The Equations of Combat
“To understand the Universe, you must understand the language in which it’s written, the language of Mathematics.” — Galileo
Mathematics is the language of nature, and fighting is a part of nature.
Just like physics describes natural phenomena in science, the same logic can describe interactions in hand-to-hand combat.
Encapsulated in this article are the field equations used to derive the principles and concepts for the strategic engagement of force.
Understanding these ideas is the key to commanding strategic and tactical advantage in martial arts.
Drawing on a developed sense of rationality, the clever man can develop, rearrange, and expand these formulas to extract the patterns of conflict.
The maximum value of these field equations is harnessed when kept within the proper perspective. Von Clausewitz says it best:
“these principles and rules are intended to provide the thinking man with a frame of reference for the movement he has been training to carry out, rather than to serve as a guide which in the moment of action lays down precisely the path he must take”
~ Carl von Clausewitz
In combat, there are three constants of success.
These are encapsulated by The Three C’s mnemonic: cunning, calculation, and commitment. The equations here are focused on the calculation portion.
For more detail, diagrams, and explanation on these field equations, please see Scott Gehring’s Strategic Engagement of Force.
The Components of Force
Physical Force = Movement + Firepower
Holistic Force = Movement + Firepower + Communication
Force Control = Speed + Direction + Essence
The 2 Kinds of Force = Contact + Field
Force per Tool = Distance / Time²
FMC² = (Movement + Firepower + Communication) ^Mass Attack
Energy
Combative State = Positioning + Attacking
Biomechanical Energy = Limb + Body
The 2 Types of Energy = Potential + Kinetic
The Behaviors of Force
Movement = Standup + Ground
Firepower = Weapons + Empty Hand
Communication = Verbal + Non-Verbal
Expressions of Force
Expression of Firepower = Tools + Path of Action + Target
Expression of Movement = Setpoint A + Transition + Setpoint B
Expression of Communication = Transmitter + Signal + Receiver
Classes of Force
Maneuver = Body + Foot
Transition = Position + Maneuver + Attributes
Standup = Setpoint A + (Position + Foot Maneuver + Attributes) + Setpoint B
Ground = Setpoint A + (Position + Body Maneuver + Attributes) + Setpoint B
Empty Hands = Grappling + Striking
Weapons = Impact + Edged + Flexible + Projectile
Verbal Communication = Linguistic + Non-Linguistic
The 7 Bases = Standup + Ground + Empty Hands + Weapons + Verbal + Non-Verbal + Mass Attacks
Paths of Action
POA = Path of Action
Path of Action = Technique + Position + Attributes
Multi-Dimensional Pathway = Centerline + Outer Rim + Path of Action
Position
Position = Distance + Angle + Aim + Balance + State
State = Physical + Mental
Opposing Force Alignment = Aim + Angle
Horizontal Force Alignment = Neutral + Angular + Net
Vertical Force Alignment = Neutral + Downward + Upward
Flow = Beats + Rhythm + Tempo + Timing + Harmony
4D Positioning = Position + Flow
Navigation = Horizontal + Vertical + Angular
Horizontal Navigation = Penetration + Clearing + Lateral
Technique
Technique = Body Mechanics + Economy of Motion + Forecasting
Technique Development = Learn + Practice + Functionalize + Master + Maintain
Attributes
Attribute Classes = Environmental + Locational + Individual
Environmental Attribute Class = Political + Topical + Social
Individual Attribute Class = Moral + Physical + Mental + Perceptual
Locational Attribute Class = Vector + Position + Flow
The 3 Mindsets = Rational + Emotional + Survival
Performance = Positive Attributes + (Negative Attributes)
Individual Physical Attributes
Power = Marriage of Gravity + Momentum + Torque + Speed
Pure Speed = Distance/Time
Holistic Speed = Metal + Physical + Perceptual
Physical Speed = Initial + Penetration + Transition + Retraction + Reaction
Penetration Speed = Distance + Velocity + Acceleration
Transition Speed = Change in Speed (Direct) + Change in Direction (Indirect) + Change in Essence (Indirect)
Tools
Tools = Range * Distance
Range Empty Hand (Parker) = Out of Contact + In Contact + Contact Penetration + Contact Manipulation
Range Empty Hand (Lee) = Kicking + Punching + Trapping + Grappling
Range Empty Hand (Parker-Lee Unified) = Out of Contact + Kicking + Punching + Trapping + Grappling
Range Ground (Hall) = Foot + Knee\Palm + Elbow + Shoulder
Range Stand up (the Five Shuffle Method) = Shuffle 0 + Shuffle 1 + Shuffle 2 + Shuffle 3 + Shuffle 4 + Shuffle 5
Range Weapons (Inosanto) = Largo Mono + Sumbrada + Hubud
Mass Attack Ranges = Swarm + Spread + Eclipse
Shuffles = Distance Unit of Measure
Beats = Time Unit of Measure
Motion
Motion = Method + Path + Direction + Dimension + Flow + Measure of Degree
Method = Circular + Linear
Path = Vertical + Horizontal + Angular
Direction = Front + Back + Left + Right Side + Up + Down
Dimensions = Height + Width + Depth + Time
Flow = Beats + Rhythm + Tempo + Timing + Harmony
Depth = Distance = Time
Targets
Targets = Zones * Dimensions
Height Zones = High + Mid + Low
Width Zones = Left outer + Left Inner + Right Inner + Right Outer
Depth Zones = Lead Wrist + Lead Elbow + Lead Shoulder + Lead Neck + Rear Neck + Rear Shoulder + Rear Ankle
Time Zones = Before + During + After
Pivot Points
The 5 Primary Pivot Points = Neck + Left Shoulder + Right Shoulder + Left Hip + Right Hip
Secondary = Left Elbow + Right Elbow + Left Wrist + Right Wrist + Left Ankle + Right Ankle + Left Knee + Right Knee + Lower Back
Frame Angulations = Left Forward + Right Forward + Flush
Arm Angulations = Bracing + 90-Degree + Spiking + Downward
Lines and Curves
Critical Distance = In Range of Firepower + Hostile Intent
Key Objective Line = Traverse + Hit + Cross
Centerline = Axis Rotation + High Reference + Low Reference
Functions for Centerline = Guidance + Measurement + Targeting + Unification
The Curve of Attack = Penetration + Point of Pressure + Clearing
The 3 Most Important Lines = Critical Distance Line + Centerline + Key Objective Line
Lines = Efficiency
Curves = Deception
Tactics
Tactical Approaches = Phase Centric + Field Centric + Combination Phase Field
Phases = Approach + Delivery + Close
The Approach = Positioning + Entry
The Delivery = Pressure + Objective
The Close = Clearing + Positioning
Tactical Paths of Action = Analysis + Preparation + Leadoff + Counter + Pressure + Blitz + Control + Damage + Fire + Move
EPOC = Entry + Pressure + Objective + Clear
Fields of Engagement
Fields of Engagement = Accordial Fields + Lateral Fields + Vertical Fields
Accordial Fields = Measure + Attack + Flank
Lateral Fields = Inside + Outside + On-Center
Vertical Fields = Standup to Standup + Ground to Ground + Ground to Standup + Standup to Ground
The Field of Positioning
Positioning = Vector 0
Vector 0 = Analysis + Preparation
States of Positioning = Structure + Lead Time
Structure = Engaged + Not Engaged
Lead Time = Scheduled + Not Scheduled
The 3 Force Engagement Patterns = Assault + Quickdraw + Sparring
Sparring = Engaged + Scheduled
Assault = Not Engaged + Not Scheduled
Quickdraw = Ambiguous Engagement + Ambiguous Scheduling
Setups = Repel + Redirect + Absorb
The 3 Where’s = Where are their hands? + Where are their friends? + Where is the exit?
The Field of Attack
The Attack = Entry + Pressure + Objective + Clear
Attack Types = Simple + Compound + Renewed + Counter
The 3 Types of Weapons Engagements = Weapons Fight + Weapons Attack + Weapons Threat
Vectors
Vectors of Attack = Entry + Pressure + Objective + Clear
The Vector Attack Chain = Vector 1 + Vector 2 + Vector 3 + Vector 4
Entry = Vector 1
Pressure = Vector 2
Objective = Vector 3
Clear = Vector 4
Vector 1 = Leadoff + Counter
Vector 2 = Blitz + Zone
Vector 2 = Objective + Control
Vector 4 = Movement + Firepower
Leadoff = Direct + Indirect + Immobilization + Combination + Independent motion + Broken Rhythm
Counter = Intercept + Destroy + Riposte
Defensive Hit Timing = Before + During + After
Defensive Footwork = Running + Holding + Jamming
Riposte = After Hit Timing + Running Footwork
Destroy = During Hit Timing + Holding Footwork
Intercept = Before Hit Timing + Jamming Footwork
The Four Pressure Patterns Movement = Blitz + Zone + Hit and Run + Stalk
Blitz = Rolling + Repeating + Figure 8 + Fanning + Expansion-Contraction + Synchronous + Spinning
Zone = Vertical + Lateral + Angular
The Time-Distance Theater
TD-theater = Distance / Time
Time = Flow + Phases + Beats
Distance = Position + Fields + Shuffles
Force per Tool = Distance / Time²
Beats = Base Unit of Measure for Time
Shuffles = Base Unit of Measure of Distance
The Hierarchy of Decisiveness
The Hierarchy of Decisiveness = Objective + Strategy + Plans + Tactics + Vectors + Paths of Actions + Targets + Tools
The Decisiveness Six = Objective + Strategy + Plans + Tactics + Vectors + Paths of Actions
The 3 Constants of Combat = Cunning + Calculation + Commitment
Tools = Range * Distance
Targets = Zones * Dimensions
Paths of Action = Position + Attributes + Technique
Strategy
The 3 Ways of Loss = Wreck + Will + Wind
OAD = Objects of Neutralization + Advantage + Deception
Objects of Neutralization = Person + Place + Thing
The 6 Advantage States = Strong + Neutral + Vulnerable + Weak + Ambiguous + Desperate
The 6 Deceptions = Disguise + Distraction + Sleight of Hand + Lure + Razzle Dazzle + Game Change
The 3 Types of Conflict = Moral + Attrition + Maneuver
OAD Triangle Principles = Attributes + The 3 Where’s + Set Point Control
OAD Person = Physical + Metal + Moral + Perceptual
OAD Place = Vector + Position + Flow
OAD Things = Friends + Hands + Exit
SEF Trinity = FMC² + EPOC + OAD
OODA Loop = Observe + Orient + Decide +Act
The Strategic Questions = Who? + What? + Where? + Why? + How? + What? + When? + How Much?
About Scott Gehring
Scott Gehring is a Senior Combat Instructor in the Art Contemporary of Jeet Kune Do, a 5th Degree Blackbelt in Kenpo Karate, and an expert in multiple mixed martial arts.
Check out the following resources to learn more about Scott:
About — Scott Gehring — Medium
They Get Their Kicks — YouTube
TheyGetTheirKicks (@GetTheirKicks) / X (twitter.com)
Strategic Engagement of Force (@force_strategic) / X (twitter.com)
