Practical Methods of Optimizing

the Maximum Range for Rockets

CRISTINA MIHAILESCU

Electromecanica Ploiesti SA

Sos. Ploiesti-Targoviste, km8, Ploiesti

ROMANIA

Abstract: - Range extension for artillery projectiles, rockets, and missiles is a problem of trajectory

important performance parameter; in others, the range can be considered as the performance parameter to be

optimized.

In this study, pulsed solid propellant rocket motor technology was considered to demonstrate a feasible method

for range extension.

For the targeted optimization problem, the influence of the thrust profile along the launching angles was

studied, and the results from the performed calculations were analyzed and discussed.

Key-Words: - Optimization design, rocket range extended, multi-pulsed solid rocket motor, rocket efficacity

Received: October 13, 2022. Revised: August 11, 2023. Accepted: September 15, 2023. Published: October 5, 2023.

systems, the SRM option is preferred because of its

simpler manufacturing technology, long-lifetime

storage, short time required for launch preparation,

ease of operation and handling, and large potential

amount of chemical energy concentrated in a

relatively small volume. In addition, lower costs are

preferred compared to other types of rocket motors.

Even with the advent of reusable rocket boosters,

SRM and its development will be essential in

ballistic technology. In counterbalance to the

engine efficiency for specific situations, payloads,

and vehicles [1]. The modern era demands

increasingly complex optimization processes with

new variable profiles that need to be monitored

using new multidisciplinary optimization

methodologies.

Because many products from artillery, projectiles,

rockets, and missiles currently use SRM, the

problem of optimizing the method of managing the

energy produced by the engine is essential [2].

domain. Because optimization methods permit

better use of the available energy, many methods

have been developed over time [3], [4].

Several methods of range extension can be

approached from different perspectives:

impulse (Isp) propellant for higher

efficiency – requires replacement of grains

and nozzle redesign;

technology is a method for optimizing SRM and can

be a simple way of extending the range [8], [9]. A

pulsed rocket motor is typically defined as a

multiple-pulse solid-fuel rocket motor. Typically, an

SRM cannot be easily shut down and reignited. The

pulse rocket motor allows the motor to burn in

segments (or pulses) until the completion of that

segment. The next segment can be ignited on

command either by an onboard device/algorithm or

in a pre-planned sequence. All the segments are

can be accomplished by the on-command ignition of

the subsequent pulses. Each pulse can have a

different thrust level and burn time and can achieve

a different specific impulse depending on the type of

propellant used, its burn rate, its grain design, and

the current nozzle throat diameter [11].

This technology is already in use, and an example is

the anti-hail rocket, which will be used as the

computational model in this study.

two-pulsed SRM created by splitting the grain into

two segments [12]. Between the two segments a

pyrotechnic delay device is placed to ensure the

rocket that contain a pyrotechnic composition with a

slow burning rate and almost no thrust.

Fig. 1 Two-pulsed rocket motor

The delay device produces a lag time t that

practically divides the thrust into two sequences

(Fig.2). The delay time can be adjusted using this

device (by varying the composition or geometric

The total energy produced by the rocket motor is

almost the same, but the profile of its use over time

is different and produces different results for the

flight parameters and implicitly, for the trajectory of

the rocket.

Fig. 2 Thrust diagrams for different delay times t

The scope of this study is to analyze the lag time t

By modifying the delay time (Fig.2), a new thrust

distribution is practically involved in the motion

equations, and implicitly results in a new flight path.

As a result, the trajectory depends on the lag time.

The obtained effect is that the trajectory of the

rocket is more flattened and elongated, which is

advantageous in some cases (guided projectiles or

missiles, hail combat).

The rocket used as an example for performing the

calculations evolved in the supersonic regime. It is

performed to flatten and lengthen the trajectory.

However, the same method can be used to optimize

the maximum range for a number of ballistic

products that use SRM.

Without this delay device, it can be seen that the

maximum range is slightly over 9 km. Another

observation from Fig. 5 is that the range initially has

Starting to increase t from 0s, the impact time will

rise to a maximum which corresponds to the

maximum range.

After a certain moment of time, when the rocket

reaches the downward part of the trajectory, any

increase in thrust will have the effect of shortening

the range and reaching the ground faster, i.e.

reducing the impact time till a minimum is reached.

Continuing to increase thet, the impact time will

Representing the range dependency of t (Fig. 7)

for different launching angles, we can see that there

Fig. 7 Maximum range dependence on t

From Fig. 7 it can be seen, with certain limitations,

that the same range can be obtained for different

launch angles by calibrating the time interval t of

the delay device.

Otherwise, we can represent the optimum values of

the maximum range dependence on t in Fig. 8.

If we analyze the influence of the delaying time t

on the velocity profile (Fig. 9) computed only for

maximum velocity of the rocket depends on t.

Fig. 9 Velocity dependence on t

For the present case, the rocket has a supersonic

evolution (Fig. 9), regardless of the t value. For

The study could be extended in the same manner for

other values of launching angles.

4 Conclusion

The first conclusion is that the delay time offers, in

a limited way, a useful instrument for controlling

the trajectory profile. The fragmentation of the grain

propellant into several segments separated by delay

devices allows a more efficient management of the

Existing pyrotechnic devices are reliable and robust,

but are also complex in manufacturing technology.

Furthermore, their installation is relatively costly

because of their hazardous characteristics.

Importantly, they also have to be regularly checked

or replaced to ensure high reliability level

requirements.

In the case of using pyrotechnic delay devices, they

have by construction a defined delay time, and

cannot be easily adjusted for each launching angle.

for example, in the case of a pyro-numerical

architecture that can initiate combustion at a

predetermined moment of time. A pyro-numeric

architecture was designed and patented by Dassault-

Aviation in 2010. This lies in the use of digital bus

for the command distribution instead of pyrotechnic

communication solutions. Digital orders are

transmitted through classical electric wires from the

numerical bus to each smart initiator which are

designed to receive, decode, and interpret the digital

[13].

The main conclusion is that this study definitely

launching angles, the maximum range could be

impact increased by 4.3%.

In the present work, the effects of using dual pulse

SRM applicable to anti-hail rocket RAG-96 were

studied. Using this technology for the operation of

SRM, the possibility of extending the maximum

range was practically demonstrated. The numerical

results were validated by experimental

measurements. In the future, the research may

continue with multi-pulse SRM studies, which will

enable a much more efficient management of the

ballistic products can be modified relatively easily

and at low cost to obtain an extension of the range

through the presented method. However, the method

is strongly influenced by the input data and the

constraints specific to each ballistic product.

Therefore, for the optimization of other projectiles

or missiles, it is necessary to study the technological

implications and the costs involved vis-à-vis the

possible benefits.

In the context of the increasingly extensive use of

References:

[1] Ahmed Mahjub, Nurul Musfirah Mazlan, M. Z.

[2] Geisler, R. L., Frederick, R. A., Jr., and Giarra,

[4] Dario Donrey Serrano, “Applications of

[5] Calabro, M., Dufour, A., and Macaire, A.,

[7] Willcox, M. A., Brewster, M. Q., Tang, K.-C.,

[8] Koehler, Frederick & Meisner, Mark & Vollin,

[10] Jensen, G.E, & Netzer D.W. Tactical Missile

[12] Gheorghiosu, Edward & Bordoş, Sorin &

[13] Guillaume TATON, Laurent RENAUD, Carole

Contribution of Individual Authors to the

Creation of a Scientific Article (Ghostwriting

Policy)

prepared the mathematical model, provided the

requirements, and the input data, carried out the

simulation and interpretation of results, and

extracted the conclusion.

Sources of Funding for Research Presented in a

Scientific Article or Scientific Article Itself

No funding was received for conducting this study.

This article is published under the terms of the

Creative Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en

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