The Physics of the Rolling Putt
The stroke gives the ball speed and spin. The green changes their balance until the ball rolls without sliding. Then the surface drains energy while gravity bends the path. At the hole, position, speed and rim contact decide the result.
Spin Changes the First Part of the Putt
The five-sevenths result holds for an ideal sphere launched without spin on a level surface. It begins pure rolling at five-sevenths of launch speed. Forward spin needs a different adjustment. A ball spinning too fast can speed up while friction trims the extra spin. A fixed skid fraction is a conditional prediction, not a universal rule.
Green Speed Is a Calibration
A Stimpmeter reports a repeatable rollout distance. Turning that into a constant slowdown assumes a certain release and surface. Two greens can read the same yet treat a slow ball differently. A rolling ball also has rotational inertia, so it speeds up downhill less than a sliding point mass would.
The Hole Has Several Capture Mechanisms
A ball may drop in, circle the lip, or hit an edge and fall. A simple fall-time calculation covers one. It does not prove a universal maximum holing speed.
Scope and Intent
Putting is a compact example of the larger problem examined throughout this site: geometry, inertia, contact, energy and control must agree within one declared model. A stroke does not determine a putt through speed alone. It establishes a state, that state selects a contact regime, and the regime determines which equations apply. The same separation is needed when interpreting a golf swing: observing motion, reconstructing forces and recommending an intervention are different tasks.
This article develops a tractable model from ground contact to the hole. It derives the level-ground slide-to-roll transition, explains what a Stimpmeter calibration can identify, includes rotational inertia in slope response, and separates a free-fall capture criterion from a historical capture fit. The calculations are conditional predictions that can be checked against measured trajectories. They are not a certification of any particular simulator. Simulating the Green provides related numerical and stochastic context; software using different contact or calibration conventions needs its own validation.
Conventions and Inputs
For level-ground examples use a right-handed frame with \(x\) forward, \(y\) up and \(z\) right. Define scalar forward-rolling spin by \(\boldsymbol\omega=-\omega\mathbf e_z\) when translation is along \(+x\). Thus \(v=R\omega\) means pure forward roll. On a tilted plane, use its outward unit normal \(\mathbf n\) and tangent vectors rather than treating vertical and surface-normal directions as interchangeable.
Write the spherical inertia as \(I=\alpha mR^2\). Numerical examples use \(\alpha=0.4\), the uniform-solid-sphere idealization. Actual layered balls need a measured inertia; a conforming diameter and mass do not determine it. We use \(m=45.93\) g and \(R=21.335\) mm as representative limiting values from the official maximum mass and minimum diameter, not as exact properties of every ball. Examples take \(g=9.81\) m/s² and hole diameter \(D_h=4.25\) in \(=107.95\) mm.
1. Impact Sets Speed and Spin
A one-dimensional impact model helps organize the variables. Let \(V\) be the striker’s normal approach speed, \(e\) the normal restitution coefficient, and \(M_{\mathrm{eff}}\) its effective mass at the contact. For an initially stationary ball, isolated normal impact gives
\[ v_0=\frac{(1+e)V}{1+m/M_{\mathrm{eff}}}. \]
This follows by combining normal impulse–momentum with the restitution relation. Effective mass is the inverse of the striker’s contact mobility in the impulse direction; even a free rigid head includes rotational effects when contact is off its centre of mass. Shaft and hand coupling depend on their dynamic response during the collision. The fraction of an arm that participates cannot be inferred just from the slower tempo of the overall putting stroke. Restitution, effective mass and a single measured launch speed are also not independently identifiable from this equation.
The normal model does not predict spin. To see why a face can generate forward spin, consider a vertical face contacting the rear of the ball at \(\mathbf r=-R\mathbf e_x\). Let its impulse on the ball be \(J_n\mathbf e_x+J_t\mathbf e_y\). Ignoring ground impulse during this illustrative collision,
\[ v_x=\frac{J_n}{m},\qquad \omega=\frac{RJ_t}{I},\qquad \frac{R\omega}{v_x}=\frac{J_t/J_n}{\alpha}. \]
An upward tangential impulse produces positive forward spin. The available impulse depends on contact friction, relative tangential motion and compliance; this example does not promise a particular spin ratio. It does show why a blanket statement that putters cannot produce topspin is incorrect. Loft, attack angle, impact height, face motion and subsequent ground contact must be considered together. Launch angle need not equal face loft.
A hopping ball needs flight and landing phases before the ground model below begins. Therefore \(v_0\) and \(\omega_0\) in the skid calculation mean the state at the start of the modeled continuous ground contact, not automatically the state immediately after face separation. Marked-ball video can distinguish these states. Start direction likewise follows the full contact impulse: the face normal is important, but a universal face/path percentage or negligible spin effect does not follow merely from low impact speed. See Impact Mechanics and Ball Flight for that decomposition.
2. Sliding Into Pure Roll
2.1 Signed Slip and the Equations of Motion
Assume straight motion on a level plane, continuous contact, constant kinetic friction \(\mu_k\), spherical inertia, and negligible rolling resistance during the short sliding phase. These are stronger assumptions than “a ball on grass.” Define the signed contact slip and its initial sign by
\[ s=v-R\omega,\qquad s_0=v_0-R\omega_0,\qquad \sigma=\operatorname{sgn}(s_0). \]
For nonzero slip, the contact force opposes slip, which need not point in the direction of centre motion. With \(A=\mu_k g\),
\[ \dot v=-\sigma A,\qquad \dot\omega=\frac{\sigma A}{\alpha R},\qquad \dot s=-\sigma A\left(1+\frac1\alpha\right). \]
Under-spin (\(s_0>0\)) slows translation and increases forward spin. Over-spin (\(s_0<0\)) speeds translation and decreases forward spin. The contact still dissipates energy in both cases. When \(s_0=0\), this sliding phase has zero duration; static traction and rolling resistance govern the subsequent motion.
2.2 Transition Speed, Distance and Dissipation
Integrating until \(s=0\) gives
\[ t_* = \frac{\alpha|s_0|}{(1+\alpha)A},\qquad v_* = \frac{v_0+\alpha R\omega_0}{1+\alpha},\qquad \omega_* = \frac{v_*}{R}. \]
The signed displacement during that interval is
\[ d_{\mathrm{skid}}=v_0t_*-\frac12\sigma A t_*^2. \]
If extreme backspin reverses the centre motion, displacement and distance traveled are different. The forward-putt examples below do not enter that regime.
A useful independent check is \(mR\dot v+I\dot\omega=0\). The combination \(mRv+I\omega\) is constant under these level, straight-contact assumptions. It is the relevant transverse angular-momentum component about a fixed surface point on the track, with weight and normal force balancing. This is not conservation of the full angular-momentum vector about every possible point on the surface.
Energy provides another check. The frictional power on the ball is \(-\mu_kmg|s|\), so the mechanical energy lost before rolling is
\[ Q=\int_0^{t_*}\mu_kmg|s|\,dt =\frac{m\alpha}{2(1+\alpha)}s_0^2\ge0. \]
Translation can gain energy during over-spin because rotation supplies more energy than friction dissipates. This distinction between a component’s energy gain and total system dissipation is also essential in swing energy-transfer arguments.
For \(\omega_0=0\) and \(\alpha=2/5\), these expressions reduce to
\[ v_* = \frac57v_0,\qquad t_* = \frac{2v_0}{7\mu_kg},\qquad d_{\mathrm{skid}}=\frac{12v_0^2}{49\mu_kg}. \]
The five-sevenths factor is exact within this model and initial condition. It does not make launch spin irrelevant. For example, at fixed \(v_0\), an initial spin ratio \(R\omega_0/v_0=0.5\) gives \(v_*/v_0=6/7\); a ratio of \(1.5\) gives \(8/7\).
3. Rolling Resistance and Green Calibration
3.1 Why Rotational Inertia Still Matters
Pure rolling constrains contact velocity; it does not remove rotation from the dynamics. On a level plane let a resisting couple of magnitude \(\tau_r\) oppose forward rotation. Let \(F\) be the signed tangential contact force. Newton’s and Euler’s equations are
\[ m\dot v=F,\qquad I\dot\omega=-RF-\tau_r,\qquad \dot v=R\dot\omega. \]
Eliminating \(F\) gives
\[ \dot v=-\frac{\tau_r}{mR(1+\alpha)}=-a_0. \]
An equivalent forward displacement \(\ell\) of the normal resultant gives \(\tau_r=N\ell\). On level ground, \(a_0=g\ell/[R(1+\alpha)]\). Thus \(a_0/g\) is an effective deceleration coefficient; it is not \(\ell/R\). Using one symbol for both would lose the inertia factor later on a slope.
In ideal no-slip contact with a stationary rigid plane, static traction does no contact-point work. The effective resisting couple represents deformation and other losses omitted from that idealization. Its power is \(-\tau_r v/R\), consistent with differentiating the total rolling kinetic energy \(\tfrac12m(1+\alpha)v^2\). One should not add a second empirical drag term for the same measured loss without recalibrating the model.
3.2 The Stimpmeter: Geometry and Procedure
The USGA describes a 36-inch bar with a 145° V-shaped groove. Its instruction booklet specifies release at approximately 20°; the standard notch is approximately 30 inches from the lower end. The procedure uses repeated rolls in opposite directions on a suitably level patch. The USGA centenary account describes averaging three rolls each way. Use the actual instruction booklet for acceptance criteria and its alternative 2X notch procedure. A single arbitrary downhill rollout is not a standard stimp reading.
For a stationary, ideal groove of opening angle \(\gamma\), elementary cross-section geometry gives the effective rolling lever arm
\[ r_c=R\sin(\gamma/2). \]
With the USGA’s 145° groove, \(r_c/R=0.9537\), rather than 0.87. No-slip motion along the groove has \(v=r_c\omega\). A lossless release through height \(h\) would therefore satisfy
\[ mgh=\frac12mv^2+\frac12I\frac{v^2}{r_c^2},\qquad v=\sqrt{\frac{2gh}{1+\alpha(R/r_c)^2}}. \]
Using the approximate values \(h=0.762\sin20^\circ\) m and \(\alpha=0.4\) yields \(v=1.885\) m/s. This is an ideal ramp calculation, not a parameter-free derivation of an exact 1.83 m/s turf-entry speed. Notch geometry, the tip transition, losses and operator motion all affect the actual initial state. The USGA’s technique study specifically identifies release technique as a source of measurement variation.
The ideal groove spin ratio relative to flat-ground rolling is \(R/r_c=1.0485\). It suggests over-spin if that speed and spin survive transfer unchanged. The real ramp-to-turf transition must be measured or modeled before assigning it a definite rollout correction. An ideal energy balance on the ramp alone cannot determine that transition.
3.3 A Useful Conditional Conversion
Take \(v_s=1.83\) m/s as a nominal reference speed entering flat pure roll. This conventional value appears in Penner’s putting treatment; it is used here as a calibration assumption. If the surface is level and deceleration remains constant until rest, a stimp distance \(S\) in feet implies
\[ a_0=\frac{v_s^2}{2(0.3048S)} =\frac{5.4936}{S}\ \mathrm{m/s^2}. \]
| Nominal Stimp \(S\) | Distance (m) | \(a_0\) (m/s²) | \(a_0/g\) |
|---|---|---|---|
| 8 | 2.438 | 0.687 | 0.0700 |
| 10 | 3.048 | 0.549 | 0.0560 |
| 12 | 3.658 | 0.458 | 0.0467 |
These values characterize this constant-loss model. They do not directly measure kinetic sliding friction, nor guarantee identical behavior at every speed and direction. If release speed is uncertain, the first-order sensitivity is \(\delta a_0/a_0\simeq2\delta v_s/v_s-\delta S/S\). Error propagation should include correlations when the same procedure affects both measurements.
3.4 One Distance Cannot Identify a Whole Resistance Law
For positive speed-dependent deceleration \(a(v)\) on a level surface, \(v\,dv/dx=-a(v)\) gives
\[ D(v_s)=\int_0^{v_s}\frac{v}{a(v)}\,dv. \]
One rollout provides one integral constraint. For a concrete counterexample, compare constant \(a_0\) with a second law having \(a(v)=2a_0\) below \(v_s/2\) and \(a(v)=6a_0/7\) above it. Integration gives the same total distance \(v_s^2/(2a_0)\) for both. Yet from \(v_s/2\) the second surface produces half the constant model’s rollout. Equal stimp therefore does not uniquely identify lower-speed behavior, even before grain, moisture, direction and spatial variation enter.
This also explains why fitting the same rollout used for calibration is not independent validation. Measure speed versus position at several initial speeds, in both directions, to test the assumed loss law. Separately observe initial spin and any hop when estimating sliding friction.
4. Worked Example: Three Metres to Rest
Consider a level, straight putt with continuous ground contact, \(\alpha=0.4\), \(\omega_0=0\) and \(\mu_k=0.4\). Set \(d_{\mathrm{skid}}+d_{\mathrm{roll}}=3\) m using the nominal calibration above. These are rest-distance calculations, not a claim that stopping exactly at a hole’s edge ensures capture.
| Quantity | Stimp 8 | Stimp 10 | Stimp 12 |
|---|---|---|---|
| Ground-contact speed \(v_0\) (m/s) | 2.629 | 2.386 | 2.200 |
| Sliding duration \(t_*\) (ms) | 191 | 174 | 160 |
| Sliding distance (cm) | 43.2 | 35.5 | 30.2 |
| Speed entering roll \(v_*\) (m/s) | 1.878 | 1.705 | 1.572 |
| Sliding share of total distance | 14.4% | 11.8% | 10.1% |
| Total travel time (s) | 2.927 | 3.277 | 3.593 |
Less resistance requires less initial speed for a fixed stopping distance, yet increases travel time. That longer exposure matters on a slope. The delivery still influences the later trajectory through the state it established: reaching pure roll does not erase initial speed, direction or the earlier displacement. A claim that the putter can no longer influence anything observed after the skid would confuse absence of ongoing contact with absence of causal influence.
5. Slope: Translation and Rotation Together
5.1 A Consistent Moving-Ball Model
Let the surface tilt by \(\beta\), with unit downhill vector \(\hat{\mathbf d}\). Gravity projected into the plane is \(\mathbf g_\parallel=g\sin\beta\,\hat{\mathbf d}\). Assume a plane, sufficient static traction for pure rolling, an isotropic resisting couple opposite the rolling component of spin, and resistance proportional to normal load. The latter choice means
\[ \tau_r=m(1+\alpha)R a_0\cos\beta. \]
For straight downhill motion the separate balances are \(m\dot v=mg\sin\beta+F\) and \(I\dot\omega=-RF-\tau_r\). Eliminating the contact force while enforcing \(\dot v=R\dot\omega\) gives the planar vector equation for nonzero velocity:
\[ \boxed{\dot{\mathbf v} =\frac{\mathbf g_\parallel}{1+\alpha} -a_0\cos\beta\,\frac{\mathbf v}{\|\mathbf v\|}.} \]
The factor \(1/(1+\alpha)\) is \(5/7\) for the ideal sphere. Even without rolling resistance, static traction is needed to accelerate rotation. Simply adding \(\mathbf g_\parallel\) to an already calibrated level deceleration would treat the slope contribution as though the ball had no rotational inertia.
This contact solution must also satisfy a static-friction capacity condition. For example, straight motion requires \(F=m\dot v-mg\sin\beta\) and \(|F|\le\mu_smg\cos\beta\). If it fails, a sliding model is needed. No-slip kinematics alone cannot supply unlimited traction.
5.2 Uphill, Downhill and the Moving Threshold
Define \(a=a_0\cos\beta\) and \(s=g\sin\beta/(1+\alpha)\). For a ball already rolling uphill, deceleration is \(a+s\); for downhill motion it is \(a-s\). Over distance \(D\) with specified arrival speed \(v_f\),
\[ v_i^2=v_f^2+2(a\pm s)D, \]
where \(+\) is uphill and \(-\) is downhill. These are rolling-phase speeds, not uncorrected putter launch speeds. A downhill ball slows only when \(a>s\). With the normal-load scaling above, equality occurs at
\[ \tan\beta_{\mathrm{crit}}=\frac{(1+\alpha)a_0}{g}. \]
The nominal critical grades are 9.80%, 7.84% and 6.53% for stimp 8, 10 and 12. At 5% downhill on the nominal stimp-12 surface, the model still predicts deceleration of about 0.107 m/s². Calling that putt intrinsically unstoppable would be wrong under these assumptions.
At equality an already rolling ball maintains speed; above it the downhill speed grows. Neither statement establishes when a resting ball starts moving. Rest requires a static resistance law, and real turf may have different initiation and motion thresholds. These model values are not course-design standards or universal safe hole-location grades.
5.3 Break Includes Lateral Resistance at First Order
For a small cross-slope perturbation, take \(x\) along the initial rolling direction and \(z\) downhill. Write the initial rolling speed as \(v_i\) and the unperturbed forward speed as \(u(t)=v_i-at>0\). If \(w=\dot z\) is small compared with \(u\), linearizing the vector equation gives
\[ \dot w+\frac{a}{u(t)}w=s,\qquad w(0)=0. \]
Lateral resistance is proportional to the first-order lateral velocity. It is therefore part of the first-order calculation, not a higher-order correction that can be discarded. Solving the equation and integrating once more yields
\[ w(t)=\frac{s}{a}u\log\frac{v_i}{u}, \]
\[ z(t)=\frac{s}{a^2}\left[ \frac{v_i^2-u^2}{4}-\frac{u^2}{2}\log\frac{v_i}{u} \right]. \]
As a modest-deflection illustration, use \(v_i=2\) m/s, \(a=0.55\) m/s², \(s=0.0701\) m/s² and \(t=2\) s. These approximate a 1% cross-slope with \(\alpha=0.4\). Then \(u=0.9\) m/s, \(x\simeq2.9\) m and \(z\simeq0.110\) m. Ignoring lateral resistance would give \(st^2/2\simeq0.140\) m; ignoring rotational inertia as well would overstate it further. Numerical integration of the full vector equation tests the perturbation rather than assuming it remains accurate at larger slopes.
The formal limit \(u\to0\) gives \(z\to s v_i^2/(4a^2)\), but \(w/u=(s/a)\log(v_i/u)\) grows without bound. The small-direction-change assumption thus fails near a dying putt’s endpoint. The limiting expression is not an exact aiming rule or a universal bound. Resolve the curved trajectory and its stopping regime numerically when finite-slope accuracy matters.
For a chosen target, aiming angle and arrival speed must be solved together. Adding pace generally changes both time on the slope and the capture window. Comparing greens without specifying whether launch speed, stopping distance or arrival speed is held fixed can hide that dependence.
6. Hole Capture: Geometry and Contact
6.1 A Finite-Ball Free-Fall Criterion
Consider a horizontal approach to an ideal level circular hole, with no flagstick. In a simplified unsupported-flight construction, the ball’s centre drops by \(R\) in time \(t_R=\sqrt{2R/g}\). The forward distance from loss of near-edge support to the far-side position at which a finite ball’s centre can reach lip height is \(D_h-R\), not the full hole diameter. The resulting central free-fall criterion is
\[ v_{\mathrm{ff}}=(D_h-R)\sqrt{\frac{g}{2R}} \simeq1.313\ \mathrm{m/s}. \]
Penner (2002), Section 3 presents this criterion and an off-centre extension, attributing the underlying capture analysis to Holmes. The original Holmes paper is not the direct source used here. The same section distinguishes free fall from lip-rolling and rebound capture. Failing the free-fall criterion therefore does not establish that capture is impossible.
For offset \(b\) and hole radius \(R_h=D_h/2\), that construction gives
\[ v_{\mathrm{ff}}(b)=\left[ \sqrt{R_h^2-b^2}+\sqrt{(R_h-R)^2-b^2} \right]\sqrt{\frac{g}{2R}}, \]
with \(|b|<R_h-R\). Outside this domain the assumed sequence of unsupported flight before far-edge interaction no longer applies. A point-particle chord calculation misses both the finite-ball clearance and this restriction.
6.2 A Historical Fit Has a Different Meaning
Penner’s Equation 23 approximates a broader level-hole capture region by
\[ v_c(b)=1.63\left[1-\left(\frac{b}{R_h}\right)^2\right]\ \mathrm{m/s}. \]
The 1.63 m/s central value includes modeled lip interactions. It is a historical model result, not a dimensional consequence of the hole diameter. Inverting this particular fit for \(0\le v\le1.63\) m/s gives \(b_{\max}=R_h\sqrt{1-v/1.63}\):
| Arrival Speed (m/s) | Full Width \(2b_{\max}\) (mm) | Status |
|---|---|---|
| 0.5 | 89.9 | Prediction of the stated fit |
| 1.0 | 67.1 | Prediction of the stated fit |
| 1.5 | 30.5 | Prediction of the stated fit |
The table is not a measured make probability. A real hole’s rim compliance, slope, spin state, edge condition and any flagstick interaction may change capture. Direct capture experiments are needed to qualify a model for those conditions. Extrapolating either the free-fall formula or this fit into a universal “hard speed ceiling” would conceal those missing mechanisms.
The useful connection to putting strategy survives these qualifications: arrival speed affects the set of offsets that can be captured. An optimal pace additionally depends on the player’s joint distribution of direction and speed errors, the surface variation and the cost of the next putt. No fixed distance past the hole follows as a universal optimum from mechanics alone.
7. Assembling the Model Without Mixing Regimes
For arbitrary planar sliding, retain vector spin. With outward normal \(\mathbf n\), the ball’s contact point is at \(-R\mathbf n\) relative to its centre, and its tangent slip is
\[ \mathbf s=\mathbf v-R\boldsymbol\omega\times\mathbf n. \]
For nonzero slip on a fixed plane, an ideal Coulomb model is
\[ \mathbf F_t=-\mu_kN\frac{\mathbf s}{\|\mathbf s\|},\qquad m\dot{\mathbf v}=m\mathbf g_\parallel+\mathbf F_t, \]
\[ I\dot{\boldsymbol\omega}=(-R\mathbf n)\times\mathbf F_t, \qquad N=mg\cos\beta. \]
Here the rolling couple is neglected during sliding, consistently with Section 2. Retaining it requires adding its torque and recalculating the transition. Scalar spin-up at a fixed sign is insufficient when slip changes direction. At pure roll, the tangent spin is \(\boldsymbol\omega_t=\mathbf n\times\mathbf v/R\); spin about \(\mathbf n\) is an additional component whose torsional resistance is absent from this point-contact model.
A practical state sequence is:
- Delivery and any flight: determine measured position, velocity and spin at continuous ground contact. Include landing impulses if needed.
- Sliding: integrate the contact balances while slip is nonzero. Detect the transition rather than stepping indefinitely through a friction sign discontinuity.
- Rolling: enforce no slip only while the required traction is feasible. Use the inertia-corrected slope equation and a calibrated resistance model.
- Rest or renewed motion: handle zero speed with an explicit static model. The direction \(\mathbf v/\|\mathbf v\|\) is undefined at rest. A numerical epsilon is a regularization, not experimental evidence for stopping behavior.
- Hole interaction: detect the approach state and apply a declared capture model, or resolve rim contacts. Do not replace the finite ball with a point chord without labeling that approximation.
One possible numerical rest convention is to allow a bounded effective resistance acceleration of magnitude \(a\) to balance the rolling gravity term when \(s\le a\). That closes the idealized rolling inclusion at rest, but assumes the static threshold equals the moving resistance. Treat it as a model choice until measured. A curved or spatially varying green additionally requires evolving tangent geometry and an appropriate normal-load calculation; the fixed-plane equations cannot be transplanted unchanged onto arbitrary terrain.
8. Assumptions and Validation
| Quantity or Mechanism | Choice Here | What Must Be Established for Prediction |
|---|---|---|
| Ball inertia | \(\alpha=0.4\) | Inertia of the tested ball |
| Ground-entry state | Measured or prescribed \(\mathbf v_0,\boldsymbol\omega_0\) | Launch, hops and landing state |
| Sliding resistance | Constant \(\mu_k=0.4\) in examples | Slip-dependent behavior on the tested turf |
| Rolling resistance | Constant level \(a_0\); normal-load scaling on slopes | Speed, direction, load and spatial dependence |
| Stimp conversion | Nominal \(v_s=1.83\) m/s already in roll | Actual release and transition repeatability |
| Pure roll | Ideal point contact with sufficient traction | Slip and static-friction capacity |
| Capture | Ideal free fall or explicitly identified historical fit | Rim, slope, spin and flagstick conditions |
The strongest tests separate these assumptions rather than fitting all of them to one final distance:
- Transition mechanics: measure translation and marked-ball spin through sliding. Compare \(v_*\) and dissipated energy with the general initial-spin formulas; test the zero-spin special case only when zero spin has been established.
- Loss law: calibrate on one release condition and predict trajectories at other speeds and directions. Equal-stimp greens with different putter rollouts do not by themselves isolate rolling-law error unless ground-entry spin, hopping and sliding have also been controlled.
- Slope response: compare measured acceleration with independently calibrated resistance, inertia and slope. Check whether static traction is sufficient and whether normal-load scaling remains appropriate.
- Break: compare full position and velocity histories, not just endpoint offset. Use the small-slope solution away from stopping as a numerical check; assess finite-slope error separately.
- Capture: vary arrival speed, offset and spin while recording rim interactions. A capture above a free-fall threshold rejects the claim of a universal threshold, not mechanics or the existence of other capture modes.
These distinctions make the model useful for investigating the swing as well as the putt. A motion can be consistent with several force histories; a calibrated parameter can absorb an omitted mechanism; and a successful outcome can occur through more than one physical route. Technical rigor comes from testing which explanation survives additional observations, while preserving the couplings that make the movement work.
References
- A. Raymond Penner. “The Physics of Putting.” Canadian Journal of Physics 80(2), 83–96 (2002), DOI: 10.1139/p01-137. Accessible manuscript, especially Sections 2–3. Used for the nominal calibration convention and explicitly attributed capture models; the balances and worked checks above are derived independently.
- USGA and R&A. Equipment Rules, Part 4: weight and size.
- USGA. Stimpmeter Instruction Booklet; instrument geometry; release-technique effects.
Citation
@online{olson2026,
author = {Olson, Dieter},
title = {The {Physics} of the {Rolling} {Putt}},
date = {2026-08-04},
url = {https://affinedrift.com/articles/putting-roll-models.html},
langid = {en}
}