Missile lofting

'''Lofting''', sometimes referred to as "'''trajectory shaping'''",<ref name=":Trajectory Shaping">{{cite report|last1=Berglund|first1=Erik|last2=Licata|first2=William|department=Swedish Defence Research Agency & Raytheon Corporation|title=Technologies for Future Precision Strike Missile Systems (ADA394520; RTO-EN-018; AC/323, SCI-087 bis; TP/37)|publisher=Research and Technology Organization of the North Atlantic Treaty Organization|location=BP 25, 7 rue Ancelle, F-92201 Neuilly-sur-Seine Cedex, France|date=July 2001|page=3-1|url=https://apps.dtic.mil/sti/tr/pdf/ADA394520.pdf|archive-url=https://archive.org/details/technologies-for-future-precision-strike-ada-394520|archive-date=20 October 2025|quote=Air-to-air missiles often employ trajectory optimisation during the mid-course. The main reason for this is to exploit the lower drag at higher altitude. Optimisation can be used to obtain minimal time of flight, maximal range, maximal terminal velocity etc.}}</ref><ref>{{cite book|last=Coté|first=Gilbert|author2=Naval Education and Training Program Development Center|title=Fire Control Technician M 3 (NAVEDTRA 10224)|publisher=Naval Education and Training Command via United States Government Printing Office|year=1981|location=United States|page=2-19|quote=SPARROW[…] utilizes trajectory shaping to greatly increase its performance envelope.|postscript=The page — "2-19" — is correct; Please do not alter it or change the parameter to "pp" or "pages." It is "2 through 19" it is labelled as "2 dash 19" and is a single page}}</ref> is a trajectory optimization technique used in some missile systems to extend range and improve target engagement effectiveness, usually in beyond-visual range scenarios.<ref name=":0">{{cite journal|last1=Shin|first1=Minjae|last2=Tahk|first2=Min-Jea|last3=Kim|first3=Boseok|last4=Lee|first4=Chang-Hun|date=2024|title=PURSUIT-BASED LONG-RANGE AIR-TO-AIR MISSILE MIDCOURSE GUIDANCE ROBUST TO CHANGES IN THE PREDICTED IMPACT POINT|url=https://www.icas.org/icas_archive/icas2024/data/papers/icas2024_0828_paper.pdf|archive-url=https://web.archive.org/web/20250430130337/https://www.icas.org/icas_archive/icas2024/data/papers/icas2024_0828_paper.pdf|archive-date=30 April 2025|journal=International Congress of the Aeronautical Sciences|page=3|quote=1 Quadratic polynomial[, peak altitude:] 33 km[;] 2 4th-order polynomial[, peak altitude:] 30 km[;] 3 4th-order polynomial[, peak altitude:] 25 km}}</ref> thumb|A US-Navy Grumman F-14A Tomcat of VF-11 launches an AIM-54 Phoenix missile, in 1982

==Method== Lofting involves a missile ascending to a higher altitude after launch,<ref>{{cite report|last1=Berglund|first1=Erik|last2=Licata|first2=William|department=Swedish Defence Research Agency & Raytheon Corporation|title=Technologies for Future Precision Strike Missile Systems (ADA394520; RTO-EN-018; AC/323, SCI-087 bis; TP/37)|publisher=Research and Technology Organization of the North Atlantic Treaty Organization|location=BP 25, 7 rue Ancelle, F-92201 Neuilly-sur-Seine Cedex, France|date=July 2001|page=2-3|url=https://apps.dtic.mil/sti/tr/pdf/ADA394520.pdf|archive-url=https://archive.org/details/technologies-for-future-precision-strike-ada-394520|archive-date=20 October 2025|quote=Flight trajectory shaping is particularly beneficial for high performance supersonic missiles, which have large propellant or fuel weight fraction. To take advantage of flight trajectory shaping, the missile must rapidly pitch up and climb to an efficient cruise altitude. During the climb, the missile angle-of-attack should be small, to minimize drag.}}</ref> creating a parabolic arc similar to ballistic missiles, before descending toward its target. This elevated flight path allows the missile to capitalize on reduced air resistance at higher altitudes, increasing both the missile's potential energy and the kinetic energy during terminal guidance, thus enabling greater range and probability of kill.<ref name=":Trajectory Shaping"></ref>

Peak altitiude of a lofted trajectory can be at altitudes ranging from {{convert|20000|-|110000|ft|km|0|abbr=on}}, with most air-to-air missiles peaking at around {{convert|80000|-|100000|ft|km|0|abbr=on}},<ref name=":0"/><ref name=":2">Karon (2019-08-29). "AIM-54 and AWG-9 WCS: Observations about Lofted Trajectory and Range". ''FlyAndWire''. Retrieved 2024-12-25.</ref> although the peaks of ballistic missiles' parabolic arcs can range from {{convert|50|km|ft|0|abbr=on}} to {{convert|1500|km|ft|0|abbr=on}}.<ref>{{Cite web |title=Prediction of Possible Intercept Time by Considering Flight Trajectory of Nodong Missile |url=https://www.koreascience.or.kr/article/JAKO201609636669772.pdf |archive-url=https://web.archive.org/web/20240904084309/https://koreascience.or.kr/article/JAKO201609636669772.pdf |archive-date=2024-09-04 |access-date=2024-12-29 |website=www.koreascience.or.kr}}</ref>

== Advantages == Lofting offers several distinct advantages compared to sea-skimming and direct-intercept trajectories, particularly in beyond-visual-range engagements.

Unlike sea-skimming, which prioritizes low-altitude flight to avoid radar detection but suffers from increased drag and limited range, lofting allows the missile to ascend to higher altitudes where air resistance is lower. This reduced drag enables greater range and energy efficiency, allowing the missile to retain more kinetic energy for terminal guidance and target interception.<ref name=":0"/>

Compared to direct-intercept trajectories, lofting also improves engagement flexibility by providing a steeper attack angle, which is particularly effective against maneuvering or high-altitude targets.

== Disadvantages == In comparison to sea-skimming trajectories, lofting lacks radar-avoidance characteristics, making it susceptible to detection by its target and potential interceptors.

Lofting is also more mathematically and technologically complex in comparison to direct-interception, and is only viable in long-range engagements.

Additionally, the thinner air which lofting utilizes to reduce drag and increase range carries the downside of impeding the ability for control surfaces to maneuver the missile. This can reduce a missile's ability to adjust for fast-moving or maneuvering targets, however can be circumvented with the use of thrust vectoring - at the downside of added cost and complexity.

== Use in Missiles == A number of missiles are known or speculated to utilize lofting techniques, such as:

*AIM-7 Sparrow (AIM-7MH variants and later) - United States<ref>{{cite tech report|title=FLIGHT MANUAL USAF SERIES F-15A/B/C/D BLOCK 7 AND UP|type=TO 1F-15A-1|author=Department of the Air Force|institution=United States Department of Defense|date=1 July 1989|url=https://usaf-sig.org/index.php/references/downloads/4-technical-orders/38-type-specific/102-f-15-eagle-strike-eagle?download=451:t-o-1f-15a-1-flight-manual-f-15a-b-c-d-block-7-up-01-07-1989-pdf|archive-url=https://web.archive.org/web/20240430083717/https://usaf-sig.org/index.php/references/downloads/4-technical-orders/38-type-specific/102-f-15-eagle-strike-eagle?download=451:t-o-1f-15a-1-flight-manual-f-15a-b-c-d-block-7-up-01-07-1989-pdf|archive-date=30 April 2024|url-status=live|access-date=2 September 2025|page=1–64E|quote="RLOFT (AIM-7MH)"}}</ref><ref>{{cite book|last=Coté|first=Gilbert|author2=Naval Education and Training Program Development Center|title=Fire Control Technician M 3 (NAVEDTRA 10224)|publisher=Naval Education and Training Command via United States Government Printing Office|year=1981|location=United States|page=2-19|quote=SPARROW[…] utilizes trajectory shaping to greatly increase its performance envelope.|postscript=The page — "2-19" — is correct; Please do not alter it or change the parameter to "pp" or "pages." It is "2 through 19" it is labelled as "2 dash 19" and is a single page}}</ref><ref>{{cite report|author1=United States Fleet Forces Command|author2=Office of Protected Resources, National Marine Fisheries Service|title=Virginia Capes Range Complex Final Environmental Impact Statement/Overseas Environmental Impact Statement (EIS/OEIS)|chapter=Volume 2, Appendices|date=March 2009|publisher=United States Department of the Navy|location=Norfolk, Virginia|url=https://www.nepa.navy.mil/Portals/20/Documents/aftteis1/virginia-capes/nepa-eo/vacapes-feis-vol2-appendices-full.pdf|archive-url=https://archive.org/details/vacapes-range-complex-final-environmental-impact-vol-2-appendices-full|archive-date=20 October 2025|quote=AIM/RIM-7M[...] Trajectory shaping[...]}}</ref> *AIM-120 AMRAAM - United States<ref>{{cite web |title=Air-to-air warfare: speed kills|last=Barrie |first=Douglas|work=IISS Military Balance Blog|publisher=International Institute for Strategic Studies|url=https://www.iiss.org/online-analysis/military-balance/2022/09/analysis-air-to-air-warfare-speed-kills|access-date=2025-10-21 |archive-url=https://web.archive.org/web/20250909040647/https://www.iiss.org/online-analysis/military-balance/2022/09/analysis-air-to-air-warfare-speed-kills|archive-date=9 September 2025|quote=The AIM-120D3 range extension is provided by trajectory shaping rather than by any solid motor modification. While this will give the missile a greater maximum range, the amount of energy it has when it reaches the target also remains important.}}</ref><ref>{{cite journal|title=Strategic Digest, Volume 32, Issues 6–12|journal=Strategic Digest|publisher=Institute for Defence Studies and Analyses|location=India|year=2002|volume=32|issue=6–12|page=1189|url=https://books.google.com/books?id=gSRNmKRVFSAC|archive-url=https://web.archive.org/web/20250824035251/https://www.google.com/books/edition/Strategic_Digest/gSRNmKRVFSAC?hl=en|archive-date=24 August 2025|access-date=2 September 2025|quote=Weapons such as the US AIM-120 AMRAAM can climb shortly after launch to high altitude, thus extending the range...}}</ref> *AIM-54 Phoenix - United States<ref name=":2"/> *AIM-260 JATM - United States *Meteor - France, Sweden, United Kingdom, Germany *R-77 - Russia *PL-15 - China *PL-17 - China<ref>{{cite web|last=Barrie|first=Douglas|title=Air-to-air missiles push the performance, payload envelope|date=29 January 2024|work=IISS Online Analysis|publisher=International Institute for Strategic Studies|url=https://www.iiss.org/online-analysis/military-balance/2024/01/air-to-air-missiles-push-the-performance-payload-envelope/|archive-url=https://web.archive.org/web/20250813135715/https://www.iiss.org/online-analysis/military-balance/2024/01/air-to-air-missiles-push-the-performance-payload-envelope/|archive-date=13 August 2025|access-date=16 October 2025|quote=The PL-17 (CH-AA-X-12) likely has a range of around 400 kilometres, using a dual-pulse solid rocket motor combined with a lofted trajectory to achieve the distance.}}</ref> *Astra Mk.2 -India<ref>{{Cite web |date=2025-12-04 |title=New Astra Mk2A Visuals Confirm India’s Leap in 240+ Range BVR Dominance Against Regional Rivals |url=https://defence.in/threads/new-astra-mk2a-visuals-confirm-indias-leap-in-240-range-bvr-dominance-against-regional-rivals.16138/ |access-date=2026-02-06 |website=Defence News India |language=en-US}}</ref><ref>{{Cite web |last=admin |date=2026-02-03 |title=Astra’s Quantum Leap: Did India’s Indigenous BVRAAM Break the 240 km Barrier Alone—or in the Shadow of a Captured Chinese PL-15? |url=https://defencesecurityasia.com/en/india-astra-missile-range-pl15-capture-operation-sindoor-analysis/ |access-date=2026-02-06 |website=Defence Security Asia |language=en-GB}}</ref>

== References ==

Category:Missile guidance Category:Missile operation Category:Missile technology Category:Tracking Category:Targeting (warfare) Category:Physics