Solid Rocket & Grain Geometry

Solid Rocket & Grain Geometry

Mihan Bandara 
Undergraduate Mechatronics Engineering Student
McMaster University
Hamilton, Canada
bandarm@mcmaster.ca    

Austin Mardon 
Faculty of Graduate Studies & Research
University of Alberta
Edmonton, Canada
mardon@ualberta.ca

Abstract - Solid rocket grain geometry refers to the pattern in which solid fuel is packed into a rocket motor. During rocket launches, different solid rocket patterns can produce different thrust patterns. These thrust patterns can correlate to specific objectives like maximizing top speed, apogee or efficiency. Customizing the grain geometry of a rocket allows its creator to have full control over these factors and more. 

I. INTRODUCTION

Newton’s third law of motion dictates that for each action, there is an equal and opposite reaction. When solid fuel grain is ignited, the propellants are exhausted out of the motor and energy is released downwards. This release of energy creates an equal and opposite reaction force called thrust which propels the rocket upwards. This is important for rocket science because rockets in space have no atmosphere pull through as a plane or helicopter can. The lack of atmosphere also means that the fuel grain contains both the fuel itself as well at the oxidizer. Some common fuel grains include black powder (gunpowder), sugar fuels, aluminum and ammonium-perchlorate, as well as dozens more.

II. FUEL GRAIN GEOMETRY

A solid rocket motor’s thrust can be controlled through its fuel grain geometry. There are two main techniques that are used to control this. The first is by layering different solid fuels, or different mixtures of the same fuel. A 2 ring motor (Figure 1) can have an inner ring of powerful but fast-burning fuel, and then a less powerful slow-burning outer ring.

The inner ring will get the rocket off the ground while the outer ring keeps the rocket at a desired speed such as orbital velocity or escape velocity. This could result in a thrust vs. time graph similar to Figure 2. 

Motors can have dozens of rings in order to produce the desired thrust pattern. Mult-ring motors are also used to create motors with constant thrust. A motor with just one ring will not produce constant thrust due to the cylindrical shape. The surface area of fuel that can combust is not constant, as time progresses and the empty core cavity grows. This means thrust will increase in a close to linear fashion until the fuel runs out (figure 3).

Using multiple rings of different fuels is not the only method used to influence thrust patterns in solid rockets. A variety of core patterns can be used in single-fuel rockets to control burn rates. The circle is the 2D shape with the least area for its perimeter. Star-shaped, plus-shaped and other core shapes increase the surface area of fuel that is burned in certain stages of the ignition period. Figure 4 shows some examples of alternate core shapes. 

Each shape can have dozens of variations like varying thickness or feature quantity (eg. prongs of a star). Just like multi-fuel motors, fuel grain geometries produce predictable thrust-time graphs. Figure 5 shows the thrust pattern produced by a rod & tube motor.

The thrust is constant because the surface area of the inner cylinder decreases at the same rate that the surface area of the outer cylinder increases. This means that the amount of fuel that is combusting at any moment is the same. Constant thrust is not always the goal, star shapes, plus signs are referred to as regressive geometries. This means that the thrust regresses, or lessens, as time passes. Shapes that produce an extreme amount of initial thrust and minimal thurst afterwards are referred to as dual thrust geometries, as they resemble the thrust pattern produced by dual-stage motors. These geometries are ones that maximize surface area, such as the multi-fin design in figure 6. 

The protrusions burn fast and produce a lot of thrust initially, while the outer ring burns slowly. Multi-fuel layering techniques can be combined with grain geometry shapes to further customize thrust patterns. The final thrust pattern customization level involves combining fuel layering and geometry to create unique graphs like the one shown in figure 6. 

This thrust pattern could be produced by a motor like the one in figure 5 with a ring of powerful fuel on the outermost part of the motor. This type of thrust pattern is similar to one you would see in a two-stage SRM. The time between the peaks can be customized by increasing or decreasing the physical gap between the end of the fin design and the start of 2nd fuel grain. 

III. ADVANTAGES & DISADVANTAGES OF SOLID ROCKETS

The first and most important advantage of solid rockets is their simplicity. Small model rocket motors need nothing more than a cardboard tube filled with black powder and an igniter. Small motors can be bought for just a couple of dollars at a hobby store. Even large-scale modern solid rocket motors (SRMs) are based around the same simple principles that the Song dynasty used in the 13th century [1]. 

Solid rockets are not widely used in the new generation of cutting-edge rocketry for a few reasons. Solid rockets are much harder to throttle and extinguish in comparison to liquid rockets that can be controlled remotely using a valve. Throttling refers to electronically controlling thrust levels either live or through a programmed computer. Thrust levels in solid rockets are designed long before launch through fuel grain geometry as described below. Many would say that once a solid rocket is ignited it cannot be stopped, while this is not entirely true the complexity makes it unfeasible for most projects [2]. 

Another disadvantage of solid rockets is that they are more tightly regulated for the average civilian. While this is not an issue for large companies, an unlicensed civilian can get into deep legal trouble for storing large amounts of solid rocket fuel or for trying to make their own. Hybrid fuel is not legally considered an explosive until it is mixed with the oxidizer, which only happens the moment before it combusts. Hobbyists and university students often start with small solid rockets but make the switch to a hybrid fuel when time, money, and experience permit.

IV. DISCLAIMER & CLOSING REMARKS

Grain geometry customization makes it easy to tailor a solid rocket motors thrust pattern to the needs of its user. The process is fairly simple in comparison to other aspects of building a rocket. Simulation software can fine-tune the design of the fuel grain and test stands can confirm these results. It is important to remember that making, buying, storing, transporting, and firing solid rocket fuel without a proper license can be illegal in many regions of the world. Always check local laws before planning any projects involving explosive materials. 

REFERENCES
[1]    T. Benson, “Brief History of Rockets,” NASA, 12-May-2021. [Online]. Available: https://www.grc.nasa.gov/www/k-12/TRC/Rockets/history_of_rockets.html#:~:text=The%20date%20reporting%20the%20first,of%20a%20solid%2Dpropellant%20rocket. [Accessed: 24-Sep-2022].
[2]    J. John, P. Nandagopalan, S. W. Baek, and A. Miglani, “Rheology of solid-like ethanol fuel for hybrid rockets: Effect of type and concentration of Gellants,” Fuel, vol. 209, pp. 96–108, 2017.