THE MOC

Time to Update the Salvo Equations

The Salvo Model of Modern Missile Combat was first fully articulated in print by their primary developer; the late Naval Postgraduate School Professor Captain Wayne P. Hughes, U.S. Navy (retired) in 1995. The product of Hughes’ research into pulsed combat actions from the Second World War through the advent of the cruise missile age, the “Salvo Equations” have since become a standard method of understanding cruise missile combat in the 21^st century. Hughes also intended the Salvo Equations to influence ship design as his research and experience suggested that warship “staying power” in combat had decreased since the end of the Second World War. The combination of advances in antiship cruise missile (ASCM) technology and the perception that U.S. warships have become “less survivable” have caused some to question the post-1991 U.S. Navy force structure of fewer, but larger and more capable warships as a viable construct for future warfare. There have been three editions of Hughes’ book Fleet Tactics (from 1986 to 2018) that developed these theories and popularized them to a wide audience. 

While there has been subsequent research into the mathematics of the Salvo equations, the “given” values for defense capability of individual or groups of ships has not received similar scrutiny. The modeling for ships’ defensive capabilities effectively stopped in 1994 without the addition of subsequent cruise missile combat in follow-on versions of the Fleet Tactics series. While the Salvo Equations remain a highly effective modeling tool for examining potential missile combat, their component that expresses the defensive capability and survivability of warships needs to be reassessed for a new era of “Great Power Competition.”

Hughes’ Logic

Hughes derived the logic from his salvo equations from multiple sources. These including the World War I Lancaster equations that measured the potential power of artillery barrages in combat and his own models of pulsed combat power as expressed by carrier air strikes during World War II. As stated by Hughes, the purpose of the salvo equations was, “to write a simple mathematical model with which to make exploratory computations that describes the offensive power of ships armed with ASCMs and the defensive power of ships defending against ASCMs.”  The offensive power of the antiship cruise missile is central to Hughes’ thesis. He described it as one where, “The possibility now exists that the striking power of a single unit armed with surface-to-surface antiship cruise missiles (ASCMs) may be strong enough to put several enemy units out of action, with profound tactical consequences.”

Warship staying power was one of the cornerstones of Hughes’ thinking behind the Salvo Equations. In one of the earliest presentations of the Salvo Equations Hughes wrote, “The purpose of this article is to offer a methodology to study modern surface combat in a form suitable to help compare the value of a modern surface warship’s principal combat characteristics. We will emphasize staying power, which we think has been neglected.” Hughes also suggested that traditional means of measuring warship survivability (in terms of armor) no longer applied as, “The case for staying power in the form of armor was muted by the atomic bomb.” Furthermore, there has not been a move to re-establish warship survivability in the wake of the Cold War nuclear weapons threat. Hughes writes, “As the threat of nuclear war wanes, corresponding interest in staying power has not been reborn.” Littoral waters are of most concern to Hughes in terms of danger to fragile ships. He further writes, “The U.S. Navy has enjoyed the luxury of contributing to decisions on land while being itself free from attacks from the land. But the sanctuary of the sea seems less secure today, along with the prospect of taking hits while fighting close against the littorals.”

The Salvo Equations

Hughes’s equations postulate that if two, equal-sized forces A and B exchange missile salvos that:

Where:

The interesting part of the salvo equations is how Hughes populated the various data fields he uses to generate missile hits resulting from salvos. He made a number of assumptions to fill some of the fields; notably those detailing what constitutes a “well aimed missile,” the number of such weapons destroyed by the defender,” and, “The staying power of a modern warship.” Hughes filled these based on data he acquired from what he calls “small missile ship types,” and, “The warships for which we have combat data.” These assumptions were (in his original 1995 thinking);

These assumptions were combined with the already referenced belief by Hughes that warship “staying power,” or what today we would call “survivability” had decreased since the end of World War II due to the rise of antiship cruise missiles. This assumption acquired from historical data of the small ship engagements for which data was available had a profound impact on the characterization of defense against cruise missiles and warship survivability in the following decades.

The Historical Basis for Modeling Defense in the Salvo Equations

Hughes derived his theories on warship survivability and cruise missile lethality from multiple sources, but one of the most significant of these was historical observation of cruise missile combat from its genesis in the late 1960’s through the writing of his second volume Fleet Tactics and Coastal Combat (2000.) One of the most significant of these was a 1994 Naval Postgraduate Thesis by Lieutenant John C. Schulte, USN, on the effectiveness of cruise missiles in littoral combat from 1967 through 1991. Schulte’s thesis was unclassified, by close held under the category of “official use only” until 2009. Hughes also drew on data collected during World War 2 on ship damage and sinking to form his theories on ship defense. Schulte’s analysis of cruise missile combat, however, seems to have an outsized role in Hughes’ thoughts as it is the modern, physical embodiment of his pulsed combat power concept.

Schulte’s thesis examined historical instances of cruise missile combat that included “defenseless” targets (that could not physically respond to an ASCM attack.) “defendable” targets that possessed systems that could defend against an ASCM attack, but were not employed (for multiple reasons,) and finally “defended” targets that physically attempted to defeat an ASCM attack with installed weapons and sensors. Schulte collected data from these ASCM attack events to generate a vulnerability index for surface warships. His 1994 data was still in use as valid in 2018 assessments.

While Schulte’s analysis was timely and useful when first published, the technology of both missile offense and defense have advanced since 1994. At the same time, there have been far fewer cruise missile engagements from which to draw useful data. Only three seem to fit within the Schulte analysis framework. These include the 2006 cruise missile attack on the Israeli corvette Hanit by the terrorist group Hezbollah in the waters off Beirut, the 2016 attack on the former US naval vessel Swift by Yemeni Houthi rebels in the Red Sea, and the closely following attack on the US destroyers Mason and Nitze in the same area as Swift by the same group., and finally the April 2022 sinking of the Russian cruiser Moskva by Ukrainian cruise missiles. Each fit within one of Schulte’s groups. Ex-Swift was unarmed and defenseless, Hanit and Moskva were defendable but did not use their defensive systems in response to the attack, and Mason and Nitze were defended units that successfully defeated cruise missile attacks.

Much of the information regarding all four of these cases remains unclear. At first glance, these cases would seem to validate the basic Schulte thesis; with the cases of Hanit and Moskva suggesting that even defendable ships had a slim chance of defeating a cruise missile attack. This inductive reasoning falls short in assessing surface ship vulnerability for many reasons. Hanit and perhaps Moskva were not expecting a cruise missile threat and appear to have been unprepared much as the U.S. Navy frigate Stark was unprepared for the Iraqi cruise missile strike that severely damaged the ship in 1987. Other warships might be equally unprepared at the outset of conflict, but what of the case of the fully prepared warship operating as part of a larger combat organization under wartime conditions? For this case we have only the HMS Sheffield Exocet cruise missile strike, and that hit resulted in part from the technical issues of early guided missile warships where systems often conflicted with each other or had low reliability. 

The Way Ahead

Unlike the Schulte report from 1994, the recent history of naval cruise missile combat offers few examples from which to draw definitive conclusions. Much of what is suggested today in terms of warship susceptibility to cruise missile attack and vulnerability to damage from cruise missile attack dates to the 1980’s and needs to be updated. The four recent cruise missile incidents offer some updated information, but still suggest that unprepared ships are more likely to get hit in surprise attacks. They do not really say anything about technological improvements in both attack and defense with and against cruise missiles. One way to better assess current conditions is to do what several testing agencies have said for years and that is to conduct a live fire cruise missile attack against an automated, defended target. One of the retiring CG-47 class cruisers might be loaded with a mix of defensive weapons and attacked with cruise missile salvos to determine the effectiveness of current AEGIS baselines. Such attacks have been simulated for decades with computers including AEGIS’ own software, but a live-fire test might better answer some of the questions that have been directed against AEGIS since the 1970’s. Regardless of such testing, however, cruise missiles, including those of the hypersonic variety continue to pose a significant threat, especially to the complacent surface vessel. The salvo equations pioneered by Captain Hughes remain an extremely useful tool in assessing the cruise missile threat, but their defensive measure “given” value needs an update.

Dr. Steven Wills is the Navalist at the Center for Maritime Strategy. His research and analysis centers on U.S. Navy strategy and policy, surface warfare programs and platforms, and military history.

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The views expressed in this piece are the sole opinions of the author and do not necessarily reflect those of the Center for Maritime Strategy or other institutions listed.