Physics Without Equations: Making Principles Executable

Why mathematical formulas don't improve execution, but physics principles translated into procedures do

The Paradox: You can read Jorgensen's The Physics of Golf, understand every equation, master the mathematical models—and still not improve your swing by a single stroke.

Meanwhile: Understanding torque, center of gravity, and kinematic constraints without any equations can directly improve your execution.

What's the difference? How physics principles are presented—as formulas to calculate, or as procedures to execute.

Two Ways to Present Physics

Physics is essential to understanding golf. Forces, torques, moments of inertia, angular momentum—these aren't optional concepts. They're the reality of how clubs and bodies move.

But there are two fundamentally different ways to present physics:

Approach 1: Physics as Mathematical Formulas

Example from academic texts:

τ = r × F
L = Iω
F_Magnus = ½ρv²AC_L

Golfer's question: "What do I do with this?"

Answer: Nothing. You can't calculate torque mid-swing.

Approach 2: Physics as Executable Principles

Same physics, different presentation:

Golfer's question: "What do I do with this?"

Answer: Follow the procedure. The physics is working for you.

The Critical Distinction

It's not physics vs. no physics. Tighter Golf is built entirely on physics principles:

Every procedure is grounded in physics. The difference is presentation:

Academic approach: Here's the physics equation → Calculate it → ??? → Execute

Tighter Golf approach: Here's the physics principle → Here's the procedure that implements it → Execute

Same physics. Different path to execution.

Why Formulas Don't Transfer to Execution

Example: Gravitational Torque

Academic presentation with formula:

τ_g = mgh sin(θ)

"Minimize gravitational torque by reducing the angle θ between the club's center of gravity vector and the shaft axis."

Golfer's reality: How do I measure θ? What's the CG height h? How do I calculate this while holding a club?

Tighter Golf's procedural translation:

"Let the club rest in your hands naturally—like balancing a broom. When it's balanced (zero twisting), the CG is aligned with the shaft. That's the torque-free position."

Same physics concept (gravitational torque). One requires calculation. The other requires feeling what you already know—balance.

The Physics is Identical

Both approaches describe the same physical reality: when the club's center of gravity is directly below the shaft axis, gravitational torque equals zero.

The formula tells you THAT this is true.
The procedure tells you HOW to achieve it.

For execution, HOW beats THAT every time.

Real Examples from Tighter Golf

Example 1: The Five-Bar Mechanism

Physics concept: The arms and shoulders form a closed kinematic chain—a spatial five-bar linkage with spherical shoulder joints and compound elbow joints. This mechanism has specific geometric properties and constraints.

With formulas (Jorgensen approach):
Derive position equations, velocity analysis, acceleration analysis using vector loop closure and Jacobian matrices.

Without formulas (Tighter Golf approach):
"When you grip the club with both hands, your arms form a connected system. This system naturally maintains its geometric relationships when you establish correct initial conditions at setup. The mechanism does the work—you just need to assemble it correctly."

Same physics. The mechanism's behavior is identical. But one approach tells you how to calculate the behavior. The other tells you how to establish the behavior.

Example 2: Line of Compression

Physics concept: During impact, the ball compresses against the clubface. The direction of this compression force determines the ball's spin axis. If the compression line is perpendicular to the clubface throughout impact, the spin axis is vertical and the ball flies straight.

With formulas (academic approach):
Impact force F(t), coefficient of restitution e, contact time Δt, spin rate ω = (v_tan × μ × t)/r

Without formulas (Tighter Golf approach):
"Maintain the original contact point between clubface and ball throughout the impact interval. The clubhead path and clubface must move together—no cutting across. When you do this, the compression stays perpendicular and the ball flies straight."

Same physics principle—normal force creates vertical spin. One describes it mathematically. The other tells you what to maintain during the swing.

Example 3: Clubhead Lag and Sweet Spot Plane

Physics concept: Centripetal force pulls the clubhead inward, causing it to lag behind the hands. This lag means the shaft plane and sweet spot plane are misaligned during the downswing. The club is designed with a "gravity angle" (hook face) to compensate—when the planes are misaligned due to lag, the face is actually square to the target.

With formulas (academic approach):
F_c = mω²r, angular momentum L = Iω, rotational kinetic energy analysis

Without formulas (Tighter Golf approach):
"The club is designed to lag. Don't fight this—work with it. Set up with the clubface on-plane (looks closed to target), and the lag during the downswing will naturally square it at impact. The club's design and physics are working together when you establish the correct initial conditions."

Same physics—centripetal force, clubhead lag, gravity angle compensation. One shows you the math. The other shows you how to set up so the physics works for you.

Why This Matters: The Cochran & Stobbs Problem

In The Search for the Perfect Swing, Cochran and Stobbs analyzed tour players with motion sensors and calculated forces and accelerations with impressive precision.

What They Provided:

What They Didn't Provide:

Result: You understand what happens in a good swing (the physics) but not how to make it happen (the procedures).

The Missing Bridge

Academic golf books describe the destination (correct physics) but don't provide directions (executable procedures).

Tighter Golf provides both: "Here's the physics principle, and here's exactly what you do to implement it."

The Translation Process

Every Tighter Golf procedure translates a physics principle into executable action:

Physics Principle: Center of Gravity Alignment

Mathematical statement: "The club's moment arm about any axis is minimized when the CG vector passes through that axis."

↓ Translation ↓

Executable procedure: "With both elbows lightly touching your torso (home position), let the club hang naturally. The butt end points at your spine, the clubhead points at the target. This is the balanced, CG-aligned reference position."

Physics Principle: Torque Balance

Mathematical statement: "The sum of all torques about the center of rotation must equal zero for uncompensated motion: Στ = 0"

↓ Translation ↓

Executable procedure: "Clear space between your trail elbow and hip before you swing (void procedure). This prevents collision-induced torque that would require compensation."

Physics Principle: Geometric Invariance

Mathematical statement: "A mechanism maintains constant geometry when coordinate transformations preserve relative positions of all links."

↓ Translation ↓

Executable procedure: "Set up the club's relationship to your body once (at address). As you shift weight from trail to lead, this relationship stays the same—like walking, where your arms maintain the same relationship to your body even as weight shifts from foot to foot."

Why Tighter Golf Uses Physics Extensively

Physics isn't optional—it's fundamental. Every procedure in Tighter Golf is grounded in physics:

Tighter Golf doesn't avoid physics—it translates physics into procedures.

The physics is why the procedures work. The procedures are how you implement the physics.

The Deliberate Design Choice

Tighter Golf could include equations for every procedure. The bibliography demonstrates engagement with physics literature. The mechanical sophistication proves understanding of the underlying mathematics.

But equations are deliberately excluded—not because they're wrong, but because they don't help execution.

Three Key Decisions:

1. Physics Principles: YES
Understanding why things work is essential. Every procedure is explained through physics principles.

2. Mathematical Formulas: NO
Calculating forces mid-swing is impossible. Formulas describe but don't guide action.

3. Executable Procedures: ESSENTIAL
Translate each physics principle into specific actions the golfer can perform.

Historical Precedent: Homer Kelley

Homer Kelley, author of The Golfing Machine, had an aerospace engineering background. He understood physics and mathematics deeply.

Yet TGM contains zero equations.

Not because Kelley didn't know the math—but because he understood that golfers need procedures, not formulas.

Kelley's approach: Identify the physics principle, then build the procedure around it. Components, imperatives, relationships—all rooted in physics, none requiring calculation.

Tighter Golf follows this model: Physics principles guide everything, but formulas don't appear because they don't aid execution.

For Technically-Minded Golfers

If you're reading this, you probably:

Tighter Golf is designed for you. It assumes you want to understand the physics—but it doesn't assume you want to calculate it.

The Technical Golfer's Question

Not: "What's the formula?"

But: "What's the principle, and how do I implement it?"

Tighter Golf answers the second question. Academic physics books answer the first.

What Transfer to Execution Requires

For knowledge to improve execution, it must be:

  1. Actionable: Tells you what to do, not just what exists
  2. Controllable: Focuses on what you can control (setup) not what you can't (mid-swing dynamics)
  3. Verifiable: You can feel/see when you've done it correctly
  4. Grounded: Based on physics principles that explain why it works

Mathematical formulas: Item 4 only
Tighter Golf procedures: All four items

The Bottom Line

Physics is essential to golf. Forces, torques, center of gravity, angular momentum—these aren't optional concepts. They're the reality of how clubs and bodies move.

But there's a crucial difference between:

Tighter Golf is built on physics principles—every single procedure implements a physics concept. The difference is presentation: instead of showing you the equation, we show you the action that implements the equation.

Same physics. Different path to execution.

The choice to present physics without formulas wasn't a simplification—it was a deliberate pedagogical decision to bridge the gap that academic books never cross: the gap between understanding what happens and knowing how to make it happen.

Physics principles guide everything. Mathematical formulas guide nothing. Procedures bridge the gap.

That's Tighter Golf: physics made executable.

Want physics-based procedures that actually transfer to execution? Explore Tighter Golf.