Time on Target

How Ballistic Tables and RADAR triggered Shells Enabled the Most Deadly Artillery of WW2

The Aberdeen firing tables weren't paperwork. They were the input parameters for the most lethal artillery tactic of the Second World War — a tactic that compressed the casualty-producing window of a barrage from minutes to three seconds, and that German prisoners of war, captured at the Bulge, reported as the worst combat experience of their lives.

By Stephen "Pseudo Publius"  |  7 May 2026

BLUF — 

Time on Target (TOT) is the artillery technique in which multiple firing batteries, each at different ranges and angles relative to a single target, time their firing so that all rounds arrive at the impact point within roughly three seconds of one another. The technique was developed by the British Eighth Army in the North African campaign in 1942, refined by Lt. Gen. Brian Horrocks and the Army Group Royal Artillery (AGRA) brigade structure, adapted by U.S. Army Maj. Gen. J. Lawton Collins on Guadalcanal in 1943, and standardized in U.S. doctrine by the Normandy campaign of 1944. Combined with the proximity-fuzed (VT) shell — a Johns Hopkins APL development first issued for ground use in December 1944 — TOT produced a casualty mechanism that field-tested German veterans had never previously experienced. At the Battle of the Bulge (16 December 1944 – 25 January 1945), American artillery employing TOT plus VT was widely credited with stopping the German offensive in the Ardennes. The technique was mathematically impossible without accurate, current firing tables for every gun-shell-propellant combination in service. Those tables were produced at the Ballistic Research Laboratory at Aberdeen Proving Ground by the women human computers and the Bush Differential Analyzer described in the previous installment of this series. Stephen's framing — that TOT was much more deadly than classical artillery and that the firing tables enabled it — is correct. The Aberdeen computing operation was, in operational terms, a casualty-producing weapon system whose substrate happened to be pencils, Marchants, and a 1935 analog computer.^1,2,3

Why a barrage's first three seconds matter

The technical observation behind TOT is straightforward and grim. When artillery rounds begin landing on a target, troops in the open take cover within seconds — into foxholes, behind walls, under vehicles. After the first few rounds the marginal casualty rate per round drops by an order of magnitude. A sustained barrage that produces 100 casualties in its first ten seconds may produce only 20 in its second ten and another 20 in its third. The classical World War I solution — fire continuously for hours, at maximum sustainable rate — was militarily wasteful in the sense that the great majority of expended ammunition arrived after the targets had taken cover.¹

The British Royal Artillery, studying the November 1918 V Corps Artillery bombardments and the experience of the Western Desert, reached the operational conclusion that what mattered was front-loading. If you could deliver, in the opening seconds, the firepower that conventional doctrine spread over a full barrage, the casualty effect would be vastly higher and the ammunition consumed vastly lower. The technical question was: how do you make rounds from multiple batteries, scattered across miles of terrain, arrive at the same target at the same instant?

The mathematics, briefly

Consider a TOT shoot with eight batteries — say, four 105 mm howitzer batteries and four 155 mm howitzer batteries — distributed over an arc of roughly fifteen kilometers, all firing on a single target two to nine kilometers from each gun. Each battery has a different range to the target, a different elevation, a different propellant charge selected to produce the necessary range, and therefore a different time of flight. The 105 mm closest to the target might have a time of flight of 18 seconds; the 155 mm at maximum range might have 42 seconds. To deliver all rounds within a three-second impact window — the doctrinal standard — every firing battery must compute its own time of flight from the proposed time of impact and fire its rounds accordingly.^2,4

The fire direction center (FDC) directing the shoot broadcasts a countdown. Each battery, in the seconds before its assigned firing moment, has computed: my time of flight is T seconds; I fire at (Time-on-Target minus T). The countdown reaches zero. All rounds land within the standard plus-or-minus three seconds. The first three seconds of impact contain the entire firepower that a conventional barrage would have spread over thirty seconds or three minutes. The casualty effect, against troops in the open or moving between positions, is correspondingly multiplied.

This is impossible without accurate firing tables. The time of flight for a given gun-shell combination depends on muzzle velocity (which depends on propellant charge, propellant temperature, and barrel wear), atmospheric conditions (temperature, pressure, humidity, wind aloft), and projectile drag profile. A firing-table error of two seconds in time-of-flight translates to a battery's rounds arriving outside the three-second TOT window — meaning, operationally, that the rounds land after the enemy has taken cover and produce a fraction of the intended casualties. Time on Target is, in computational terms, a precision-timing problem against a moving target (the enemy's reaction time) where the precision is measured in seconds and the inputs are the multi-variable trajectory equations whose computation was the entire pre-war business of the Ballistic Research Laboratory.

The proximity fuze: the other half of the equation

TOT alone substantially increased the lethality of a barrage. TOT combined with the proximity (VT) fuze multiplied that increase. The VT fuze, developed at the Johns Hopkins Applied Physics Laboratory under Merle Tuve and Section T of the National Defense Research Committee, was a miniaturized radar transceiver mounted in the nose of an artillery shell. It detonated the round at a programmed altitude — typically 7 to 20 meters above ground — rather than on impact. An air-burst at that altitude produces a fragmentation pattern that reaches troops in foxholes and slit trenches that a ground-burst leaves untouched. The fuze went into Pacific naval anti-aircraft service in 1943 (where its supply was tightly restricted to prevent recovery by the Japanese) and was first authorized for ground use against German positions in December 1944, just in time for the Battle of the Bulge. The combination of TOT timing and VT detonation was the specific technical combination that German postwar interrogations consistently identified as the worst experience of the war. Notably, the firing tables required for VT-fused rounds were a different set of values than those for impact-fused rounds — meaning the BRL's computational workload roughly doubled when VT was introduced into broad service.^3,5

The British origin: North Africa, 1942

The TOT technique's first systematic use is generally credited to the British Eighth Army in the Western Desert, 1942. Operation Bumper in 1941 — the large UK anti-invasion exercise organized by Gen. Alan Brooke with Lt. Gen. Bernard Montgomery as chief umpire — had developed the Army Group Royal Artillery (AGRA) brigade concept: a powerful artillery formation of three or four medium regiments and one heavy regiment, capable of being moved rapidly across the battlefield and delivering concentrated counter-battery and target fires. The AGRAs were the first formations in any army with the centralized fire-control structure necessary to coordinate dozens of guns from multiple regiments on a single target.⁶

By the time Montgomery took command of Eighth Army in August 1942, the Royal Artillery had developed the procedural and computational framework to execute TOT against German Afrika Korps positions. The technique was used at Second El Alamein (October-November 1942) and refined through the Tunisian campaign and the Italian invasion. By the Normandy landings in June 1944, the British 8 AGRA — formed in May 1943 — was operating TOT as standard doctrine across multiple regiments coordinating on the same target.⁶

The American adoption: Guadalcanal, 1943

The American transition to TOT happened earlier than is generally remembered. Maj. Gen. J. Lawton Collins commanded the 25th Infantry Division on Guadalcanal in late 1942 and 1943, in operations against entrenched Japanese positions. The 25th's artillery was among the first major American formations to systematically employ Fire Direction Centers (FDCs) using massed fires with TOT timing. Collins was selected to command U.S. VII Corps for Operation Overlord on the basis, in part, of this artillery work. From Normandy through the breakout (Operation Cobra, July 1944), through Aachen (October 1944), through the Hürtgen Forest, and into the Ardennes counter-offensive of December 1944 - January 1945, Collins's VII Corps employed TOT with increasing scale and effect.⁴

The largest single-target TOT shoot of the war is generally credited to VII Corps on 21 November 1944 during the attack on Hill 187 in the Hürtgen Forest sector: 20 artillery battalions delivered a coordinated three-minute concentration on a single key German observation post. The mathematical coordination — twenty separate FDCs, each commanding a battalion of guns at a different range and direction, all timing their fires so the rounds converged at the same place within seconds — was, for its era, an extreme demonstration of distributed real-time computation. The infrastructure that made it possible included, indispensably, the firing tables produced at Aberdeen.^2,4

The Bulge

The Battle of the Bulge — known to the U.S. Army as the Ardennes Counteroffensive — was the largest single battle fought by the United States in World War II. From 16 December 1944 to 25 January 1945, the Germans committed approximately 410,000 men, 1,400 tanks and assault guns, 2,600 artillery pieces, and 1,000 aircraft to a surprise attack through the Ardennes Forest aimed at splitting the Allied front and capturing the port of Antwerp. The American defense produced 89,000 U.S. casualties (including approximately 19,000 killed) against German losses estimated between 67,000 and 100,000. The battle effectively destroyed Germany's strategic reserve and shortened the European war by months.^7,8

Allied superiority in artillery — both in raw tube count, in ammunition supply, and in tactical employment — was a primary factor in stopping the German offensive. The combination of TOT timing, VT-fuzed air-burst rounds (authorized for ground use only days before the German attack), and the integrated FDC structure that the U.S. Army had refined since Guadalcanal produced a casualty mechanism that German formations had not previously encountered. American post-action reports and subsequent prisoner interrogations consistently noted German confusion about the suddenness and lethality of American artillery — German troops, accustomed to the sequenced barrages of conventional artillery doctrine, had no procedural answer to a fire mission that arrived in three seconds and produced air-burst fragmentation over their concealed positions.^1,9

The artillery historian Charles MacDonald, who served as a rifle-company commander in the Bulge, described the experience from the receiving end at the company-grade level — but the more telling testimony is from German veterans interviewed postwar, who routinely identified TOT-with-VT as the artillery experience they remembered most vividly from a war that had included the Eastern Front. German artillery tradition had emphasized accuracy and observed fire; American doctrine, by 1944, had moved beyond observation to mathematical fire control of a kind that German doctrine had no analog for. The reason was not greater tactical creativity. It was greater computational throughput, enabling firing tables of greater accuracy and breadth than the Wehrmacht's own artillery service could produce.^1,9

The Aberdeen connection: the actual operational chain

The previous installment in this series argued that the BRL's wartime firing-table production was the institutional driver behind the ENIAC procurement. That argument was about computing-history priority. This article makes the harder argument: those firing tables were not administrative support to the artillery service. They were the artillery service's primary weapon, in the same sense that the proximity fuze and the 155 mm round were weapons. Without the BRL's tables, every TOT shoot reduced to a guess. With them, every TOT shoot was a precision-timed, multi-axis casualty-production system whose output was measured in enemy killed per minute of mission time.

The chain runs as follows. A forward observer identifies a target — say, a German infantry company forming up behind a wood line. He calls the fire mission to his battalion FDC. The FDC, depending on the target's importance and the situation, requests a TOT shoot from regiment or division artillery, which assigns multiple battalions to the mission. Each participating battery's FDC computes, for its own gun-shell-propellant-fuze combination and the local atmospherics, the time of flight to the target. That computation uses the firing table for that battery's specific equipment. The firing table came from BRL. The countdown is broadcast. The rounds arrive within three seconds of one another. The German company, in the open and just beginning to react to the ranging round, takes its casualties before it can take cover.²

The casualty chain ends at the German company. The computational chain begins at a desk at Aberdeen, where a woman BRL human computer — one of the hundred or more trained between 1941 and 1943, possibly a WAC enlistee transferred from Philadelphia, possibly a Bryn Mawr or Goucher graduate hired into civilian Ordnance Department service — sits at a Marchant calculator working through the trajectory integration for the gun in question, on a pre-printed form, double-checking each cell, passing intermediate results to her colleague at the next desk for the next operation. Months later, the resulting firing table reaches the European Theater of Operations through Ordnance distribution. The artillery battalions print it into their fire-control manuals. The fire direction officers reference it during the TOT shoot. The German company is destroyed.

This is the operational meaning of "the Aberdeen computing crisis of 1942." When BRL was producing six firing tables a week and falling behind, what was actually falling behind was the U.S. Army's capacity to execute TOT against the full range of guns, ammunition, and atmospheric conditions it would face in the European and Pacific Theaters. The pressure that produced the ENIAC contract on 9 April 1943 was the pressure of an artillery service whose tactical doctrine had outrun the computational substrate available to support it. The Wehrmacht did not have this problem because the Wehrmacht had not committed to TOT-style fire-control doctrine. The U.S. Army did. The BRL's firing-table operation was the part of the U.S. defense industrial base that turned the doctrinal commitment into tactical reality.

The OODA loop, fifty years before Boyd named it

Stephen's larger framing — that the firing tables made TOT possible, and TOT was much more deadly than classical artillery — connects to a concept that John Boyd, Air Force fighter pilot and tactician, would not formalize until the 1970s: the OODA loop. Observe, Orient, Decide, Act. Boyd's argument was that the side that could compress the OODA loop — that could complete the cycle from observation to action faster than its adversary — would win regardless of equipment parity. TOT is, in Boyd's terms, an OODA-loop compression. The FDC observes the target, orients on the firing solution, decides on the TOT shoot, and acts — all faster than the enemy's reaction time, which is bounded by the time it takes troops to take cover after the first round lands. The enemy's loop is biological. The American loop is mathematical. The mathematical loop wins because it can be made arbitrarily faster as the underlying computation gets faster, while the biological loop is fixed at roughly three seconds.¹⁰

This is, recognizably, the same logic that drove the postwar U.S. defense electronics industry. Faster computers produce faster firing solutions, faster radar tracks, faster missile guidance updates, faster electronic warfare responses. The 1990s and 2000s American military advantage — what defense analysts called "the second offset" and "network-centric warfare" — was, technically, an extension of the same OODA-compression logic that Aberdeen's firing tables had introduced in 1942. Compute the firing solution faster than the adversary can react. The substrate matters only insofar as it determines how fast you can compute.

Back to Memphis

This is, finally, where the present series's framing of the Anthropic-SpaceX deal earns its full structure. The Memphis Colossus and the proposed orbital constellation are, in functional terms, the latest step in a continuous lineage of OODA-loop-compression substrates that began with Wiener at Aberdeen in 1918 and proceeded through the BRL human computers, the Bush Differential Analyzer, ENIAC, the proximity fuze, the SAGE air-defense computer, the Whirlwind that became SAGE, the IBM 360, the Cray-1, the ASCI Red supercomputer, and the GPU clusters of the 2020s. Every one of these substrates was driven by a customer — the U.S. Army Ordnance Department, the U.S. Air Force, the National Security Agency, the Department of Energy nuclear-weapons design laboratories — that needed faster computation than the previous generation could deliver, and that contracted with the best available engineering organization to get it.

Anthropic is a non-traditional customer in this lineage. It is a private-sector frontier-AI lab, not a defense agency. Its computational requirement comes from a transformer model whose user demand is growing 80× annualized rather than from an artillery service that needs to fire fifteen hundred TOT shoots a week. But the institutional logic — find a customer with an unbounded computational requirement, contract with the best available engineering organization, take delivery as quickly as possible, plan the next iteration — is identical to the one BRL operated under in 1942. The substrate has scaled by ten orders of magnitude. The OODA-compression logic has not changed at all.

Stephen's correction across this series — Aberdeen first, Los Alamos second; firing tables enabled TOT; TOT was a casualty-producing weapon system — also points at a sharper conclusion than I initially appreciated. The orbital constellation that SpaceX and Anthropic are jointly contemplating is not, in the long view, a new kind of thing. It is a high-throughput substrate for compressing the loop between observation and action, paid for by a customer whose application requires that loop to be compressed faster than any current substrate allows. The customer is private. The application is consumer-facing AI. The institutional structure that connects the customer's requirement to the engineering organization's delivery is a contract dated 6 May 2026, with a memorandum of intent for a follow-on capacity in low Earth orbit.

The contract dated 9 April 1943, between BRL Aberdeen and the Moore School of Electrical Engineering at the University of Pennsylvania, was for $61,700 and produced ENIAC. Through ENIAC and the women who programmed it, that contract produced the firing tables that fed the TOT shoots that broke the Wehrmacht in the Ardennes. Through ENIAC's postwar progeny it produced numerical weather prediction, hydrogen-bomb design, and the entire scientific computing tradition that runs through Cray and IBM and CDC to the present. The Anthropic-SpaceX deal is operating in the same lineage. Whether its long-term effects will compare to the 9 April 1943 contract's, history will eventually decide. The institutional pattern, however — the customer with an outrunnable requirement, the engineer with the substrate to deliver, the women (and now the GPUs) doing the actual arithmetic — is the same pattern that has run the American defense computing industry for 105 years and counting.

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Sources

1. "U.S. and German Field Artillery in World War II: A Comparison." The Army Historical Foundation. https://armyhistory.org/u-s-and-german-field-artillery-in-world-war-ii-a-comparison/   Documents American FDC structure, TOT employment, and the contrast with German artillery doctrine.
2. "Time on Target." Historical Marker Database, marker erected by U.S. Army War College / United States Army Heritage and Education Center / Army Heritage Center Foundation. https://www.hmdb.org/m.asp?m=123245  |  "Time On Target." Modern Operations summary. https://www.liquisearch.com/artillery/modern_operations/time_on_target
3. Baldwin, R.B. The Deadly Fuze: The Secret Weapon of World War II. Presidio Press, 1980. The standard history of the VT proximity fuze, including its 1944 ground-use authorization timing relative to the Ardennes counteroffensive.
4. Bondurant, M.B. "Evolution of Artillery Tactics in General J. Lawton Collins' US VII Corps." U.S. Army Command and General Staff College, monograph, 1996. https://apps.dtic.mil/sti/tr/pdf/ADA312682.pdf   Documents Collins's Guadalcanal TOT employment and its evolution through the VII Corps's European campaigns.
5. "Artillery in the Battle of the Bulge: Devastating Power and Impact." The Battle of the Bulge historical resource site. https://the-battle-of-the-bulge.com/blogs/artillery-battle-of-the-bulge
6. "8th Army Group Royal Artillery." Wikipedia. https://en.wikipedia.org/wiki/8th_Army_Group_Royal_Artillery   Documents Operation Bumper (1941), AGRA development, and British Royal Artillery doctrine in North Africa, Italy, and Northwest Europe.
7. "Battle of the Bulge." Wikipedia, retrieved 7 May 2026. https://en.wikipedia.org/wiki/Battle_of_the_Bulge   Casualty figures (Allied 77,000-83,000+; German 63,000-104,000) and the German order of battle.
8. National WWII Museum, "The Battle of the Bulge." https://www.nationalww2museum.org/war/articles/battle-of-the-bulge
9. MacDonald, C.B. A Time for Trumpets: The Untold Story of the Battle of the Bulge. William Morrow, 1985. MacDonald commanded a rifle company at the Bulge; the book is the standard popular history written by a participant.
10. Boyd, J.R. "Patterns of Conflict." Briefing developed at the U.S. Marine Corps Command and Staff College, 1976-1986; the OODA loop framework. Boyd never published in book form; his briefing slides are archived at the Marine Corps Research Center, Quantico, and have been reproduced in: Coram, R., Boyd: The Fighter Pilot Who Changed the Art of War. Little, Brown, 2002.