Analytical Calculation On Rocket Stability

Keywords

Center or Mass, Center-of-Pressure, Static Margin, Fins.

Introduction

The definition for model rocket stability is when the Center-of- Gravity (CG) is in front of the Center-of-Pressure (CP). The further distance the CG is in front of the CP, the more stable the rocket will be [1].

Metrology

Center or mass (CM) is the average location of all the mass of an object. For fully symmetrical objects the CG will be at the geometric center.

Ways to locate the CG

• List the mass of each component,

Mass of rocket body or chamber plus propellant = 981 kg
Mass of nosecone with payload = 34.69326615 kg
Mass of nozzle = 1.4 kg, since nozzle is not exposed component
we can ignore for CP and for CG value it is relatively very small let’s compensate its effect on stability by further analysis.

• Calculate the “CG station” of every component.

−X CGi is its CG location with respect to a fixed origin Equations for solid or hollow cylinders





Center of pressure (CP) is the average location of all the aerodynamic forces acting on an object as it travels through the air. we will focus just on components of aerodynamic forces that are “normal” to the body as opposed to the drag forces which point backward, parallel to the rocket body [2].

Ways to locate the CPCG

• List the normal force coefficient of every exposed component





Static Margin (SM) is characterizes the tendency of a rocket to self-correct its direction of travel back towards nose, first if it is disturbed for any reason while in flight.It is a dimensionless number found by dividing the distance between the Center of Gravity (CG) and the Center of Pressure (CP) by the body tube diameter, the worst-case scenario is to use the largest diameter of the rocket [3].

Here are those conditions that can cause uncontrolled pitch in a model rocket [4].

 Basic instability in the design
 Imperfection in construction
 Fly in the excessive wind

Fins

Fins should be constructed so that they can withstand the forces expected during flight. The materials and methods of construction determine how much force they can withstand. Very small models do not need very strong fins, and simple cardboard or balsa fins will suffice. Large models and those intended to fly at extremely high velocities will need more strength.

The following list gives several materials and construction methods, in order of increasing strength [1]:

• Thick cardboard (not corrugated)
• Balsa wood fins
• Plastic fins
• Balsa wood with paper reinforcing
• Balsa with spruce wood reinforcing
• Built-up fins
• Foam core fins
• Fiberglass reinforced fins
• Plywood

Balsa wood is a very good material for fins as its strong and light, and perfect for rockets up to around D impulse. Balsa has a tendency to dent or split if it’s handled roughly, and some rocket fliers use basswood as a stronger alternative. Some model shops stock thin plywood, which makes excellent fin material for rockets in the E to H impulse range. Sheet plastic can also be useful as a fin material in low power rockets, though it can be quite flexible which precludes its use for large fins. Fibre glass is very common for F motors and above as it is light, stiff and strong. Glueing plastic and fibre glass to cardboard tubes can be quite difficult, so most low and medium power rockets use wooden fins [5].

let take U type or 1,310,000 to 2,620,000 total impulse classifieds is fiber glass.

Various alternative fin shapes can be used during the rocket design process considering the mission requirements. The most commonly used fin types are clipped delta, swept, trapezoidal and triangular. Each of them can be sized using different number of geometric sizing parameters such as: span length, root chord length, tip chord length, sweep angle, and thickness. Within the content of this research the four fin shapes illustrated in figure 1 are examined.

Each fin shape is sized using different number of parameters. Clipped delta fin and trapezoidal fin have 4 different sizing parameters that are root chord, span, tip chord, and thickness. Swept fin has 5 different sizing parameters that are sweep angle, root chord, span, tip chord, and thickness. Triangular fin has only 3 different sizing parameters that are root chord, span, and thickness [6].

Fins thickness

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Figure 1

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Figure 1. Frequently Used Fin Shapes and Geometric Sizing Parameters.

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Figure 2

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Figure 2. fins dimension.

Ways to locate the CP

• Normal coefficients for n “clipped delta” fins where N = 4 fins.



• Calculate a sum of the normal force coefficients

Fin correction and stabilizations

CG.

mass

Mass of rocket body or chamber plus propellant = 981 kg
Mass of nosecone with payload = 34.69326615 kg
Mass of nozzle = 1.4 kg
Mass of fin =7.6347 kg

CG stations



CP

Normal force coefficient of every exposed component.

Acknowledgement

They author of this paper appreciate Space Engineering Research and Development Department, Ethiopia Space Science and Technology institution, Addis Ababa, Ethiopia for their valuable advice.