Sydney harbour is a beautiful place

One of the trips I am known to take is to Manly for lunch.

Above is a pic taken whilst waiting for the train home at Circular Quay. On the right is the ferry Freshwater arriving from Manly. The Opera House is just visible on the right north of the ‘toaster’ (one of the eyesores on the harbour).

It was a sparkling day on the harbour (Port Jackson) which bought back memories of many happy days boating and sailing, it is a beautiful waterway.

Manly is about 30min north east, 12km over the water, just on the north side of Sydney heads.

It is challenging to get pics on the ferry as tourists push their phone in front of your face to take videos, 5 to 10 minutes as a time.

Above, the route is from home to Bowral station by car, diesel train (Endeavor railcar) to Central, electric train on the Sydney underground to Circular Quay, and ferry to Manly. The return journey was similar but electric train from Circular Quay to Campbelltown then diesel train to Bowral. The round trip is just on 300km and nearly three hours for each direction of travel.

An interactive zoomable map is available. Zooming in around Sydney and a little south will show track jumps due to underground rail.

The track was captured with a Holux RCV-3000 GPS logger, logs downloaded with BT747 (Chinese firm Holux is defunct and so is their application which is now locked out of its maps provider).

Leaflet / OpenStreetMap map rendering on devices with tiny pixels

I wrote an application that presents maps on a webpage using Leaflet and OpenStreetMaps, and some readers commented that the text was hard to read on their devices.

It turns out that this issue seems present on devices with high resolution small screen (ie high pixels/mm or small pixel size).

The reports raise the question of whether it is the compatibility of the device and the user’s Visual Accuity (VA).

VA is often assessed on the familiar Snellen chart which has characters of a 5×5 grid and normal vision is indicated by reading characters that subtend 5 minutes of arc (MOA), or 1MOA for each ‘pixel’ (px).

An example phone screen calculation

My Huawei dub-lx2 has a screen height of 1520 px and 144mm, so the px size is 95µm. Keep in mind that the size of this pic may be much smaller on the phone that on your viewing device. Continue reading Leaflet / OpenStreetMap map rendering on devices with tiny pixels

Simsmith bimetal line type – revision #1

This article is a revision of an article Simsmith bimetal line type for Simsmith v17.2 and revisions to my own model for current distribution in a conductor.

This article discusses various measurements and models of Wireman 551 windowed ladder line, including adapting Simsmith’s bimetal line type to bear on the problem.


A starting point for characterising the matched line loss (MLL) of the very popular Wireman 551 (W551) windowed ladder line is the extrapolation of measurements by (Stewart 1999) to 1.8MHz. Since the measurements were made at and above 50MHz where the W551 has copper like performance, this is likely to underestimate actual MLL and such wide extrapolation introduces its own uncertainty. Nevertheless, the datapoint is MLL=0.00227dB/m.

This is a revision of an article written in Feb 2020, capturing revision of Simsmith to v17.2 and revision of my own current distribution model.

Dan Maquire recently posted a chart summarising measurements of these lines.

For the purposes of this article, let’s tabulate the MLL at 1.8MHz in dB/m. Continue reading Simsmith bimetal line type – revision #1

A model of current distribution in copper clad steel conductors at RF – capturing conductor curvature

A model of current distribution in copper clad steel conductors at RF laid out a model for current distribution, though ignoring curvature of the conductor in calculating current density vs depth.

A model for current distribution in a conductor is that for a homogenous conducting half space with surface current parallel to the interface. Current density at depth d is given by the expression \(J_r=J_R\frac{J_0(kr)}{J_0(kR)}\) where δ is the skin depth \(δ=(ω \cdot µ \cdot σ)^{0.5}\) and \(k=\frac{1-\jmath}{\delta}\), σ is the conductivity). This takes into account curvature of the conductor surface, albeit with slower compute time.

Let’s compare the two algorithms on a test case at 1.8MHz being copper cladding of 67µm copper over a steel core for an overall diameter of 1.024mm (#18).

Above is a stacked image, the simpler algorithm is the feint plot.

There is a quite small difference in this case. When the expected loss of 400Ω line using the conductor is calculated, the result with the simpler algorithm is 1.3% less than the later one using the Bessel distribution.

Distance to fault in submarine telegraph cables ca 1871 – the leap expanded

Distance to fault in submarine telegraph cables ca 1871 gave a mathematical explanation of the location of fault…

Now it is in terms of the three known values u,v,w and unknown x.


\(x^2-2wx+vw+uw-uv=0\) from which you can find the roots.

\(x=w – \sqrt{(w-v)(w-u)}\\\)

I have been asked to expand the last ‘leap’.

So we have \(x^2-2wx+vw+uw-uv=0\) which is a quadratic, a polynomial of order 2.

The solution or roots of a quadratic \(ax^2+bx+c=0\) are given by \(x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\).

So, for our quadratic \(a=1, b=-2w,c=vw+uw-uv\), so \(x=\frac{2w \pm \sqrt{(2w)^2-4(vw+uw-uv)}}{2}\).

Dividing the top and bottom by 2 we get \(x=w \pm \sqrt{w^2-(vw+uw-uv)}\) which can be rewritten as \(x=w \pm \sqrt{(w-v)(w-u)}\).

We want the lesser square root \(x_-=w-\sqrt{(w-v)(w-u)}\) because x must be less than w, a constraint of the physical problem.

So when measurements gave \(v=1040 \Omega\) and \(w=970 \Omega\) we can calculate that the distance to fault is the lesser root, 210.3km from Newbiggen-by-the-sea. (The greater root would imply a -ve value for x or y which is not physically possible.)