The Physics of Arrow Penetration in Bow Hunting

Understanding why some arrows punch clean through game while others barely penetrate comes down to physics. In bowhunting, there has long been a debate about whether an arrow’s speed and kinetic energy (KE) or its momentum is more important for penetration. Modern science and real-world hunting tests show that momentum, essentially the arrow’s “weight in motion,” plays the dominant role in driving broadheads deep.

As a retired U.S. Army Green Beret, I was getting tired of hearing the debate over speed, kinetic energy (KE), and momentum. So, I did a deep dive into the hows, whats, and whys of hunting arrows and found the answers that both science and real-world testing have proven.

Below, we explore scientific studies, practical examples, key formulas, and counterarguments to clearly show why a high-momentum arrow penetrates better than one relying on speed alone.

Want to see how this applies to your hunting arrows? Start the Performance-Driven Arrow Build Series here.

Speed, Kinetic Energy, and Momentum: What Science Says

Kinetic energy is the energy of motion. It depends on an object’s mass and especially its velocity (speed). In fact, the formula for kinetic energy is KE = ½ × mass × velocity². This means if you double an arrow’s speed, its kinetic energy quadruples (because velocity is squared). By contrast, momentum is simply mass × velocity (no squaring).

If you double speed, you only double momentum; if you double the mass, momentum also doubles. An arrow’s momentum is essentially how much “push” it carries in the direction of travel. In physics terms, momentum tells us how much force over time the arrow can exert to keep moving forward.

Many archers talk about kinetic energy because it’s easy to calculate and is often used for bullets. However, experts note that kinetic energy is not a direct indicator of arrow penetration. Dr. Ed Ashby, who conducted 30 years of arrow performance research, explains that an arrow’s KE includes all kinds of motion energy (like the arrow flexing, vibrating, or making noise) that don’t help it cut through an animal.

In other words, an arrow can have high KE but waste much of that energy in forms that don’t aid penetration. Momentum, on the other hand, is a measure focused on the arrow’s forward drive (a “unidirectional” push) that actually carries the arrow through flesh and bone.

It’s helpful to compare arrows to bullets here. Kinetic energy as a killing mechanism was popularized by gun researchers studying hydrostatic shock – the destructive shockwave effect fast bullets have in flesh. Bullets traveling over about 2,500 feet per second can cause massive tissue damage beyond the bullet’s path due to this shock.

The formula for this shock effect was kinetic energy (KE). But arrows travel far slower (usually 200–300 fps, not thousands), so they cannot cause a hydrostatic shock wave. As a bowhunting resource notes, using kinetic energy as a yardstick for arrow performance below firearm speeds has “absolutely no indication of penetration”.

Instead of shock, arrows kill by slicing through vital organs (hemorrhage). This means what matters is how far the arrow penetrates, not the “shock” it delivers.

READ: Best Arrow Weight for Deer Hunting: Balancing Speed and Penetration

Physics studies on penetration support this focus on momentum and mass. For example, researchers have observed that if you increase only an arrow’s mass (making it heavier but keeping speed the same), both its KE and momentum go up, and penetration definitely increases.

But if you increase only speed (making a lighter arrow faster), it’s not guaranteed to penetrate much more. The target material can resist high-speed impacts disproportionately, sometimes negating the advantage of higher KE. In simpler terms, a lighter arrow going super fast might stop more quickly on impact than a heavier arrow that hits a bit slower.

The heavy arrow’s greater momentum helps it plow ahead consistently, whereas a fast, light arrow can shed its energy in a flash. As one physics answer put it, the target’s resistance can rise with impact speed, so beyond a point, just speeding up a light arrow doesn’t yield deeper penetration.

Another basic physics concept is force = mass × acceleration. When an arrow hits an animal, it starts decelerating (slowing down) as it cuts through tissue. A high-momentum arrow (heavy and reasonably fast) decelerates more slowly – it’s like a freight train that’s hard to slow down.

A low-momentum arrow (light but very fast) slows down very quickly once it hits something solid. Dr. Ashby illustrated this by showing that two arrows can have the same momentum but different weights: the heavier arrow will slow down more gradually in the animal, taking longer to come to a stop.

That means it keeps pushing forward longer, resulting in deeper penetration. A blog for bowhunters boiled it down with a driver’s ed analogy: imagine a small car and a big semi-truck both moving at 65 mph – if they hit the brakes at the same time, the truck travels farther before stopping*. The truck’s greater momentum carries it forward. In the same way, a heavy, high-momentum arrow keeps driving through an animal, whereas a lighter arrow (even with high initial KE) can grind to a halt sooner.

It’s important to note that other factors also influence penetration. Arrow broadhead design and sharpness, arrow flight stability, and the arrow’s diameter all matter. For instance, a long, sharp broadhead with fewer blades has a higher mechanical advantage – it splits tissue with less force needed.

If an arrow isn’t flying straight (hits at an angle or wobbles), it won’t penetrate well, no matter the momentum. In Dr. Ashby’s reports, broadhead integrity (not bending or breaking) and perfect arrow flight were among the top factors for penetration success.

So, momentum isn’t the only piece of the puzzle, but given a well-tuned arrow setup with a strong broadhead, momentum is the driving force that pushes that setup to its maximum potential.

Real-World Bowhunting Examples of Penetration

Theory is convincing, but real-world hunting results truly drive the point home. Seasoned bowhunters and controlled tests have repeatedly shown that arrows with higher momentum (often from greater mass) penetrate better on game animals:

Heavy Arrow vs. Light Arrow on Big Game

Experienced hunters have seen slower, heavier arrows punch through large animals where fast, light arrows failed. One hunter recounted shooting completely through a large moose with a traditional bow using a very heavy arrow, whereas he’s seen high-speed, light arrows (with much more KE on paper) stop short when hitting the moose’s shoulder bone.

In the same comparison, a tiny .22 caliber rifle bullet (40 grains at ~1250 fps) carries nearly double the kinetic energy of that heavy arrow. Yet no one would hunt a moose with a .22 bullet – it lacks the momentum and mass to penetrate deeply. The heavy arrow, despite lower KE, drove deep and even broke bone, while the lighter, high-KE projectiles failed to penetrate enough.

This real scenario shows that a big animal’s resistance can negate high kinetic energy if the momentum (and mass) behind the arrow isn’t sufficient.

Cape Buffalo “Baseball” Example

To legally hunt Cape buffalo in South Africa with a bow, the law requires at least 80 ft-lbs of kinetic energy at impact. Some bow setups can reach this, and it sounds like a lot. But consider a Major League baseball weighing 2300 grains thrown at 100 mph – it has about 114 ft-lbs of kinetic energy, well above that requirement.

By the KE standard, a fastball pitcher could legally hunt buffalo with a baseball! Of course, a blunt baseball would just bounce off a buffalo, doing almost no harm. This absurd example (KE = 114 ft-lbs, zero penetration) proves that without momentum in the right direction and a penetrating shape, kinetic energy means little.

It’s the arrow’s focused momentum and sharp point that drives into a buffalo, not just raw energy numbers.

Dr. Ashby’s Big Game Studies

Dr. Ed Ashby’s exhaustive field studies on African game animals provide some of the most compelling data. Over decades of testing arrows on species like buffalo, giraffe, and large antelope, Ashby observed clear trends. He found that arrow setups above a certain weight threshold (around 650 grains total) performed far better, especially when bones were hit.

In heavy bone impacts, arrows below ~650 grains often failed to penetrate deeply, whereas those above 650 gr (with sturdy single-blade broadheads) consistently penetrated enough to be lethal. This roughly corresponds to about 0.5+ pound-seconds of momentum at impact in his tests. He noted that the deepest penetrations – and highest percentages of pass-through shots – occurred with high-momentum arrows.

In fact, deeper arrow penetration was directly linked to higher odds of a quick kill. The takeaway: on tough game, a massive, high-momentum arrow (e.g. 650–900+ grains) is far more reliable for driving through hide, muscle, and bone than a lightweight, high-speed arrow.

Many bowhunters chasing big game have since adopted Ashby’s heavy-arrow principles to ensure they get two holes (entry and exit wounds) on animals for better blood trails and recovery.

Bullet vs. Arrow Penetration

Even outside of hunting, experiments illustrate the momentum advantage of arrows. In one test, a .357 Magnum handgun bullet (158 grains at ~1250 fps) and a heavy hunting arrow were fired into a sand-filled bucket. The bullet had ten times the kinetic energy of the arrow (over 500 ft-lbs vs about 52 ft-lbs), and also higher momentum (0.83 vs 0.57 lb·s).

Even so, the arrow burrowed completely through the bucket, while the high-energy bullet was stopped in the sand. The arrow’s long, slender shape and steady momentum let it penetrate where the bullet’s energy was expended almost instantly in a splash of sand.

While bullets and arrows are different tools, this shows how penetration is about more than energy alone – the projectile must carry its force in the right form (momentum and shape) to continue pushing through a medium.

Every Day Bowhunting Outcomes

Countless bowhunters can share anecdotes of arrows performing better when they emphasize weight over speed. Many who switched to a heavier arrow setup (for example, going from a 350-grain arrow to a 500-grain arrow) noticed more pass-through hits on deer and other game.

The arrows may fly slightly slower, but they hit with a harder “punch.” As one archery company states, “Momentum at impact has a direct correlation to penetration, not kinetic energy.” In the field, a slower arrow that blows through both lungs is far deadlier than a fast arrow that only penetrates one lung.

The deeper the arrow goes, the more vital tissues it cuts – and the quicker the animal falls.

An arrow that blew through a bull and kept going. High-momentum arrows often achieve complete pass-throughs (“two holes”), leading to better blood trails and quicker kills. This arrow’s deep penetration was no accident – it had the mass and momentum to drive on through.

Key Formulas and Simple Calculations

Understanding the math behind kinetic energy and momentum can help clear up why momentum matters so much. Don’t worry – it’s not too complicated:

• Kinetic Energy (KE) is given by the formula ½ × m × v². In words: half the mass times velocity squared.
  • This means speed affects KE a lot. (For bowhunting units, you can use a simplified formula: KE (ft·lbs) = (ArrowWeight (grains) × Velocity² (fps)) / 450,240.)
  • It’s measured in foot-pounds for arrows. For example, a 350-grain arrow at 300 feet per second has about 70 ft-lbs of kinetic energy.
• Momentum (p) is given by m × v (mass times velocity). There’s no squaring – both mass and speed contribute evenly.
  • In bowhunting, we often talk about momentum in pound-seconds. Using consistent units, momentum (lb·s) can be calculated as (ArrowWeight (grains) × Velocity (fps)) / 225,400 (approximately).
  • The 350-grain arrow at 300 fps above has a momentum of around 0.47 lb·s (pound-seconds).

*Remember, you can always use my Arrow Speed, Kinetic Energy, and Momentum Calculator to see what your numbers are.

Comparing Light and Heavy Arrows

Let’s compare two arrows to see the difference. Arrow A is light and fast: 350 grains at 300 fps (a common deer setup for a compound bow). Arrow B is heavy and slower: 600 grains at about 230 fps (this could be a heavy setup from a similar bow).

• Arrow A (350 gr @ 300 fps): KE ≈ 70 ft-lbs, Momentum ≈ 0.47 lb·s.
• Arrow B (600 gr @ ~230 fps): KE ≈ 70 ft-lbs, Momentum ≈ 0.61 lb·s.

Notice how both arrows carry roughly the same kinetic energy (we intentionally chose Arrow B’s speed to give ~70 ft-lbs as well). But Arrow B has about 30% more momentum (0.61 vs 0.47) thanks to its extra mass. That means when these arrows hit a target, Arrow B will be harder to slow down.

Even if Arrow B had a bit less energy than Arrow A, it can still penetrate more because its momentum is higher. In real shooting, a 600-grain arrow might actually retain energy better on impact anyway, since it doesn’t shed speed as violently.

To put things in perspective, let’s bring back the firearm comparison:

• A 40-grain .22LR bullet at 1250 fps has around 139 ft-lbs of KE, which is nearly double our Arrow A’s energy.
  • However, its momentum is only about 0.22 lb·s (much lower than either arrow). It zips in with lots of energy but also loses that energy almost immediately on impact, creating a tiny wound channel.
• Our heavy Arrow B (600 gr @ 230 fps) has only ~70 ft-lbs KE, but ~0.61 lb·s momentum. That’s nearly three times the momentum of the .22 bullet. So the arrow just keeps driving forward where the small bullet would stop.
  • Even a modern hunting arrow of ~700 grains at 180 fps has been shown to have about the same momentum (~0.57 lb·s) as a .22 Hornet rifle bullet traveling over 2600 fps! Momentum is the great equalizer that allows a slower arrow to compete in penetration.

What do these numbers mean for a bowhunter?

Essentially, momentum tells you how hard it is to stop the arrow. An arrow with 0.6–0.7+ lb·s of momentum is a workhorse – ideal for punching through big animals or bone hits. Lower momentum (say 0.3–0.4) might be fine for smaller game or perfect broadside shots, but it leaves less margin if you hit heavy muscle or angled shots.

Kinetic energy alone might make Arrow A sound impressive, but it doesn’t guarantee how far it will go in the animal. The momentum number is more directly tied to that penetration depth.

Lastly, recall that penetration isn’t solely physics numbers – arrow design matters too. A sharp cut-on-contact broadhead with a high mechanical advantage will convert an arrow’s momentum into cutting action more efficiently.

A dull or very short/blunt broadhead might waste even a high-momentum arrow’s potential. Always consider the whole system: a heavy, high-momentum arrow + a sharp, sturdy broadhead + good arrow flight = maximum penetration.

Want to dig into how this affects your arrows? Start here: Part 1: Momentum Explained: How Arrow Weight Impacts Penetration

Debunking Myths: Why Momentum Matters More Than KE

Despite the evidence, some bowhunters still focus on kinetic energy as the end-all measure of arrow performance. Let’s address a few common arguments and misconceptions from the “KE is king” camp, using physics and facts:

Myth 1: “Kinetic energy determines penetration because it’s the energy available to do work (cutting).”

It’s true that an arrow needs energy to cut tissue. However, energy can be spent in many ways, and not all of it goes into cutting straight through. Kinetic energy is a broad measure and does not account for how that energy is used. An arrow’s KE can be siphoned into flexing the shaft, making noise, or deforming the broadhead, none of which helps penetration.

Also, as mentioned, arrows move too slowly to cause the kind of shock damage that high-energy bullets do. The key is delivering force in the right direction for a long enough time, which is exactly what momentum represents. Think of KE as the size of the “gas tank,” and momentum as how effectively that gas can be used to push the arrow forward.

A sports car and a tractor might have the same horsepower (energy), but the tractor applies its power more steadily to pull heavy weight – that’s momentum at work in penetration. As Dr. Ashby concluded, simply citing an arrow’s kinetic energy is misleading as a predictor of penetration. Real penetration combines momentum with arrow design and target factors.

Myth 2: “A faster arrow (higher KE) will always out-penetrate a slower arrow.”

Not necessarily. Speed without sufficient mass can be a liability. The faster a lightweight arrow goes, the more quickly it tends to shed its speed upon impact. It’s like throwing a ping-pong ball versus a heavier dart. The ping-pong (very fast, very low mass) might sting on impact, but stops almost immediately. The dart (slower, heavier) keeps driving in.

High velocity does increase energy, but unless paired with enough mass, the arrow may lack the momentum to continue deep. We saw in the examples: a lighter arrow with 80+ ft-lbs of KE might not penetrate as well as a heavy arrow with 60 ft-lbs of KE. One reason is that tissues (or any target) offer resistance.

At high speed, resistance (and drag) can increase greatly, acting like an emergency brake on the arrow. The heavier arrow at a lower speed experiences a gentler slowdown, maintaining its movement. As a result, heavier arrows consistently penetrate better in practical tests because they carry more momentum into the target.

The momentum means more force is required to halt the arrow’s motion, so it goes farther in. Bowhunters who have tried super-light, fast arrows often report superficial hits on tough animals, whereas slightly slower, heavier arrows pass through vitals. In short, speed is only one part of the equation – without mass, it loses steam quickly.

Myth 3: “Energy is energy – if an arrow has the same KE as another, they’ll penetrate the same.”

If all else is truly equal (same broadhead, angle, etc.), two arrows with equal momentum tend to penetrate similarly. But two arrows with equal KE can actually have very different momentum values. For example, recall Arrow A vs Arrow B above: both ~70 ft-lbs KE, but one had ~30% more momentum.

In that case, we would expect the higher-momentum arrow to penetrate deeper, and indeed, field experience shows it would. The confusion comes from assuming energy alone drives penetration. In reality, penetration is a function of force over distance. An arrow stops when its kinetic energy has been used up against resistance.

A lighter, faster arrow might hit with a big initial force (energy), but then quickly run out of “gas” as resistance slows it down within a short distance. The heavier arrow applies a more sustained push, so it keeps doing work (cutting) over a longer distance, thus penetrating further. In physics terms, the lighter arrow experiences a larger deceleration (negative acceleration) because $F = ma$ and it has less mass.

The heavier arrow, with more mass, doesn’t slow as abruptly under the same force. All this means that matching KE numbers is not a guarantee of equal penetration if the momentum behind them differs. Momentum is a more reliable gauge for penetration potential, as it directly relates to how hard it is to stop the arrow.

Myth 4: “I need high KE for big game.”

Bow manufacturers and even regulations often quote kinetic energy recommendations (like 50+ ft-lbs for deer, 65+ for elk, etc.). While having sufficient overall energy is important (you can’t have good momentum without some energy too), focusing on a KE threshold alone can be misleading.

It’s possible to have high KE with a very fast, light arrow, but such an arrow might lack the mass to penetrate a big animal reliably. Instead, many experienced hunters now look at momentum or total arrow weight recommendations for big game. For example, Ashby’s research suggests ~0.5 lb·s of momentum (around a 650-grain arrow at ~180 fps) as a minimum for large, heavy-boned game.

Some African game laws even specify a minimum arrow weight in addition to (or instead of) energy. The reason is that a heavier arrow retains its penetrating power better on impact. In practical terms, if you’re after large game like elk, moose, or buffalo, you should prioritize a heavier arrow with a solid broadhead.

Ensure your setup can still shoot that arrow accurately, of course, but do not worry if the speed is lower. As long as the arrow flies well, the added weight will deliver more dependable penetration. Kinetic energy numbers by themselves don’t kill animals; cutting through vital organs does, and for that, you want momentum on your side.

Finally, it’s worth noting that modern bowhunting literature has been shifting toward momentum-based thinking. Even some arrow manufacturers who used to push KE are acknowledging that momentum and arrow construction are bigger factors in lethality.

The goal is always a quick, ethical kill – and that means an arrow that penetrates deep enough to hit the vitals and (ideally) exits to leave a good blood trail. All the evidence – scientific and anecdotal – points to momentum as the key to achieving that goal consistently.

Finding the Right Balance: Practical Arrow Weight Selection

Ultimately, momentum is the driving factor in how deep an arrow penetrates, not just raw speed or kinetic energy. That’s why a heavier arrow, even if it’s slower, will often punch through farther: it carries more momentum and loses speed more gradually on impact, delivering a longer-lasting push through flesh and bone.

Of course, making your arrow ultra-heavy comes with a trade-off: a slower, more arcing trajectory that can make long shots trickier. Many bowhunters, therefore, aim for a happy medium—enough arrow mass for lethal momentum but still a flat-shooting setup for accuracy at range.

For a practical guide on achieving that balance, check out my post: Best Arrow Weight for Deer Hunting: Balancing Speed and Penetration, which walks you through choosing the ideal arrow weight for your setup based on these principles.

Or, use the Shortcut I created here.

Conclusion

In summary, while speed and kinetic energy sound exciting, they are not the best predictors of arrow penetration in bowhunting. Momentum – the combination of an arrow’s mass and speed – is a more faithful measure of an arrow’s ability to drive through an animal.

High-momentum arrows (often heavier) behave like a punch from a heavyweight boxer: they hit hard and keep driving in one direction. Lighter, high-KE arrows can be like a quick jab – sharp at first impact but quick to slow down. Science backs this up: momentum is directly related to the force needed to stop the arrow, and heavy arrows maintain their velocity longer upon impact.

Real-world hunting experiences, from whitetails to Cape buffalo, have proven that arrows with greater momentum routinely penetrate deeper and achieve more pass-through shots, leading to higher success rates.

For bowhunters, the take-home message is clear: don’t get obsessed with speed and kinetic energy alone. An arrow that is slightly slower but heavier (with a sharp fixed-blade broadhead) will more reliably penetrate vitals than an ultra-light rocket arrow that might stop short on a shoulder bone.

By choosing adequate arrow mass and optimizing momentum, you set yourself up for deeper penetration and cleaner kills. In the end, an ethical hunter wants an arrow that can reach the vital organs from any reasonable angle. Physics overwhelmingly shows that momentum is the bowhunter’s best friend in achieving that goal.

So the next time someone brags about arrow speed or KE, you’ll know the real secret: it’s the unstoppable momentum that truly brings home the trophy.

Want to see how this applies to your hunting arrows? Start the Performance-Driven Arrow Build Series here.