https://orcid.org/0009-0008-2364-3208
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Abstract
After the start of the Russian invasion of Ukraine in 2022, missile defense systems became more prominent and sought after on a global scale. In 2023, Germany decided to purchase the Israeli Arrow missile defense system. This article derives technical capabilities of the Arrow missile defense system from publicly available information, with a focus on the Arrow 3 interceptor. This information is the basis for an analysis of Arrow’s utility to defend Germany within a larger European context against existing and potential future missile threats from Russia. The interceptor’s capabilities are assessed using a newly developed missile defense footprint calculation and comparison program. The program calculates trajectories of missiles and interceptors, and sectoral footprints. The results suggest that Arrow 3 is theoretically capable of intercepting Russia’s current long-range and potential future intermediate-range ballistic missiles. It will be of no use against existing Russian short-range ballistic missiles and of limited use against existing medium-range ballistic missiles.
Acknowledgements
The authors would like to thank Zia Mian for suggesting the development of the Missile Defense Footprint Calculation and Comparison (MD FCC), the Program on Science and Global Security at Princeton University for funding the initial development phase, David Wright and Jürgen Altmann for input regarding the physics and software development, as well as Pavel Podvig and two anonymous reviewers for valuable comments on the manuscript.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Notes
1 Sebastian Sprenger and Seth J. Frantzman, “German Air Force Banks on Israel’s Arrow-3 for National Missile Shield,” DefenseNews, 6 April 2002, https://www.defensenews.com/global/europe/2022/04/06/german-air-force-banks-on-israels-arrow-3-for-national-missile-shield/.
2 Deutscher Bundestag, “Tagesordnung für 9. Sitzung des Verteidigungsausschusses am 06.04.2022,” https://www.bundestag.de/resource/blob/887764/864a958606d2ae95169ba14bc947d416/to_09_sitzung_06-04-2022-data.pdf.
3 “Gaza-Krieg: Israel will Raketenabwehrsystem Arrow 3 pünktlich an Deutschland liefern,” RedaktionsNetzwerk Deutschland, 4 December 2023, https://www.rnd.de/politik/gaza-krieg-israel-will-raketenabwehrsystem-arrow-3-puenktlich-an-deutschland-liefern-2R47QBXFEBOZJILKDRTM3NDRO4.html.
4 CNN reporting on the consequences of a massive Russian attack on Ukraine on 2 January 2024: “…Patriot batteries have been successful in destroying Kinzhal missiles, according to US officials” – according to Ukrainian officials, air defense downed “10 out of 10” Kinzhal missiles, Christian Edwards, Maria Kostenko, and Jennifer Hauser, “Poland activates fighter jets to protect airspace as Russia pounds Ukraine with missiles,” CNN, 2 January 2024, https://edition.cnn.com/2024/01/02/europe/poland-jets-russia-missiles-ukraine-intl/index.html; on earlier occasions see e.g. Ellen Mitchell, “Pentagon confirms Ukraine downed Russian missile with Patriot system,” The Hill, 9 May 2023, https://thehill.com/policy/defense/3996387-pentagon-confirms-ukraine-downed-russian-missile-with-patriot-system/; and a report that after a concentrated attack against a Patriot installation near Kyiv, the damage to the system was minimal: Natasha Bertrand, Oren Liebermann, and Jim Sciutto, “US officials say damage to Patriot missile defense system was minimal following Russian attack near Kyiv,” CNN, 17 May 2023, https://edition.cnn.com/2023/05/16/politics/patriot-missile-damage-ukraine; first operational use of Arrow 3: “The Arrow 3 System’s First Successful Operational Interception,” Israeli Defense Forces, 10 November 2023, https://www.idf.il/en/mini-sites/idf-press-releases-regarding-the-hamas-israel-war/the-arrow-3-system-s-first-successful-operational-interception/. See also an analysis of the Iranian 13–14 April 2024 missile attack on Israel: Uzi Rubin, “Operation ‘True Promise’: Iran’s Missile Attack on Israel,” BESA Center Perspectives Paper No. 2, 281, 18 June 2024.
5 Cf. Missile Survey: Ballistic and Cruise Missiles of Selected Foreign Countries”, CRS Report, updated 26 July 2005, https://crsreports.congress.gov/product/pdf/RL/RL30427/3.
6 Bundesministerium der Verteidigung, “European Sky Shield – die Initiative im Überblick, Bundesministerium der Verteidigung,” https://www.bmvg.de/de/aktuelles/european-sky-shield-die-initiative-im-ueberblick-5511066.
7 “Germany, 14 NATO allies agree to procure air defense systems,” Deutsche Welle, 13 October 2022, https://www.dw.com/en/germany-14-nato-allies-agree-to-procure-air-defense-systems/a-63423028, Ralf Bosen “Sky Shield Initiative: Can it protect Europe?,” Deutsche Welle, 8 August 2023, https://www.dw.com/en/sky-shield-initiative-can-it-protect-europe/a-66900967.
8 Frank Kuhn, “Das Raketenabwehrsystem Arrow 3: Eine fragliche Beschaffung,” 25 August 2023, PRIF Blog, https://blog.prif.org/2023/08/25/das-raketenabwehrsystem-arrow-3-eine-fragliche-beschaffung/; Sven Arnold and Torben Arnold, “Germany’s Fragile Leadership Role in European Air Defence,” Stiftung Wissenschaft und Politik, 2 February 2023, https://www.swp-berlin.org/10.18449/2023C06/.
9 Missile Defense Project, “Arrow 3 (Israel),” Missile Threat, Center for Strategic and International Studies, 11 August 2016, last modified 16 July 2021, https://missilethreat.csis.org/defsys/arrow-3/.
10 Additional parameters influence the overall effectiveness of the system and are discussed in the next section.
12 David Wright, Laura Grego, and Lisbeth Gronlund, The Physics of Space Security: A Reference Manual (Cambridge, Mass: American Academy of Arts and Sciences, 2005), https://www.ucsusa.org/resources/physics-space-security.
13 The comparison of missile defense to “hitting a bullet with a bullet” apparently goes back to at least 1962, see e.g., R. James Walker, Lewis Bernstein, and Sharon Lang, “Seize the High Ground: The Army in Space and Missile Defense,” Historical Office U.S. Army Space and Missile Defense Command 2003, 46, https://history.army.mil/html/books/070/70-88-1/index.html.
14 Area outside of the footprint also includes areas unreachable by attacking missile.
15 Jürgen Altmann, “SDI for Europe? Technical Aspects of Ballistic Missile Defenses.” PRIF Research Report, 3/1988.
16 Parameters of missiles and interceptors used to calculate footprints presented in the paper are provided in the Appendix B.
17 The program uses a tool called geojson.io for that, but there are other tools that can read this format.
18 This section is based on Jürgen Altmann, “SDI for Europe,” 179–182. For software for a detailed analysis of missile trajectories, see e.g. Geoffrey Forden, “GUI_Missile_Flyout: A General Program for Simulating Ballistic Missiles,” Science & Global Security, 15, no. 2 (2007): 133–146, https://doi.org/10.1080/08929880701609170.
19 The V2 curve is based on a chart (Figure 4-4) in: George P. Sutton and Oscar Biblarz, Rocket Propulsion Elements, 9th ed. (Hoboken, NJ: Wiley, 2017), 105; the other two curves were provided by David Wright, personal communication.
20 Re-entry vehicle’s drag coefficient can be estimated using a chart (Figure 6.11) in Frank J. Regan, Re-Entry Vehicle Dynamics (AIAA, Inc., 1984), 139.
21 Jürgen Altmann, “SDI for Europe,” 181.
22 The program uses the “Ambiance” Python module (https://ambiance.readthedocs.io/) for altitudes up to 80 km, and “National Aeronautics and Space Administration: U.S. Standard Atmosphere,” 1976 (https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770009539.pdf) for altitudes from 80 to 100 km.
23 Missile vertical launch altitude and initial gravity turn angle are determined by the missile’s thrust-to-weight ratio and desired flight trajectory. MD FCC provides a module that facilitates finding a combination of these parameters that result in maximum range (approximating MET). For other types of trajectories desired range or apogee are usually attained by increasing or decreasing gravity turn angle from the value corresponding to MET and using user’s best judgement.
24 A model of an exo-atmospheric interceptor with this type of trajectory is described in Paul Zarchan, “Midcourse Guidance Strategies for Exoatmospheric Intercept,” Charles Stark Draper Laboratory, Inc., Cambridge, Massachusetts, 1998. The exoatmospheric interceptor is launched straight up for 1–2 s and then pitches over to the desired flight path angle using a simple linear control law. The same control law was implemented in MD FCC for testing purposes, and the difference to simply assuming the desired flight path angle at 100 m altitude was found to be negligible.
25 For calculation of footprints covering a range of directions (sector) see section “Sectoral Footprints” in Appendix A.
26 More accurately, φ is the dihedral angle between two planes: the one points O, A and earth center belong to, and the one points O, D and earth center belong to. Points O, D and A form a spherical triangle, which is resolved using spherical law of cosines (see e.g., https://mathworld.wolfram.com/SphericalTrigonometry.html).
27 More accurately, ω is the dihedral angle between two planes: the one points O, A and earth center belong to, and the missile trajectory plane (to which points D, A and earth center belong to). Points O, D and A form a spherical triangle, which is resolved using spherical law of cosines (see previous endnote).
28 The maximum value for OA is set to be the sum of maximum interceptor range and missile range, the minimum is set to 1 km.
29 Depending on the shape of the footprint and on the required accuracy of calculation, brute force approach can be significantly more computationally intensive than respective algorithmic method: the number of points to probe is proportional to linear size of the footprint divided by required accuracy, i.e. it grows linearly with inverted accuracy, while for algorithmic approach the number of points to calculate grows as logarithm of that number.
30 Estimating figures is very difficult, most data sources must be considered highly uncertain. Already in March 2022, a U.S. official talked about more than 1100 missiles: “Senior Defense Official Holds a Background Briefing,” Transcript, U.S. Department of Defense, 21 March 2022,.
https://www.defense.gov/News/Transcripts/Transcript/Article/2973395/senior-defense-official-holds-a-background-briefing/. Additional reporting on the Russian use of missiles in Ukraine can be found for example in Williams, Ian. “Russia’s Strike Campaign in Ukraine,” Report of the CSIS Missile Defense Project. Center for Strategic and International Studies, 2023, https://www.csis.org/analysis/putins-missile-war. There exist also online data sets reporting missile use, for example “Massive Missile Attacks on Ukraine,” https://www.kaggle.com/datasets/piterfm/massive-missile-attacks-on-ukraine.
31 Williams, “Russia’s Strike Campaign in Ukraine.”
32 “Russia’s new missile does not violate INF Treaty—top brass,” TASS, 23 January 2019, https://tass.com/defense/1041348; “Russian Compliance with the Intermediate Range Nuclear Forces (INF) Treaty: Background and Issues for Congress”, CRS Report, Updated 2 August 2019, https://crsreports.congress.gov/product/pdf/R/R43832.
33 “Небесные точки: «Кинжальные» МиГи переходят в автоматический режим,” Известия, 26 August 2021, https://iz.ru/1212509/roman-kretcul-aleksei-ramm/nebesnye-tochki-kinzhalnye-migi-perekhodiat-v-avtomaticheskii-rezhim.
34 “Названа боевая дальность ракеты “Кинжал”,” Российская газета, 18 July 2018, https://rg.ru/2018/07/18/nazvana-boevaia-dalnost-rakety-kinzhal.html; “Источник: дальность применения “Кинжала” увеличится на 1000 км с бомбардировщиком Ту-22М3,” TASS, 18 July 2018, https://tass.ru/armiya-i-opk/5383655.
35 “Разработка стратегической ракеты РС-26 - один из ответных шагов на развертывание ПРО США - источник в Минобороны РФ,” Interfax, 25 March 2015, https://www.militarynews.ru/story.asp?rid=1&nid=370944&lang=RU.
36 Ibid.
37 “RS-26 and other intermediate-range ICBMs,” Russian strategic nuclear forces, 18 July 2017, https://russianforces.org/blog/2017/07/rs-26_and_other_intermediate-r.shtml.
38 “Источник: комплекс “Авангард” заменил “Рубеж” в госпрограмме вооружения до 2027 года,” TASS, 22 March 2018, https://tass.ru/armiya-i-opk/5055517.
39 “Источник: первыми носителями гиперзвуковых блоков “Авангард” станут ракеты УР-100Н УТТХ,” TASS, 20 March 2018, https://tass.ru/armiya-i-opk/5047200.
40 The table is based on the “Missile Threat” data published by the CSIS Missile Defense Project https://missilethreat.csis.org/country/russia/.
41 Presented are maximum reported ranges.
42 Russia claims this missile has a range of 480 km, e.g. “Russia’s new missile does not violate INF Treaty—top brass,” while Western sources estimate its range being over 2,000 km, e.g. “Russland verfügt über mehr Raketen als bislang bekannt,” Frankfurter Allgemeine Zeitung, 10 February 2019, https://www.faz.net/aktuell/politik/ausland/russland-verfuegt-ueber-mehr-raketen-als-bislang-bekannt-16032894.html.
43 “3M55 Oniks Russian Short-Range Anti-Ship Cruise Missile,” OE Data Integration Network, https://odin.tradoc.army.mil/WEG/Asset/3M55_Oniks_Russian_Short-Range_Anti-Ship_Cruise_Missile.
44 Nikolai Litovkin, “New Russian cruise missiles to hit targets from 130,000 feet,” UPI, 30 August 2016, https://www.upi.com/Defense-News/2016/08/30/New-Russian-cruise-missiles-to-hit-targets-from-130000-feet/4301472562569/.
45 The system’s reported 2,000 km range includes carrier’s (MIG-31K jet fighter) range. Missile’s range is 3 times longer than that of 9M723 ballistic missile, i.e. 1,500 km, see “Названа боевая дальность ракеты ‘Кинжал’,” Российская газета, 18 July 2018, https://rg.ru/2018/07/18/nazvana-boevaia-dalnost-rakety-kinzhal.html. On a depressed trajectory with apogee below 100 km the missile’s range is estimated to be 1,000 km.
46 During a successful flight test in May 2012 the missile flew from Plesetsk to Kura, a distance of approximately 5,800 km, see e.g., “Russian Compliance with the Intermediate Range Nuclear Forces (INF) Treaty: Background and Issues for Congress,” CRS Report, 2 July 2019, https://crsreports.congress.gov/product/pdf/R/R43832.
47 This weapon has been announced and used by Russia on 21 November 2024 against the Ukrainian city of Dnipro. Many details about the missile are still unclear.
48 According to a statement by Commander of the Strategic Missile Forces Sergei Karakayev that the missile “can strike targets across the entire territory of Europe”. To do that the missile needs to have a range of at least 3,000 km. Since the missile is likely to be a variant of RS-26, its maximum range must be higher than that, see “Совещание с руководством Минобороны, представителями ВПК и разработчиками ракетных систем,” Москва, Кремль, 22 November 2024, http://kremlin.ru/events/president/news/75623 and C. Todd Lopez, “Russians Launch New Missile at Dnipro, U.S. Provides Ukraine With New Tactical Weapons,” DOD News, 21 November 2024, https://www.defense.gov/News/News-Stories/Article/article/3975321/russians-launch-new-missile-at-dnipro-us-provides-ukraine-with-new-tactical-wea/.
49 See e.g., “Минобороны РФ заявило об установке в шахту очередной стратегической ракеты “Ярс”,” Interfax, 11 November 2023, https://www.interfax.ru/russia/931618.
50 “First test launch of Sarmat ICBM due this fall,” TASS, 4 August 2021, https://tass.com/defense/1322397, ““Роскосмос”: Комплекс “Сармат” поставлен на боевое дежурство,” DW, 1 September 2023, https://www.dw.com/ru/roskosmos-kompleks-sarmat-postavlen-na-boevoe-dezurstvo/a-66696577.
51 “‘Булава’ пролетела 9,3 тыс. км,” Известия, 27 August 2011, https://iz.ru/news/498708.
52 “Гиперзвуковой стратегический ракетный комплекс “Авангард” (объект 4202),” Новости ВПК, https://vpk.name/library/f/avangard-mbr.html. HGV Avangard is being deployed with SS-19 boosters, and is planned to be deployed with SS-29 boosters, see e.g. “Россия показала США ракетный комплекс “Авангард”,” TASS, 26 November 2019, https://tass.ru/armiya-i-opk/7202227, and “РВСН: ракета “Сармат” может нести несколько блоков “Авангард”,” RIA Novosti, 4 April 2022, https://ria.ru/20220424/sarmat-1785181058.html.
53 E.g., Paul Zarchan, Tactical and Strategic Missile Guidance, 6th ed (Reston, VA: American Institute of Aeronautics and Astronautics, Inc., 2012), 968.
54 Lisbeth Gronlund and David C. Wright, “Depressed Trajectory SLBMS: A Technical Evaluation and Arms Control Possibilities.” Science & Global Security 3, no. 1–2 (1992): 101–159. https://doi.org/10.1080/08929889208426380.
55 Israeli Aerospace Industries, Arrow Weapon System, n.d., https://www.iai.co.il/sites/default/files/2020-05/Arrow%20Brochure_0.pdf.
56 Barbara Opall-Rome, “US-Israel Arrow-3 Intercepts Target in Space,” Defense News, 10 December 2015, https://www.defensenews.com/air/2015/12/10/us-israel-arrow-3-intercepts-target-in-space/.
57 “Green Pine Radar (Israel),” Missile Defense Advocacy Alliance, December 2018, https://missiledefenseadvocacy.org/defense-systems/green-pine-radar-elm-2080-israel/. The detection range depends on the target’s radar cross section. It is assumed that in all cases considered in this paper targets have a cross section large enough to be detectable within the vendor-specified range.
58 Calculated assuming 0 degrees minimum elevation, and assuming that the object sits at an altitude of 100 km, and the radar sits on the surface, without considering refraction in the atmosphere.
59 Israeli Aerospace Industries, Arrow Weapon System, n.d.
60 “DSP [satellite] takes 40–50 seconds to detect a missile launch and determine its course, while SBIRS High was being designed to make those determinations and relay warnings to ground forces in 10–20 seconds,” Marcia S. Smith, “Military Space Programs: Issues Concerning DOD’s SBIRS and STSS Programs,” CRS Report, Updated 30 January 2006, https://sgp.fas.org/crs/weapons/RS21148.pdf. If a forward-based ground radar is used instead, this delay should be set accordingly, for example as time for the missile to rise over that radar’s horizon.
61 Israeli Aerospace Industries, Arrow Weapon System, n.d.
62 Christopher F. Foss and James C. O’Halloran (ed.), “Arrow Weapon System (AWS),” in IHS Jane’s Land Warfare Platforms: Artillery and Air Defence 2012–13 (United Kingdom: IHS, 2013), 692–695. This is also illustrated by a video released by IAI in 2016: https://www.youtube.com/watch?v=0hdMJZ6RQNY, and can be inferred from the images of the interceptor body and the kill vehicle in the brochure.
63 Israeli Aerospace Industries, Arrow Weapon System, n.d.
64 Alexander Budweg, “Wie ‘Arrow 3’ Deutschland schützen soll,” Tagesschau, https://www.tagesschau.de/inland/innenpolitik/arrow-flugabwehr-100.html, “Experte: Arrow 3 schließt Bedrohungslücke,” ZDF, 17 August 2023, https://www.zdf.de/nachrichten/politik/arrow-3-deutschland-raketen-abwehr-gressel-100.html.
65 Henrik Bahlmann, “Was kann der Raketenschutzschirm Arrow 3 – und wie teuer ist er wirklich?” Der Spiegel, 17 August 2023, https://www.spiegel.de/wissenschaft/arrow-3-in-deutschland-was-kann-der-raketenschutzschirm-und-wie-teuer-ist-er-wirklich-a-bc8ff34d-d66c-48b5-9cc2-168e32c5229e.
66 Ibid.
67 Israeli Aerospace Industries, “Arrow Weapon System,” 23 June 2016, https://www.youtube.com/watch?v=0hdMJZ6RQNY.
68 Israeli Aerospace Industries, Arrow Weapon System, n.d.
69 This is discussed for the U.S. Ground-Based Interceptor in Andrew M. Sessler, et al., Countermeasures: The Operational Effectiveness of the Planned US National Missile Defense System (Cambridge, MA: Union of Concerned Scientists and MIT Security Studies Program, 2000), 28, https://www.ucsusa.org/sites/default/files/2019-09/countermeasures.pdf. Heating is discussed on page 27. The minimum height given there is 130 km (page 28).
70 See, e.g., Theodore A. Postol and George N. Lewis, “Illusion of Missile Defense: Why THAAD Will Not Protect South Korea,” Global Asia, 11, no. 3 (2016) https://www.globalasia.org/v11no3/feature/illusion-of-missile-defense-why-thaad-will-not-protect-south-korea_theodore-a-postol-george-n-lewis.
71 Yaakov Lappin, “Arrow 3 missile defense system successfully intercepts target in space in critical test,” The Jerusalem Post, 10 December 2015, Updated: 11 December 2015, https://www.jpost.com/israel-news/defense-ministry-carries-out-critical-trial-of-arrow-3-missile-defense-system-436880.
72 Elbit Systems, “Elbit Systems Land Tank Ammunition Portfolio,” 4, https://elbitsystems.com/media/Catalog-Tanks_17_noIMI_Web_compressed.pdf.
73 Marco Evers, “So soll das Raketenabwehrsystem ‘Arrow 3’ aus Israel Deutschland schützen,” Der Spiegel, 28 March 2022, https://www.spiegel.de/wissenschaft/technik/schutzschild-fuer-deutschland-was-kann-das-abwehrsystem-arrow-3-aus-israel-a-dc103bac-9dc2-44a0-816e-e8ed59de7a70.
74 Mass of Arrow 3 is described as “nearly half” of Arrow 2 in Barbara Opall-Rome, “Iran Threat Speeds Arrow-3 Effort,” Defense News, 22 March 2010, https://archive.ph/20130121114610/http://www.defensenews.com/story.php?i=4548013&c=FEA&s=SPE, and as “less than half” in Herb Keinon, Yaakov Lappin, “Netanyahu: Arrow will help us on peace, or defense,” The Jerusalem Post, 25 February 2013, https://www.jpost.com/defense/netanyahu-arrow-will-help-us-on-peace-or-defense.
75 Foss and O’Halloran, “Arrow Weapon System (AWS),” 692–695.
76 Missile Defense Project, “Arrow 2 (Israel),” Missile Threat, Center for Strategic and International Studies, 14 April 2016, last modified 23 July 2021, https://missilethreat.csis.org/defsys/arrow-2/, Airforce Technology, “Arrow 3 Air Defence Missile System, Israel,” 16 September 2022, https://www.airforce-technology.com/projects/arrow-3-air-defence-missile-system-israel/.
77 Airforce Technology, “Arrow 3 Air Defence Missile System, Israel.”
78 Sutton and Biblarz, Rocket Propulsion Elements, 467.
79 Sutton and Biblarz, Rocket Propulsion Elements, 469, Table 12-4.
80 Corresponding to propellant volumetric fractions of 0.55 and 0.98.
81 Specific impulse is assumed to be roughly equal (slightly higher) to that of the Minuteman 1 first stage motor, see Sutton and Biblarz, Rocket Propulsion Elements, 442.
82 “RAW VIDEO: Arrow 3 missile test in Alaska,” CBS 17, 28 July 2019, https://www.youtube.com/watch?v=cUQ4UlvSHzo.
83 In this example booster propellant mass is 800 kg, and total interceptor mass is chosen so that on the maximum range trajectory burnout speed of the interceptor using just the booster is 3,400 m/s.
84 Using the kill vehicle as the second stage for reaching maximum flyout range.
85 For calculation details see section “Sectoral Footprints” in Appendix A.
86 As mentioned earlier, Kinzhal has a range of 1,500 km after being launched from its carrier, i.e. this number does not include carrier’s range.
87 Maps were created using geojson.io, powered by Mapbox and OpenStreetMap.
88 NATO, “Ballistic missile defence,” last updated: 26 July 2023, https://www.nato.int/cps/en/natolive/topics_49635.htm.
89 See e.g., Missile Defense Project, “The Evolution of Homeland Missile Defense,” Missile Threat, Center for Strategic and International Studies, 7 April 2017, last modified 27 April 2021, https://missilethreat.csis.org/evolution-homeland-missile-defense/.
90 NATO, “Ballistic missile defence;” Heather Mongilio, “U.S., Spain Agree to Host Two More Warships in Rota,” USNI News, 9 May 2023, https://news.usni.org/2023/05/09/u-s-spain-agree-to-host-two-more-warships-in-rota.
91 Intersection of spherical polygons is calculated using “SphericalGeometry” Python package, https://spherical-geometry.readthedocs.io/.
92 The 11,000 km missile data from: Altmann, “SDI for Europe”; the 4,000 km and 1,000 km missiles data were provided by David Wright, personal communication. The 1,000 km missile is based on Scud-ER data from: Markus Schiller and Robert H. Schmucker, “Flashback to the Past: North Korea’s ‘New’ Extended-Range Scud,” 38 North, 8 November 2016, https://www.38north.org/2016/11/scuder110816/. Iskander M and Kinzhal models are based on data from: Sam Cranny-Evans and Dr Sidharth Kaushal, “The Iskander-M and Iskander-K: A Technical Profile”, 8 August 2022, RUSI, https://rusi.org/explore-our-research/publications/commentary/iskander-m-and-iskander-k-technical-profile, and Stefan Forss, The Russian Operational-Tactical Iskander Missile System (Helsinki: National Defense University, 2012), https://doria.fi/handle/10024/84362.
93 Gravity turn height for all missiles is set to 0.
94 The Kinzhal model used is launched (as from its carrier aircraft) at an altitude of 20 km, at an angle of 41 degrees from vertical and speed 830 m/s.
95 The interceptor with burnout speed 2.6 km/s data from: Altmann, “SDI for Europe”; the interceptor with burnout speed 4.5 km/s data were provided by David Wright, personal communication. Patriot PAC-3 MSE model is based on a model of Patriot PAC-3 CRI provided by David Wright, personal communication, and Jon Hawkes “Patriot games: Raytheon’s Air-Defence System Continues to Proliferate,” Jane’s International Defence Review 52 (2019), https://web.archive.org/web/20191019003835/https://www.raytheon.com/sites/default/files/2018-12/Raytheon_article%20reprint_IDR%201901.pdf.