The Invisible Arc
At the heart of every pole vault is a curve.
Not the bend of the pole, nor the shape of the athlete’s body in flight, but the invisible path traced by the athlete’s center of mass (CoM). That path, at its simplest, is a parabola. At its most complex, it’s a differential equation.
The Myth of the Perfect Parabola
In physics, a parabola is the path followed by any object moving through the air under the influence of gravity alone. Throw a javelin, put a shot, or toss a discus — its flight path is a perfect arc: symmetrical and predictable.
But pole vaulters are not simply projectiles. Not at first.
Until the moment a vaulter releases the pole — or the pole finishes transferring its energy — they remain tethered to a complex, dynamic system of forces. The pole acts as both guide and engine, redirecting the horizontal speed of the run into vertical lift. As a result, the vaulter’s center of mass follows a far more chaotic trajectory before that final moment of release.
In reality, the vaulter’s flight is a composite motion: part mechanical propulsion from the pole, part human athleticism, part projectile. In essence, it’s a differential equation — a dynamic system with many inputs, where small changes can lead to massively different outcomes.
Forces in Play
Prior to release, the CoM is manipulated by a tightly interwoven set of variables — each one capable of shifting the shape and timing of the vault:
Approach speed – Determines available kinetic energy
Grip height – Influences leverage and pole bend depth
Pole stiffness – Dictates how much energy is stored and how quickly it’s returned
Pole drop timing and control – Affects balance and posture in final strides
Plant timing and location – Determines pole angle, depth, and recoil timing
Takeoff angle and last step mechanics – Shape the launch vector and affect vertical lift
Body posture, bottom arm action, and stretch reflex – Control efficiency of energy transfer into swing
Swing timing and trail leg engagement – Influence how and when the pole recoils
Inversion and turn mechanics – Govern vertical alignment and bar clearance trajectory
Wind conditions and environmental effects – Modify approach, plant, and pole drop
Standard placement – Alters where the vaulter peaks relative to the bar
Mental state, rhythm, and focus – Often overlooked, but critical for coordination and timing
Each of these variables is part of the system. Change one, and the outcome changes.
Add tension in the shoulders, and you block the swing. Go off balance at takeoff, and the launch vector flattens. Delay the turn, and you miss the window to finesse around the crossbar.
This stage is not parabolic. It’s dynamic, directional, and alive — more like a gymnast on a high bar, building momentum with each swing, shaping their body to add energy, and launching skyward into a release. The pole may store and return energy, but it’s your movement — the swing, the timing, the posture — that injects even more. Done right, you don’t just ride the recoil. You accelerate it.
The Moment of Transition
Once the vaulter disconnects from the pole—either physically or mechanically—the only force left acting is gravity. The athlete is now in pure projectile motion. From this point forward, the CoM will trace a true parabola, governed by the laws of physics:
Where:
Variables
v is the velocity at release (a result of approach speed and pole recoil
θ is the angle of release (launch vector)
g is gravity
This equation reveals something critical: mass cancels out. Whether you’re a 115-pound female or a 180-pound male, the shape of your parabola is determined not by your size, but by your speed and takeoff angle.
Shaping the Parabola
The true art of pole vaulting is shaping the final arc so that the center of mass crests just below the bar — not before it, not after. Everything the vaulter does up to the moment of release is designed to control that arc and time its peak more precisely.
More speed yields greater vertical potential — as long as it’s applied with the correct timing.
A higher grip gives you more potential height, but only if you can handle the extra bend in the pole.
A stiffer pole gives more back — but only if your technique holds up under pressure.
A dynamic, well-timed plant activates the stretch reflex, adding power and preserving momentum into takeoff.
A clean swing and powerful inversion harness the pole’s energy, converting recoil into lift and maximizing height.
Standard placement tunes the position of the bar relative to the peak of the parabola.
Every cue you’ve trained — counting steps, holding posture at takeoff, delaying the swing, finishing the turn — was never just a drill. Each one was a tool for shaping the parabola.
Pole vaulting isn’t about muscling over a bar. It’s about sculpting a trajectory.
And if you can master that — not just the pieces, but how they fit together — the bar will start to feel less like a barrier… and more like a checkpoint on a flight path you’ve already chosen.
Seeing the Invisible
When you watch elite vaulters, you’re not just seeing power or speed. You’re seeing artistry — the ability to shape a flight path with precision. Mondo Duplantis doesn’t just run fast or swing beautifully. He carves a parabola so perfectly that his chest crests just above the bar while his center of mass passes cleanly below it.
What sets him apart isn’t just his physical gifts — it’s his ability to adjust the equation in real time. His steps, his takeoff angle, the delay of his swing, the tempo of his turn — all of it is a response to the pole, the wind, the runway, even the placement of the standards. He’s solving a complex, dynamic system mid-air, shaping the parabola with every micro-adjustment. It’s not guesswork. It’s mastery.
For developing vaulters, that kind of precision takes time. Early in the journey, the CoM may peak too early, or too late. The bar is still cleared — sometimes through grit, sometimes through timing — but rarely with full control. And that’s okay. Learning to see and shape the invisible arc is what turns potential into consistency.
And consistency changes everything. When you can shape the parabola with purpose, you stop hoping for a good vault — and start creating one.
Final Thoughts
Pole vaulting is physics, no doubt. But it’s also poetry.
Every phase of the vault—run, plant, swing, invert, turn, and fly—is about bending forces to your will. Your job is to master them not separately, but as a system—one whose goal is to deliver you into that perfect arc.
So remember this: the bar is constant, but everything else — the approach, the plant, the swing, the timing, your focus — those are variables. And they’re in your control.
Master the shape of the arc, and you master the vault.
Sources:
Linthorne, N. P. (2000). Energy Loss in the Pole Vault Take-off and the Advantage of the Flexible Pole. Sports Engineering, 3(4), 205–218.
Schade, F., & Arampatzis, A. (2012). Biomechanical Analysis of the Pole Vault Jump of the World’s Best Athletes. Journal of Sports Sciences, 30(9), 899–906.
Coaches Insider. (2023). Pole Vaulting: Mechanical Goals and Technical Strategy.
Red Bull. The Technique Behind Mondo Duplantis’ Pole Vault World Record.
SimpliFaster (2019). Data‑Driven Coaching in the Pole Vault.