Fire Effectively First: CAPT Wayne Hughes and Salvo Equations

Captain Wayne Hughes holds a position of prominence in the field of naval theorists and thinkers. A luminary and highly influential war quant, Captain Hughes imbued his theories with a concrete, quantitative rigor that has contributed to the prestige and the staying power of his ideas. Captain Hughes began his career as a practitioner, spending over 30 years on active duty in the United States Navy as a surface warfare officer before beginning a second career as a naval scholar, serving as a professor of Operations Research at the Naval Postgraduate School from 1980 until his passing in 2019. He is best known as the author of Fleet Tactics¹ and for his salvo equations, which describe naval combat in the age of missiles. Hughes’ rich research and deep understanding of modern naval conflict is masterfully distilled into his most often quoted phrase, “fire effectively first.”

Portrait of CAPT Wayne Hughes. Source: Naval Postgraduate School.

Captain Hughes’ work challenged some of the prevailing thought paradigms in the United States Navy and influenced recent US naval concepts like distributed maritime operations (DMO), littoral operations in contested environments (LOCE), and the Marine Corps’ Tentative Manual for Expeditionary Advanced Base Operations and A Concept for Stand-in Forces.

The Origin of the Hughes Salvo Equations

By his own account, CAPT Hughes began his work on salvo equations with a specific goal in mind. Like most Naval officers of the time, he was convinced that the future superiority of the US Navy required a blue water navy replete with capital ships. In his time working as an analyst at OPNAV N96, Hughes encountered proponents of a contrary idea: that the Navy should be more focused on building greater quantities of smaller ships. Captain Hughes intuitively believed that this was the wrong approach, and later undertook research at the Naval Postgraduate School to prove the superiority of a capital asset-heavy blue water navy over a larger force comprised of smaller, less capable warships. Hughes would ultimately culminate this line of inquiry with his creation of the salvo equations and in the process unexpectedly convince himself of the opposite position, upending the conventional wisdom of the day.²

“Numerical superiority is the force attribute that is consistently most advantageous.” -CAPT Wayne Hughes

Hughes’ research showed that the size and capability of a single ship was less important than the ability of a formation of ships to mass fires and (if necessary) withstand adversary fires. His equations demonstrate that capital ships may be vulnerable to asymmetric threats from adversaries that can mass fires from numerous distributed platforms, especially in littoral regions.³

Deconstructing the Salvo Equations

Captain Hughes’ salvo equations build upon the famous Lanchester equations that describe ground combat. However, Hughes noted a fundamental difference between modern naval and ground combat: naval missile combat is not characterized by continuous fire, as modeled in Lanchester equations. Rather, naval fires occur in pulses. Single missiles or small salvos often prove ineffective, since many adversaries can employ defensive measures to intercept incoming missiles. To overcome these countermeasures, attackers must mass sufficiently large salvos. In another departure from ground combat, when a missile strikes a ship, there is potentially a large, discrete change in combat power for the victim. The salvo equations accommodate these discrete changes, which differ from ground combat models where combat power changes are smaller and can be approximated by continuous functions.

The salvo equations for force A and force be B are given below:

The the variables and parameters of the model are defined as follows:

Implications of the Salvo Equation Model

Hughes used the basic model above to describe many possible circumstances. Notably, he demonstrated a number of outcomes where a force made up of seemingly inferior ships could damage or defeat a force of ships with comparably superior staying firepower and defenses. In such cases, the force of weaker ships can still mass a salvo of sufficient size to hold the superior force at risk, even if the superior force can destroy the weaker force many times over. If the weaker force can do sufficient damage to the stronger force and can do so affordably, it may achieve its objectives at a discount.

Hughes’ basic salvo model can also support a variety of additions and enhancements. For instance, warships no longer line up and exchange simultaneous salvos — rather, naval forces seek advantage by detecting the enemy and firing preemptively before the adversary can react. To accommodate this tactic, Hughes introduces parameters for the scouting abilities of each force. This parameter reinforces that a force of less capable ships can inflict great damage on, or indeed defeat, a force comprised of superior ships especially if scouting gives that force a first-strike advantage.

Hughes explored many other force combinations and many scholars and thinkers have extensively adapted the salvo equations to describe novel capabilities and theories. Indeed, Hughes’ work has been impactful enough that any work done on Naval concepts or force structure would be incomplete without viewing the proposed concept or ship design through the lens of the salvo equations.

For all the impact of his work, Hughes remained keenly aware of the critical distinction between theory and practice. He notes that there have always been variables in combat that escape foresight, planning, and theory: “If there were no variables in battle, we theorists could win the battles.”⁴

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The views and opinions expressed on War Quants are those of the authors and do not necessarily reflect the official policy or position of the United States Government, the Department of Defense, or any other agency or organization.

1. Three editions. First edition was printed in 1986. The Third Edition:
Fleet tactics and naval operations. By Wayne P. Hughes and Robert P. Girrier. Third edition. Annapolis, MD: Naval Institute Press. 2018

2. Story summarized from CAPT Wayne Hughes interview with Naval Post Graduate School’s Seapower Conversations.

3. A salvo model of warships in missile combat used to evaluate their staying power. By Wayne P. Hughes. Naval Research Logistics, 42: 267-289. https://doi.org/10.1002/1520-6750(199503)42:2<267::AID-NAV3220420209>3.0.CO;2-Y

4. Quote from interview with Naval Post Graduate School’s Seapower Conversations.