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Solid Propellant Application in

High Speed Underwater Projectiles and Bullets

Mohammad Hassan Ziraksaz *

Islamic Azad University, Science & Research Branch, Tehran, IRAN

Studying the probability of using solid propellant in a bullet or projectile,

shooting from an underwater gun, to approach higher velocities is the

subject of this paper. Providing supercavitation jacket all over the bullet is

the solution but it requires not only higher initial velocity but also

continues gradual thrust. Since the size of the bullet is too small to install a

common propulsion system inside, therefore a micro solid propellant

system is designed. Since the bullet outer profile has a key role in

providing the supercavity jacket, the matter is studied in the other paper.

Nomenclature: •

m Burning mass flow rate

bA

Burning Area

r Total Burning Rate

er Erosive Burning Rate

οr Neutral Burning Rate

bρ Solid Density

P Chamber Pressure

n Burning Rate Exponent

a Empirical Coefficient

pσ

Temperature Sensitivity of Burning Rate

kπ Temperature Sensitivity of Pressure

G Mass Flow Velocity per unit Area

D Characteristic Dimension of Port Passage

α Empirically Constant

β

Empirically Constant

Introduction: The study is performed on two

individual subjects: A high speed

minesweeper and a high speed underwater

bullet. Although the minesweeper is

applicable for both air to water and water

to water shooting, but in this study both

bullet and minesweeper are used as

underwater subjects. In fact they are

considered as underwater solid rockets.

The drag forces on a moving bullet

and projectile through water especially,

deep water, is so high that they have to

stop very fast. While they can travel

through air so far and fast. Equipping

them with solid propellant propulsion

engine, make them to behave as a solid

rocket, therefore they can travel so faster

and longer. The problem arises, when the

bullet tries to approach high velocity after

shooting from a personal underwater gun.

Bullet travels through a high viscous

liquid therefore approaching higher

velocity, higher drag forces creates over

the bullet. Drag forces are so high that the

bullet has to stop very soon. The bullet is

not able to travel as long as or as fast as it

travels through air. On the other hand not

only its velocity and affective distance

decreases but also penetration decreases

too. Designing a high velocity bullet that

travels longer than the other with high

penetration factor is the desire.

*PhD Student, Faculty member of Aerospace

Engineering Division, Ziraksaz@mstco.net

Copyright © 2008 by the American Institute of

Aeronautics and Astronautics, Inc. All rights

reserved.

AIAA-2008-4975

44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit21 - 23 July 2008, Hartford, CT

AIAA 2008-4975

Copyright © 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

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To do so a micro engine must be

installed in the bullet to make it a

propulsive subject. Both bullet and

projectile has small size, therefore

installing a micro engine makes several

problems. To approach higher speeds, the

solid propellant engine is suggested. Solid

propellant engines have short operation

time because of their high burning rate

but their specific impulse and thrust

production is higher instead.

Now, the problem is to design a small

solid propellant engine to be installed in a

bullet or in a projectile. Of course several

restrictions arise consequently in design

process. The bullet initial velocity is

provided by the personal underwater gun.

The velocity is not so high to make the

bullet to travel so far, therefore it must be

accelerated by an extra propulsion

system.

In fact the bullet acts as a solid

propellant rocket after shooting. The

propulsive force helps it to approach

higher velocity and the bullet outer shape

helps it to reduce Drag forces by creating

supercavitation jacket, which is not the

subject of this study.

Mission: A moving underwater bullet may

have low velocity and therefore low

penetration. It means that the bullet can

not travel so fast or travel a long distance

underwater. Then it is not able to

effectively damage the subjects it is

shooting to.

To develop the underwater bullets, its

motion must be so faster than it is. It must

approach higher velocity ranges. But

higher speeds, higher drag forces.

Therefore a high velocity bullet will be

decelerate and stop because of water

viscosity.

Using supercavitation phenomena,

the bullet speed not only never decelerate

but also may be accelerated because of a

water vapor jacket formation all around

the bullet. Since the jacket cover all the

bullet except of its nose, therefore the

bullet is traveling through water vapor (a

nearly gas) instead of water with high

viscosity and then high drag forces.

The bullet can approach higher

velocity and consequently its effective

motion distance and its effective

penetration into the subject shooting to

increases because of water vapor jacket

which is formed all around the bullet. To

approach higher velocity, the initial

velocity must be so fast that

supercavitation phenomena created.

Using solid propellant will satisfy the

required velocity.

Therefore, the mission is to use solid

propellant motor to satisfy the velocity

required to produce a supercavitation

water vapor jacket all around the bullet to

increase not only the effective motion

distance but also the effective penetration

distance.

Sketch: Since the studied bullet is designed as

a solid propellant rocket then S.P.R

considerations must be studied. The

parameters can be classified in two

groups, the first one are the parameters

that satisfy the applicability of the solid

propellants in this case while the second

group are the parameters which must be

studied or design to prepare the sufficient

condition. Propellant composition,

burning rate, Grain and sI are the most

important parameters while the other

parameters such as Igniter, Bullet

Chamber, Nozzle, Exhaust Cap, Jet

Plume and the Case are the secondary

group. Here the first group is studied

because of the importance.

Burning rate

This parameter is a function of

propellant composition, which can be

developed in several methods. decreasing

the oxidizer percentage and size, using

metal staples in the propellant, increasing

the chamber pressure, increasing the

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combustion gas temperature, increasing

the gas flow velocity parallel to the

burning surface, acceleration and spinning

the bullet during its travel are some

common methods to develop the burning

rate.

On the other hand the burning rate is

a sensitive parameter that depends on

several thermodynamics properties such

as temperature and pressure while its

dependence on mass flow rate must be

high lighted too.

bbrAm ρ=•

Where:

bA = )( 2m

r = )/( Secm

bρ = )/( 3mKg

Then the total effective mass will be:

dtrAdtmm bb ... ∫∫ ==•

ρ

In which both bA and r vary with time.

On the other hand: naPr =

Where:

r = )/()/( SecinorSecCm

P = PsiorMpa

n = Non Dimensional

a = Non Dimensional

n depends on grain initial

temperature.

Stable operation 10 ⟨⟨n

Unstable operation 0≈n

No change over a wide range of

Pressure 0=n

Re-startable 0⟨n

The burning rate varies with

temperature too. The chamber

temperature affects the chemical reaction

while propellant temperature prior to

combustion affects the burning rate. For

composite propellant in range of 219K –

344K, there are 20-35% changes in

chamber pressure and 20-30% changes in

operation time. To consider temperature

effects one must consider:

kk

k

pp

p

T

P

PT

P

T

r

rT

r

∂∂

=

∂∂

=

∂∂

=

∂∂

=

1ln

1ln

π

σ

Where:

pσ expresses the percentage changes

of burning rate to degree changes of

temperature and kπ expresses the

percentage changes of chamber pressure

to degree changes of temperature.

Erosive burning

Erosive burning refers to the increase

in the propellant burning rate caused by

the high velocity flow of combustion

gases, over the burning propellant surface.

It occurs when the cross section area

is smaller than throat area. Erosive

burning cause not only mass flow rate

increases but also chamber pressure and

thrust increase in early portion of burning.

When the passage increases, the erosive

reduces without any major increase in

burning rate area, mass flow rate,

chamber pressure and thrust reduces.

Therefore:

( )GrDGaPr

rrr

b

n

e

ρβα −+=

+=− exp2.08.0

ο

Grain

The other most important parameter

is the grain or the shaped mass of

processed solid propellant which is a cast,

molded or extruded body. Once ignited, it

will burn on all its exposed surfaces to

form hot gases. Grain is held in the case

via two methods either case and grain

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manufactured separately and then

assembling or case is used as mold and

grain is casted into it. In the case of aging,

the first type is preferred.

Although the shape of the initial

burning surface of the grain as it is

intended to operate in the motor is very

important but the effects of the other

parameters never must be ignored. Grain

perforation or the flow passage of

propellant grain, the grain cross section

changes along the axis, burning situation

including Neutral, Progressive or

Regressive are important too. In addition

to above parameters there are additional

elements which affect the solid motor

performance.

Inhibitors or the layer of coating of

slow or non burning material applied to a

part of the grain propellant surface to

prevent burning on that surface.

a) Wagon wheel b) End burning

c) Multi perforated d) Internal burning

e) Dog bone f) Slots and tube

g) dendrite h) Star

Fig.1 different grain cross sections

Liner or the sticky non-self burning

thin layer of polymer type material is

applied to the cases prior to casting the

propellant in order to promote good

bonding between the propellant and the

case or the insulator.

Insulator or the internal layer

between the case and the propellant grain

made of an adhesive, thermally insulating

material that will not burn rapidly. Web

thickness, b or the minimum thickness of

the grain from the initial burning surface

to the insulated case wall. Web

fraction, fb , or the ratio of the web

thickness (b) to the outer radius of the

grain.

a) Single grain bust with radial burning

b) Two different propellant with simple grain

c) Single grain boost with large burning area and

sustain with small burning area.

d) Boost- Sustain-Boost with different burning

areas

Fig.2. mixed grains.

The cross section of the grain

propellant is very important. Using

similar solid propellant with two different

grains, make the solid propellant motor to

act differently. Some of the most common

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grain profiles are illustrated in Fig.1. a, b,

f and h are some neutral grains while d is

progressive and c is progressive

regressive. On the other hand based on

the requirements and desire performance

one can use mixed grain as shown in

Fig.2. In grain part several considerations

must be concerned:

1. Solid motor requirements are

determined from the mission.

2. The grain geometry is selected to

fit these requirements.

3. The propellant is usually selected

on the basis of its performance,

capability, mechanical properties,

ballistic properties, manufacturing

characteristics, the propellant

formulate.

4. The grain structural integrity.

5. The complex internal cavity

volume of perforation slots, ports,

fins, increases with burning time.

6. The processing of the grain and

the fabrication of the propellant

should be simple and low cost.

Propellant

There are several classifications for

solid propellant. One can classify them

based on their application but more

general classification is based on the

arrangement of fuel and oxidizer as well

as the ingredients. Therefore we can use

Double base and composite solid

propellant.

The first one is a homogeneous

propellant including both fuel and

oxidizer. The arrangement is so that it is

the same as in each portion of the

propellant while the second one is a

heterogeneous propellant with different

ingredients. The second one is more

preferred since not only it is possible to

use some explosive binder instead of the

simple one but also using some special

ingredients is possible. That is why there

are several types of composite solid

propellants including low and high energy

propellants. Some of the most desire

characteristics are listed as:

1. Low moisture absorption.

2. Low pressure sensitivity.

3. High specific Impulse.

4. High mechanical strength.

5. High density.

6. Stable combustion.

7. High aging.

8. Deflagration not Detonation.

In all cases one must select correct

ingredients with proper percentage of the

oxidizer, fuel-binder, metal fuel, burning

rate modifier, explosive filler, and

plasticizer.

Igniter

The igniter mass is too small to be

considered in total impulse. Its mass must

be big enough to provide the ignition and

to satisfy the combustion process

initiating. There are several Igniter

locations, but the forward installation is

the best because of the combustion flow

over the burning surface. Pyrothecnic and

pyrogen igniters can both use but the first

one is preferred for small devices. The

desire is:

1. Fast high heat release.

2. Low sensitive to pressure and

temperature.

3. Rapid burning.

4. Low moisture absorption.

5. high aging

6. Stable over a wide rang of

operation condition.

Nozzle and Cap

Since the total length is very small

then, a fixed bell shaped nozzle based on

characteristics method with the minimum

length is considered for the system. A cap

equipped with a small igniter is installed

at the nozzle exit to not only prevent

water flow inside the bullet through the

nozzle but also to provide suitable

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Fig.3. Cartridge Schematic Diagram

including the Case and the Bullet

Fig.4. Bullet Schematic Diagram

including the bullet and Grain Cross sections

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ignition as well as increasing the chamber

pressure.

Underwater Bullet: The main underwater cartridge includes

the bullet and the case as well as the gun

powder and the accessories Fig. 3. The

cartridge is so sealed that the igniter and

the gun powder can not get wet.

Therefore, it can burn properly to provide

desire pressure not only to shoot the bullet

but also to initiate the bullet solid

propellant ignition while water is the

environment.

The shooting process performs in two

steps. Firstly the underwater gun acts to

initiate the cartridge main igniter.

Initiating the ignition the gun powder will

burn and the case pressure increases to

not only shoot the bullet out side but also

provide sufficient pressure over the cap,

the flexible disk covers the bullet end or

the exhaust nozzle. Secondly the pressure

makes the cap to actuate the solid

propellant igniter. Initiating the solid

propellant ignition, while the bullet is

moving through water, causes the bullet

internal pressure increases. Since the

bullet is equipped with solid propellant,

the pressure will increase rapidly and the

final pressure is very higher than its

primary value. Therefore the cap which is

installed on the nozzle exhaust will be

pushed out side and the solid propellant

burning gases flows through the bullet

inside.

The bullet moves through water by

its primary inertial pressure before bullet

internal engine initiate. But it will find

additional thrust by itself when its internal

solid propellant initiate. It means that the

bullet will force to speed faster not only

because of solid propellant burning but

also because of bullet mass decrement.

The internal solid propellant includes

not only two different solid propellants

but also two different grain types. For the

first stage a conventional water resistant

solid propellant with some metal

ingredients can be used with neutral

burning rate therefore the grain type can

be a star type to help the bullet outer

profile to make up the separation bubble

smoothly. But the second stage can be a

progressive type, therefore the solid

propellant must be a high energy material

included, while the grain has to be an

internal-tube-burning stage.

The bullet and its relevant grain cross

sections are demonstrated in Fig.4.

Moving through root to tip, the outer and

inner diameter of the bullet decreases and

therefore internal volume decreases and

less propellant can be installed there.

Using star shape grain helps the grain to

burn neutrally with higher values at the

root and lower values in section number

5, where the first stage ends and the

second stage with different grain and

propellant starts.

Conclusion: Considering the above underwater sketch,

some points must be considered:

• The cartridge must be sealed

completely especially in igniter and

the bullet junction.

• The gun powder must include high

energy materials to provide

sufficiently high pressure.

• The initial provided pressure must

be so high that the bullet speed out

in such a way that the primary

bubble forms right over the bullet

nose.

• As the primary bubble forms, the

bullet internal engine first stage

must be initiated and burn neutrally

to help the bubble increases.

• As the bubble covers the bullet nose, the second stage must be

initiated progressively to develop

the bubble and form the water vapor

jacket covering almost the entire

bullet rapidly.

• The pyrotechnic igniter used in

bullet internal engine must be

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pressurized sensitive.

• The cap must be so strength to

avoid water penetration inside the

bullet after shooting and so flexible

to burn, burst or pop off the bullet

exhaust nozzle.

• The nozzle must be designed for

regular water depth shooting

because of plum changes in various

water depths.

• As propellant is burning, the CG, CJ and HC changes and therefore the

outer ballistics will change. To

avoid changes, using different metal

with higher density in section 9 to

11 is recommended.

References: • M.J.L.turner, Rocket and Space

craft Propulsion, Springer, 2006.

• G.P.Sutton., Rocket propulsion

elements 7th Edition, John Wily and

Sons, 2001.

• H.E.Malone, The analysis of rocket

propellant, Academic press Inc,

1976.

• Ihor Nesteruk, Drag Reduction

Tools in High-Speed

Hydrodynamics: Supercavitation or

Unseparated Shapes, Institute of

Hydromechanics NASU.

• Vladimir Serebryakov, Problems of

Hydrodynamics for High Speed

Motion in Water With

Supercavitation, Institute of

Hydromechanics of NASU,

UKRAINE.

• Yuriy N. Savchenko,

Supercavitation – Problems and

Perspectives,

• National Academy of Sciences -

Institute of Hydromechanics, Kyiv,

Ukraine,2003.

• Eric A. Euteneuer, Further Studies into the Dynamics of a

Supercavitating, Torpedo,

University of Minnesota, 2003.