# Newton impact depth and ballistic gel penetration. Why does it not work? **URL:** \ **Category:** Factual Questions\ **Created:** [February 1, 2024, 5:37pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978 "2024-02-01T17:37:27Z")\ **Posts on this page:** 15\ **Page:** 1
**Author:** ![Hermitian](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hermitian/32/470_2.png) [@Hermitian](https://boards.straightdope.com/u/Hermitian)\ **Post date:** [February 1, 2024, 5:37pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/1 "2024-02-01T17:37:27Z")
In simple terms Newton’s impact depth approximation says that “For a cylindrical impactor, by the time it stops, it will have penetrated to a depth that is equal to its own length times its relative density with respect to the target material.” So this means that if a material and the penetrator are the same density, regardless of speed, the projectile will only penetrate into the material the length of the projectile. This makes sense. Now if the projectile is more dense, it should penetrate into its length times the difference in densities. (This should only hold up as long as the speed of the projectile is less than the speed of sound within the target or projectile material. For bullets and ballistic gel, this is true.) So lets try some calculations that I have found. Density of ballistic gel: 1,060 kg/m^3 Density of lead: 11,400 kg/m^3 So the ratio difference between lead and ballistic gel is approximately 10.75. So all lead bullets should go ~10-11 times deeper into gel than their length. Lets look at a 9mm 115grain bullet: Length of bullet: 0.551" Predicted penetration into ballistic gel: 0.551" \* 10.75 = 5.9" Actual penetration: 11-13" (multiple test sources online) So it is almost double what it should be? Here is a fun example. I noticed this while watching a [slow mo guys video](https://youtu.be/nsJGJHkJolI?si=E3N7JcKGo4ow51Jl&t=498). They shoot a .577 T-rex round. I did a freeze frame and measured lengths of bullet vs. gel. The bullet goes through almost exactly 20 times its length and leaves the 32" of ballistic gel still going 869 mph. So it easily more than twice what it should be. Now, I know the impact depth formula is an approximation, so I expected it to be off by 10-30%. But it is off by 100% and more. Any thoughts why? ---
**Author:** ![FrenchDunadan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frenchdunadan/32/5449_2.png) [@FrenchDunadan](https://boards.straightdope.com/u/FrenchDunadan)\ **Post date:** [February 1, 2024, 5:54pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/2 "2024-02-01T17:54:55Z")
Is it restricted to solid/solid interaction? Does the diameter or shape import? Does it vary with the plasticity of the material? if you shoot a bullet in water, the penetration will be minimal. ---
**Author:** ![eburacum45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eburacum45/32/8690_2.png) [@eburacum45](https://boards.straightdope.com/u/eburacum45)\ **Post date:** [February 1, 2024, 5:58pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/3 "2024-02-01T17:58:10Z")
Bullets are pointed. ---
**Author:** ![running\_coach](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/running_coach/32/15836_2.png) [@running\_coach](https://boards.straightdope.com/u/running_coach)\ **Post date:** [February 1, 2024, 6:12pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/4 "2024-02-01T18:12:49Z")
> [@FrenchDunadan](#): > > Does it vary with the plasticity of the material? if you shoot a bullet in water, the penetration will be minimal. - > **[MythBusters Episode 34: Bulletproof Water](https://mythresults.com/episode34)** > > The MythBusters test if diving under water will protect you from bullets, and if it is possible to swing over the top of a swing set. > All supersonic bullets (up to .50-caliber) disintegrated in less than 3 feet (90 cm) of water, but slower velocity bullets, like pistol rounds, need up to 8 feet (2.4 m) of water to slow to non-lethal speeds. ---
**Author:** ![FrenchDunadan](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/frenchdunadan/32/5449_2.png) [@FrenchDunadan](https://boards.straightdope.com/u/FrenchDunadan)\ **Post date:** [February 1, 2024, 6:20pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/5 "2024-02-01T18:20:59Z")
8 feet of water is 16 times the 5.9" of the OP, is it? that’s effectively a lot more than expected. If there was less penetration, that could be from unaccounted contact forces, but more penetration than the ideal case means something is wrong in the approximation. ---
**Author:** ![74westy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/74westy/32/3950_2.png) [@74westy](https://boards.straightdope.com/u/74westy)\ **Post date:** [February 1, 2024, 8:52pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/6 "2024-02-01T20:52:13Z")
> [@Hermitian](#): > > (This should only hold up as long as the speed of the projectile is less than the speed of sound within the target or projectile material. For bullets and ballistic gel, this is true.) … ---
**Author:** ![DPRK](https://avatars.discourse-cdn.com/v4/letter/d/4491bb/32.png) [@DPRK](https://boards.straightdope.com/u/DPRK)\ **Post date:** [February 1, 2024, 9:40pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/7 "2024-02-01T21:40:43Z")
> [@FrenchDunadan](#): > > Is it restricted to solid/solid interaction? > Does the diameter or shape import? > Does it vary with the plasticity of the material? if you shoot a bullet in water, the penetration will be minimal. In the regime of validity of Newton’s approximation law, that stuff does not matter, NB the target by definition is not “solid” in that case. In other cases, the penetrability of the target and the shape of the projectile do matter. ---
**Author:** ![Hermitian](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hermitian/32/470_2.png) [@Hermitian](https://boards.straightdope.com/u/Hermitian)\ **Post date:** [February 1, 2024, 9:42pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/8 "2024-02-01T21:42:30Z")
I don’t think the shape matters significantly, but I could be wrong. ---
**Author:** ![eburacum45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eburacum45/32/8690_2.png) [@eburacum45](https://boards.straightdope.com/u/eburacum45)\ **Post date:** [February 1, 2024, 9:45pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/9 "2024-02-01T21:45:03Z")
One way to test this would be to make some perfectly cylindrical bullets with flat ends and test them against pointed, bullet-shaped bullets. The shape may have no effect, but my intuition causes me to doubt that. ---
**Author:** ![gnoitall](https://avatars.discourse-cdn.com/v4/letter/g/bb73d2/32.png) [@gnoitall](https://boards.straightdope.com/u/gnoitall)\ **Post date:** [February 1, 2024, 9:49pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/10 "2024-02-01T21:49:22Z")
> [@eburacum45](#): > > perfectly cylindrical bullets I.e., wadcutters. > **[Wadcutter](https://en.wikipedia.org/wiki/Wadcutter)** > > A wadcutter is a special-purpose flat-fronted bullet specifically designed for shooting paper targets, usually at close range and at subsonic velocities typically under approximately 270 metres per second (890 ft/s). Wadcutters have also found favor for use in self-defense guns, such as .38 caliber snubnosed revolvers, due to shorter barrel lengths, lower bullet velocities, and improved lethality. Wadcutters are often used in handgun and airgun competitions. > A wadcutter has a flat or nearly fla... ---
**Author:** ![mixdenny](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mixdenny/32/2962_2.png) [@mixdenny](https://boards.straightdope.com/u/mixdenny)\ **Post date:** [February 1, 2024, 10:01pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/11 "2024-02-01T22:01:20Z")
Many years ago I tested some water cubes for resistance to penetration from high speed projectiles. Each box was a cardboard cubic foot and had a plastic bladder to hold the water. I shot at them at point blank range with a 30-06. That’s a .30" diameter bullet at about 2800 fps. Since the projectiles we were concerned with were not ogive tipped cylinders I also pulled the bullets and turned them around and fired them base first. With my simple test I could not tell a difference. Both types of bullets made it through a single water cube and neither made it out second cube. I also tried 12 gauge, double aught buckshot with a similar result. Don’t fuck with water. ---
**Author:** ![MikeF](https://avatars.discourse-cdn.com/v4/letter/m/45deac/32.png) [@MikeF](https://boards.straightdope.com/u/MikeF)\ **Post date:** [February 1, 2024, 10:57pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/12 "2024-02-01T22:57:33Z")
Interesting. Intuitively, I’d think that velocity would play a major factor in penetration depth. The faster projectile has more energy and would go further. More speed=more drag=faster stopping? Where is this extra energy dissipated? Heat? ---
**Author:** ![eburacum45](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/eburacum45/32/8690_2.png) [@eburacum45](https://boards.straightdope.com/u/eburacum45)\ **Post date:** [February 1, 2024, 11:07pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/13 "2024-02-01T23:07:43Z")
It certainly is dissipated in heat when applied to meteors penetrating the atmosphere. A meteor typically penetrates the atmosphere approximately in line with Newton’s approximation, and all the excess energy is dissipated as heat and light. ---
**Author:** ![markn\_1](https://avatars.discourse-cdn.com/v4/letter/m/f9ae1b/32.png) [@markn\_1](https://boards.straightdope.com/u/markn_1)\ **Post date:** [February 1, 2024, 11:33pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/14 "2024-02-01T23:33:03Z")
There is a somewhat mediocre [Wikipedia article](https://en.wikipedia.org/wiki/Impact_depth) about the topic. Newton’s analysis just looks at the momentum of the impactor. For the impactor to stop, its momentum must be zero, so all its initial momentum must be transferred to the medium. In the conditions where Newton’s approximation is valid, the medium has no cohesion, so all the momentum must be transferred to the medium directly in front of the impactor. When the mass of the medium thus pushed forward is equal to the mass of the impactor, all the momentum has been transferred. That happens when it has penetrated to a depth equal to its length multiplied by the density ratio. ---
**Author:** ![mixdenny](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/mixdenny/32/2962_2.png) [@mixdenny](https://boards.straightdope.com/u/mixdenny)\ **Post date:** [February 2, 2024, 6:34pm UTC](https://boards.straightdope.com/t/newton-impact-depth-and-ballistic-gel-penetration-why-does-it-not-work/996978/15 "2024-02-02T18:34:05Z")
> [@MikeF](#): > > Interesting. Intuitively, I’d think that velocity would play a major factor in penetration depth. The faster projectile has more energy and would go further. More speed=more drag=faster stopping? Where is this extra energy dissipated? Heat? The bullets deform significantly or tear apart. If they stay together they expand to maybe 3 times the original diameter.