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Daring Descent: Having Fun with Friction

November 21, 2012 4Comments

I’ve always enjoyed having fun outdoors, and recently I’ve started to branch out of my usual “going for a walk in the park” comfort zone. My latest adventure took place in the wonderful state of Alabama at a location I wouldn’t have pictured myself being had you asked me a few months ago– a cave. Not just any old, regular cave that people wander into to make-out and spray-paint the walls, but a vertical cave with a super cool 100 ft drop called Sheldon’s Cave.

Photo by Nima Yazdanpanah

For the avid caver, or spelunker if you prefer, 100 ft may not be very exciting, but to me, I was stoked… and nervous. I had gone exploring in horizontal caves before, but had never done any descending (except for my days of rock climbing several years ago). We had some practice at a rock climbing wall, but I was still nervous for the real descent. It is a very uneasy feeling having to rely on a skinny rope to hold your weight as you ease over the edge of  cliff. “Oh, just lean back and trust the rope.” Trust the rope?! But we just met! So, with my left hand in a death grip on the rappel rack and my right hand in a death grip on the loose end of the rope, I (very slowly) made my way over the edge of the cave and down the side. By the time I got about half way or so, I eased up and realized how awesome it was that I was descending below ground level, about to go exploring another cave.

You may be thinking, “What the heck is this rappel rack she is talking about?” A rappel rack (see one in action here) is a J-shaped device made out of aluminum and/or steel with bars running between the two sides of the device. The rope gets woven between each bar to create a friction force which counteracts the force of gravity and slows the descent. The speed of the descent can be adjusted by either adding or removing bars or by sliding the bars up or down. Adding bars increases the surface area in contact with the rope, increasing the amount of friction between the rope and the rappel rack, decreasing speed. Sliding the bars up increases the angle of contact between the rope and bars, once again increasing the amount of friction and decreasing speed. This idea of angle of contact is best exemplified in pulleys, where the tension (pull) of one side of the rope can be calculated using the tension of the other side of the rope and the degree of contact the rope has with the edge of the pulley (Capstan equation).

The diagram above shows the amount of contact the rope has with the rappel rack for the given configuration; areas of rope within the angles shown are places where the rope is in contact with the bars and normal (contact) force is being applied. This is how I had my rappel rack set up for the descent, and being a scaredy cat, I was definitely not about to take off any bars in order go faster. I was perfectly content with my snails pace. I could have gone even slower had I slid up the bars, but I didn’t want to look TOO much like a newb.

At a stand still, the net force on the system (me and the rope) is zero, so the amount of friction supplied by the rappel rack would be equal in magnitude to the amount of gravitational force on my body (assuming an ideal situation without any deformation of the rope). Assuming the static friction coefficient for the rope against the steel rappel rack is 0.25, the minimum amount of normal force required to counteract gravity and keep the rope from sliding can be calculated. Since I weigh about 150 pounds (68 kilograms), the amount of gravitational force on my body equals about 666 Newtons. What a lucky number! Setting this equal to the amount of friction required, the amount of normal force the rappel rack must supply against the rope is 2665.6 Newtons. Dang! That’s a lot of Newtons, seeing as one Newton is about equal to the amount of weight of one apple. That’s enough apples to make a whole lot of pie!

The rappel rack doesn’t actually supply this much normal force alone, which is why I still moved down the rope even with all of the bars on the rack. This is where my hand holding on to the rope came into play. If I ever got to going too fast, I would squeeze the rope with my right hand and would stop moving (or slow down, depending on how hard I squeezed). Just like the rappel rack, my hand supplied a normal force against the rope which created friction and counter-acted the force of gravity.

Now that I have blown your minds with my awesome tale of caving and physics, enjoy these great pictures taken by cave master (joking), Colin Lehman:

Pretty foliage!
Oh, don’t mind me! I’m just going down into this deep, dark hole!
The inside of the majestic cave.
One caver made a new friend… with a bat!
The path to the cave was covered with cotton. It had all been harvested by the time we got back.
The cave master making his way down.
Sweet view!
A fellow caver moving up!

 

Source:

The Mechanics of Friction in Rope Rescue by Stephen Attaway, Ph.D. (Find it here)

Photos by Colin Lehman and Nima Yazdanpanah

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Katelyn Sturdivant
About Author

Katelyn is in her 4th year at Georgia Tech. In her spare time, she likes to hang out with her family, volunteer at Kennestone Hospital, and be crafty. She is a pescatarian and is currently trying to learn the F chord on her acoustic guitar, Gretchen. Katelyn hopes to attend both medical school and graduate school (for a Master's in Public Health).

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  Timothy Durham was convicted of rape when a test showed his DNA genotype matched the DNA recovered from the crime scene. Eye witnesses testified that Durham was in a different state at the time of the incident, but he wasn’t exonerated from his 3000 year sentence until follow up DNA analysis showed that the preliminary forensic analysis used in the trial was misinterpreted (Thomas et al.). DNA testing serves an invaluable part in our criminal justice system, but it comes with complications and bias that can lead to wrongful convictions and misinformed juries.  

Background:

Forensic genetics aims to identify the origin of a biological sample. It can be traced back to Karl Landsteiner who discovered human ABO blood groups. With blood groups, suspects could be eliminated based on their blood type. For example, if a suspect had type A blood and there was type B blood left at the scene by the perpetrator, the investigators could rule out the suspect. Unfortunately, the reverse didn’t work. If the suspect and perpetrator both had the same blood type, it can’t be concluded that the suspect was guilty. Blood identifiers evolved into 8 distinct categories which improved the ability to eliminate suspects, but could only conclude that (if the system matched) it might be the perpetrator or this person might be related to the perpetrator (Jobling and Gill). The field evolved in the 1980s with the discovery of Minisatellites, lines of repetitive DNA that don’t encode proteins. Minisatellite patterns in DNA create what we know today as the DNA fingerprint, and it has a much higher accuracy rate than previous methods (Augustyn et al.). Around the same time, a breakthrough for victims of sexual assault was discovered. In the case of assault, bodily fluids of both the victim and the assaulter can get mixed. A process called differential lysis was created which could selectively increase the concentration of sperm in a fluid sample thereby allowing for accurate DNA testing (Jobling and Gill). Forensics evolved to use single-locus probe testing after several years because of its ease of interpretation. It looked at specific minisatellites that had high variability between subjects. This was the first DNA-based method to be used in a criminal investigation. Two murder homicides from several years apart were connected using DNA evidence. The evidence was then used to exonerate an innocent man, and the guilty party was found when he tried to evade mandatory DNA testing for all men in the small town. His guilt was then reinforced when the DNA profiles matched, and he gave a confession (Jobling and Gill). Finding DNA at a crime scene doesn’t guarantee that you’ll find a murderer. There are issues with non-pure samples and limited samples that make DNA work difficult, and accreditation of facilities and new techniques and take time (Jobling and Gill).  

Subjectivity of DNA Interpretation:

In a 2009 publication, the National Academy of Science discusses the possibility for subjective influence in lab based forensics. The interpretation bias happens in complex cases where, for example, there could be a mixture of DNA. A study published in 2011 looked specifically at this issue. A gang rape happened in Georgia, and the mixture in DNA from the case was used to prosecute one suspect after another suspect took a plea bargain to testify against him. With DNA mixtures, there are three possible conclusions: suspect excluded, suspect cannot be excluded, and inconclusive. If the suspect is excluded, it means that there’s little to no possibility that his DNA is part of the sample. If the suspect cannot be excluded, it means that there’s a possibility that his DNA is part of the sample. In the trial, the DNA examiners who knew the context of the case concluded that the suspect being prosecuted could not be excluded. The 2011 study gave the DNA evidence from this case and the DNA profiles of the suspects to 17 forensic examiners. These examiners had no context of the case, and they all worked independently. Of the 17, only 1 came to the same conclusion (suspect cannot be excluded) as the examiners who knew the context of the case. Twelve of the 17 concluded that the suspect who was prosecuted and convicted had no relation to the DNA found in the sample. Not only does this show that subjectivity occurs due to the context of the case, but the 17 examiners came up with different findings based on their past experiences meaning that not all DNA analysis is objective. Some organizations like the Scientific Working Group on DNA Analysis Methods say that quantitative statistical evidence should be presented with every categorical conclusion, but the US doesn’t require this (Dror and Hampikian).

False Positives:

There are two categories that cause wrongful identification in a DNA report: coincidental matches and false positives. Coincidental matches are DNA matches between two unrelated people. The probability of these matches is about 1 to 500,000 for white individuals and about 1 to 350,000 for black individuals. This small probability of coincidental matches makes people feel confident in DNA evidence. False positives, on the other hand, are matches between DNA and test DNA that result from issues in the forensics lab. There have been multiple cases of forensics labs accidentally switching victim and suspected rapist DNA which lead to convictions that were later overturned when the lab realized the error. There are also cases of misreading or misunderstanding a sample. In a case from 1993, a man was convicted of rape because someone interpreted a mixed sample of victim and perpetrator DNA as an individual sample. The conviction was again overturned. To prevent false convictions, retesting DNA is allowed, but it’s not an efficient solution. Many people are pushing for statistical information on the probability of false positives, so that the jurors can make accurate judgements based on DNA evidence (Thomas et al.).  

Conclusion:

DNA analysis is a useful tool for the criminal justice system, but subjectivity can be an issue in forensic testing. To combat wrongful convictions, there are organizations like The Innocence Project who use DNA testing to free the innocent, but reformed forensic testing standards should be put in place to prevent subjectivity and to ensure juries are correctly informed during trials. https://www.innocenceproject.org/    

Citation:

Augustyn , Adam, et al. “DNA Finerprinting.” Encyclopedia Britannica , 26 Apr. 2018, www.britannica.com/science/DNA-fingerprinting#ref153186. Dror, Itiel E., and Greg Hampikian. “Subjectivity and Bias in Forensic DNA Mixture Interpretation.” Science & Justice, vol. 51, no. 4, 2011, pp. 204–208., doi:10.1016/j.scijus.2011.08.004. Jobling, Mark A., and Peter Gill. “Encoded Evidence: DNA in Forensic Analysis.” Nature Reviews: Genetics, vol. 5, no. 10, Oct. 2004, pp. 739–751., doi:10.1038/nrg1455. Thompson, William C, et al. “How the Probability of a False Positive Affects the Value of DNA Evidence.” Journal of Forensic Sciences, vol. 48, no. 1, Jan. 2003, pp. 1–8., doi:10.1520/jfs2001171.