Lofting, sometimes referred to as "trajectory shaping", [1] is a trajectory optimization technique used in some missile systems to extend range and improve target engagement effectiveness, usually in beyond-visual range scenarios. [2]
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Lofting, sometimes referred to as "trajectory shaping", [1] is a trajectory optimization technique used in some missile systems to extend range and improve target engagement effectiveness, usually in beyond-visual range scenarios. [2]
Lofting involves a missile ascending to a higher altitude after launch, [3] 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. [4]
Peak altitiude of a lofted trajectory can be at altitudes ranging from 20,000–110,000 ft (6–34 km), with most air-to-air missiles peaking at around 80,000–100,000 ft (24–30 km), [2] [5] although the peaks of ballistic missiles' parabolic arcs can range from 50 km (164,042 ft) to 1,500 km (4,921,260 ft). [6]
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. [2]
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.
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.
A number of missiles are known or speculated to utilize lofting techniques, such as:
SPARROW[…] utilizes trajectory shaping to greatly increase its performance envelope.
1 Quadratic polynomial[, peak altitude:] 33 km[;] 2 4th-order polynomial[, peak altitude:] 30 km[;] 3 4th-order polynomial[, peak altitude:] 25 km
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.
{{cite report}}: CS1 maint: location (link)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.
{{cite report}}: CS1 maint: location (link)RLOFT (AIM-7MH)
SPARROW[…] utilizes trajectory shaping to greatly increase its performance envelope.
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.
Weapons such as the US AIM-120 AMRAAM can climb shortly after launch to high altitude, thus extending the range...
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.