## Calculating Average Speed

I have absolutely NO opinion about whether Mark Lundy is guilty or not, but the Crown case was NOT the sound basis for a conviction. I will not reiterate the points raised by others, but there is one technical point that was made by the Crown prosecutor in his summation that was deeply misleading to the jury.

He stated " the average speed for the entire round journey only had to be 120km/hr".

What this is playing to is the sense that most people have is that it is easy enough to drive at 120k, even 130+ for short periods of time, so the jury was mislead into thinking that the high speed trip was possible. In fact this is not the case at all. If I ask you, for example, what is my average speed if I travel from Wellington to Palmerston at say 100 km/hr, and then turn around and return the same journey at say 200km/hr? Most people immediately answer 150k/hr. Try this and see.

In fact the correct answer is something called the harmonic mean calculated as 133km/hr !. This is remarkably slower than most people imagine.

See this link http://en.wikipedia.org/wiki/Harmonic_mean.

The effect of this is critical to understanding the absurdity of the Crown claiming that Mark only had to average 120 km/hr for the whole journey. On your website I see you state

I am not certain where the figure of 150kph has come from, but I would expect that if we take the total of 2hr 58 min = 178 min, then subtract a conservative 30min lost for Mark to walk 1km, commit two murders, clean up , and reset a computer time, the balance for travel time is 148 min. To travel 300km in 148 min gives a simple "arithmetic mean speed" of about 121 km/hr.

I assume this is how the Crown came to claim this speed.

Of course critical to this simple analysis is the non-travel time we have to guess at for Mark to have walked 1 km and committed the murders. 30 minutes seems to me an conservative minimum, any longer and the travel time mean speed needs to increase.

But as anyone knows it is impossible to drive from Petone to Palmerston North non stop at 120kph. There are traffic lights, many corners, and at least six major 50 kph zones where sustained speeds in excess of 80kph are very unlikely. I would estimate that around 35% of the entire trip length is limited to 80kph. The effect of the harmonic mean is that time spent travelling at less than the "mean speed" demands far more time spent at a much higher speed than the mean, in order to achieve the mean speed for the whole trip.

This is hard to convey in words, but the arithmetic is convincing

If Mark travelled 35% of 300km at say 80 kph, then this would take 78 minutes.

This now leaves (148 - 78)= 70 min to achieve the rest of the journey.

In order to do this he now needs to travel 200km in 70 minutes, demanding that he now travels at an

Of course it is impossible to know the exact speeds and times that might have been travelled at, but the idea that Mark might have driven 200km of busy open road at an average speed of 170kph, without being noticed by either the police or ANY other member of the public is frankly ludicrous.

And this is the crucial point where the Crown absolutely mislead the jury.

He stated " the average speed for the entire round journey only had to be 120km/hr".

What this is playing to is the sense that most people have is that it is easy enough to drive at 120k, even 130+ for short periods of time, so the jury was mislead into thinking that the high speed trip was possible. In fact this is not the case at all. If I ask you, for example, what is my average speed if I travel from Wellington to Palmerston at say 100 km/hr, and then turn around and return the same journey at say 200km/hr? Most people immediately answer 150k/hr. Try this and see.

In fact the correct answer is something called the harmonic mean calculated as 133km/hr !. This is remarkably slower than most people imagine.

See this link http://en.wikipedia.org/wiki/Harmonic_mean.

The effect of this is critical to understanding the absurdity of the Crown claiming that Mark only had to average 120 km/hr for the whole journey. On your website I see you state

"Is it possible to cover the 150 kilometers distance between Petone and Palmerston North, commit two murders, manipulate a computer, hobble 500 meters to and from a car, clean up and dispose of all evidence, in 2Hrs 58 minutes?"Is it possible to cover the 150 kilometers distance between Petone and Palmerston North, commit two murders, manipulate a computer, hobble 500 meters to and from a car, clean up and dispose of all evidence, in 2Hrs 58 minutes?

Why did no-one see or report a vehicle being driven at high speed through Wellington peak traffic, avoiding all police and speed cameras, at an average speed of over 150kph?"

Why did no-one see or report a vehicle being driven at high speed through Wellington peak traffic, avoiding all police and speed cameras, at an average speed of over 150kph?"

I am not certain where the figure of 150kph has come from, but I would expect that if we take the total of 2hr 58 min = 178 min, then subtract a conservative 30min lost for Mark to walk 1km, commit two murders, clean up , and reset a computer time, the balance for travel time is 148 min. To travel 300km in 148 min gives a simple "arithmetic mean speed" of about 121 km/hr.

I assume this is how the Crown came to claim this speed.

Of course critical to this simple analysis is the non-travel time we have to guess at for Mark to have walked 1 km and committed the murders. 30 minutes seems to me an conservative minimum, any longer and the travel time mean speed needs to increase.

But as anyone knows it is impossible to drive from Petone to Palmerston North non stop at 120kph. There are traffic lights, many corners, and at least six major 50 kph zones where sustained speeds in excess of 80kph are very unlikely. I would estimate that around 35% of the entire trip length is limited to 80kph. The effect of the harmonic mean is that time spent travelling at less than the "mean speed" demands far more time spent at a much higher speed than the mean, in order to achieve the mean speed for the whole trip.

This is hard to convey in words, but the arithmetic is convincing

If Mark travelled 35% of 300km at say 80 kph, then this would take 78 minutes.

This now leaves (148 - 78)= 70 min to achieve the rest of the journey.

In order to do this he now needs to travel 200km in 70 minutes, demanding that he now travels at an

**average of**(200/70)* 60 =**171 kph**for this high speed segment.Of course it is impossible to know the exact speeds and times that might have been travelled at, but the idea that Mark might have driven 200km of busy open road at an average speed of 170kph, without being noticed by either the police or ANY other member of the public is frankly ludicrous.

And this is the crucial point where the Crown absolutely mislead the jury.

The mean speed for the whole journey in no way indicates the actual speeds needed to be achieved.The mean speed for the whole journey in no way indicates the actual speeds needed to be achieved.

**Careful analysis of this matter reveals clear legal grounds for retrial.**

**Note from FACTUAL comittee:**

*The eye witness stated that the "runner" was seen at between 7:15 and 7:20 pm, so allowing the runner to get into the car and turn it around to head back to Petone, a start time of 7:20 could be assumed. Mark was in Petone talking on the phone at 8:28 pm according to cellphone records. This gives and average speed of 135 kph. There is reason to believe that the voice message on Mark's phone at 8:13 was in Petone and at the same place as when Mark cleared his messages. This would mean a return time of under 1 hour for 150km, therefore an average speed of over 150 kph.*

*Whatever the alleged start and finish times, the claimed average speeds all require*

**sustained high speed driving in traffic and over roads that make it inconceivable**)No comments