Attachment 4 continued ARSP-2 Vol II Edition A Version 1 Draft 4.pdf

NATO UNCLASSIFIED

NATO STANDARD

ARSP–2 Volume II

GUIDANCE ON THE DEVELOPMENT OF

WEAPON DANGER AREAS/ZONES

PROBABILISTIC METHODOLOGY –

APPLICATION TO UNGUIDED WEAPONS

Edition (A) Version (1)

MARCH 2017

NORTH ATLANTIC TREATY ORGANIZATION

ALLIED RANGE SAFETY PUBLICATION

Published by the

NATO STANDARDIZATION OFFICE (NSO)

© NATO/OTAN

INTENTIONALLY BLANK

NORTH ATLANTIC TREATY ORGANIZATION (NATO)

NATO STANDARDIZATION OFFICE (NSO)

NATO LETTER OF PROMULGATION

1 March 2017

1. The enclosed Allied Range Safety Publication ARSP-2 Volume II, Edition (A), Version (1), GUIDANCE ON THE DEVELOPMENT OF WEAPON DANGER

AREAS/ZONES — PROBABILISTIC METHODOLOGY — APPLICATION TO

UNGUIDED WEAPONS, which has been approved by the nations in the MCLSB, is promulgated herewith. The agreement of interested nations to use this publication is recorded in STANAG 2470.

2. No part of this publication may be reproduced, stored in a retrieval system, used commercially, adapted, or transmitted in any form or by any means, electronic, mechanical, photo-copying, recording or otherwise, without the prior permission of the publisher. With the exception of commercial sales, this does not apply to member nations and Partnership for Peace countries, or NATO commands and bodies.

3. This publication shall be handled in accordance with C-M(2002)60.

Edvardas MAŽEIKIS, Major General, LTUAF Director NATO Standardization Office

ARSP-2 VOL II

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RESERVED FOR NATIONAL LETTER OF PROMULGATION

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RECORD OF RESERVATIONS

CHAPTER RECORD OF RESERVATIONS BY NATIONS

Note: The reservations listed on this page include only those that were recorded at time of promulgation and may not be complete. Refer to the NATO Standardization Document Database for the complete list of existing reservations.

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RECORD OF SPECIFIC RESERVATIONS

[nation] [detail of reservation]

Note: The reservations listed on this page include only those that were recorded at time of promulgation and may not be complete. Refer to the NATO Standardization Document Database for the complete list of existing reservations.

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TABLE OF CONTENTS

Chapter 1 General

1.1. Introduction ………………….…………………….…………………….……….………. 1-1

1.2. Aim ………………….…………………….………………………….…………………... 1-1

1.3. Scope ………………….…………………….………………………….………………... 1-1

1.4. Vocabulary and abbreviations ...……………….…………………….……………....... 1-1

1.5. Related documents …………….…………………….…………………………………. 1-2

Chapter 2 Methodology

2.1. Introduction .…….…….…….…………………….………………………….………….. 2-1

2.2. A small arms example …………...………….………………………….………………. 2-1

2.3. A carrier shell/submunition example ………..……………………….……….............. 2-2

Chapter 3 Terrain models – topography, surface type and surface roughness

3.1. Introduction ….…….…….…………………….………………………….……………... 3-1

3.2. Coordinate systems …………... 3-1

3.3. Topography ...….…….…………………….………………………….……………….… 3-1

3.4. Surface type …...………………………………………………………...……….……… 3-2

3.5. Surface roughness …………………………………………………...……………….… 3-3

3.6. Terrain survey data …..….…………………….………….……………….……………. 3-3

3.7. Digital terrain data ….…….…………………….………………………….……………. 3-5

Chapter 4 Object models — hard targets and structures

4.1. Introduction .…….…….…….…………………….…………………………….……….. 4-1

4.2. Cuboid objects ……………………………………………………………….………….. 4-1

4.3. Simple polyhedra ………………………………………….…………………………….. 4-1

4.4. Groups of objects ……………………………………………………………………….. 4-2

Chapter 5 Meteorology models

5.1. Introduction …….…….…….…………………….………………………….…………... 5-1

5.2. Coordinate systems .……………..………………..…………..……………………….. 5-1

5.3. The ICAO standard atmosphere ..…………..…………..…………..………………… 5-1

5.4. A generalized standard atmosphere ……..…………..…………..…………………… 5-2

5.5. Wind models .………..…………..…………..…………..…………..………………….. 5-3

5.6. Tabulated meteorology data .…..…………..…………..…………..…………………. 5-4

Chapter 6 Firer models — firing points, target positions and aimer deviations

6.1. Introduction …….…….…….…………………….…………………….……….……….. 6-1

6.2. Static firing points ………………..…………..………….…..…………..……………… 6-1

6.3. Static target positions ………………..…………..………….…..…………..………….. 6-2

6.4. Dynamic firing positions…………..…………..………….…..…………..……………...

6.5. Dynamic target positions …..………..…………..………….…..…………..…………..

6.6. Firing and target lines and areas …..…………..………….…..…………..…………..

6.7. Aimer deviations ………….………..…………..………….…..…………..…………..

Chapter 7 Projectile models — launch and free flight

7.1. Introduction .…….…….…….…………………….…………………………….……….. 7-1

7.2. Projectile properties including muzzle velocity …....…………..…………………….. 7-1

7.3. Aerodynamic forces ………………..…………..…………..…………..………………. 7-1

7.4. Gravity …………………………………………………………..……………………….. 7-2

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Chapter 8 Fuze models

8.1. Introduction .…….…….…….…………………….…………………………….………..

8.2. Time, point detonating, proximity and multi-role fuzes ………..…………………….. A-1

8.3. Premature and early bursts ………..…………..…………..…………..………………. A-1

8.4. Delayed action and non-function …………………………..……………………….. A-2

Chapter 9 Warhead models — fragmentation, shaped charges and submunitions

9.1. Introduction .…….…….…….…………………….…………………………….………..

9.2. Fragmentation ……………………………………………………..…………………….. B-1

9.3. Shaped charges ……………...……..…………..…………..…………..………………. B-1

9.4. Submunitions ………………………….………………………..……………………….. B-1

Chapter 10 Impact model — ricochet and break-up

10.1. Introduction ….…….……..…………………….…………………….……….……….. 6-1

10.2. General assumptions …………..…………..………….…..…………..……………… 6-1

10.3. Impact angles ..……………………..…………..………….…..…………..………….. 6-2

10.4. Surface roughness …….………..…………..………….…..…………..……………...

10.5. Probability of ricochet and probability of break-up .…….…..…………..…………..

10.6. Ricochet …………………………......…………..………….…..…………..…………..

10.7. Break-up ………..………….………..…………..………….…..…………..…………..

Chapter 11 Post-impact models — post-ricochet and post-break-up flight

6.1. Introduction …….…….…….…………………….…………………….……….……….. 6-1

6.2. General assumptions ..…………..…………..………….…..…………..……………… 6-1

6.3. Turn angle ………………..…………………..…..………….…..…………..………….. 6-2

6.4. Drag ………………………………..…………..………….…..…………..……………...

6.5. Curvature ………………..…..………..…………..………….…..…………..…………..

6.6. Sampling ………………………….…..…………..………….…..…………..…………..

Annex A Coordinate systems

10.1. Introduction ….…….……..…………………….…………………….……….……….. 6-1

10.2. WGS 84 Cartesian coordinates .…………..………….…..…………..……………… 6-1

10.3. Geoids, ellipsoids, and geodetic coordinates ..………….…..…………..………….. 6-2

10.4. Grids and grid coordinates ……..…………..………….…..…………..……………...

10.5. Grid reference systems ……………………………..…….…..…………..…………..

10.6. Conversion/transformation between Cartesian, geodetic and grid coordinates ...

Annex B Terrain models

10.1. Introduction ….…….……..………………….….…………………….……….……….. 6-1

10.2. Coordinate and grid reference systems ….………….…..…………..……………… 6-1

10.3. Irregular rectangular ………………..…………..………….…..…………..………….. 6-2

10.4. Triangulation ………..….………..…………..………….…..…………..……………...

10.5. Regular rectangular grid …………………………….…….…..…………..…………..

10.6. Terrain survey data ….…………......…………..………….…..…………..…………..

10.7. Digital Terrain Elevation Data (DTED) ...……..………….…..…………..…………..

10.8. Ordnance Survey Land-Form Profile (LFP) Digital Terrain Model (DTM) ………..

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Annex C Object models

C.1. Introduction …….…….…….…………………….….………………………….……….. C-1 C.2. Cuboids …..………..…………..…………..……….……..…………..………………… C-1

C.3. Simple polyhedra .…..…………..…………..………….…..…………..………………. C-1

C.4. Groups of objects ………………………………………………………………………..

Annex D Meteorology models

D.1. Introduction …….…….…….…………………….………….………………….……….. D-1 D.2. The ICAO standard atmosphere …………..……………..………………………….... D-2

D.3. A generalized standard atmosphere ………………..………………………………… D-3

D.4. Wind models ….…………………….………….………………….……………………..

D.5. Tabulated data models ….…………………….………….………………….…………

Annex E Firer Models

E.1. Introduction …….…….…….…………………….…………………………….………... E-1 E.2. Static firing points …………..…………..…………………….……………..………….. E-2

E.3. Static target positions …………..…………..…………..………………………………. E-3

E.4. Dynamic firing positions …………..…………..…………..……………………………. E-4

E.5. Dynamic target positions …………..…………..………………………………………. E-5

E.6. Firer-target combinations …………..…………..………………………………………. E-6

E.7. Aimer deviations …………..…………..………………………………………………… E-8

E.8. Calculation of initial angles …………..…………..………………….......................... E-9

Annex F Projectile models

F.1. Introduction …….…….…….…………………….…………………………….………... E-1 F.2. Point-mass models ..………..…………..…………………….……………..………….. E-2

F.3. Modified point-mass models …..…………..…………..………………………………. E-3

F.4. Aerodynamic coefficients .………..…………..…………..……………………………. E-4

F.5. Gravity ………………………………..…………..………………………………………. E-5

F.6. Coriolis …………………...…………..…………..………………………………………. E-6

Annex G Fuze models

G.1. Introduction ...….…….…….…………………….…………………………….………... E-1 G.2. Time fuzes …………..…………………..…………………….……………..………….. E-2

G.3. Point detonating fuzes ..………..…………..…………..………………………………. E-3

G.4. Proximity fuzes ...………..…………..……………...……..……………………………. E-4

G.5. Multi-role fuzes …………..……………………..………………………………………. E-5

G.6. Premature and early bursts ...……..…………..………………………………………. E-6

G.7. Delayed actions ....………..…………..………………………………………………… E-8

Annex H Warhead models — fragmentation, shaped charges, and submunitions

H.1. Introduction …….…….…….…………………….…………………………….………... E-1 H.2. the warhead coordinate system ..……..…………………….……………..………….. E-2

H.3. A “spider” fragmentation model .…………..…………..………………………………. E-3

H.4. A preformed fragmentation model …………..…………..……………………………. E-4

H.5. A shaped charge model ….………..…………..………………………………………. E-5

H.6. A submunition model …………..…..…………..………………………………………. E-6

Annex I Impact models

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I.1. Introduction …….…….……..…………………….…………………………….………... E-1 I.2. Spin stabilized projectiles …..…………..…………………….……………..………….. E-2

I.3. Fin stabilized projectiles ….……..…………..…………..………………………………. E-3

Annex J Post-impact models

J.1. Introduction …….…….…….…………………….…………………………….………... E-1 J.2. Spin stabilized projectiles ....…………..…………………….……………..………….. E-2

J.3. Fin stabilized projectiles ...……..…………..…………..………………………………. E-3

Lexicon …………..…………..…………..…………..…………..…………..………………… L-1

References …………..…………..…………..…………..…………..…………..……………..

R-1

LIST OF FIGURES

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CHAPTER 1

GENERAL

1.1. INTRODUCTION

1. A Weapon Danger Area (WDA) is that area associated with firing a weapon where the risk of death or injury exceeds some threshold. The risk outside the WDA does not exceed this threshold and hence the risk to people outside the WDA is acceptable or tolerable. A Weapon Danger Zone (WDZ) extends this into three dimensions. Traditionally, WDA have been developed using deterministic methodology and WDA are extended into WDZ by using a constant height above the WDA. In both cases the level of risk associated with the area or zone has been assessed as acceptable or tolerable, but has not been explicitly quantified. In order to quantify the levels of risk we have to use a probabilistic methodology.

2. Weapon Danger Area/Zones (WDA/Z) encompass the ground and airspace for lateral and vertical containment of projectiles, fragments, debris, and components resulting from the firing, launching, and/or detonation of ordnance. WDA/Z account for weapon accuracy, failures, ricochets, and broaches/porpoising of a specific weapon/munition type. WDA/Z developed using deterministic principles, where a number of worst case assumptions are used, are usually bigger than they need to be, and this often results in the use of large areas and can constrain training. The probabilistic methodology can be used to handle more complex situations:

3. Specific range danger areas/zones (RDA/Z) to account, for example, for local terrain and local met conditions can be developed;

a. The methodology can be applied to the specific situation using realistic data so that range space can be optimized;

b. Ranges can be designed to contain projectiles;

c. Probabilistic analyses can provide information that can be used for other risk management purposes, for example to quantify the risk to range infrastructure;

d. Probabilistic analyses can provide information that can be used to diagnose problems for conceptual or existing ranges.

4. It is important to note that the use of a probabilistic methodology is not a universal remedy. Whilst is has many advantages over deterministic methodology, probabilistic models have to be developed and data needs to be gathered and analyzed for use in these models and this may not be a simple process.

1.2. AIM

1. Whereas WDA are traditionally classified by weapon type and role, the general principles described here apply to all weapon systems and no such distinctions need to be introduced. This aim of this document is to describe these general principles so that they may be applied for all weapon systems and appropriate WDA/Z may be developed.

1.3. SCOPE

1. This publication is relevant to the development of WDA/Z for all weapon systems.

Although the description here is based on ballistic weapons the principles apply to all weapon systems and lasers (either used as part of a system or as weapons). Specific information for various categories of weapon systems is given in related publications.

1.4. VOCABULARY AND ABBREVIATIONS

1. A list of terms and abbreviations used in this publication are provided in the Lexicon.

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1.5. RELATED DOCUMENTS

1. This is one of a sequence of Allied Range Safety Publications (ARSPs) that are concerned with the development of WDA/Z for a variety of weapon systems for use by NATO forces in a variety of roles. The framework is shown in Figure 1.1. Brief descriptions of each ARSP are given below:

a. Volumes in STANAG 2401 (Reference 1) with ARSP-1 cover the deterministic methodology:

(1) Volume I (Reference 2) contains a description of the factors that are relevant to the use of unguided weapons.

(2) Volume II (Reference 3) contains a description of the application of the factors from Volume I, and provides generic danger area outlines together with nation dependent numerical values for the factors.

b. Volumes in STANAG 2470 (Reference 4) with ARSP-2 cover the probabilistic methodology:

(1) Volume II (Reference 5) contains a description of the application of these principles to unguided weapons. It includes descriptions, and in some cases detailed specifications, of the models that may be used when applying the probabilistic methodology to the factors in ARSP-1 Volume I.

(2) Volume III (Reference 6) contains a description of the application of these principles to guided weapons (GW).

(3) Volume IV contains a description of the application of these principles to unmanned aerial vehicles (UAVs). This is an update of STANAG 2402, Edition 2 (Reference 7).

c. Volumes in ARSP-3 cover the acquisition and analysis of data for use with both deterministic and probabilistic methodologies:

(1) Volume I contains a description of the general principles of data acquisition and analysis and a description of existing methodologies, such as those for aimer deviations and free flight data.

(2) Volume III contains a description of trials procedures and data analysis for impact and post-impact models.

d. STANAG 3606 (Reference 8) with ARSP-4 (Reference 9) covers the factors relevant to lasers and the application of deterministic and probabilistic methods to lasers.

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Figure 1.1 — Framework of Allied Range Safety Publications.

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Equation Section (Next)CHAPTER 1

METHODOLOGY

2.1. INTRODUCTION

1. The general principles of the probabilistic methodology are described in ARSP 2 Volume I (Reference 1). Here we provide an outline of the methodology and two examples that illustrate the application of the methodology to unguided weapon systems.

2. Most applications are concerned with the distribution of trajectories, in the same way that estimates of effectiveness are. The estimation of effectiveness is generally concerned with the distribution assuming that weapons work as they should, with for instance models for dispersion about the optimal trajectory. In the development of WDA/Z additional allowances have to be made for faults in performance and the models are generalizations of those used for the estimation of effectiveness. Some examples are:

a. The firer does not necessarily aim at the correct target.

b. The tracer in small arms ammunition fails to ignite and burn.

c. Fuzes function between arming and the intended point of functioning.

d. Fuzes fail to function as intended.

4. With the probabilistic methodology a direct estimate of risk is attempted. There are a number of measures of risk that are used in developing WDA/Z:

a. Probability of escape, which is related to the distribution of the final resting places of projectiles or their components.

b. Individual risk of death, which is related to the locations where projectiles would be lethal and where people are present.

c. Measures related to individual risk of death, where for instance only hit, or injury is considered.

5. The methodology, outlined in Figure 2.1, may involve a number of stages:

a. A simulation of the use of a weapon system for a single firing position and single target position is carried out to produce histogram representations of the estimates of the distributions of interest (See Chapter 5 in ARSP 2 Volume I). Note that it is possible to estimate all the distributions a., b., and c. in 3 above from a single simulation.

b. Histogram representations of the population exposure, or the probability of being present at a particular location, both of which are related to population density, may be created (see Chapter 4 in ARSP 2 Volume I).

c. The histogram representations from a. and b. may be combined to produce new histograms that represent estimates of the distributions of interest for multiple firing positions and/or multiple target positions or individual risk of hit, injury, or death (see Chapter 4 in ARSP 2 Volume I). Note that these histogram representations may themselves be combined again to produce new histogram representations corresponding to ever more complex scenarios.

d. The final histogram representations may be processed to develop WDA/Z. This usually involves the calculation of contours in the distribution of interest or calculations of the risk associated with given WDA/Z (see Chapter 6 in ARSP 2 Volume I).

6. In this volume we are only concerned with 4 a. and this involves the trajectory simulation phase of the process shown in Figure 2.1. Two examples that illustrate this for unguided weapon systems are given below. The first is a simple small arms example, which only

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involves inert ammunition being used on a standard range. The second is a complex example for an artillery shell that releases submunitions as its fuze functions. These submunitions in turn detonate and produce fragments when their fuzes function. By studying this second example it can be seen how all the relevant models can be used to build a simulation for any conceivable weapon system.

2.2. A SMALL ARMS EXAMPLE

1. A simulation of the use of 7.62 mm ball ammunition from a single 200 metre firing point, with a single target on a gallery range, is being made. A summary of the data required is given below:

a. The terrain is modelled using survey data overlaid on digital terrain data. The survey has been carried out to pick up the small scale detail present on the (constructed) gallery range. This picks up the firing points, for example at the 100 meter firing point, and the mantlet that protects the target gallery. The digital terrain data sits beneath the survey data and is used when locations are outside the survey.

b. There are a few sections of brick walls present to the right of the mantlet and these are modelled as objects.

c. Meteorology is modelled using a generalized ICAO atmosphere that is based on the worst case conditions of high temperature and low pressure that occur on this range. It is assumed that there is no wind.

d. The firer’s position is assumed to be in a particular lane at the 200 metre firing point but an allowance is made for him moving sideways within his lane. He is assumed to aim at the correct target most of the time, but occasionally makes mistakes and aims at the targets either side of the correct one. The distributions of launch angles about the line of sight (between the firing position and the centre of the target he aims at) are assumed to be normally distributed with mean zero and a small standard deviation.

e. The projectile is a standard one for which free-flight data including the distribution in muzzle velocity, and impact, and post-impact data have been collected from trials with a sand target. The impact and post-impact models used treat the terrain as if it were sand.

2. A large number of trajectories are simulated. Each trajectory involves the following:

a. The firer’s position is determined within the lane.

b. The launch elevation and azimuth are determined by sampling from the aimer deviation distributions and combining these with the line of sight.

c. The values from a. and b. are combined with the muzzle velocity, sampled from its distribution, and this provides the initial conditions for the trajectory.

d. The trajectory is calculated:

(1) Its intersection with the terrain is determined and the trajectory is truncated here. Note that this may be before the target and could even be before, or at, the 100 metre firing point.

(2) The truncated trajectory is checked to see if it intersects the objects, i.e. the brick walls that are at the sides of the mantlet. If it does the trajectory is truncated here.

e. Impact is modelled with either the terrain or the object, depending on where the trajectory was terminated in d. There are three possible outcomes of this:

(1) The projectile comes to rest in the terrain or in the object.

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(2) The projectile ricochets and a further trajectory results.

(3) The projectile breaks up into pieces and trajectories for the pieces result.

f. Where trajectories result the impact and post-impact models are used to determine the initial conditions and flight characteristics for the trajectories. For each of these trajectories we return to d. and repeat until all trajectories terminate and the projectile or its parts come to rest.

g. The locations of all impacts are processed to add to the histogram representation of the distribution of final resting places and the probabilities of hitting the objects.

h. Each of the trajectories is processed to determine where the projectile would hit a man stood on the terrain. Where they would hit a man, it is determined whether the man would be injured or killed by the projectile. At locations where this would occur we add to the histogram representations of the probability of injury and death given that a person would be present at each location.

3. The resulting histograms are scaled and stored for further processing (see Chapters 6 and 7 of ARSP 2 Volume I).

2.3. A CARRIER SHELL/SUBMUNITION EXAMPLE

1. A simulation of the use of a 155 mm carrier shell being fired in indirect mode at a point target 15 km down range is being made. A summary of the data required is given below:

a. The terrain is modelled using digital terrain data. There is no need for survey data as there is no need to consider small scale detail.

b. There are no objects of concern.

c. Meteorology is modelled using tabulated data from an artillery meteorology message that is based on the particular conditions that prevail when the firing is to take place.

d. The gun and target positions are assumed fixed and are given as grid references.

The mean elevation and azimuth are obtained from a fire-control calculation that uses the meteorology model and the mean muzzle velocity for the ammunition. It is assumed that the deviations about these mean angles are independently normally distributed.

e. The projectile is a standard one for which free-flight data including the distribution in muzzle velocity, and the free-flight data for the submunitions is available. There is no impact, or post-impact data, for either the complete projectile or the submunitions as it had been assumed during procurement that both the shell and submunitions fuzes would function correctly every time and data would not be required. Data for a similar complete artillery shell will be used in the event of an impact of a complete shell being modelled. Data for a simple fragment will be used in the event of an impact of a submunition being modelled.

f. The fuze is set to function at a particular time of flight that corresponds to the optimal position for the release of the submunitions to engage the area round the target position. If the fuze functions correctly the distribution about this time of flight is assumed to be normally distributed with a known standard deviation. The fuze may also function before it should and this early function is assumed to be uniformly distributed in time of flight between arming and the correct time of flight.

g. The submunitions have impact fuzes and are supposed to function correctly every time. However, there is a failure rate for these fuzes and the failure rate data is available.

2. A large number of trajectories are simulated. Each trajectory involves the following:

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a. The launch elevation and azimuth are determined by sampling from the aimer deviation distributions and combining these with the fire-control solution, which is calculated using the mean muzzle velocity.

b. When combined the values from a. are combined with the muzzle velocity, sampled from its distribution, this provides the initial conditions for the trajectory.

c. The trajectory is calculated:

(1) The intersection of the trajectory of the complete shell with the terrain is determined and the trajectory is truncated here.

(2) The fuze is modelled to see if it functions either early or correctly. If it does the trajectory is truncated here.

d. If the fuze has functioned submunition release is modelled. This results in the initial conditions for the trajectories of each submunition, as well as the initial conditions for the parts of the carrier itself, being generated.

(1) The trajectories for the carrier parts are calculated and the intersections of the trajectories with the terrain are determined. Impact with the terrain is assumed to result in the carrier parts coming to rest.

(2) The trajectories for each of the submunitions are calculated and the intersection of the trajectory of the submunition with the terrain is determined and this trajectory is truncated here.

(3) The submunition fuze is modelled to see if it functions.

(4) If this fuze functions fragmentation of the submunition is modelled and this results in the masses and initial conditions of each fragment being generated.

(a) The trajectories of each fragment are calculated to find the intersection with the terrain and the trajectories are truncated.

(5) If the fuze does not function impact with the terrain is modelled. There are two possible outcomes of this:

(a) The submunition comes to rest in or on the terrain.

(b) The submunition ricochets and a further trajectory results. This trajectory is calculated to find the intersection with the terrain and the trajectory is terminated. We repeat (4) and (5) until all projectiles (submunition and fragments) come to rest.

e. Where the carrier fuze did not function, impact of the complete shell with the terrain is modelled with the terrain. There are three possible outcomes of this:

(1) The projectile comes to rest in the terrain.

(2) The projectile ricochets and a further trajectory results.

(3) The projectile breaks up and trajectories for the parts including the carrier body and submunitions result.

f. Where trajectories result, the impact and post-impact models are used to determine the initial conditions and flight characteristics for the trajectories. For each trajectory of a complete shell we return to d. and repeat until all trajectories terminate and the projectile or its parts come to rest. Where the projectile breaks up we similarly model the trajectories until all projectiles (carrier parts, submunitions, and fragments) come to rest.

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g. The locations of all impacts (complete shells, carrier parts, submunitions, and fragments) are processed to add to the histogram representation of the distribution of final resting places. It is useful to keep a separate histogram for the submunitions as these are potential hazards and the information may be required for clearance operations.

h. Each of the trajectories is processed to determine where the projectile would hit a man stood on the terrain. Where they would hit a man, it is determined whether the man would be injured or killed by each projectile. At locations where this would occur we add to the histogram representations of the probability of injury and death given that a person would be present at each location.

3. The resulting histograms are scaled and stored for further processing (see Chapters 6 and 7 of ARSP 2 Volume I).

4. This example is complex and it is difficult to write down a clear description of the process. However, once each of the models is implemented in a computer program it is relatively straightforward to keep track of all the projectiles. As well as estimating the numbers of projectiles coming to rest at particular locations it is possible to make a minor modification to the method to estimate the mass of projectiles that come to rest, which may provide useful information for environmental assessments.

Deleted: described as an algorithm and

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Figure 2.1 Trajectory simulation and post-processing framework.

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Equation Section (Next)CHAPTER 3

TERRAIN — TOPOGRAPHY, SURFACE TYPE

AND SURFACE ROUGHNESS

3.1. INTRODUCTION

1. Terrain models provide a representation of the surface of the ground over which firing takes place. Topography refers to the height and implicitly the slopes of the ground and surface type refers to the material type, e.g. turf, sand, concrete. Surface roughness is an artificial attribute that is used to model local undulations below the scale of the representation of the topography.

2. The height is used to detect intersections of trajectories with the ground surface. The slopes are used, together with the velocity of a projectile or fragment, to calculate the impact angle (the angle between the trajectory and the ground surface).

3. The generic information that is required for the terrain models is described in clauses 302 to 305. There are two principal sources of terrain data — survey and digital terrain — and methods for converting this raw data into a format that matches the models are described in clause 306.

4. The specific models that should be implemented, which are specified in Annex B, are:

a. Terrain defined on an irregular rectangular grid;

b. Terrain defined on a triangulation;

c. Terrain defined on a regular rectangular grid.

5. Annex B also contains specifications for methods for converting raw data to match one of these three models:

a. Survey data gathered on a rectangular grid to either 4a or 4c;

b. Survey data gathered at scattered data points to 4b;

c. Digital Terrain Elevation Data (DTED) to 4c;

d. Ordnance Survey Land Form Profile data to 4c.

3.2. COORDINATE SYSTEMS

1. Trajectories are calculated in a local Cartesian coordinate system and hence the terrain representation is defined in this same system. The y axis is aligned with the local vertical with its origin at mean sea level. The local vertical is the line that the gravitational force acts along at mean sea level. A local horizontal plane is perpendicular to the y axis and the x and z axes are chosen according to the application.

2. The choice of x and z axes in the local horizontal plane is arbitrary. Two methods that are in widespread use for the choice of direction and origins of the coordinate axes are specified. The first uses a line of fire for the x axis, such as that between one of the firing positions and its corresponding target position, with the origin chosen either at the firing position or the target position. The second uses an x axis aligned with the grid coordinate system in use in the relevant mapping system.

3. In either case the area over which the terrain representation is provided should be large enough so that attempts are not made to reference the terrain outside its definition. Where such attempts arise a method should be provided for recording and reporting the limits that occur so that a corrected definition can be determined.

4. Relevant coordinate systems that are required to handle terrain data are described in Annex A, with the methods for constructing the local coordinate system given with the detailed terrain models in Annex B.

Deleted: (known as model type 2)

Deleted: (known as model type 3)

Deleted: (known as model type 4)

Deleted: model types 2 or 4

Deleted: model type 3

Deleted: model type 4

Deleted: model type 4

Comment [SE2]: equation

Comment [SE3]: equation

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3,3. TOPOGRAPHY

1. The height, y and slopes, xy and zy along the coordinate axes are defined as functions of position ( ),x z :

x z y y x z y y x z x y y x z z

. (2.1)

2. It is assumed that the height is single valued and continuous. The slopes may be discontinuous.

3.4. SURFACE TYPE

1. The surface type, S , is an integer index to a material type. This is used within the impact models, where models and data are expected to be available for a number of different materials. As with the height and slopes the surface type is defined as a function of position

( ),x z :

( ),S S x z= . (2.2)

3.5. SURFACE ROUGHNESS

1. In order to allow for local undulations below the scale of the representation of the topography, models are provided that alter the ground slopes. This changes the impact angle used within the impact models and hence may affect the outcome of an impact.

2. Originally it had been intended to specify that a single surface roughness model would be available and it would be either used, or not used, over the whole range surface. A more flexible approach has been adopted and the surface roughness R is an integer index to different models to be used allowing these to be applied in different areas of the surface. As with surface type the surface roughness index is defined as a function of position ( ),x z :

( ),R R x z= . (2.3)

3.6. TERRAIN SURVEY DATA

1. On many ranges a survey has to be carried out to gather terrain data. This is most likely on small arms ranges, which are often constructed, as these contain detailed features below the resolution of digital terrain models. The area surveyed usually should include all those features that are likely to be used for modelling impact where the slopes play an important part.

2. The survey data has to be converted into one of the standard model types. The most general format is model type 3 and a standardized process for carrying out this conversion has been created by GBR. The survey data is automatically downloaded into an AutoCAD drawing; triangulation constraints (representing for instance firing points) are added manually, before the data is triangulated subject to the constraints and written to file for use by computer programs. This process, including relevant coordinate transformations, is described in more detail in Annex B.

3.7. DIGITAL TERRAIN DATA

1. Digital terrain data is obtained from external sources. It is usually produced for general purpose use and is usually low resolution i.e. there are often topographic features that are not represented as they are too small. This data has two main uses. Firstly it can be used to

Comment [CAM4]: Types to be listed

Comment [CAM5]: Explanation in Impact Model

Comment [CAM6]: Circulate the svy tasking docs

Comment [CAM7]: Change

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model terrain outside the area included in a terrain survey. Secondly it can be used on its own when developing WDA/Z for medium and large calibre weapons, where small features have little effect on the results. There are many sources and formats for digital terrain data. Initially we only propose to work with two if these:

a. Digital Terrain Elevation Data (DTED) is available from the (United States Department of Defense) Defense Mapping Agency. It provides a uniform matrix of terrain elevation values and allows basic quantitative data such as slope and/or surface roughness information to be derived.

b. Land-Form PROFILE (LFP) Digital Terrain Models (DTMs) are available from the Ordnance Survey, which provides geographical data for Great Britain. LFP is a digital height dataset covering the whole of Great Britain and is available either as contours or DTMs. The DTMs consist of a grid of height values defined on the British National Grid at approximately 10m intervals.

2. Both these formats provide the terrain elevation in “tiles” that cover small areas. They could be used in their original format but this would require transformations from the trajectory coordinate system to the coordinate system used for the digital terrain data plus the location of an appropriate tile every time the surface was referenced. As the surface is referenced hundreds of times in each trajectory and a single simulation can generate millions of trajectories this is extremely inefficient.

3. In order to use this data efficiently it should be transformed into one of the standard formats. Because it is low resolution data the format chosen is that of a regular rectangular grid as this is the most efficient model. The grid should be chosen at a resolution related to that of the digital terrain data. For DTED level 1 a resolution of 60 metres by 60 metres is suitable and for DTED level 2 a resolution of 20 metres by 20 metres is suitable. For LFP the original resolution of 10 metres should be used.

4. The coordinate transformations and the procedure for converting into the standard model are specified in detail in Annex B.

Deleted: The heights have been mathematically interpolated from the contour data

Comment [CAM8]: LIDAR/ArcGrid and ASCII

Deleted: .

Comment [CAM9]: Include Irish National Grid, ED50, Tokyo datum

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Equation Section (Next)CHAPTER 4

OBJECT MODELS — HARD TARGETS AND STRUCTURES

4.1. INTRODUCTION

1. Object models provide a representation of hard targets and structures, such as tank hulks used as targets, or supporting walls that are part of a constructed range. Sometimes these can be modelled as part of the terrain but the restriction that the terrain definition should be single valued can cause problems, for instance simple vertical walls do not meet this restriction.

2. The objects can be hit by projectiles and the models are simple enough to allow the detection of hits, yet complicated enough to allow reasonably complex objects to be modelled.

A single object is assumed to be a solid object that is made of a single material so that impact and post-impact can be modelled using the same models that are used for the terrain. More complex impact models that, for instance, allow projectiles to perforate the objects and/or allow the fragmentation of the object are not considered in this publication.

3. The models, which are specified in Annex C, are:

a. Cuboid objects that are aligned with the coordinate axes.

b. Simple polyhedra that are constructed from simple polygons. The adjective simple here is used in its mathematical sense — a simple polyhedron is constructed from planar polygons that do not intersect except at their boundaries.

4. These two specific models are described in clauses 402 and 403. It is useful to be able to collect these simple objects into groups so that, for example, standard building configurations can be positioned at more than one position. The specification for groups of objects is described in clause 404.

4.2. CUBOID OBJECTS

1. A cuboid object is a cuboid that is aligned with the x, y, and z axes i.e. each of its six faces lies in one of the x-y, x-z, or y-z planes. A cuboid object is specified by the origin of its front, bottom, left hand corner ( )0 0 0, ,x y z and its dimensions of depth, height, and width

( ), ,d h w .

2. Each cuboid object is assumed to be solid and constructed from a single material. A material type is provided as an integer index. As with the terrain surface type it is used within the impact models, where models are expected to be available for a number of different materials.

3. Because of the use of a Cartesian coordinate system cuboid objects are only of use for short range problems where the discrepancy between the y axis and the local vertical is negligible.

4.3. SIMPLE POLYHEDRA

1. A simple polyhedron is constructed from simple planar simple polygons. A polyhedron is specified by providing a list of coordinates for vertices in either Cartesian or grid coordinates

1 1 1 1 1 1

2 2 2 2 2 2 or2

V V V V V V

V V V V V V

V i i i i i i

V n n n n n n i x y z e n h x y z e n h x y z e n h n x y z e n h (3.1) and a list of indexes to points for each polygon, for example:

Deleted: that should be implemented

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1 2 3 4 5

11 21 31

12 22 32 42 52

1 2 3 4

1 3

2 5

P

P P P P

P Vi

P n n n n i n V V V V V

V V V

V V V V V n V V V V

(3.2) where there are Vn vertices, Pn polygons, and polygon Pi has iPVn vertices given by indices 1 2, , , ViPiP iP n iPV V V . For example, in (3.2) polygon 2 has 5 vertices given by indices 12 22 52, , ,V V V .

2. A homogeneous coordinate transformation may be specified for each polyhedron. This may be used to scale, rotate, and shift the polyhedron. This allows a library of standard polyhedra to be used to build models of common objects from standard shapes.

4.4. GROUPS OF OBJECTS

1. It is useful to be able to combine objects to model more complex objects. A group of objects consists of a collection of previously defined cuboid objects and polyhedra. A further homogeneous coordinate transformation may be specified for each group of objects. This allows a complex object group to be built and positioned anywhere.

Deleted: and

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Equation Section (Next)CHAPTER 5

METEOROLOGY MODELS

5.1. INTRODUCTION

1. Meteorology models provide a representation of the properties of the atmosphere.

These properties, such as air density and wind speed, are required in the projectile models.

Two types of model are in common use — analytical models and tabulated data models.

2. In the analytical models the properties are derived from ideal equations and simplifying assumptions are made about the properties of air, the gravity model, and temperature profiles.

The assumptions made allow analytical formulae to be derived for air density, air pressure, and local speed of sound as functions of geopotential height (see clause 503) relative to mean sea level. The addition of a uniform wind profile completes these meteorology models.

3. For tabulated data models the required properties are simply tabulated as functions of height relative to mean sea level. Interpolation within the tables allows the required properties to be calculated at any height.

4. Relevant coordinate systems are described in clause 502. Standard analytical atmospheres and a generalization of these are described in clauses 503 and 504. The tabulated data models are described in clause 505. The specific models are provided in Annex D.

5.2. COORDINATE SYSTEMS

1. The meteorology models are specified as functions of height with respect to mean sea level but are used in the Cartesian coordinate system that trajectories are calculated in. A general description of coordinate systems is provided in Annex A, whilst the specific details required to use the meteorology models is provided with the details of the models in Annex D.

5.3. THE ICAO STANDARD ATMOSPHERE

1. In STANAG 4044 (Reference 10), NATO adopted the International Civil Aviation Authority (ICAO) standard atmosphere (Reference 4). The ICAO standard atmosphere is identical to the International Organization for Standardization (ISO) standard atmosphere (References 15 and 16).

2. The ICAO manual states that “this standard atmosphere is intended for use in calculations in the design of aircraft; in presenting test results of aircraft and their components under identical conditions, and to facilitate standardization in the development and calibration of instruments. Its use is also recommended in the processing of data from geophysical and meteorological observations.” It is in widespread use for calculating trajectories in “standard” conditions.

3. Annex C contains a complete derivation of the standard atmosphere. Here the key points are listed:

a. The air is assumed to be dry and of constant composition;

b. A standard gravity model corresponding to latitude 45.5425 degrees, which ignores centrifugal acceleration and uses only Newton’s gravitation law, is assumed and used to derive an analytic relationship between geometric height and geopotential height;

c. The atmosphere is assumed to consist of eight layers between geopotential heights of -5 km and +80 km, with each layer having its own constant temperature gradient;

d. Analytic expressions for pressure as a function of geopotential height are derived;

e. Density is obtained from pressure and temperature using the perfect gas law;

Deleted: described

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f. Tables of temperature, pressure, density and several other derived quantities as functions of geopotential height are provided.

When using this standard atmosphere there are a number of common methods for dealing with the difference between geometric and geopotential height.

a. Use geometric height as geopotential height i.e. ignore the difference and look up the required properties as functions of geometric height;

b. Use the standard latitude of 45.5425 degrees and the relationship presented in the ICAO standard to convert geometric height to geopotential height before looking up the required properties;

c. Use the actual latitude and use the gravity model for that latitude to convert geometric height to geopotential height before looking up the required properties.

4. It is rarely clear from any particular reference to the use of the ICAO standard atmosphere, which method is being used here we should allow any of these methods to be used.

5.4. A GENERALIZED STANDARD ATMOSPHERE

1. The ICAO standard atmosphere may be generalized to produce atmosphere models that are more suitable for safety purposes. Here we allow two modifications:

a. The atmosphere may be set with reference to a set of pressure, temperature, and relative humidity values for a particular geometric height;

b. The specifications for the eight layers of the atmosphere may be changed so that the heights and temperature gradients are different from those used in the ICAO derivation.

2. A full derivation of this generalized atmosphere is provided in Annex C. It should be noted that in calculating trajectories the use of a combination of low pressures and high temperatures produces the longest ranges, which are often of interest in producing “worst case” danger areas/zones.

5.5. A WIND MODEL

1. Both the ICAO standard atmosphere and the generalized standard atmosphere do not provide any wind data. Wind can be added in many ways. Here we use a simple model that is uniform at all locations and altitudes for each trajectory. However, to handle the random nature of wind, it is allowed to vary from trajectory to trajectory.

2. The wind is specified by providing a wind speed and direction for the prevailing wind and a standard deviation for headwind and crosswind. The wind profile for each trajectory is obtained by generating random headwind and crosswind values, which are then added to the prevailing wind. This wind is assumed constant with respect to altitude.

5.6. TABULATED METEOROLOGY DATA

1. For the tabulated meteorology model the required properties, including wind, are simply tabulated as functions of geometric height. Properties at intermediate heights are calculated using linear interpolation. A complete description of this tabulated form is provided in Annex D.

Comment [CAM11]: Explain conversion from ballistic met

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Equation Section (Next)CHAPTER 6

FIRER MODELS – FIRING POSITIONS, TARGET POSITIONS

AND AIMER DEVIATIONS

6.1. INTRODUCTION

1. Firer models contribute to the representation of the initial conditions for trajectories. A firer model consists of a set of firing positions, a set of target positions, a specification of the method for calculating reference angles and the distribution of aimer deviations from these.

The term aimer errors is not used as it has become evident that in many cases range users deliberately fire at the wrong target and the more general term is used to cover this situation.

2. In the simplest case there is a single static firing position and a single static target position. This is modelled by providing a probabilistic specification of the position of both the firing position and target position.

3. The use of static firing positions, which may be anywhere within a prescribed area, and/or the use of static target positions that may be anywhere within another prescribed area, can be handled by allowing this probabilistic specification of position to include uniform…