Arrow Speed vs FOC: Why Momentum Matters More Than KE
Bikash Roy
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Full bio →The Debate Every Bowhunter Faces
Two ways to measure arrow striking force appear constantly in archery discussions:
Kinetic Energy (KE): KE = ½mv². Favors fast, light arrows — velocity is squared, so speed has double the impact on KE compared to mass.
Momentum (p): p = mv. Mass and velocity are equally weighted — a heavier, slower arrow retains momentum better through impact.
Both numbers are printed on product pages, calculator outputs, and hunting forums. But only one is the better predictor of what actually matters in bowhunting: arrow penetration through tissue and bone.
The answer matters because FOC — and the weight you add to achieve it — directly trades away speed for mass. Understanding which metric matters more tells you whether that trade is worth making.
Use the FOC Calculator to check your current FOC. This article explains why the physics behind it favors momentum.
The Physics: Why Momentum Wins in Tissue
Kinetic energy is a measure of the total work the arrow can do — theoretically. Momentum is the arrow’s resistance to deceleration — how hard it is to stop.
When an arrow enters an animal’s body, resistance forces (hide, muscle, bone, organs) act against it. These forces work to decelerate the arrow. The arrow’s ability to continue penetrating despite these forces is its momentum — not its kinetic energy.
The critical insight: velocity decreases faster than momentum during penetration.
- KE = ½mv² — as the arrow slows, KE drops by the square of velocity loss
- p = mv — as the arrow slows, momentum drops linearly with velocity loss
A fast, light arrow that loses 20% of its velocity has lost 36% of its kinetic energy but only 20% of its momentum. A slow, heavy arrow that loses 20% of its velocity has lost the same 20% of its momentum.
In practice: fast, light arrows “run out of steam” sooner in tissue than slow, heavy arrows with the same or even slightly lower KE.
The Numbers: Same KE, Different Penetration
Arrow A: 350 grains at 280 fps → KE = 61.0 ft-lbs, momentum = 0.263 slug-ft/s
Arrow B: 550 grains at 225 fps → KE = 61.8 ft-lbs, momentum = 0.337 slug-ft/s
Both arrows have essentially the same kinetic energy. Arrow B has 28% more momentum. In tissue, Arrow B will penetrate significantly further despite flying slower and having identical KE.
This is not theoretical. Multiple independent archery penetration studies — most comprehensively Dr. Ed Ashby’s 30-year terminal performance research across thousands of shots on large and dangerous game — confirm that heavier arrows with higher momentum penetrate more deeply and consistently, even when matched for KE.
Where FOC Fits In
FOC amplifies the penetration advantage of heavy arrows in two ways:
1. Directional stability at impact: An arrow with high FOC maintains its direction better as it meets resistance. The heavy front drives straight through. An arrow with low FOC tends to “fishtail” at impact, with the rear angling sideways as resistance slows the tip — this reduces effective penetration depth and can cause the broadhead to redirect off the intended path.
2. Preserved sectional density: High-FOC heavy arrows have more weight concentrated at the point, which means more force concentrated per unit area at the cutting edge. The broadhead drives into the tissue rather than riding on top of it.
These two effects work with momentum to make heavy, high-FOC arrows penetrate more reliably — especially through bone, thick muscle, or when an angle shot requires the arrow to travel through more material.
The Speed Trade-Off: What You Actually Give Up
Adding weight to reach higher FOC costs speed. The rule of thumb: approximately 1 fps lost per 3 grains of arrow weight added (varies by bow, arrow, and draw length).
Trajectory impact:
| Arrow weight increase | Speed lost (approx) | Hold-over at 50 yards (Std arrow drops ~4”) |
|---|---|---|
| +50 grains | ~17 fps | Additional ~0.5” drop |
| +100 grains | ~33 fps | Additional ~1” drop |
| +150 grains | ~50 fps | Additional ~1.5” drop |
These are small numbers if you range carefully. The trajectory argument against high FOC — “I’ll miss a deer at 50 yards because of the extra drop” — only holds if you refuse to compensate for the known trajectory change. Any rangefinder and pin adjustment handles this trivially.
The KE Minimums Myth
KE minimums (the common chart showing 25 ft-lbs for small game, 65 ft-lbs for elk, etc.) are widely cited as hard hunting requirements. These numbers are useful as rough baselines but do not distinguish between two arrows with the same KE and very different momentum.
An arrow with 65 ft-lbs of KE from a 350-grain shaft at 300 fps has a momentum of 0.286 slug-ft/s.
An arrow with 65 ft-lbs of KE from a 530-grain shaft at 245 fps has a momentum of 0.353 slug-ft/s — 23% more.
Both clear the “65 ft-lbs for elk” threshold. The second arrow penetrates reliably through an elk shoulder. The first may not.
KE thresholds are not wrong — they’re just incomplete. For game where penetration depth matters (elk, bear, thick-skinned animals), momentum is a better selection criterion.
Practical Decision Framework
| Priority | Arrow choice | FOC implication |
|---|---|---|
| Maximum range (speed) | Lighter arrow | Lower FOC unless added with heavy inserts/screws |
| Maximum penetration | Heavier arrow | Higher FOC naturally; build for 15–22%+ |
| Balanced close-range hunting | Mid-weight | 13–17% FOC typical |
| Specific game: elk, bear, boar | Heavy momentum build | 18–25%+ FOC |
For game-specific FOC recommendations, see FOC for Big Game Hunting. For the comparison between high and standard FOC setups with specific speed/penetration numbers, see High FOC vs Standard FOC.