The thought occurred to me as I was reading the autopsy report. I couldn't understand why someone would strangle her and then bash her head in after she was dead.

The autopsy report says, "This grossly appears to be fresh hemorrhage with no evidence of organization."

The term "fresh" caught my eye and made me wonder. I tried to put myself into John's shoes. From his description of finding her, he was pretty much hysterical, not thinking clearly, and just rushed her upstairs. He and Linda Arndt described how he carried her, and that her head was turned to the right. The injury was on the right side as well.

So I wondered if maybe he didn't accidently bump her head on something on his way through the basement or up the stairs. I have a feeling that he wouldn't have even noticed if his hair was on fire at the time.

I spent alot of time learning what the different terms in the autopsy report meant (specifically regarding her head injury) and I haven't learned anything that would medically rule the possibility out. I don't know what changes take place in a child's skull strength after death (if it weakens) or how much force would be necessary to cause such an extensive fracture.

So would it be medically possible for something like that to have happened?

And then if it is medically possible, I guess someone would need to know how tall John is. He held her by the waist, facing him, with her head above his according to descriptions. Someone would need to know what obstacles would be at that height on the route from the cellar to the upstairs. In some pictures I saw ductwork along the ceiling and whatnot. Maybe there is something up there that could produce a similar type injury? (I'm thinking about the depressed portion of her skull.) Maybe an electrical plug-in thingy or something on the top part of a door frame? I suppose it's also possible that he started out carrying her a different way, so maybe a corner or something along the way was sticking out?

I realize that this scenario is unlikely but I think it's worth considering so it can be ruled out or not. It's one that I haven't seen mentioned and considering how hysterical John apparently was, he may not have noticed if he bumped her head on something in his rush to get her upstairs. It seems plausible anyway.

Thanks in advance for your comments, and hello from a new member. :-)

Miz

Dead people do not bleed, nor do they bruise in the typical manner of living persons. There were signs of fresh bleeding and bruising in the brain.

Pathologists learn to determine whether damage to a body is antemortem,perimortem or postmortem. Bones broken prior to death differ in color than bones broken after death, and the manner in which they break is also different.

Rainsong

"Do you know how much force is necessary to cause the injuries she sustained to her head?"

Yes I do (see below) and so do others who have read the note below or have done their own calculations.

"I have learned that such extensive injuries can happen with relatively little force, as well as great force."

Not true. The punched-out injury requires a tremendous impulse.

"I also learned that a child's skull is not fully formed, so more prone to fracture than an adult skull."

Not true. Whether one is "more prone" than the other depends upon the specific type of fracture, how it happens, and so on. No such general claim can be made.

"I do not know if 12 some hours of death would compromise the strength of a skull."

Extremely unlikely.

"So, if he was running through the basement then her head may have whacked something (HARD) along the way. Due to her stiffness, particularly in her neck, there would have been no "give", thus increasing the force. If he was running then that very well could have been sufficient force to cause her head injuries."

Not true (see below).

"I'm not saying that is what happened. What I'm saying is that it's a plausible scenario if you sit and think about it..."

No it isn't if you know anything at all about the physics involved (see below).

------------------------------------------

The JonBenét Ramsey Case:

On the Physical Impossibility
of Detective Steve Thomas' Envisionment

08 July 2001, 10 July 2001

Introduction

Herein it is shown that the scenario envisioned by former Detective Steve Thomas of the Boulder Police Department, regarding the murder of JonBenét Ramsey in late 1996, is in all likelihood physically impossible. After a very brief summary of Thomas' envisioned scenario, calculations of the required impact are presented which show that the injury to JonBenét's skull require far more force than can be developed by a fall, an enhanced fall such as by being shoved, slammed, or similar physical action by Patsy Ramsey.

Background

Former Detective Steve Thomas' envisioned scenario <1> is that Patsy Ramsey, JonBenét's mother, "slammed" JonBenét into a hard object such as the edge of a bathtub, causing JonBenét's severe skull injury. Subsequently, Patsy covered up this incident by staging a kidnapping and murder by an unknown intruder in order to distract attention from her own involvement in her daughter's death.

According to the coroner's autopsy report <2>, there was a displaced skull fragment measuring approximately 1.75 inches by 0.5 inches (4.4 cm x 1.3 cm). The area of this fragment is, therefore, slightly less than one square inch (5.6 cm2 or 5.6x10-4 m2).

According to studies on the strength of bone <3>, the ultimate strength of human bone is on the order of 100 MPa (mega-Pascal, or millions of Newtons per square meter).

Simple Fall

In order to introduce some of the relevant physics, let us first consider the fall of a 6.5 year-old female. Her weight, if average, would be on the order of 46 pounds (21 Kg) <4>. Her expected height is 45.5 inches, (3' 9.5" or 1.16 m). If we consider that her center of gravity is approximately half her height, then her center of gravity is 23 inches (0.58 m) above the ground. Her potential energy is, given Earth's gravitational field and switching to metric units exclusively, m*g*h or (21 Kg) * (9.8 m/sec2) * (0.58 m) = 119 J. If she were to fall completely to the ground (center of gravity at 0.0 m, not at bathtub height) from an initial standing position, the kinetic energy developed would be this same number, namely 119 J. Her velocity at impact with the ground can be calculated from K.E. = 0.5 * m * v2. This gives about 3.4 m/sec for her velocity at impact with the ground.

A typical impulse time used for studying skull fractures is on the order of 10 milliseconds (10 msec) <5>, and about 2 msec for a very hard surface <6>. During a time period of 2 msec, a velocity of 3.4 m/sec going uniformly to zero requires a deceleration of 1700 m/sec2. If a force of mass * acceleration (21 Kg * 1700 m/sec2) is judiciously applied to the falling child discussed above, she could be stopped in 2 msec. This force is approximately 36,000 Newtons. If we ludicrously and carelessly applied 100% of this force to an area equivalent to the area of the displaced skull fragment reported by Dr. Meyer in his coroner's autopsy report, we have 36,000 Newtons / 5.6x10-4 m2 = 64 MPa. This is somewhat below the 100 MPa required for the ultimate strength of bone. But what does the assumption of 100% of the force to the area of the displaced fragment imply? It implies that the child's body was completely halted by that impulse applied to the small area of the skull, further implying that the child's body is completely rigid. This just simply is not true.

More reasonable would be to assume that the child's head was completely stopped by the impact to the skull, but that her torso, arms, and legs were stopped by impact with other surfaces. A young child's head is approximately 25% or one-fourth of his/her body weight, so we can crudely adjust the result of 64 MPa above by simply dividing 64 MPa by the mass ratio of four (or multiplying by 0.25). This results in 16 MPa, which is far below the force required to cause a punching out of a skull fragment of the size reported. So we would not expect an average child to have a skull fragment of approximately one square inch in area punched out by a fall of one meter to a hard surface with their head striking a part of the surface 1.75 inches by 0.5 inches. Indeed, experience shows us that one meter is about the minimum-distance fall onto a hard surface for which a person can sustain any kind of skull fracture at all <7>, but this is a completely different situation than having a small section of the skull completely punched out.

Enhanced Fall

Let us now consider an enhanced fall. Let us first consider merely doubling the stress of 16 MPa above to 32 MPa and try to determine what changes are required to the initial problem of a simple fall. The first thing to note is that if we are talking about motion of the child's entire body, then we can simply double the deceleration above so that we would achieve a stress of 32 MPa for her head. The resulting deceleration is therefore 3400 m/sec2 (obtained by doubling 1700 m/sec2). Again using 2 msec as the time over which this uniform deceleration occurred <8>, we have an initial velocity of 6.8 m/sec. The kinetic energy just prior to impact would, in this second case, be (0.5) * (21 Kg) * (6.8 m/sec)2 or about 480 J. Doubling the impact velocity results in an increase in kinetic energy of roughly 360 J (quadrupling the total energy). This extra energy is the additional energy beyond that of a simple fall that would be required to be supplied by the person pushing or throwing a child into something and resulting in a stress of 32 MPa.

How much energy is this extra amount? It is the energy used to raise a 74 Kg object (162 pounds) one-half meter (slightly more than eighteen inches). If Patsy Ramsey can benchpress over 160 pounds, (my athletically fit wife can not do this) then she could possibly have pushed JonBenét at the doubled velocity into a hard surface, but this action would result in an impulse which is still far too small (to repeat, only 32 MPa). We need to, at the very least, double the force again, and this would quadruple the energy again. This second doubling results in an increase in kinetic energy of roughly 1800 J from where we initially started (119 J). 1800 J is the energy used to raise a 367 Kg object (808 pounds) one-half meter. We're still not there yet. We're at 64 MPa, and we need 100 MPa. Suffice it to say that it's physically impossible that JonBenét's displaced skull fragment was caused by Patsy throwing her whole body against something or by shoving her whole body hard enough.

Falls and enhanced falls such as by shoving by Patsy Ramsey are therefore excluded on physical grounds.

Slamming

Now if we assume that Patsy "slammed" JonBenét against something, we have to consider that she probably didn't slam her whole body against the hard surface, probably only her head. Her head is a fraction of 21 Kg, perhaps 4 or 5 Kg. In order to obtain a stress of 100 MPa over an area of the displaced skull fragment, we need a force of 56,000 Newtons. This means that the deceleration needs to be (for 4.5 Kg) 12,400 m/sec2. A uniform deceleration of 12,400 m/sec2 over a period of 2 msec implies that the initial velocity is about 25 m/sec (56 mph). For this to be possible, Patsy would have had to accelerate JonBenét's head to about 25 m/sec in approximately one meter, the maximum distance over which Patsy could have reasonably be expected to have applied the acceleration. (Even this would require acceleration and movement of a large portion of the rest of the body, but we'll neglect that for now.) This acceleration is 312 m/sec2, which for a 4.5 Kg mass implies a force of about 1400 Newtons (317 pounds!).

Patsy, or anyone else for that matter, would have had to push JonBenét's head with 317 pounds of force (over a distance of about three feet) to cause the reported skull fragment displacement, and this act would have had to have been performed with 100% efficiency, meaning that the entire impulse would have had to have been applied directly towards completely punching out that particular fragment of skull. Although it's conceivable that someone very strong, capable of benchpressing hundreds of pounds, could get within range of this, it's highly unlikely that Patsy Ramsey could have done this.

Weapons

More likely a weapon of some sort was used. People can swing golf clubs at speeds over 100 mph and baseball bats at speeds in excess of 75 mph <9>, respectively (45 m/sec and 34 m/sec). A uniform deceleration from 45 m/sec (100 mph) to zero in 2 msec is 22,500 m/sec2. Developing a stress of 100 MPa over the area of the skull fragment requires a mass of only about 2.5 Kg (about 5.5 pounds). This is heavier than a baseball bat or a golf club, but it's the correct order of magnitude for those objects. It is also the case that using a weapon allows for the attacker to direct a deadly impulse to a specific area, a serious problem especially for a falling or a shoving/falling scenario.

This latter calculation demonstrates that even if a weapon was used, it was used with great force. Whoever wielded this weapon was probably physically quite strong. The weapon was also probably somewhat long to achieve a very high speed, not as short as a flashlight, for example. It also had to be relatively hard to achieve a very short deceleration (deformation) time.

Future Work

Finite element codes are available which could be used to more accurately simulate an injury to the skull. Here we have merely shown with simple analytical calculations that any pushing, shoving, or "slamming" actions by Patsy cannot come even remotely close to generating the kind of force necessary to have caused the JonBenét's skull injury. More accurate simulations could potentially rule out other scenarios.

More accurate analytical calculations could be done, especially those taking into account suture lines and so forth to determine exactly what kind of weapon is reasonable. That is to say that a more careful consideration of the skull fragment may result in a better understanding of what actually occurred. It seems highly unlikely, however, that the primary conclusion that Patsy could not have possibly done this in the manner envisioned by Steve Thomas would be changed in the slightest.

Conclusion

Although it is possible that someone very, very strong could have killed JonBenét Ramsey in the fashion described by former Detective Steve Thomas, the blow inflicted on JonBenét was almost certainly an extremely violent blow to the head using a weapon. The scenario envisioned by former Detective Steve Thomas, specifically involving Patsy Ramsey slamming JonBenét against something, is hereby shown to be physically impossible.

References and Notes (Links may no longer be valid - Sept 2006)

<1> Steve Thomas. JonBenét: Inside the Ramsey Murder Investigation. St. Martin's Press, 2000, pages 286-289 (hardcover).

<2> John E. Meyer. Autopsy Report: JonBenét Ramsey. 27 December 1996.
http://www.courttv.com/casefiles/jonbenet/autopsy.html

<3> D. T. Reilly and A. H. Burstein. The classical and ultimate properties of compact bone tissue. Journal of Biomechanics, Volume 8, 1995, page 393. As cited in: Stephen C. Cowin. Bone Mechanics. CRC Press, 1989, page 115.

<4> The World Almanac and Book of Facts: 1995. World Almanac, 1995, page 972.

<5> B. V. Mehta, R. Mulabagula, and J. V. Patel. Finite element analysis of the human skull considering the brain and bone material properties. In J. Middleton, M.L. Jones, and G.N. Pande (editors), Computer Methods in Biomechanics and Biomedical Engineering, Gordon and Breach Publishers, 1996, pages 217-228.
http://www.ent.ohiou.edu/~mehta/skulluk.html

<6> John Plunkett. Shaken Baby Syndrome and Other Mysteries. Submitted to American Journal of Forensic Medicine and Pathology, 1998.
http://www.portia.org/chapter8/mystery.html

<7> D. W. Sadler. Head Injuries. University of Dundee, 1999.
http://www.dundee.ac.uk/forensicmedicine/llb/heading.htm

<8> Here we assume a constant deceleration time rather than a constant deformation distance, consistent with the assumption that higher velocities would result in more deformation and roughly the same deformation time.

<9> Knowledge Daily, 08 July 2001.
http://www.knowledgedaily.com/index.asp?st=mcgwire

<10> The actual energy required to displace the skull fragment at its maximum possible displacement prior to fracture, relying on thin-plate theory which isn't actually applicable here, is quite small, less than 10 J. The impulse required, however, is very large. Energy calculations alone won't reveal what is possible and what is not.

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