirements, similar products do not exist in the market. However, there are attributes, parts, or ideas that do help design a competing rocket. Sources for these design inspirations come from rocket teams who have competed in the past as well as our mentor who led a group of BSU students in creating high-powered rocket during the 2014 spring semester.

Areas in which these insights are invaluable are:

• Materials for the body frame (both interior and exterior)
• Grain design, impulse, and thrust ranges required from a motor
• Parachute deployment methods and parachute design
• Fin designs and construction (fixed vs. free, permanent vs. replaceable)

Materials utilized in constructing the airframe must withstand the stress of flight, yet be light enough to optimize the performance of the motor. Materials investigated for the airframe include:

• Carbon Fiber (strong, expensive, but can interfere with wireless radio-frequency transmission)
• Aluminum alloys (strong enough to withstand impact if recovery fails, yet light enough for flight)
• Wood or paper (light, inexpensive, but could result in catastrophic failure if an impact or fire occurs)
• Fiberglass (strong, less expensive than carbon fiber, does not interfere with RF signals, and within an acceptable weight limit).

There are several possibilities regarding parachute design, these include:

• Dual deployment (drogue deploys at apogee to reduce the impact on the main chute when it deploys at a lower altitude)
• Dual parachutes (two main chutes are deployed simultaneously to reduce spin and swing during descent)

Regarding fins, there are several ideas including:

• Individually detachable (increases ease of replacement)
• Mounted on a free spinning base (reducing stresses placed between the fins and the body of the airframe, adds complexity)
• Various shapes (designs are endless, a catalog found at aerotech-rocketry.com describes many of the fin shapes often utilized)

It is apparent that the cost of a rocket designed to meet the specifications for the advanced category is dependent on many different factors. With the possibility of utilizing parts from the rocket BSU designed last year (specifically the flight module) and the possibility of having a motor/motor materials donated, it is not possible to establish a solid estimate on cost. It should be noted that a similar rocket launched in the 7th IREC was quoted to have cost around $5000.