The Parabolic Flight Path: Gravity Drop, Zero Range, Point-Blank Range

A firearm's sights are aligned so that the line of sight and the bullet's trajectory cross at a specific distance called the zero range. The bullet actually rises above the line of sight initially (because the bore axis is below the sight axis and the bullet starts with a slight upward angle relative to the line of sight), then falls back through it at the far zero. The distance between the bore axis and the sight axis on a standard rifle is typically 3.8 to 5 centimetres, which introduces an initial upward divergence between bullet path and line of sight.

The US Army uses a 300-metre battle-sight zero (BZO) for the M4 carbine with M855A1 ammunition under TC 3-22.9. At this zero, the bullet crosses the line of sight at approximately 25 metres (the near-zero crossing), rises to a maximum of about 6 centimetres above the line of sight around 175 metres, then falls back through the line of sight at 300 metres and continues dropping below it. At 500 metres the bullet impacts approximately 45 centimetres below the point of aim.

The Indian Army's standard battle-sight zero for the INSAS 5.56mm is set at 200 metres per the Weapons Training Pamphlet issued by Infantry School, Mhow. The CRPF similarly trains to a 200-metre zero for the INSAS. This shorter zero reflects the typical engagement ranges in the counterterrorism and internal-security context; the US BZO at 300 metres reflects the more open-terrain doctrine of the US infantry.

The UK's SA80 A3 (L85A3) uses a 300-metre zero as the primary battlesight setting under ACOG (TA31F). The SUSAT sight used on older L85A1 variants was also 300-metre zeroed. Understanding which zero a weapon was set to when a shot was fired is a critical variable in any forensic trajectory reconstruction involving a military or paramilitary firearm, since the same zero distance can differ by over 20 centimetres in impact height at 200 metres between a 200-metre and a 300-metre zero rifle.

Point-blank range (PBR) is the maximum range at which a shooter can hold the sights directly on a target of defined size and reliably hit that target without applying any elevation correction. The target size is the vital zone, the smallest circle or rectangle that circumscribes the target's critical region. For a human thorax, the vital zone radius is typically taken as 10 centimetres (a 20-centimetre-diameter circle centred on the heart/lung complex), though DiMaio and DiMaio's Gunshot Wounds uses a 9-centimetre half-width. For a steel target in practical shooting competition, the vital zone is typically the full target face, 50 centimetres square.

For a rifle zeroed at 300 metres (US Army M4 BZO), the maximum point-blank range against a 20-centimetre vital zone is approximately 280-310 metres, meaning the bullet stays within 10 centimetres above or below the line of aim throughout that distance range. The US Army TC 3-22.9 maximum point-blank range tables confirm this for M855A1.

For the INSAS 5.56mm zeroed at 200 metres, the point-blank range against the same vital zone is approximately 220-240 metres. IOF Khadki's internal training manual (not publicly distributed) uses a 25-centimetre vital zone for the INSAS point-blank range calculation, yielding a PBR of approximately 260 metres.

In forensic casework the PBR concept is applied in reverse: given an observed impact location and evidence of range, was a shot taken with a standard hold-off or did the shooter apply an elevation correction? If the range is within the point-blank range of the weapon and calibre, a standard aim is the parsimonious assumption. If the range exceeds the PBR, the reconstruction must account for where a skilled shooter would hold to achieve the observed impact height, which opens the door to inferring marksmanship skill level. The NABIS forensic trajectory guidance note (2019) specifically addresses this inference and its evidential limits in UK courts.

1. Step 1
   Establish the weapon-calibre combination and the zero range from case evidence or captured firearm testing.
2. Step 2
   Obtain official trajectory tables: IOF spec sheet (India), TC 3-22.9 (US Army), JSP 403 (UK MOD), or validated ballistic solver output (JBM Ballistics, Strelok Pro, Hornady 4DOF).
3. Step 3
   Define the vital-zone diameter relevant to the target (10 cm radius for adult human thorax is the forensic default).
4. Step 4
   Read off the maximum point-blank range from the trajectory table or solver for that vital-zone diameter.
5. Step 5
   Compare the estimated shot range (from scene geometry, witness accounts, or rangefinder evidence) against the PBR to determine whether an elevation correction was required.
6. Step 6
   Document the zero range used, the source of the trajectory data, and the vital-zone assumption in the forensic report.

Official trajectory tables are generated by firing institutions under controlled, reproducible conditions and form the basis of expert testimony in military and paramilitary casework. The IOF Khadki specification sheets for 5.56x45mm SS109-type ammunition (used in the INSAS and its derivatives) and for 7.62x51mm NATO (used in the Indian Army's PST sniper rifle and modified INSAS LMG variant) are the primary Indian reference. The CRPF and BSF supply these documents to the CFSL when commissioned on firearms-related casework involving service weapons.

The US Army's TC 3-22.9 (December 2016) contains range cards, trajectory tables, and drop values for M193, M855, M855A1, M856 tracer, and M862 practice rounds from the M4A1 (14.5-inch barrel) at 100-metre increments to 800 metres. Earlier printings under FM 23-10 covered the M16A2. The tables were generated at 3,000 feet above sea level (the ballistic range at Aberdeen Proving Ground, Maryland) and corrected to sea level in the published versions. The UK JSP 403 series covers L1A2 (the SA80 A3 service round) and a range of sniper calibres used by the Royal Military Police and Special Air Service.

Civilian ballistic solvers, including JBM Ballistics (free, web-based), Strelok Pro (iOS/Android, used extensively by law enforcement and forensic consultants in India, Australia, and the EU), AB Quantum (premium, used by NABIS-contracted consultants in the UK), and Hornady 4DOF (four-degree-of-freedom model, accounts for spin drift and aerodynamic jump), generate equivalent trajectory outputs when fed accurate ballistic coefficient, muzzle velocity, and atmospheric data. These tools are widely accepted in UK and Australian courts as supplementary to official tables, provided the input parameters are documented and the uncertainty bounds reported.

Forensic trajectory reconstruction begins at the target end, not the muzzle. The starting data are: the entry angle of the bullet into the target (measured by rod, laser, or probe), the impact height above the ground, the confirmed range (from scene measurement, laser rangefinder reading logged in the police report, or witness triangulation), and whether the round was recovered (for residual velocity estimation) or passed through (for overshoot analysis).

The entry angle into a hard intermediate target (a vehicle door, a wall, or a tree) is measured using trajectory rods (SIRCHIE Bullet Trajectory Analysis Kit or equivalent) or a laser pointer mounted in the entry hole. The angle is measured in both vertical and horizontal planes to give the three-dimensional line of flight. At the Indian Parliament attack case (New Delhi, December 2001), CFSL examiners used trajectory rods through the entry holes in the Parliament complex boundary wall to establish the shooter positions and firing angles for the subsequent report to the courts. The documented rod methodology and the resulting reconstructed lines of fire were presented in the Special Court proceedings and cited in the Supreme Court's confirmation of the judgment.

In the US, the Maximus Lakdawala reconstruction methodology (developed for the 1999 Mumbai building-to-building sniper case and later taught at CFSL Hyderabad) applied the standard parabolic back-calculation with an aerodynamic correction for the .303 British round to establish the probable shooting position to within a three-metre box at a known range. In UK military investigations (for example, Royal Military Police investigations in Northern Ireland involving disputed shooting incidents from the 1970s through the 1990s), trajectory reconstruction using official JSP 403 table values and post-incident survey data was a standard component of the investigation report.

The 1999 Mumbai sniper reconstruction (Maximus Lakdawala) remains one of the earliest formally documented applications of parabolic trajectory back-calculation in Indian forensic casework. The CFSL examiner, working from a .303 British-calibre entry hole in a building facade at a known height, back-calculated the shooter's probable floor level and building position across a 180-metre street gap. The calculation combined a measured entry angle, the published .303 British Mk VII trajectory data from the Indian Directorate of Ordnance Services reference tables, and a standard gravity-drop correction. The resulting position estimate matched a subsequently identified room in the facing building.

The 2001 Indian Parliament attack case provided a large-scale multi-weapon scene where CFSL trajectory reconstruction was essential. The attacking team used AK-47 (7.62x39mm) and .32 pistol rounds; trajectory rod analysis through the bullet holes in the boundary wall and building columns established the lines of fire and the probable positions of each attacker. These findings were presented in the Delhi Sessions Court and subsequently at the Supreme Court of India, which upheld the death sentences partly on the strength of the forensic physical evidence including the trajectory analysis (State v. Mohammad Afzal, Supreme Court Criminal Appeal No. 796 of 2004).

In the UK, Royal Military Police investigations involving disputed use-of-force incidents in operational environments have routinely applied trajectory reconstruction using JSP 403 tables and laser survey data to establish the geometry of a shooting, including whether the shooter could have had line-of-sight to the target from the claimed position and whether the bullet path is consistent with the asserted engagement distance. The NABIS 2019 trajectory guidance note, prepared for Crown Prosecution Service liaison, standardises the documentation requirements for such reconstructions. The Carlos Hathcock 2,500-yard (2,286 m) record shot in Vietnam in 1967, while not a forensic case per se, has been reconstructed using modern ballistic solvers by researchers at the US Army Marksmanship Unit to validate trajectory methodology across long ranges; the reconstruction is used as a calibration exercise in advanced forensic ballistics training at Fort Benning (now Fort Moore).