Justice Lang has no questions, thanks Beatty and says he's free to go.

"Members of the jury, we'll call it a day."

He tells them we won't be sitting on Thursday because some of the jurors have other commitments.

The trial will resume 10am tomorrow, as will the Herald's live coverage.

Prosecutor Brian Dickey is on his feet for cross-examination. He indicates he can probably finish with Beatty this afternoon.

Dickey asks about the condensation on the jug that was mentioned.

Dickey refers to the metadata on the photo of the jug in his report, and it shows the photo is not actually taken on the morning of April 5.

Were we just saying that if the washing machine ran on the morning of April 5, it would mean that one or other of the appliances weren't used? asks Dickey.

"We don't know the mix of electricity," says Beatty.

Beatty says he doesn't think the April 5 data would be sufficient for a washing machine.

Dickey says the Crown's power usage expert Paul Smith of Consumer NZ said it's possible the washing machine could have run that morning.

"I would exclude it," says Beatty.

Paul Smith thought one of the kettle or toaster might have run, but not both.

"It's too refined an analysis," Beatty says. 

"We don't know how much water is actually in the jug," and we don't know the setting on the toaster either, says Beatty.

Asked about the small rise at 6am, which he took to be LED lights switched on by Polkinghorne in his bedroom when he rose, Beatty agrees he can't say who switched the lights on, or in fact where in the house the lights might have been switched on that morning.

Dickey asks about how Beatty knew the underfloor heating was on that morning in 2021.

"The floor was on when I was there," says Beatty.

When was that?

"It was this year."

No further questions from Dickey. 

Harrison Smith is back up. He must have questions in reply.

Smith asks about photographs Beatty was referred to by Dickey of condensation that could be seen on the jug.

What evidence did you consider when considering whether the jug might have been used on April 5, 2021? Smith asks.

One is the quantity of electricity used and the other is the condensation, Beatty says.

Putting the photograph aside, says Smith, what does the data say about the jug being used that morning?

"Given the data, my view would have been that it was certainly the jug that was turned on because of the quantity of energy that's actually being used," Beatty says.

In addition to the jug and the toaster, Beatty confirms he was also asked if the washing machine could have been used between April 4 and 5.

If the washing machine had been used, he would have expected to see the washing machine turning off in the data on April 5, he says. 

But the data does not show it turning off on April 5.

Beatty says the washing machine could only have run on the evening of April 4, in his view.

He says he can't be more specific than anywhere between the 6pm to 11.30pm period on April 4.

There's no evidence in the data, in Beatty's view, of the washing machine being used on the morning of April 5. There's also no sign of it being used in the morning on other days, he says.

Two sheets and two pillow cases are about 6kg of wet weight, close to a machine's maximum load, he says.

"I don't believe the washing machine cycle started on Monday the 5th of April," Beatty says.

What about the dryer? asks Harrison Smith.

There is potential for the dryer, the washing machine and many other appliances to be used on April 4, Beatty says, any time in the same period of high electricity consumption from 6pm to 1130pm already referred to at length.

What about on April 5?

"The fifth of April, definitely the dryer could not have run," Beatty says. He says there is insufficient consumption evident in the graphs for the dryer to have been used.

Beatty says the jug and toaster could have been turned on just before 8am as well, given consumption data can span multiple periods. It could have been either appliance or both in combination, he agrees.

Ronald Beatty, an electrical engineer with expertise in forensic data analysis,  wants to give the court a lesson on reading graphs.

"I call this a load profile," he says. "We have 48 metered half-hour periods."

He's used red arrows to show the standing load overnight.
Then about 7.30am, the load starts to increase slightly, "because someone has got up and turned something on" or an automatic appliance has started.

The load has gone up from a bout 0.5kWh to about 0.75 to 0.8kWh.

The difference between those two figures tells us how much additional electricity was being applied, Beatty says.

You can take the shape and super-impose it over other days to see how regular the usage is, Beatty explains.

Harrison Smith moves the witness to his analysis of April 4 and 5, 2021.

Beatty is comparing Sunday March 14 to Monday April 5 (which was Easter Monday, hence the Sunday comparison).

On April 5, there was a standing load until about 6am, when there's a step increase.

Beatty's view is that Polkinghorne rose then and turned on some lights.

"It supports Dr Polkinghorne's statement that he got up and turned some lights on," he says.

About 8am, there's another increase. Beatty says his view is Polkinghorne got up and came down the stairs and – Brian Dickey objects, saying he couldn't know from the power data if he went down the stairs. 

Justice Graham Lang agrees and Harrison Smith asks Beatty to stick to his opinion on what the deviations in the graph show.

The increase in load of about 6am was followed by a larger increase about 8am, too great to just be lighting. It needed to be other appliances turned on at 8am, he says.

Beatty can't tell us what appliances specifically were used, he says, but is able to use a list of appliances to determine whether or not they may have been used in that period.

"But it also relies on the history of data," he says, in that the load on Monday April 5 is not too dissimilar to the load on other days.

"It indicates a regular pattern of electricity consumption."

The increase about 8am is consistent with boiling an electric jug, he says.

On Sunday, April 4, there is quite widely divergent electricity consumption during the day and into the night, Beatty says.

During the night period, a big lump on the right of the usage graph, we don't know what's in there, Beatty says, but it's of such a size that it would support the dryer running, the dishwasher and washing machine.

The block at the right of the graph starts at 6pm and runs to 11.30pm.

"That is a lot of electricity to use," Beatty says.

To use that amount, all of those appliances would have to have run.

Smith moves to the April 5, 2021 usage graph, starting at midnight.

Beatty says you can see a minor change in the standing load up until 6am. Some of that would be the underfloor heating switching on and off with its thermostatic control.

Load from a refrigerator would also cycle, as the compressor switches on and off.

"And these variances create a little bit of a ripple," he says.

At 6am, there is an increase beyond the ripple. That tells us extra load was applied then, Beatty says.

It won't have been underfloor heating because that would have been seen earlier, he says.

At 8am, the average load remains higher than what it was overnight, telling us there was additional electrical load that turned on and stayed on, Beatty says.

Then at 8am, there's a "sharp increase in load", the first of two spikes.

That tells us, Beatty says, that someone has turned some more electrical load on.

At 8.30am, the load is turned off.

Asked if the 8am load could have been both the jug and the toaster, Beatty says "we just don't know".

"I noted that the setting on the toaster was down to very low," he says.

The police photo of the jug had condensation showing it had been run.

The photo of the toaster also showed it was set very low, he says.

"The time that the toaster would have actually been on would have been quite limited."

Smith asks about the condensation on the jug again and Justice Lang interjects, asking if he can comment on that as an expert, and Beatty says he can't.

Ronald Beatty, an electrical engineer with expertise in forensic data analysis, is now showing the court a photo of the smart meter at his house, via the television screens in the courtroom.

In most homes, the electricity demand is very low, says Beatty. So the devices have to be accurate over a wide range, from as low as 0.25kWh or right up to 12kWh when the oven and other appliances are switched on. Smart meters are accurate to +/- 1% or less, says Beatty, so very accurate. 

That accuracy is important for us to understand in this particular case, Beatty says, because we are looking at very minor increases, of just 0.05kWh between one half hour period and the next, so you need to be assured of the accuracy of the meter.

Polkinghorne's meter had a current certification so its data will be accurate, says Beatty.

Beatty shows the court a graph.

The red arrows show "standing load", the amount of power usage in the background without any other activity, such as devices left on standby like computers, television sets, fridges, microwaves: anything that's always on.

What we see at the Polkinghorne home is a flat standing load around 0.4 to 0.45kWh. That is high for a domestic home, and that could be due to electric underfloor heating, says Beatty.

Beatty has been to the Upland Rd home, where he surveyed the electrical devices and fixtures.

"I was particularly interested in the lighting," he says, given Polkinghorne's statement that he rose and sat in his bed reading, which would have needed the lights to be on.

He also took note of the setting on the toaster.

Did you factor in the sunlight on the morning of April 5? asks Harrison Smith.

No, says Beatty, it's very hard to get Niwa irradiance data.

Moving on to his analysis of electrical usage data. Beatty used data from December 1, 2020, to April 5, 2021 (when Pauline Hanna was reported dead).

Each month has about 1700 data points, he says.

"It's important to actually establish trends," says Beatty.

Beatty says he's trying to establish from the half-hourly data, which is not particular granular, just what could have actually happened that morning.

The trends he was looking for were mornings very similar to April 5, by comparing the shape of consumption evident from the power curves.

His view is the data on April 5 supports Polkinghorne rising early, turning on a few lights, then more load being applied about 8am.

He doesn't think the washing machine ran on the morning of April 5, but it did run on the morning of April 4.

To recap – police found a slightly damp top sheet in the dryer when they arrived at the home. A top sheet was missing from the room where Polkinghorne said Hanna spent her final night.

Police instructed Paul Smith from Consumer NZ to look at usage data from Polkinghorne's home in Remuera's Upland Rd.

The defence instructed Ronald Beatty to perform a similar exercise to see if Polkinghorne's explanation matched the power usage data.

Beatty says the electricity industry settles in 30-minute increments, so it's not possible to look at one or two days to  consider what could have happened within the premises as well. A wider set of data has to be used, he says, but we can never actually say what exactly happened on any given day.

Smith's report looked only at one or two days of consumption, and didn't look at what happened on similar days in the past.

"That is, I think, a failing actually of that side of the investigation," says Beatty.

There are issues with some of the figures Smith used too, says Beatty.

The washing machine used in his modelling wasn't the same as Polkinghorne's, he says.

In addition, there were assumptions around the jug. The test Smith carried out was with 1L of hot water, but we don't know how much water was in the kettle, making the energy consumption figures for the kettle an assumption.

Beatty moves on to his findings.

"My view, taking into account data and trends that I noted actually from 1 December 2020 through to 5 April 2021, is the data does support Mr Polkinghorne rising early, turning on a few lights and he was obviously very energy conscious, the data shows a small increment which could be LED lights actually turning on and then at about 8am, it actually shows an increase in load, which could be consistent with boiling an electric jug and perhaps even running a toaster."

One issue, says Beatty, is that the half-hourly increments of electricity measurement mean that an appliance switched on in one period could continue being used into another period, making it very difficult work out exactly what was used when.

Now Ronald Beatty is talking about what he says is his "crowning glory".

Two of the projects he worked on were put forward for energy excellence awards, New Zealand's largest battery, the Rotohiko battery, and a Kāinga Ora project to sell surplus solar power back to the grid.

"This is very interesting," says Justice Graham Lang, but the judge says he's just not sure a detailed explanation of the Kāinga Ora solar energy project is required for this trial.

The defence moves on after producing Beatty's CV as an exhibit.

Court has resumed for the final session of the day.

Harrison Smith, one of the barristers assisting defence lawyer Ron Mansfield, has called the next witness for the defence, Ronald Beatty.

Beatty is an electrical engineer with expertise in forensic data analysis.

He has 52 years experience in the electricity industry.

Beatty has got NZC electrical, is a registered engineering associate and has some endorsements around radiation as well, he tells the court.

Beatty says he's worked through every tier of the electricity industry and has a lot of experience in regulation, data and metering.

Beatty was previously employed by the Electricity Commission, the regulator pre-dating what is now the Electricity Authority.

He spent 16 years with the regulator.

Beatty says he was responsible for metering at the commission, among other things.

More recently, he was the principal adviser market operations at the Electricity Authority.

Since December 12, 2021, the anniversary of his 50 years in the electricity industry, he has been retired. Since then he's worked as a private consultant, from hydrogen legislation right through to "highly detailed data transfer protocols".

The trial is about to resume and the public are filtering into the gallery. The defence will call a new witness when proceedings begin again. Who will it be? The jury have not been told.

Crown prosecutor Brian Dickey begins his cross-examination and references the evidence of Stephen MacIntyre, another Rings neighbour, who was a Crown witness and who said Polkinghorne had acted erratically in the years before his death, and he suspected he was on drugs.

Foote saw nothing of the sort.

"He was in bed by 9.30 every night for two and a half decades, even on New Year's Eve."

No further questions and Foote is free to go.

We are taking the afternoon break early to prepare for the next witness. Court will resume about 3.35pm.