There are a few different models, of course; one could argue that Ranma's toughness is consciously controlled via ki despite the fact that there is absolutely no evidence of this anywhere in the manga and a good bit of counter-evidence. Some people argue that Ranma's toughness is due to some sort of ki-shielding, despite tons of counter-evidence in the manga. Some people have proposed that Ranma jumps high by manipulating gravity/adjusting his weight, but that is also unsupported; that would result in the Chinese-Wu-Shu style "floating through the air" jumps that take a long time to land... which we don't see in the Ranma manga or anime. We, instead, take the approach that Ranma's toughness and strength (and relevant jumping and punching ability) is enhanced throughout his body in a straightforward manner... and that the cause is possibly (but not necessarily) related to ki and spirit. This fits easily with evidence in the manga and with intuition. Further, it's a good model in a crossover where guns are used.

On the most basic level, Ranma needs to have a level of toughness and strength where someone of his own strength is capable of harming himself with punches and kicks. Further, he needs to have a level of strength and fitness capable of performing the many feats he is seen performing in the manga (like jumping high, etc.) In humans, the ability to punch hard is limited only by /power/ output - the ability to accelerate one's fist when it is already moving at a high velocity. The best way to obtain power outputs in humans is jumping ability. A 10m moderate jump (9m is easily enough to leap into a 3rd floor window) would have a corresponding max jump near 16m (4th floor). Those might be a little high for Ranma, but I'd consider them reasonable. This takes about 160000 W output (or about 210 horsepower.)

As a note: "Fit human": jumping output is up to 2500W. (55cm/22" vertical jump).

"Super-fit human:" jumping output is 4000W (91cm/36" jump).

In comparison, the average adult male has a 17" jump, and world-record vertical jumps are 48".

Now, Ranma would have 40x the power of the super-fit human and 64x the power of the fit human... but after scaling for differences in mass, Ranma has 50x the power/kilogram of the super-fit human and 80x the power/kilogram of the fit human. (Ranma and Ryouga are smaller than the 70kg human the other numbers are based from.) Since Ranma vs. Ryouga doesn't end up with shattered arms and broken teeth, it's more like a fight between "Fit" humans than anything else. So, relative to toughness, Ranma and Ryouga have to be able to take blows generated with around 80x more power than normal humans can withstand. If they were much tougher than that, then they could never take damage from their own blows, which is not supported by the manga. If they are much less tough than that, then they'd be casually breaking each other's bodies and their own bodies with the forces generated when they punch or kick or jump. There is, of course, leeway for variance; Ryouga is probably tougher than Ranma, after all. However, it provides a baseline.

Now... when you generate blows with 80x the power, you get the cube-root of that enhancement to velocity and the 2-3rds root of that enhancement to energy. That is, without using any special or especially exhausting techniques (e.g. Amaguriken) Ranma could punch 4.3x as often and 18.6x as hard. (This should make sense; if you can punch 18.6x as hard and 4.3x as often, then your total power output is 4.3*18.6 = 80 times as high.) Amaguriken seems to be a technique that enhances speed without enhancing how "hard" a punch is, so it should be treated as something different.

Anyhow, if one can perform blows that are 18.6x as hard, the most reasonable conclusion is that one needs to be 18.6x as tough in order to take them.

Of course, Ranma is also taking 4.3x as many blows per unit time as a normal fighter, so he must be able to recover from them and react to them much faster too... and endurance is probably higher (allowing Ranma to take more damage before going down). (If you don't know, Toughness reduces damage while Endurance allows you to suffer more of it and keep moving.)

Now, when we say 18.6x as hard, here... we mean 18.6x as hard as skilled, fit +martial artists+ can punch... not 18.6x as hard as an untrained, fit +normal person+ can punch.

Below, a more "conservative" estimate of 15x toughness was used. This would be the absolute minimum relative toughness Ranma possesses. (Much lower than this, and Ranma's fist would be capable of punching holes in Ranma's flesh.) The higher 18.6x toughness, however, is enough to reduce penetrations a decent amount for bullets that already weren't penetrating very deeply.

--

Anyhow, here are some considerations:

The amount of energy in Ranma's fist is a primary factor in the damage it will inflict. Ranma's fist is getting a total output of about 15x the total relative energy as a normal high-caliber martial artist's fist... or about 1700 Joules rather than 120 Joules, then scaled down for Ranma's smaller size... call it 1500 Joules. However, it inflicts only as much damage to himself as is dealt by a blow from one expert martial artist to another. We're simply assuming Ranma is as much more capable of absorbing energy-damage as Ranma is of inflicting it.

The average /pressure/ from a blow is equal to Energy/(Area*Stopping Distance). This is also equal to 15x for Ranma as it is for a normal human. In the literature, it takes 1 N to push a 22-guage needle (0.7mm outer, 0.4mm inner) into a normal human's flesh - corresponding to a pressure-resistance of 4 MPa. (This also determines scratch-resistance of flesh such.) The 15x factor, for Ranma, brings this up to 60 MPa. Of course, that assumes a very low stretch-factor for the flesh, which isn't the case when handling things of wider-caliber. (I.e. the flesh will give more when you press a finger into it than, say, a needle...).

If Ranma's fist is about ~10 square centimeters. E/A = 150 Joules/cm^2 = 1.5 MJ/m^2. If you assume a stopping-distance of 3cm against, say, Ryouga, the total pressure on Ryouga would be 1.5 MJ/m^2 * 1/0.03m = 50 MPa. Comparing human (real-life!) martial-artist to martial-artist, the pressure would be 12 Joules/cm^2 * 1/0.03m = 0.12 MJ/m^2 * 1/0.03m = 4 MPa. Obviously this is the same pressure as a needle... but we know the fist doesn't penetrate. That means the stopping-distance must be greater, or, at least, that the flesh is capable of giving yet more before the fist is stopped... which is likely the case. By using a finger-punch (spear-hand) the pressures here can be tripled; it is perfectly reasonable that one upper-level martial artist might be able to pierce another's flesh with such a technique.

Relative to bullets: if the flesh can't stop a 19mm long bullet in about 3cm, it is very reasonable to assume that it has already penetrated. Bullets are a lot narrower and sharper than fists, after all... and it is likely more true if the bullet beats the needle by a high numerical factor. Anyhow, a typical 9mm Luger round has ~570 Joules of energy and punches a 9mm hole in the opponent. Even ignoring its rounded head (which will help penetration the same way the edge of a katana does) that results in a whopping 900 Joules/cm^2 = 9 MJ/m^2. To stop this in 3 cm would require Ranma's flesh be able to handle 300 MPa. The only reasonable conclusion is that Ranma's skin won't stop the bullet!

Thus Ranma isn't bullet-proof.

What about the JHP (Jacketed Hollow Point) that already penetrated the table? Those would be expanded by the impact by at least half a caliber and up to a full caliber (14mm to 18mm) depending on the nature of the round. Further, they would have lost energy to the table... even ignoring the air in the way. Assuming the table is 30 mm thick (1.2"), the bullet has about 270 Joules left upon striking Ranma. This results in a much lower 110 J/cm^2 to 180 J/cm^2... about the same as Ranma's fist. To stop these in 3cm would require 40-60 MPa... just below the toughness of Ranma's flesh. It is, thus, quite possible that those pre-expanded and slowed JHP would fail to penetrate... but is is a very borderline case.

Anyhow, the general conclusion is that Ranma isn't Bullet-proof.

Well, if Ranma is 15x as Energy and pressure-resistant even AFTER you penetrate his skin, then this gives an internal pressure value about 15x higher against continued piercing even after the bullet cuts into the body. Unfortunately, I haven't a clue about the math relating internal pressure-resistance to bullet-penetration... there are a lot of differential equations involved. So I used a ballistics calculator: http://home.snafu.de/l.moeller/Englisch/Penetration_Calculator_2.html (dont'cha just love those Germans?)

Anyhow, fill in the values:

bullet = 9mm, 8grams, 390 m/s

materials: (C1 and Density)

natural diamond (pull-strength = 90,000 kp/cm^2 to 170,000 kp/cm^2, density 3.5 g/cm^3, ... fragile!)

Aluminum Oxide (= ruby, saphire) (pull-strength = 30,000 kp/cm^2, density 3.97 g/cm^3, ... fragile!)

high-strength steel (pull-strength = 17,000 kp/cm^2, density 7.8 g/cm^3, ... fragile! used in top-level gun barrels)

titanium alloys (pull-strength = 7000 kp/cm^2 to 14,000 kp/cm^2, density 4.5 g/cm^3)

RHA Steel (pull-strength = 7500 kp/cm^2, density 7.8 g/cm^3) (/old/ armors were made from RHA steel.)

soft steel (pull-strength = 5000 kp/cm^2, density 7.8 g/cm^3)

aluminum alloys (pull-strength = 1000 to 4000 kp/cm^2, density 1.5 g/cm^3)

granite (pull-strength = 2000 kp/cm^2, density 2.7 g/cm^3)

rolled copper (pull-strength = 1720 kp/cm^2, density 8.96g/cm^3)* (FMJ bullets using copper will deform against harder materials)

bone (pull-strength = 1700 kp/cm^2 (1000 to 2000, density 2.0 g/cm^3, ... fragile!)

brick (pull-strength = 500 kp/cm^2... 100 to 1000 kp/cm^2, density 2.0 g/cm^3 to 2.8 g/cm^3 )

concrete (pull-strength = 280 kp/cm^2, 2.3 g/cm^3)

marble (pull-strength = 150 kp/cm^2, density 2.5 g/cm^3)

wood: (150-600 kp/cm^2 parallel to grain, 20-100 kp/cm^2 perpendicular to grain, density ~0.9... prone to splitting when struck parallel to the grain!)

rubber: (90 kp/cm^2, 1.0 g/cm^3)

soil: (50 kp/cm^2, 1.2 g/cm^3)

human flesh: (40 kp/cm^2, 1.0 g/cm^3) -- at the bottom of the totem-pole!

(Bones and Diamond have about the same fracture toughness).

Pull-strength is "strength under pressure" 1 kp/cm^2 = 1 kilopond ~= 1 atmosphere or 100 kPa. As with everything else, we multiplied these by 15x for Ranma. As a result, we get 600 kp/cm^2 = 60 MPa for flesh (note that it is tougher than stone... no nurse is putting a 22 guage needle into Ranma w/o slamming it in) and 25000 kp/cm^2 (2500 MPa) for bone... enough to casually bend steel without breaking, which Ranma does canonically on at least one occasion.

Note: Ranma's bones would be among the tougher materials in OUR world... though carbon super-composites put Ranma's bones to shame. A bullet, even an FMJ bullet, hitting Ranma's bones will yield before Ranma's bones do... most of the bullet's energy will be reflected back on the bullet, just like when a bullet hits an armored car, or when a normal person punches a steel plate. However, against heavy bullets, the bones are likely to fracture... and even against lesser bullets, the bones can bruise or fracture.

And, of course, magically enhanced materials (or ki-enhanced like Ryouga's bandannas) can be harder than than they are naturally by large factors...

Ah... well, I got side-tracked there. Ultimately, HOW WELL DO BULLETS DO AGAINST RANMA?

Well, according the the ballistics calculator (assuming a shot to Ranma's flesh, not bone):

9x19mm Luger FMJ = 12 cm (4.7"... not enough to be deadly without a direct shot to vitals)

9x19mm Luger JHP (3mm crimp) = 4.7 cm

9x19mm Luger JHP - Pre-expanded: = 4.1 cm

9x19mm Luger JHP - Pre-expanded after hitting table: = 3.1 cm

9x23mm Winchester FMJ: = 14.5 cm (6")

9x23mm Winchester Fragmenting (assuming 2/3 mass loss): = 5.7 cm

.44 JSP - 7.6 cm (expanding to 20 mm caliber! yeouch! but not deadly.)

.454 Casull JSP - 8.2 cm (expanding to 22mm caliber! 3.2" deep and .85" diameter)

.44 Magnum (hard core): = 17.5-22.1 cm (7"-9" depending on load (Magnum bullets are often hand-made), starting to get deadly)

.454 Casull (hard core): = 26-30 cm (10"-12"... now that's stopping power even against Ranma... so long as you hit no bones.)

Note that the Casull actually has almost twice as much raw energy in its bullet as Ranma has in his punch... 2700 Joules as compared to 1500. Even the magnum has more energy than Ranma's fist... though it is much closer (~2000 Joules for a high-power magnum bullet). Thus these guns hit as hard as Ranma does, but to an area the size of Ranma's finger.

Note that even the powerful Casull and .44 Magnum aren't particularly deadly to Ranma when loaded with expanding rounds... which are, by far, for these guns, the most common. Even Alucard uses expanding rounds for his Jackal and Casull. However, while not deadly, they'll effin' hurt!

5.56mm NATO: = 53 cm

7.62mm NATO: = 53 cm

(in one side, out the other, assuming no yaw, fragmentation, or tumbling... but that's unreasonable; the 5.56mm bullet, at least, is designed to do all of the above.)

.50 BMG (Browning Machine Gun): = 90 cm

Hitting Ranma's Bones (ignoring reflected damage/flattening of bullet!):

9x19mm Luger JHP: = 1.3 mm (assuming it just flattens upon hitting Ranma's head)

9x19mm Luger FMJ: = 3.8 mm

.454 Casull: = 9.9 mm (Enough to break any bone or puncture Ranma's skull)

7.62mm NATO: = 25 mm (will tear through all but the thickest bones)

.50 BMG: = 44 mm (in one side... out the other. Period.)

Realistically, we'd see a lot more deformation when these bullets hit bones. For example, the 7.62 mm NATO is known to only penetrate 12mm of RHA steel... which indicates it is deforming, since without deformation it would penetrate about 40mm of RHA steel. Of course, it makes sense that these deform... hitting harder steel with soft lead surrounded by a soft copper jacket is guaranteed to deform; even steel core bullets have the potential to deform (though they'll deform far less!) If you want to get these high penetration values on Ranma, you need an armor-penetrating bullet... a tungsten carbide tip would work.

Anyhow, the average cranial thickness in an adult human is about 5mm. This indicates that a .454 Casull (assuming no deformation) would definitely be deadly to Ranma with a direct hit to the head. Even adding deformation to the bullet only brings it down to 7.5mm or 6.3mm depending on how much it crimps... so it is deadly even for a soft-point Casull round (the likes of which Alucard uses.)

However, Ranma would require /multiple shots/ to the skull to be seriously hurt by 9mm Luger enhanced armor-piercing rounds (e.g. with tungsten carbide tips!). And, most importantly, any indirect/glancing hit to Ranma's skull is going to end up with that bullet performing a ricochet. In either case, the damage from a non-penetrating blow from a Luger is going to be /far less/ (1/3rd the energy) than Ranma getting punched in the head by another high-level martial artist.

To kill Ranma with 9mm Luger FMJ, you'll need to hit his neck (arteries) or his eyes, or aim for the heart and pray the bullet passes between ribs. This is a very difficult task when accounting for Ranma's range; his jumping acceleration is at a level good enough to /barely/ dodge a shot to the head from a range of 10 meters (assuming zero reaction time...). If you account for his danger sense or his eyes being able to see your trigger-finger and barrel aim, he might even get negative reaction time to your shot. The time it takes to aim a gun and the time it takes for Ranma to dodge that aim will be very significant...

Conclusion: Ranma is /not/ going to be taken down with bullets from a weak pistol. To do it at all, you'd need complete surprise and plenty of time to aim for a vulnerable spot... or have Ranma tied up, literally. Big-ass pistols and Rifles, however, are a different story.

As a side note: Ranma isn't particularly well known for his toughness among the other martial artists... Alexander Anderson and Ryouga have the potential to be considerably more resilient, especially since they have technologies and techniques associated with toughness.

As obsidian_fox said: Realistically, bullets will deform against bones.

The truth of this statement can be varified quite easily. A 5.56mm round fired from an M16 (920 m/s, 4.0 grams) has been verified in the real world as penetrating ~6mm of steel. However, according to the ballistics calculator the same round will penetrate ~36mm through steel. To say this disparity is significant is an understatement. So the question becomes, why?

Well, the problem is apparent, the ballistic's calculator assumes, unless you enter otherwise, that the bullet leaves as prestine as it entered. However, all but the best designed armor piercing rounds /deform/ when penetrating steel. Equally, Ranma's bones apply as great, or greater force back on the bullet as does steel. Thus, we can assume that a bullet will deform similarly.

However, the rate of deformation is unknown, and the only penetration values I could garner are: 6mm steel for the 5.56x45mm (920 m/s, 4.0 grams) and 12mm for the 7.62x51mm (840 m/s, 9.33 grams). As such, I will /attempt/ to reconstruct information from this and this alone...

*******

Methodology: to attempt reconstruct this I used a simple mechanism. That is, I determined what crimp, the expansion of the bullet caliber, is necessary for each of the rounds to stop at their real world designated value.

5.56x45mm = Penetration 6mm through steel = crimp: 13.5, expansion factor 2.4x, end expanded caliber 20.17mm

7.62x51mm = Penetration 12mm through steel = crimp: 7.5, expansion factor 0.98x, end expanded caliber 19.50 mm

Note the closeness of the end expanded caliber. They are both almost equal to 20mm. For a moment let's take the /large/ assumption that an expansion to ~20mm is to be expected before the bullet comes to a rest in steel. Using this I can construct an assumed penetration through steel, and crimp factor for the following bullets:

9x19mm Luger = Penetration 3.5mm through steel, crimp: 29mm

9x23mm Winchester = Penetration 4.2mm through steel, crimp 24mm

.454 Cassull = Penetration 10.4mm through steel, crimp 9.5mm

Note, that these results are not outside of expectations. The 9x19mm Luger and the 9x23mm Winchester rounds are penetrating less than the 5.56mm M16 rifle rounds, which is almost certianly correct. However, the .454 Casull's penetration seems a bit high, but it is well within expectation, especially given that high momentum weapons tend to penetrate more effectively against dense materials. Keep in mind, all of these penetrations assume ordinary bullets, tungstun and other armor penetrating materials will preform much better due to greater resistance to deformation.

Now, using these /loosely/ reconstructed values, we will /assume/ that the deformation on Ranma's bones will be the same as that when penetrating Armor grade steel. Given the strength values of Ranma's bones this statement is not out of line. As such, we will use the same rounds against Ranma's bone: 25,000 kp/cm^2 pull, 2 g/cm^3 density, Cd: 1, and the crimps above.

9x19mm Luger = (crimp 29mm): 2.0 mm penetration

9x23mm Winchester = (crimp 24mm): 2.5 mm penetration

.454 Cassull = (crimp 9.5mm): 6.4 mm penetration

5.56x45mm = (crimp 13.5mm): 5 mm penetration

7.62x51mm = (crimp 7.5 mm): 9.4 mm penetration

Now again, these are /loosely/ constructed, but are undoubtedly far more correct than the unconstructed values. Note also that of the listed rounds only the .454 Cassull, and 7.62x51mm will fully penetrate Ranma's skull. For these I will include additional /flesh/ penetration after punching through 5mm of bone.

.454 Cassull = 5mm bone + 48 mm flesh (1.9")

7.62x51mm = 5mm bone + 125 mm flesh (4.9")

Notice that the 7.62x51mm has enough penetration capabilities even after slicing through 5mm bone to threaten organs, though the penetration is still quite low. Further, even 7mm of bone drops flesh penetration to 65 cm (2.6"). Further note, that while none many rounds might not /penetrate/ bone there is still little stopping them from fracturing or even shattering bone.

For my story I've been using the GURPS role playing system to model the characters and have been modeling the canon chi techniques with psi powers, with many limitations on their use. For instance Cologne has shown some very powerful Telekinesis in her techniques, and Ranma has shown ESP, Telekinesis, Cyrokinesis, and even Photokinesis. My version of Ranma has undergone Genma's version of the Bakusai Tenketsu training and has probably recieved at least the basics of the Iron Skin technique while in China, this has made Ranma's subconcious use Telekinesis to reinforce his skin to resist penetration and harden the muscles underneath to resist blunt trama damage, this makes him resistant to fragmentation and .22 rimfire and .25 pistol rounds, and .38 and 9mm would only produce very shallow wounds. As a side note, Akane has aided his training in resisting head trauma, thus his skull is being subconciously reinforced with his TK powers and his brain is cushioned to resist concusions, ie he is uninjured by anyone with less than gorilla strength with a sledge hammer, or would only suffer a graze from a .454 bullet as it ricocheas from his skull.

Physics trumps GURPS rules!

My question to the authors, does Ranma have any control over his toughness? There would be times (getting a shot with a needle at the doctors) when the ability to lower his toughness would be an asset.

Whether it is Ranma's chi or something else that results in Ranma's toughness, the facts are that:

1) Ranma is difficult to scratch, hurt with punches, etc.

2) Ranma takes fairly consistent damage from attacks, so it is not something that he can casually control.

3) Ranma takes considerably less damage from blows than non-martial-artists would.

4) Ranma can crush steel and crumble concrete with ease.

5) Ranma displays no "shielding" style effect. He can be scratched easily by other martial artists.

6) There is no evidence that Ranma's toughness decreases when he is exhausted.

7) Ranma's toughness remains the same when unconscious.

Note that we didn't make Ranma's bones or flesh any denser. We just made it tougher. The result meets all the observed qualities about Ranma's capacities.

I'm not of the belief that GURPS modeling with psionic powers is appropriate for the task. The idea that Ranma's strength and protection comes from some obscure use of chi is not supported in Ranma canon.

Note that a .454 hitting the skull will hit with about the same overall power as Akane's mallet... but to an area the size of a finger. It should -not- ricochet from Ranma's head in your story... unless you are using much higher estimates for Ranma and company, or if the shot hit at a shallow angle (which may have been what you meant).

Yes, Ranma would have troubles getting a shot... it would take about 15N (3.3 pounds) force to push a 22-guage needle into the body, and that would stress it and potentially break it... but it would be doable with a strong needle and syringe.

Can only remember Cologne and Tofu applying pressure points in the manga, not sure if there is any supporting evidence either way.

For the ki-based pressure points and esoteric things (e.g. ultimate weakness moxibustion), it wouldn't matter.

Applies to other sorts of pressure, too. If you want to give Ranma a backrub, you've got to have strong hands!

This is not shiatsu. AFAIK, shiatsu is an exclusively Japanese concept of manipulating individual nerve pathways to affect energy flow. However, there are Chinese styes that focus on manipualting pressure points.

An easy example is the spot behind the thumb, which if pinched, causes debilitating pain, and the inability to use the hand.

The only thing I disagree with it on is the fist speed, which seems way too fast to me, though I'd think your estimate would be a tad slow. Be that as it may I think his estimates for Ranma's strength is good. And the example it gives of being punched into the mountain is excellent. It would take a hell of a lot of energy to displace that much rock. Yet Ranma is barely phased.

That site uses rather poor examples for Ranma's strength, speed, power, etc (examples where determining objective numbers is very difficult) then proceeds to use bad physics in order to perform the calculations.

Example 1: Power - the 100m number was pulled directly from ass. The 45 m/s landing is incorrect once accounting for air friction, which doesn't allow for a fall much faster than 60 m/s given the formation in which Ranma carries the girls. Finally, and most fundamentally, Ranma's muscle power can't be estimated by landing... only by jumping. Landing is a bone and muscle stress test... but even a statue can land, and statues have no power at all.

As a stress test, it has some value; clearly, at that amount of damage, Ranma broke bones.

Example 2: Fist speed. It is known that Amaguriken to one spot looks like an elongated, blurred punch. This means it is happening longer than a frame for the human eye. It is also known that Ranma has shouted Katchuu Tenshin Amaguriken during the maneuver in a late manga volume... which means it can take up to 2 seconds to execute. Finally, it is known that Akane can't count the punches; to her, it looks like one punch. She couldn't even count the seven kicks against Kuno when Ranma was slower. Thus, Akane is apocryphal; it could be 100 punches in 0.1 seconds like they say... but it could also be 100 punches in 1 second.

Example 3: Body speed... actually comes up equivalent to our own... though we expect 28 m/s would be an exhausting pace for Ranma to maintain (and 20 m/s would be a more casual running speed).

Example 4: Body damage. No evidence that rock was compressed (in fact, it can't be; it has to be a shockwave blast, or there has to be hollow behind the rock face and it caved.) Damage to the rock is damage not done to Ranma's body. As it is, our measurements make him harder than stone... so utilizing his body to inflict damage like that would be rather casual.

(And, of course, we can't forget that Ryouga is a rock-blasting specialist...)

Rock compression would result in Ranma-imprint.

The only thing I disagree with it on is the fist speed, which seems way too fast to me, though I'd think your estimate would be a tad slow. Be that as it may I think his estimates for Ranma's strength is good. And the example it gives of being punched into the mountain is excellent. It would take a hell of a lot of energy to displace that much rock. Yet Ranma is barely phased.

Our estimate for fist speed still allows Ranma to perform every act he was ever shown to perform in the manga, surprisingly enough. The difficulty here is scale; we're running Ranma as a scaled up outstanding-martial-artist from our world, and even IRL these outstanding-martial-artists can do things that completely defy what you'd think reasonable - like cutting freely-moving bricks in half with a crescent kick. Ranma's power is such that he throws punches at a considerably greater velocity. It is very difficult to put that in perspective. I don't imagine you can really think something is a tad slow unless you really know how everything interacts.

Now, some people run Ranma as a cartoon-punk with cartoon-physics. That works too, so long as the internal physics are consistent within the cartoon-physics laws.

I hate to say it, but that site grossly over exagerates Ranma's capabilities. It pushes everything to the point, and beyond reasonable guesstimate, and then uses numbers to even further overly bloat estimated capabilities. Finally, the mathimatics are often quite shaky, and the physics very hocky.

Take for instance this:

"Using falling approximately 100m while carrying 4 girls (Akane, Shampoo, Pink and Rink) in V29.7 page 113-114."

You can /clearly/ see Ranma rise 1.5x - 2x the height of Furiken Highschool. Thats around 20 to 30 meters... an inaccuracy of ~only~ /300% to 500%/

This is neither the first, nor the last example of inaccuracy, often times /DRASTIC/

"taking total weight to be 300Kg"

Try 55 Kg Ranma, ~45 Kg x4 or around 235 Kg. (Doesn't seem like much, but thats another: 25% over estimate)

"Using the PE equation, to estimate maximum weight he could lift above his head (ie 2m):"

This is pure bullshit. You can't estimate lifting capacity via power. There is no direct relationship.

" In comparison Lime catches a boulder (V24.10 p154) in one hand which would weigh (taking radius as 1.5m, density as 5tons/m³ ) about 60 tons."

Again, these numbers are absurd. First, the boulder is 1.1 - 1.2m radius. Second, this 'rock' has a tree growing out of it, indicating that it is rock/wood/and soil. A rather /GENEROUS/ density is around 2,500 kg / m^3. Note that 5000 kg / m^3 is 25% denser than the most dense of real rock (3000 kg / m^3 would be a fair estimate for most dense rock).

Estimating: v = 4/3 * pie * r^3; v = 4/3 * pie * (1.15)^3

6.35 m^3 or 16 metric tons for Lime, one handed. (Factor of four differance...)

To put it simply, most of his calculations are pure crap. Further, there is no attempt to relate these numbers to real world numbers.

Back to you:

The only thing I disagree with it on is the fist speed

Which shouldn't be surprising, given how absurd his other calculations are.

Lets take a quick look shall we:

"Now, in V6 (Viz GN5) when Ranma is fighting Ryöga who's just learned the Bakusai Tenketsu, Ranma hits Ryöga several 100 times so fast it looks like one punch."

The value "Hundreds of times" is heresay from a character that directly admited to being unable to tell how many punches are being thrown. Hundreds, must therefore, be considered an entirely meaningless value.

FURTHER, Ryouga, who would be in a better position to know how many punches Ranma threw, says after Ranma uses a few Arigumi Ken (of /indeterminate length/) "Tired after throwing a few hundred punches?"

This clearly indicates that his raw number of punches is already wrong by at least a factor of 2.

EVEN FURTHER, Ranma would appear to be throwing a 'deep punch' in the end, a time frame of 0.5 to 1 second would not be unreasonable guess. The later amagurikens could be far longer.

It would take a hell of a lot of energy to displace that much rock. Yet Ranma is barely phased.

Moving Rock doesn't require a whole lot of energy. Especially given all the rock would be moving down...

(Of course, slightly less conservative Ranma's can have 14x toughness and 52x power, or 15x toughness and 58x power, or 16x toughness and 64x power... etc. power-factor^(2/3) would be relative toughness.)

Some more math considerations vary the numbers again. This time the concern addressed is that toughness is rated off the expectation that Ranma could do as much damage to himself as a Superfit-Olympic-Martial-Artist-Freakazoid, which while human, pushes the upper limits of human capability. However, Obsidian, correctly, expressed concern that a Superfit-Olympic-Martial-Artist-Freakazoid attacking another Superfit-Olympic-Martial-Artist-Freakazoid would be doing incredible damage. Shattered bones, blood, teeth on the floor wouldn't be out of line. We just don't see Ranma and Ryouga doing that kind of damage to eachother.

So instead, toughness was recalibrated off of a more /normal/ fit human (instead of super freakazoid). This raises the toughness factor for a conservative Ranma up to about x18, slightly higher than the original x15. This will make a small difference, about 10-15% smaller penetrations. However, that is about all.

60 km/h = 17 m/s. Ranma can run himself into walls at a higher speed than that. At worst, Ranma would have a bleeding nose and welts in the shape of a grate and maybe a few bruises (what you'd expect a high-caliber martial artist to suffer from running full speed, face-first into the same surface - that's what Ranma would suffer... supposing the surface didn't yield under Ranma.) If Ranma or the martial artist expected such a blow, there would be almost no damage at all (due to slight adjustments to muscles, keeping face away from the trailer, etc.)

Basically, Ranma would be immune to accidents up to some level. Now... if someone dropped a bridge on top of him, or hit him with a jet plane, that's a different story. There are always orders-of-magnitude issues.

... you had originally stated something about how Ranma would absorb 7500 Joules and the car would absorb the other half, and that it would be like you or I was hitting the ground after falling out of bed.)

--

Hmmm... energy dumps from inelastic Carmageddon collisions: (assuming victim isn't moving prior to encounter)

(a) m_car * v_car = (m_car + m_victim) * v_final (Conservation of momentum)

(b) v_final = m_car*v_car / (m_car+m_victim) (follows (a))

(c) 1/2*m_car*v_car^2 = (1/2*(m_car + m_victim) * v_final^2) + DAMAGE (Conservation of Energy)

(d) DAMAGE = 1/2*(m_car)*(v_car)^2 - 1/2*(m_car+m_victim)*v_final^2 (follows (c))

(e) 2*DAMAGE = (m_car)*(v_car)^2 - (m_car+m_victim)*((m_car*v_car)/(m_car+m_victim))^2

= m_car*v_car^2 - (m_car*v_car)^2/(m_car+m_victim)

= m_car*v_car^2 - m_car*v_car^2 * (m_car / (m_car + m_victim))

= m_car*v_car^2 * (1 - (m_car / (m_car + m_victim)))

= m_car*v_car^2 * ((m_car+m_victim)/(m_car+m_victim) - m_car / (m_car + m_victim)))

= m_car*v_car^2 * (m_victim)/(m_car+m_victim)

(follows from (d) and (b))

(f) DAMAGE = KE_CAR * m_victim / (m_car + m_victim)

= 1/2*v_car^2*(m_car*m_victim) / (m_car + m_victim)

Actually, that should apply to all sorts of inelastic collisions.

A 4000kg truck speeding on the highway at 33.5 m/s (75mph or 120 km/h) strikes Ranma dead on:

Damage = 1/2*33.5^2*4000*55/(4055) = 30kJ.

lim (x-oo) of x*y/(x+y) = y. Thus, for really big things (like trains, wrecking balls, etc.) the damage the person suffers is always proportional to his own mass. I.e. it becomes more and more like falling onto the ground at a speed equal to the speed of the car.

Anyhow, a hefty blow WILL usually damage the car (which is not damage to Ranma). However, suppose all the damage went to Ranma. Would he stand up and dust himself off? It's equivalent to a 55 meter fall - it would certainly knock Ranma silly. But if that damage were spread (diffuse) over, say, a portion of Ranma's torso (maybe 2000cm^2 - a 40cm*50cm area) then the energy per unit area would be only 15 J/cm^2 - completely unable to break Ranma's bones or penetrate his skin. Ranma would be bruised and rather disoriented. So, after any diziness wears off, Ranma WILL just get back up and brush himself off (... supposing he doesn't guilt-trip the driver into giving free meals or something).

Above was a direct hit to the torso from a speeding truck on the highway (e.g. imagine falling out of a bunk-bed directly onto your back). It is possible to take a hit -much- better... and -much- worse. Landing straight on the head would -really- hurt and possibly break the back or cause a concussion. Landing on fingers can break fingers. Catching oneself with one's arms or legs, however, can significantly reduce -real- damage from being suffered. (-Real- damage is characterized by compression and breaking of things that are not acceptable to compress or break... like bones, as opposed to force applied against muscles.) The same is true for Ranma. Even for the truck, a "good" strike will be like landing at 33 m/s on a surface (eqv. to a 108m fall, or a fall from a 27 story building.) Relative to you or me, that is like a fall from 6 meters (20 feet, or the top edge of a second-story window.) Use of his legs or arms to prevent damage will likely have moderate success, but he's not going to suffer overly much in any case unless he lands very badly.

While it is possible to try for intuition by comparing it to our own falls, one must also remember that, because Ranma can handle the higher fall as though it were (for us) a lower fall, he also has additional advantages in that the ground will seem "softer" to him when he hits it than when we hit it. With an impact from 108 meters, he can crack the cement... which saps more damage away from Ranma himself. For high-speed impacts, things simply seem 18x softer to Ranma than they do to you or me. (Of course, that doesn't make beds feel any softer - it's a different sort of softness, since beds must feel soft under gravity, not impact.) For Ranma, falling 108 meters onto concrete is more equivalent to you or me falling 6 meters onto soft soil.

So I guess one could quickly and safely assume that should Ranma ever go threw some psychological episode and begin raping the various girls after him that he could safely force them to suck him off and not have any fear of having "it" bitten off, right? Or do we have to consider the girls (Shampoo, Ukyo, Akane, various other female martial artists) jaw strength? I'm not too sure, but I don't think I've ever heard of any martial style that focuses on biting their opponents.

You know, just for... a story idea... ehhhh.

Well anyways, am I right?

While obsidian and Xylix probably could write a long and undesciphrable rant about that subject; that only would be understood by themselves.

Now, we are talking about super fit martial artist in the two parts, So IMHO, the bite power would scale accordingly, specially after seeing Ranma insanely fast meals. To eat that quickly, one has to have it's jaw muscles well developed. Therefore, it wouldn't surprise me that she could chew a rubber car tire, or crush rocks with her teeth. (Ryoga does so with a finger.)

In the other part, There is no bone in there, And Imho, if you search in google, I found at least one precedent of one such Case, So what you ask IS possible

(In the other hand, I don't even want to try searching for "masculine reproductory organ toughness factor" in google, the results, most certainly WON'T be what i want)

But IMHO, Even if the girls couldn't cut it off; it will still hurt like HELL. Severe hemorrage for sure.

(I hope Obsidian, Xylix would ignore this part of the post. God, I feel dirty)

First: *Ewwwww*. For god's sake you could have just asked if they could sink their teeth into Ranma's flesh! It'd have answered your question...

Okay, now that I'm beyond /that/.

---

Jaw strength scales with all other ki-adept strength. A ki-adept can bite into the flesh of another ki-adept, just as well as normal human can bite into a normal human. Though, in the case of Ryouga (super high toughness) and a weak ki-adepts like Ukyou, Shampoo or especially Akane..., the girls might not be strong enough to penetrate flesh (It'd still hurt though!).

In the case of a truely normal human girl, yes, a normal human girl could not bite through Ranma's flesh, and probably couldn't even cause more than minor pain with the attempt.

On the other hand, if Ranma ever took such action there would be plenty of people, including Ryouga, that would be willing to handle the casteration in their stead.

I figured since Ranma will be spending a good deal of time in the Wizarding community, (s)he's likely to run into such things since technology reacts badly with magic, and I doubt that ALL wizards and witches are as reliant on their wands as some seem to be.

In a lot of ways, thrusting a knive into Ranma would be kinda like thrusting it into a wooden board. That is, for a normal human, it isn't going to work too well. However if a sharp knife, that can sustain that kind of force on the tip is thrust into Ranma /hard/ it will penetrate. My own numbers indicate anywhere from 20 lbs to 100 lbs of constant force being required to sink a knife into Ranma (point first)..., with most knives being 60+ lbs. This is sufficient that most individuals will have a very difficult time doing so... but it is still possible.

A bow is a significantly powerful weapon. A good bow can penetrate through full plate armor, and has characteristics similar to a pistol. A modest 100 lbs pull bow, (at 80cm draw), will store: 1/2 ( (100/.8) * (10/2.2)) *.8^2 = ~180J

Thats as much energy as low end hand guns, and will certainly penetrate Ranma if shot head on. This is because bullets are fundementally poor penetrators for their energy -- having a blunt face, and low momentum -- where as arrows are fundementally excellent penetrators. Powerful long bows can be significantly stronger, and the same is true of some short hunting bows. Some of the strongest composite bows have circa 220 lbs pulls, and have historically punched through more than an inch of brass. As an additional note, most historic long bows could punch through all but the /best/ plate armors.

I figured since Ranma will be spending a good deal of time in the Wizarding community, (s)he's likely to run into such things since technology reacts badly with magic, and I doubt that ALL wizards and witches are as reliant on their wands as some seem to be.

The vast majority of wizards are as familiar with most ancient muggle weapons as we are today. However, some individuals do carry such weapons around. Hagrid for instance, carries a heavy crossbow when he goes out to the forest.

In any case, Ranma is likely to encounter such weapons, because they are standard fare in Ranma 1/2 as well, and tend to be more more potent in the hands of ki-adepts and other supernaturally strong creatures. (A bow built for a ki-adept will have energies rivaling or surpassing most combat rifles!).

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