## How Maths Solved a Real Murder!

October 1, 2009

It is the aim of Mathspig to show you maths as it is used in the real world.  As this is a REAL murder conviction we will be very serious in our comments.

A woman was found dead at the bottom of The Gap at Sydney’s Watson Bay in 1995. It wasn’t until 1997 that University of Sydney physicist, Rod Cross, was asked if the victim could have jumped off the cliff.  In 1998, the coroner declared an open finding in the death of Byrne.

It wasn’t until 2003, however, that the police contacted Ross to check the maths. He said that Caroline Byrne couldn’t have slipped or jumped.  The case was reopened and in 2006 Byrne’s ex-boyfriend Gordon Wood was arrested in London and eventually found guilty of her murder. Wood was sentenced last year to 17 years in jail with a non-parole period of 13 years.

Why we are interested in this case, mathspigs, is because Cross, The Physicist, made the comment when asked during the trial (See The Australian Wednes 30th Sept 2009 ) that the maths involved was not rocket science but maths high school students would be able to master. Can we?

Here is some information you might need:

Height of cliff = 29m later found to be 25.4m

Distance from base of cliff (of body) = 11.8 m

Weight of body = 57 kg

We will assume  influences of weather or air resistance are not significant. We will not include the sloping rock surface at the bottom of the cliff in the calculations.

So mathspigs, you can do it? And keep in mind this is a real case. It’s not Numb3rs or NCIS.

You know y (Height of the cliff) so you can calculate x (Position of body from cliff) for different velocities (Vx) of a person leaving the cliff. There was a limitation on the speed of someone running off the cliff as there was only a 3 – 4 m lead up to the cliff edge. Here are some known running speeds:

Speed of fastest man on earth = 10.4 m/sec       Usain Bolt ,Jamaica  running 100m in 9.58 sec (@  37.4 kph)

Speed of fastest woman on earth = 9.29 m/sec   Evelyn Ashford, USA running 100m in 10.76 sec ( @ 33.4 kph)

Speed of average sprinter = 19 – 24 kph

These calculations alone did not bring about the conviction. The prosecution then had to prove that a person could be thrown at sufficient speed to land 11.8m from the cliff base. To do this Cross re-enacted the experiment with two policemen and a policewoman of similar size to the victim. The policewoman was thrown into an Olympic Pool. The policemen could achieve an exit velocity of the policewoman of 4.15 m/sec, 4.37 m/sec and eventually using the strongest thrower 4.85 m/sec.

Could your maths put a murderer behind bars, mathspigs?

For more information see Rod Cross’s book, Evidence for Murder: How Physics convicted a Killer published next month. ( New South Books  )

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# Wood Aquitted

On the 3rd DEC 2008 Gordon Wood was sentenced to 13 years jail for the 1995 cliff top murder of Caroline Byrne.

On 24th FEB 2012 Wood was acquitted on the murder charge in an unanimous decision by three Appeal Court judges. Justice McClellan said Wood’s behaviour around the time of the death had “raised suspicions”. The prosecution case was based on evidence given by Associate Professor Cross, but the Court of Appeal labelled his evidence biased as he had later written a book titled Evidence for Murder: How Physics Convicted a Killer. Justice McClellan noted in his judgement that “suicide could not be ruled out” and that “suspicion, even a high level of suspicion, was not enough” to convict someone of murder.

Of course, Caroline Byrne, may have been murdered. The question that remains unanswered is ‘By whom?’

1. Great post Kerry! By coincidence today I was searching the web for info re the trajectory of a lawn bowl and came across Rod Cross’ homepage. Great example for kids to see the relevance and importance of Mathematics. I will be showing my students this post tomorrow. Thanks, keep the great blog posts coming….

• Hey Jeff,
Thanks for the info. I hadn’t found Rod Cross’ homepage. I also appreciate the feedback. It keeps me on track regarding maths stories that work in the classroom. Cheers Mathspig

2. […] Mathematics Solved a Real Murder Posted on October 13, 2009 by Jason Dyer At Mathspig blog: A woman was found dead at the bottom of The Gap at Sydney’s Watson Bay in 1995. It wasn’t […]

3. […] You'll have to check it out and see!].  It’s got some cool stuff, including a post about using math to solve a murder case [but can they really neglect air resistance?  Wouldn't that make a difference, and maybe make it […]

4. Topical once again, now that Wood has been acquitted. So if Caroline Byrne couldn’t run and jump 11.8m out, wasn’t thrown off the cliff, what happened?

• Interesting comment. As I wasn’t at the trial, I can only use the judges comment as stated in response.
I’ll upgrade the post. Thanks. Mathspig

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