A number of things crossed my mind as I watched the reenactment.
A number of things crossed my mind as I watched the reenactment.
Firstly, I was disgusted, yet again, with law enforcement in this case. We are watching a low budget reenactment with issues stemming from the lack of access to the crime scene when the opportunity to do a proper reenactment was squandered by the SDCSD.
The CBS8 reenactment was an unusual mix of attention to detail in some areas and oversights in others.
The most impressive bit of detective work was tracking down the maker of the bed frame.
The chief oversight can be summed up in one word friction. Unfortunately, this severely damaged the validity of the reenactment.
There are three areas where friction would play an important part in the crime scene.
The point of contact between the rope and railing.
The point of contact between the rope and the closed balcony door.
The coefficient of friction (COF) between the bed and the rug.
In physics, the coefficient of friction is important and there are tables to show how different substances interact. The table below gives a sampling and show the difference between getting two things to begin to move (coefficient of static friction) while in contact with each other and the change in friction once movement has begun (coefficient of kinetic friction.)
Usually, although there are exceptions, the force required to initially move an object and overcome the forces of friction and gravity are higher than the force required to keep it moving.
In a situation such as we find in the crime scene there would definitely be a higher static coefficient of friction between the bed and rug because the bed had sunk into the rug over time.
Any difference between the crime scene and the reenactment with respect to kinetic or sliding friction would be down to the pile depth and material type of the rugs which may or may not be significant.
http://www.freeonlineresearchpapers.com/friction-sports
Just as a further illustration, if the bed was on a hard marble floor, it would have of course slid much further.
The rope is exposed to two areas in which it contacts other items and would be subject to friction.
The first contact is with the closed door on the balcony. This is about a 10 degree angle of contact with the edge of the wood door.
The second contact is with the top of the 1 inch iron balcony railing. This is a very significant source of braking friction in the crime scene.
The rope contacts the inner edge of the railing at about a 11 degree angle and then forms a 90 degree angle with the outer edge.
If the rope was going over a round tube, rather than the two relatively harsh edges of the railing, there would be a nice formula to determine the amount of force transmitted from the fall back to the bed.
That formula is FORCE@BED= FORCE * e^- coefficient of friction * angle of contact
http://www.girep.org/proceedings/se...perimental_Example_from_Physics_in_Sports.pdf
http://www.engineeringtoolbox.com/bollard-force-d_1296.html
http://www.engineeringtoolbox.com/friction-coefficients-d_778.html
http://www.engineershandbook.com/Tables/frictioncoefficients.htm
The reenactment differs in two important respects:
The rope does not make contact with an obstructing door edge and a sharp-angled railing edge, but rather only with a well rounded beam shown in the picture below.
If this difference created a difference in the coefficient of friction of 0.2 (as an example,) then the change in force would be a huge 42%
Another less important difference is that the point where the rope was tied to the bed and the contact point over the railing are offset in the crime scene but directly in line in the reenactment.
There also appears to be a considerable difference in the dimensions of the rooms involved.
At the Spreckels mansion, the distance from the where the rope was tied to the bed and the railing was about 15 feet and 7.5 inches (before the bed moved 7.5 inches) and in the reenactment, I would say that the distance would be about 8 or 9 feet. The distance of the drop was 9 feet and 2 inches as opposed to 7 feet and that doesnt take into consideration the differences in the center of gravity between RZ and the dimensions of the punching bag used in the reenactment. This means different rope lengths; 24.5 feet in the RZ case versus about 15 or 16 feet in the reenactment. (The longer the length of the rope, the more strain energy it is able to absorb.)
The shorter distance also changed some angles. In the screen shot below you will see that the rope makes an angle of about 20 degrees from the bedpost up toward the balcony.
This would be consistent with my guess of an approximate 8 foot distance from the bed to the rail.
Mathematically, a right angle triangle with sides, 8 feet, 3 feet and 8.5 feet will have an angle of 20.5 degrees.
The crime scene had an angle of about 11 degrees.
This affects the amount of force required to move the bed by about 15% (However, because of the 11 degree contact between the closed door and the rope in the crime scene, as opposed to no such contact in the reenactment, the overall difference would be zero.)
Earlier I spoke of the coefficient of friction (COF) with respect to the rug. Unquestionably, the fact that the bed had sunk into the rug would mean that there would be a higher static coefficient of friction.
By way of comparison, the primary change that the reenactment tried to make in order to prove that the bed would move a significant distance was adding weight to increase the overall weight of the bed to 400 pounds in tests 2 and 3. This change would mean that 20% more force would be required to move the bed.
Because of the issues Ive previously outlined, a change in the weight of the bed would help but in order to begin to approximate the force required, the overall weight needed would likely be as high as 550 pounds and that would be just to compensate for a static COF difference of 0.3 between rugs and the lack of an indentation from the bed sinking in.
I admire the time and effort that was put forth in undertaking the reenactment, but its unfortunate that they didnt work with a technical consultant or engineer in order to more accurately simulate the incident.
I agree about the need to take friction and room dimensions into account for a more accurate re-enactment and analysis. I haven't been able to keep track of this case (and I daresay many others that I try to follow).
I understand there are some Dr. Phil episodes that have aired recently and wonder if they will be archived (online) so I can watch.
IMO, the most accurate way to determine the feasibility of a 7.5 inch bed movement would be a reenactment at the crime scene with another rope of the precise type that was used.Thanks Cynic for the comprehensive analysis!
Can you use pure math & physics with what you know about the room, Rebecca Zahau, the doors, etc. to determine whether the 7.5 inches of bed shift was possible without having to re-enact entire crime scene?
Welcome to Websleuths, ufos8mycow!
I presume she was concerned her DNA or fingerprints might be found on the phone. Of course she was concerned for nothing, as LE decided this was suicide and probably didn't test the phone for DNA and fingerprints at all.
