Improving Punching "Power": Reconsidering the roles of initial strike velocity and effective mass

Joseph L. Natale

REVIEW 2 major objections 5 minor 71 references

Improving Punching "Power": Reconsidering the roles of initial strike velocity and effective mass

T0 review · 2 major / 5 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read Raising the effective mass of a punch can increase the target's post-impact velocity as much as or more than raising punch speed, within realistic combat ranges.

desk verdict Sound textbook math, honest about its own limits, but the practical punchline depends on an untested training assumption that the paper itself flags. read the letter →

arxiv 2607.18276 v1 pith:ZMEM25QU submitted 2026-06-25 physics.pop-ph physics.data-anphysics.med-phphysics.soc-ph

Joseph L. Natale This is my paper · ORCID

classification physics.pop-phphysics.data-anphysics.med-phphysics.soc-ph

keywords effectivemasspunchingpowerelasticcollisiontargetvelocitycombatsportsstrikespeedkineticenergytransferbiomechanics

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that the post-collision speed of a stationary target in a one-dimensional elastic collision depends on both the strike's speed and its effective mass, but real fighters occupy a narrow speed band of roughly 6–10 m/s. Because speed improvements saturate around a factor of 1.67, while effective mass could plausibly be multiplied by 2–5 through technique or training, mass gains can rival or exceed speed gains in driving target velocity. The paper further shows that, within combat-relevant mass ranges, increasing effective mass can increase the target's kinetic energy by an order of magnitude, comparable to the entire achievable speed-driven increase despite K ∝ v². If correct, this would shift training emphasis from hand speed toward mass recruitment and make effective mass a central quantity for assessing strike efficacy.

What carries the argument

The load-bearing object is the classical elastic collision solution for two point masses: Vf = [2m/(m+M)]v, often written with mass ratio u = m/M, together with the fold-change formula k = c(u+1)/(cu+1) for a c-fold increase in effective mass. This identity separates the linear, unbounded-in-principle influence of speed v from the saturating, ratio-dependent influence of mass m. The paper then imposes realistic dynamical bounds (v ≈ 6–10 m/s, m from roughly 5 kg to 20–60 kg, M ≈ 60 kg) to argue that within the occupied region of parameter space, mass can match or exceed speed as a lever on target velocity and energy.

What would settle it

Measure effective mass and punch speed of a cohort before and after a training intervention aimed at mass recruitment. If the maximum c achieved is ≤ 1.5 while speed can still be improved by up to 1.67-fold, then the claim that mass can rival speed collapses for practical training; likewise, if instrumented targets never show target-velocity fold increases above 1.5 for any recorded technique, the regime the paper relies on would be empirically absent.

Watch

Extended reading notes

Core claim

The central claim is that the post-collision speed of a stationary target, Vf = [2m/(m+M)]v, responds linearly to strike speed v, but the realizable range of v is narrow (roughly 6–10 m/s), capping the maximum speed-driven gain at about 1.67-fold. By contrast, the effective striking mass m, though loosely defined and hard to measure, may be trainable from a roughly 5 kg baseline to several-fold multiples (c ∈ [2,5)). Within intermediate mass ratios u = m/M, this yields fold-increases k = c(u+1)/(cu+1) in Vf that rival or exceed the speed-driven gain. Numerical evaluation for a 60 kg target and m from 5 to 20 kg at fixed speeds 6–10 m/s shows target kinetic energy increasing by an order of ma

Load-bearing premise

The central practical premise is that a fighter can raise effective mass by a factor of at least 1.75, and perhaps 2–5, through training or technique; the paper provides no data or mechanical mechanism for this, only a hypothesis deferred to future work.

Editorial extensions

If this is right

If a fighter can raise effective mass from about 5 kg to 10–20 kg (c = 2–4), the post-impact target speed gain matches or exceeds the maximum realistic speed gain of about 1.67-fold at speeds of 6–10 m/s.
For a roughly 60 kg target, increasing m from 5 to 20 kg at fixed v raises the target's post-collision kinetic energy by roughly an order of magnitude, comparable to the entire achievable speed-driven range.
Real strike speeds have a bounded improvement ceiling of about b = 1.67, so any training that achieves c ≥ 1.75 gives at least the same target velocity as the maximum usable speed increase.
A coach can use the presence of strong whiplash motion of the target, rather than quantitative velocity data, as a practical indicator that the incoming effective mass is comparable to the target mass.
For head-like small targets (roughly 5 kg), strikes can exceed concussion-level accelerations even at speeds below the median measured punch speed, provided contact times are about 10 ms or less.
Even within an elastic model, the limiting bounds on speed and mass show that the effective striking mass matters as much as, or more than, strike velocity for determining target acceleration and injury risk in realistic combat.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the central claim is right, the most direct testable extension is a training study: one group trained to maximize effective-mass recruitment, another to maximize hand speed, with target velocity measured on an instrumented target. The model predicts mass-trained fighters would match or beat speed-trained fighters in target velocity.
The paper's logic implies that current effective-mass estimates near 5–10% of bodyweight may be measuring the wrong thing; if c ≥ 2 is achievable through technique, standardized protocols for measuring effective mass would become as important as speed measurement for assessing strike quality.
A cross-weight-class implication left implicit by the author is that because k saturates when m ≫ M, heavier effective masses confer diminishing returns in target velocity, so the biggest payoff is for fighters whose current masses sit near the low end (about 5 kg) rather than those already near 20 kg.
The same collision identity could be repurposed for protective-equipment design: materials that selectively absorb energy to reduce target velocity would weaken the mass leverage identified here, meaning padding research should report effective-mass ratios, not just peak forces.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague — here's my read of arXiv:2607.18276. The one thing you should know: the math is all textbook (Eqs. 3–8 are standard 1D elastic collision results), and what's new is the contextual scaling argument. Over the range of realistic combat parameters (m≈5 kg, M≈60 kg, v≈6–10 m/s), the paper shows that a fold increase in effective mass c can produce target-velocity gains comparable to or larger than the maximum practical speed gain of b≈1.67. That is a genuine and useful reminder: because u=m/M is small, Vf ≈ 2u v, so the mass ratio enters linearly, while v is bounded by physiology.

The paper does several things well. It correctly identifies that v factors out of the post-collision target velocity and that the mass ratio u is the real control parameter. It gives a clean derivation of the fold-change relation k=(u+1)/(u+1/c). It performs numerical sweeps over realistic ranges and shows where the mass effect dominates. And it is honest about its own load-bearing assumption: Section II.C explicitly notes that muscle-mass gain saturates at c≤1.5, and Section IV says the c∈[2,5) range is a hypothesis, deferred to the author's future work [25].

The soft spot is not the math; it's the bridge from 'in principle' to 'in practice.' The practical punchline—training can make mass gains rival speed gains—rests entirely on the untested claim that a fighter can raise effective mass by c≥1.75 to maybe 5. The only citation for higher effective mass is a single paper series [35] without independent replication. If the realistic ceiling is c≈1.5, then for the paper's own baselines the speed gain b≈1.67 still produces a larger Vf gain. The stress-test note is right about that. The paper does not pretend otherwise; it flags exactly this gap. But the title and abstract may still mislead a casual reader into thinking the training effect is established.

Two smaller concerns. First, the paper leans heavily on the author's own in-preparation work (refs 24, 25, 27, 42, 48, 49, 53) for measurement methods, the trainable mechanism, and even contact-time estimates; that is a weak citation pattern for a standalone paper. Second, the choice of baseline m0=5 kg and M=60 kg is plausible but not inevitable; with M=40 kg or m=10 kg the comparison shifts, though the broad qualitative picture across the explored parameter space still holds. So I'd call it a sensitivity issue rather than circularity.

Who should read this? Combat-sports biomechanics people and strength-and-conditioning coaches will get a clear, correct analysis of why effective mass matters and why the fold-change comparison is the right way to frame it. They should read the trainability claim as a hypothesis, not a result. The paper deserves a serious referee: the algebra is sound, the question is worthwhile, and the author is explicit about the missing evidence. I'd send it to review, with the expectation that the referee pushes for either independent data on trainability or a more conservative framing that separates the theoretical scaling from the training claim.

Referee Report

2 major / 5 minor

Summary. The paper models a punch as a one-dimensional elastic collision between an incoming effective mass m moving at speed v and a stationary target mass M. It derives the post-collision target velocity V_f = 2m v/(m+M), the fold-change k = c(u+1)/(c u+1) under m→c m, and corresponding scalings for kinetic energy and target acceleration. It argues that because realistic strike speeds are effectively bounded to a fold-increase of roughly b≈1.67 (from ~6 to ~10 m/s), while effective mass might be trainable by c∈[2,5), mass increases can match or exceed speed increases in raising V_f, particularly for a baseline m≈5 kg and a target M≈60 kg. The paper also discusses whiplash, kinetic energy as a damage proxy, the inelastic variant, and concussion-acceleration thresholds. The central practical conclusion is that increasing effective mass through training could produce target-velocity gains comparable to or larger than the maximum practical speed improvement.

Significance. The algebraic core (Eqs. 1–8 and Eq. 10) is correct and clearly presented. The observation that, for small u=m/M, the fold-change k is nearly linear in the mass multiplier c is a useful corrective to the common heuristic that velocity dominates because kinetic energy scales as v². If the trainability of effective mass were established, the practical implications for combat-sports training would be substantial. The paper is also commendable for providing explicit numerical analyses and for distinguishing the 'in principle' claim from the trainability assumption, although that distinction is not carried through consistently in the abstract and summary. The main weakness is that the load-bearing practical premise—that a fighter can raise effective mass by c≥1.75–5—is unsupported and explicitly deferred to future work.

major comments (2)

[Eq. (8) and Sec. II C] The claim that mass fold-changes can rival velocity fold-changes is an artifact of the chosen baseline u=m/M≈1/12. From Eq. (8), k=c(u+1)/(cu+1). For the paper's m=5 kg, M=60 kg, u≈0.083, so k≈c. But for a less favorable baseline, say m=20 kg and M=40 kg (u=0.5), k=2c/(c+2), which for c=5 is only 1.43 and cannot match b=1.67. The abstract's statement that effective mass 'can, in principle, match or exceed' strike velocity is therefore not a general property but a property of the selected normalization. The parameter dependence should be stated explicitly, and the claimed regimes should be qualified accordingly.
[Secs. II C, IV, and Summary item 7] The practical conclusion that training can raise effective mass by c≥1.75–5 is unsupported. The paper itself notes that muscle-mass gain saturates at c≤1.5 and states 'All that remains to be seen is whether any training-mediated increases in effective mass ... can approximate c≥1.75' (Sec. II C), and in Sec. IV it says 'We hypothesize that such transformations c are still a possibility in practice' with a deferral to the author's own future work [25]. Without independent evidence for c≥1.75, the speed improvement b≈1.67 yields a V_f gain of ≈2.35 m/s at baseline m=5 kg, which exceeds the gains from any mass transformation at the currently supported ceiling. The abstract and Summary item 7 should either present the trainability claim as a conditional hypothesis clearly separated from the established algebra, or provide supporting data; as written, the central practical message is not esta

minor comments (5)

[Section III A] There is a typo: '(see Section Za)' should be a proper reference to the relevant section or appendix.
[Section IV, final paragraph] The text refers to 'the set of curves in Fig V'—this should be 'Fig. 7'.
[References] Several load-bearing premises and proposed measurement protocols are delegated to unpublished or in-preparation manuscripts ([24], [25], [27], [42], [48], [49], [53]). These cannot be checked by the reader and should either be made available or removed from the argument; at minimum, the dependence on unpublished work should be flagged in the abstract.
[Section II B] The statement that doubling the mass from m=M to m=2M gives 'V_f →1.3V_f' is approximate; Eq. (4) gives exactly 4/3. Consider writing 4/3 or '≈1.33'.
[Section IV] The sentence 'the leftmost values of k in Fig. 4 appear artificially than the reference values' appears to be missing a word (likely 'larger').

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the core collision algebra is derived from conservation laws, and the trainability of c is explicitly left as an open hypothesis rather than a predicted result.

full rationale

The central derivation chain is Eqs. (1)-(4), which follow directly from conservation of momentum and kinetic energy for a 1D elastic collision, and Eqs. (5)-(8), which are algebraic manipulations of Eq. (4). No parameter is fitted to data and then re-presented as a prediction; no equation is simultaneously used as input and output. The k-vs-b comparison (Eq. 8) is a conditional sensitivity statement: the paper itself notes that k≈c only for small u≡m/M and that the comparison depends on the chosen ranges (m=5 kg, M=60 kg, c∈[2,5), b≈1.67). Different baselines would change the numerical conclusion, but this is a parameterization/robustness concern, not circularity. The practical weak point is the assumption that a fighter can raise effective mass to c≥1.75 through training. The paper flags this as unresolved: 'All that remains to be seen is whether any training-mediated increases in effective mass [39] can approximate c≥1.75; even maximizing muscle-mass gain [40] saturates c≤1.5.' It then labels the mechanism as a hypothesis: 'We hypothesize that such transformations c are still a possibility in practice... we explore one promising mechanism – and a trainable protocol – for augmenting m, potentially to c≥3, in ongoing work [25].' This is an explicit evidence gap and a deferral to the author's own future work, but it is not a circular reduction: no result is derived from [25], and the algebra stands independently of whether c is trainable. The numerous self-citations ([24], [25], [27], [42], [48], [49], [53]) concern measurement methodology, follow-up studies, and future mechanisms; they do not carry the derivation of Eqs. (1)-(8). Under the required standard of quotable reduction (Eq. X = Eq. Y by construction, or fitted parameter renamed as a prediction), no circular step exists. The manuscript's own limitation statements are flagged here and weighed: they reduce the practical, empirical force of the 'trainable goal' claim, but they do not make the theoretical derivation circular.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. Its quantitative comparison is driven by four chosen numbers (m0, M, b, c). The first three are literature/plausibility ranges, while the c range is a pure hypothesis. That makes the practical conclusion substantially more fragile than the underlying algebra, which is standard.

free parameters (5)

baseline effective mass m0 = 4.9 kg ≈ 5 kg (7% of a 70 kg fighter)
Set in Sec IV as the default baseline. The small u=m/M≈1/12 is what makes k≈c in Eq. 8, so the mass-vs-speed conclusion depends on this baseline.
target effective mass M = 60 kg
Chosen in Sec IV as a 'worst-case' large body target. With M=5 kg (head), the paper's own Fig. 8 shows acceleration is dominated by v, not m, so the central comparison is regime-dependent.
accessible velocity improvement factor b = max ≈1.67 (v from 6 to 10 m/s)
Sec II C bounds repeatable punching speed to 6-10 m/s. A wider range (e.g., 6-14 m/s) would make velocity gains larger and weaken the central comparison.
accessible mass improvement factor c = c≥1.75 threshold; c∈[2,5) hypothesized
No empirical support in this paper; feasibility is deferred to the author's future work [25] and to [39]. This parameter drives the practical conclusion that mass can match or exceed speed.
collision time t_coll = ≈10 ms
Used for acceleration-threshold comparisons in Sec III E and Fig. 7-8; taken from Lee & McGill glove data and doubled. Acceleration scales as 1/t_coll, so this choice strongly affects concussion-risk conclusions.

assumptions (5)

standard math Collision is one-dimensional and perfectly elastic between point masses; momentum and kinetic energy are conserved (Eqs 1-2, 3-4).
Sec II A; textbook result. Real tissue, gloves, and ground coupling are inelastic, but the paper treats this as the baseline model and provides an inelastic variant in Eq. 10.
domain assumption A stationary human target can be represented by a single effective mass M≈60 kg that remains fixed during the collision.
Sec IV default. Real targets have coupled segments, ground contact, and deformation; the paper's own whiplash model in Sec III A introduces additional degrees of freedom.
domain assumption Post-collision target velocity Vf is a useful proxy for punch efficacy and damage, and maximizing Vf maximizes impulse for fixed M.
Sec III A, Eq. 9. Damage actually involves acceleration, local deformation, and inelastic energy dissipation; the paper argues but does not validate the proxy.
domain assumption Effective mass is a well-defined quantity that can be meaningfully compared across studies despite the lack of a standardized measurement protocol.
Sec I acknowledges inconsistent definitions and protocols, yet the numerical ranges m≈5-30 kg are drawn from that literature and treated as comparable.
ad hoc to paper Training or technique can multiply effective mass by c≈1.75-5 without compromising balance or form.
Sec IV-V; explicitly called a hypothesis and deferred to the author's future work [25]. No data or mechanical mechanism is provided in this preprint.

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Cite this review

Pith. "Pith review of Improving Punching "Power": Reconsidering the roles of initial strike velocity and effective mass." pith.science (2026). https://pith.science/paper/ZMEM25QU

@misc{pith2026260718276,
  author       = {Pith},
  title        = {Pith review of: Improving Punching "Power": Reconsidering the roles of initial strike velocity and effective mass},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZMEM25QU}},
  note         = {Machine review of arXiv:2607.18276}
}

read the original abstract

We review the principal features of one-dimensional, elastic collisions pertinent to modeling strike-mediated impacts in martial arts and combat sports contexts. Arguing for the post-collision velocity of a stationary, target mass as a useful proxy for determining overall punch efficacy, we demonstrate that pre-collision velocities for real strikes are bounded, such that speed prior to impact has a more limited effect on the impulse experienced by said target than suggested by supporting literature. We find that the value of incoming, "effective" mass -- despite eluding uniform establishment criteria or measurement protocols across the same body of literature -- exerts an independent influence on the target velocity which can, in principle, match or exceed that of the strike speed. We perform explicit numerical analyses to supplement these theoretical considerations, in dynamical regimes relevant to real human combat, and then briefly discuss the potential for a given fighter to attain a fold-increase in effective mass (from a reasonable baseline value based on bodyweight, and supported by previous work) sufficient to realize limits for upper-limb strikes to the body, in practice, as a trainable goal.

Figures

Figures reproduced from arXiv: 2607.18276 by the authors.

**Figure 2.** FIG. 2. The variation in post-collision target velocity [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** FIG. 3. Swapping the horizontal and vertical axes of Fig. 2 [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

Figures from the paper (5 more)

**Figure 4.** Figure 4: FIG. 4. Considering [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]

**Figure 5.** Figure 5: FIG. 5. Kinetic energy values for the target mass [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 7.** Figure 7: FIG. 7. Given a fixed collision time of 10 [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]

**Figure 6.** Figure 6: FIG. 6. Another presentation of a subset of the data in Fig. 5 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 8.** Figure 8: FIG. 8. Nearly any value of the incoming, effective mass [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]

Discussion (0). Continue with ORCID to comment.

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[3] [1]

The effective, striking mass exerts an effect entirely independentof that exerted by the incoming strike velocity on the post-collision velocity gained by the target mass, for a stationary target of any size

[4] [2]

Recoil, or any negative change to the initial speed of a strike, is experienced by the striking implement exclusively when that strike is delivered to atarget whose mass exceeds that of theincomingmass

[5] [3]

whiplash

The opposite scenario – of no recoil, and possibly the continuation of movement of the incoming mass malong the line of impact – guaranteesm≥M; this may be experienced as a “whiplash”-like effect, from the perspective ofM, if the target is composed of coupled components far from the impact point

[6] [4]

upstream

The accessible values of bothabsolutechanges and fold-changes in the inducible post-collision, target velocities corresponding to any “upstream” changes in effective striking mass tend to be of magnitudes similar to those associated with upstream changes in the initial strike speed, over a broad input space comprising nearly the full range of realizable v...

[7] [5]

There exist regimes – well within the subspaces of reasonable parameter values, representative of real human combat – where the kinetic energy gained by a stationary target can also be increased by the same order of magnitude as it would by varyingv, but by increasingminstead (despite thatK∝v 2)

[8] [6]

At strike durations this short, even moderate values ofmare implicated in risking neurological damage

The accelerationaof any stationary targetMsmall enough to model a defender’s head (i.e, the cranium and its organic contents, including the brain) – in collision with a moving mass (striking implement) at least as massive – can grow sufficiently large that it crosses the previously-established thresholds for inducing mild traumatic brain injury (concussio...