Vintage Calculators

Vintage calculator dating from 1977. © Eugene Brennan

My first calculator from 1977 with a fluorescent display. Who can guess what the "D" button is for? The next one is a scientific calculator from 1984 when I started college and cost £5. Still my favourite, the Sharp EL-506P, although I use a calculator app now. This model had an immediate entry mode which I find more convenient than the more modern expression input.

Sharp scientific calculator model EL 506 with immediate mode data entry. © Eugene Brennan

 

Using Trimble Sketchup for Mould Dimensions

© Eugene Brennan

I made up a mould and cast the cappings for my gate piers. They probably wouldn't have cost much to buy, but it was just an interesting project to make them from scratch. I could have used trigonometry to work out the sizes of the triangles for the mould's pyramid faces, knowing the overall height, but I drew it in Sketchup, a free 3D CAD application, and then just measured the side lengths with the tape measure tool in the application. I used my old kitchen cupboard panels to line the mould to get a smooth finish on the concrete. This would have been great for the pillars themselves, but I just used shutter ply (which cost more than the 2.5 tonnes of concrete).

 

© Eugene Brennan

© Eugene Brennan

© Eugene Brennan

© Eugene Brennan

© Eugene Brennan

 

Numerical Analysis

 

The advent of computers allowed us to use algorithms to rapidly work out solutions to maths problems. E.g. working out square roots of numbers or finding roots of equations (where a graph of the equation crosses the x-axis). The solutions are often approximate to a desired level of accuracy, rather than an exact analytical solution. This area of maths, using algorithms to solve problems is called numerical analysis. If you've ever wondered how a scientific calculator works out e.g. the sine of an angle, it just uses an infinite series or other technique and does lots of simple arithmetic to add each element of the series together. The most basic microprocessors can only do simple arithmetic such as addition and subtraction of integers (whole numbers), so anything more complex such as multiplication, division and the handling of decimal numbers must be done using algorithms. For example, multiplication can be thought of as adding numbers multiple times (e.g. 4 x 3 = 4 + 4 + 4). In the 80s, math coprocessors became common as separate integrated circuits (ICs) or "chips", dedicated to doing faster maths calculations in hardware rather than software. These could be bought as an upgrade for PCs. Eventually the functionality of these chips was built into the main processor.

This article from Medium shows how the square root of a number can be calculated using the Newton Raphson algorithm:

 

https://surajregmi.medium.com/how-to-calculate-the-square...

Heavy Engineering — Drop Hammers and Hydraulic Presses

 

They began as steam or drop hammers, first used in the 1840s for forging large components or driving piles. Steam was used to raise the hammer which was then dropped. Hydraulic presses take a more gentle and less noisy approach, slowly squeezing white hot pieces of steel which can be massive. They also put less stress on the material being forged, shaping it uniformly and reducing the likelihood of flaws. Steam hammers are still used for pile driving.

Inventory of Power Stations

Image created using Bing Image Creator

A list of electrical power generating sites in Ireland from a Wikipedia article and written answers from a Dáil Éireann debate of Tuesday, 26 Jan 2010 on the Oireachtais.ie website. There may be sites that generate lower output, not listed in these resources. According to a list referred to by Minister Eamon Ryan and provided by EirGrid and ESB Networks, Drummond Mills in Athgarvan was generating 20 kW from its small hydro turbine. (The owner showed me this 20 years ago, but I can't remember anything about it). Also Silliot Hill was generating 1.255 MW from methane produced by the landfill. An installation at Celbridge Mills was listed as generating 55 kW.

Oireachtas debate Tuesday, 26 Jan 2010

 

List of power stations in the Republic of Ireland from Wikipedia

Samples of the Elements

Image created on request by Bing Image Creator.

For people who have everything. One of many eBay stores that sells samples of the elements. Some are hazardous, so they're either not available (the radioactive ones) or enclosed in glass ampoules (sealed vials, don't let the toddler chew them). Whether you're getting the genuine article is another question. Some research to find reputable companies first might be a good idea. What are elements? Chemical elements are the fundamental substances from which all materials are made. They can't be broken into simpler substances. So for instance water is made from the elemental gases hydrogen and oxygen and has the formula H₂0 . All materials are made from atoms and molecules which are like the Lego building blocks of matter (although they don't look like bricks. In fact atoms can't be "seen" as such because light doesn't work at such small dimensions). A molecule is a collection of atoms and the subscript "2" in H₂0 means that each molecule of water is made from two hydrogen atoms and one oxygen atom. Other examples of compounds, substances made from two or more elements are carbon dioxide CO₂ which is one carbon and two oxygen atoms and common table salt NaCl (A molecule consisting of one sodium atom Na and one chlorine atom Cl).

Image created on request by Bing Image Creator.

Nova Elements store on eBay.

Why is DC Used for Long Distance Power Transmission?

Pylon at Dunstown Wood, carrying 400 kV AC lines from Moneypoint Power Station to Dunstown 400 kV Substation. Photo © Eugene Brennan

Before reading this, you might like to read my article which explains the difference between AC and DC.

 

In a previous article I explained why we use AC and very high voltages for electricity transmission because of the ease with which voltages can be stepped up or down using a device called a transformer. Also this reduces power loss. I also mentioned The War of the Currents in the late 19th century, which was a series of events surrounding the introduction of Edison's DC and George Westinghouse's competing AC electric transmission systems. Edison’s DC was inefficient, requiring generating sources to be located close to locations to reduce voltage drop. DC also suffered from power loss in lines, whereas AC could be stepped up or down to raise voltage, reduce current and significantly reduce this problem. During the War of the Currents, Edison supporters staged publicity stunts, electrocuting dogs, calves and a horse to show how AC was more dangerous than DC, although in truth they’re equally lethal at high voltages.

 

Capacitive losses 

 

Every object has a property known as capacitance which allows it to store electric charge, simply due to the accumulation or removal of electrons. If you rub a ballpoint pen on your hair, you can pick up small pieces of kitchen towel with it or bend a narrow stream of water running from a kitchen tap. Similarly for a balloon. This is due to electrons being added to or stripped from the plastic. The charge on the material creates an electric field and a force that can attract other items. If you take two sheets of aluminium foil and sandwich a sheet of paper between them, you’ve made a device called a capacitor which can store charge when connected to a DC voltage source. Capacitors are also used as components in most electronic gadgets and appliances. Power transmission lines have capacitance between each other and also the ground. When AC electricity flows on the lines, it can also flow through this capacitance to the other lines and also the ground, causing a loss of power.

 

Inductive losses

 

Every conductor has inductance. Take a piece of wire and wind it into a coil shape by wrapping it around e.g. a pencil. You’ve created an inductor. Connecting a voltage source to a wire causes a current to flow. Current flowing through a wire creates a magnetic field. If the current is changing, the magnetic field is changing also. However a magnetic field that changes in magnitude induces a voltage in a conductor (which is how generators work) which is in the opposite direction to the voltage that created the current in the first place. This property is called inductance and inductors are components used in many electronic devices, e.g. your phone charger. All conductors have inductance, not just ones where the wire is wrapped into a coil form, but even straight wires. Power lines that use AC have inductance and this inductance causes power loss and heating of the wire. 

 

The solution, use DC

 

If electricity needs to be sent over a distance of greater than 600 km, the solution is to use DC for transmission. In the past, converting from one AC voltage to a higher or lower one was simply done with transformers, but this was more complicated for DC. It required a converter system where the input voltage drove a motor which was coupled by a shaft to a generator that output DC at the required level. This was costly, more complex than a transformer and the conversion wasn’t 100% efficient, resulting in a waste of power. Modern power electronics makes it easier to do DC to DC, DC to AC or AC to DC conversion. 

 

Is DC transmission used in Ireland? 

 

Yes, there is one DC interconnector currently in operation between Ireland and Britain: The East West Interconnector (EWIC) which connects the east coast to Wales. A second interconnector, the Greenlink Interconnector, is due to be completed by the end of 2024 and a third interconnector will connect Ireland to the north coast of France. This is under construction with a completion date of 2026. A fourth interconnector, the Moyle Interconnector, connects Northern Ireland to Scotland.

This Eirgrid page explains all the details of existing and under construction interconnectors:

 

https://www.eirgrid.ie/industry/interconnection

Boyle's Law, Volume and Pressure

GIF image courtesy NASA's Glenn Research Center, Public domain, via Wikimedia Commons

 

A nice little animation from Wikipedia showing the relationship between pressure and volume of a gas. If you studied science at school, you may remember this relationship is described by Boyle's Law which states that at constant temperature, the absolute pressure of a gas is inversely proportional to the volume. So if you squash a gas into half the original volume, the pressure doubles. If the volume is made ten times smaller, the pressure becomes ten times higher and so on. The law was formulated by Robert Boyle, a 17th century scientist from Lismore in Waterford. If P is the pressure and V is the volume of a gas, then:

 

P ∝ 1/V

 

Absolute and gauge pressure

 

Absolute pressure is pressure above vacuum and gauge pressure is pressure above atmospheric pressure. So for instance if I have a container and I put a lid on it and the container is fitted with a pressure gauge, the gauge will read zero because it only reads pressure above atmospheric. (A tyre pressure gauge does this and if a tyre is completely flat, the gauge will read zero) However the air inside the container and all the air around us is at at an absolute pressure greater than zero due to the weight of the atmosphere. That pressure is approximately 15 pounds per square inch (psi) absolute or in metric 101,325 pascals (Pa). Atmospheric pressure is also indicated as 1 bar or 1 atm. See this link:

 

https://en.wikipedia.org/wiki/Standard_atmosphere_(unit)

 

Constant temperature in the law

 

The law states that the inverse pressure/gas relationship is at constant temperature. This means that it's only true if temperature is kept constant. In reality, if a gas is compressed, it actually gets hot because of gas molecules becoming closer together (just like the way a bicycle tyre gets hot when you pump it up).

 

GIF image courtesy NASA's Glenn Research Center, Public domain, via Wikimedia Commons

Kildare DC Electric Station

Image courtesy Brian Murphy, KILDARE DC ELECTRICITY STATION, Cill Dara Historical Society: Kildare Town Heritage Series No. 37 (https://www.facebook.com/kildaretownfootprints/posts/147252716928373) - Accessed 16/10/24

 

Nowadays we use natural gas in our homes and industry. It comes from natural gas deposits such as the offshore Corrib gas field off the coast of Mayo and previously from the Kinsale Head gas field which is now depleted. We also import gas from the UK and mainland Europe through several gas interconnectors. Natural gas is pretty much odourless methane, with an odoriser added for safety reasons.

 

Coal gas

 

Before the advent of natural gas, cities and many towns had their own gasworks. Coal was roasted to create a gas which could be stored in large tanks called gasometers and coke and tar remained as by-products. Tar could be used for road building and coke used as a fuel domestically or in foundries for smelting iron ore.

 

The Kildare DC Electricity Station

 

In the Kildare station, just like in a gasworks, gas was produced from coal in a gas plant room. The article doesn't mention how the liquid fuel was obtained, but presumably the gas that was created from roasted coal was distilled and condensed to a liquid that could be stored and used to power the engines. This process known as gasification isn't limited to coal as a raw product. In fact any biomass can be used that contains cellulose, such as wood chip. During WW2 when there were fuel shortages, modified "wood gas cars" and buses ran on such fuels, with an onboard or towed gasifier generating the fuel gas.

 

This article about the Kildare DC Station by Brian Murphy was first published in the Kildare Nationalist in 2009.

Sink Hole, Impact Crater or Turlough?

Image courtesy Google Maps and Maxar Technologies

I've often wondered about this circular pond area at the back of what's called "Brownstown House" on the first edition c. 1837 OSI map or 19 Mile House Inn on earlier maps, once the meeting place of 1798 rebels and a home of the McDonnell family in past decades. The Geological Survey of Ireland interactive map however doesn't show any magnetic anomalies which I think would be the case if it was a mini crater site, meteorites often being made of iron. But not all of them are. Maybe the circular shape is man-made or a natural phenomenon due to the edges falling in uniformly all around the perimeter because of erosion and sheep wandering around it over time.

Does anyone know anything about it?
Maybe it's a turlough?

 

There is a red "hotspot" of magnetic intensity further east, but I think that may be due to the covered KTK landfill (Planning permission has now been lodged for a solar farm there). When I zoom into the map, the shading disappears, so I can't identify whether it aligns with the landfill. I've queried this bug with the GSI.

 

Edit: This EPA report from 2011 mentions "..reclamation of metals and metal compounds" at the KTK landfill.

 

https://epawebapp.epa.ie/.../lic_eDMS/090151b2804386da.pdf

 

A close-up of the pond. Image courtesy Google Maps and Maxar Technologies

  

6" c. 1837 map, courtesy OSI (Tailte Éireann)

The red area shows a region of higher magnetic intensity. Map courtesy GSI (Tailte Éireann)

Kilcullen Sewerage Infrastructure Maps

Image  © Tailte Éireann | Geological Survey Ireland & Marine Institute | Geological Survey

 

Some interesting maps of sewerage and water infrastructure and other information here in a site investigation report prepared on behalf of Nicholas O'Dwyer Ltd Consulting Engineers and Kildare County Council. This was in advance of the the Kilcullen Sewerage Improvement Scheme in the late 90s. The report is accessible by clicking on the red outlines on the GSI interactive map.

Maps can be accessed here.

Metal Fatigue and Saddle Repair

© Eugene Brennan

 

The results of 6000 miles on bad roads and trails on the spring bar of my mountain bike saddle! The saddle was nice and comfortable, so as a challenge, I decided to weld it with stainless steel rods. I lost the other section, but replaced it with a piece of similar diameter spring bar from a camp bed. The other bar in the saddle broke later from fatigue, but I didn't lose the bar and was able to weld it too. This was in 2014 and so far so good, it hasn't broken since. The reason it broke was probably because I had the seat cantilevered too far backwards on the supporting clamp.

 

© Eugene Brennan

 

 

Metal fatigue occurs when a material is repeatedly stressed, potentially resulting in failure (like when you bend a piece of wire or paper clip backwards and forwards and it eventually snaps). Critical components in structures and aircraft need to be inspected regularly and often X-rayed to establish whether there are any fatigue issues.

 

© Eugene Brennan

© Eugene Brennan

© Eugene Brennan

 

Superconducting Cables

Image attribution: Created by Rama. Creative Commons Attribution-Share Alike 2.0 France via Wikimedia Commons

All electrical conductors have resistance. This can be useful (E.g. electric elements which get hot for boiling water or room heating) or a disadvantage (resulting in waste of power in transmission cables). Because of electrical resistance, we have to use thicker cables to carry larger currents. Superconductors are materials that have zero resistance and huge currents can be carried by thin cables. Currently, superconductive properties only exist at very low temperatures and liquid helium or liquid nitrogen must be used to cool the materials. A common use of superconductors is for the coils of the electromagnets of MRI machines, allowing huge currents to be carried by reasonably sized conductors. These magnets are necessary for generating the strong magnetic fields required for imaging. They're also a component of the electromagnets that generate the magnetic fields in particle accelerators. The image shows a section of a superconducting cable capable of carrying 12,500 amps and used for the Large Hadron Collider at CERN. The top image is of an older conventional cable that could carry the same current, requiring 25 heavy gauge individual cores.

 

An electromagnet in its simplest form is a coil of wire, wrapped around a former. You can make one by wrapping a couple of hundred of turns of wire around a nail and connecting it to an AA cell. The magnet's strength depends on the number of turns and also the magnitude of the current. All electric motors use electromagnets to create the forces required for motion of the shaft.

 

Energy Units, Specific Heat Capacity and Sea Breezes

Image created by Bing Image Creator

Compared to other substances, water has a huge specific heat capacity. This means it takes a relatively large amount of heat transferred to it to raise its temperature. Specific heat capacity is defined as the amount of heat energy required to raise the temperature of one kilogram of a material by one degree kelvin. I.e. 1 °K (which is the same as 1 °C). Whereas the zero point on the Celsius temperature scale starts at the freezing point of water which is 0 °C, the Kelvin temperature scale starts at absolute zero when the motion of all atoms ceases. 0 °K is equivalent to −273.15 °C. However a difference in temperature of 1 °C = 1 °K, so the divisions on both scales are the same magnitude.

 

What are calories?

 

The joule is the metric unit of energy, although the calorie is still used in some countries and in the context of food or heating systems (The British Thermal Unit or BTU is also used). The kilocalorie, also known as the kilogram calorie, great calorie or large calorie is what's marked on food products however and is one thousand small calories. One large calorie is the energy required to heat 1 l of water by 1 °C. One full sized Mars bar has 260 calories so it has enough energy to boil two full kettles of water if burned and all the energy transferred as heat to the water

 

This is how the calorific heat content of materials was traditionally measured in a lab: Burn a known weight of material in an insulated chamber called a bomb calorimeter and measure by how much it raises the temperature of a known quantity of water.

 

The joule, the metric unit of energy

 

Back to metric. Energy in the SI system is measured in joules. The symbol for joules is J, watts is W and seconds is S, so 1 J equals 1 W for 1 S. A one bar electric fire with a 1000 W bar uses 1000 J in 1 S. Similarly a 20 W LED bulb uses 20 J in 1 S.

Water has a specific heat capacity of 4200 J/kg °K. (read as "joules per kilogram per degree kelvin). Compare this to iron for instance which only has a SHC of 451 J/kg °K. Soil has a SHC of between 800 and 1480 J/kg °K, depending on whether it's dry or wet. The high SHC of water has several consequences. It's responsible for our mild climate because the Atlantic Ocean holds a lot of heat and keeps us relatively warm in winter. In the summer, the ocean prevents the air temperature from becoming too high. However regions that are a long distance inland and far from the ocean have a continental climate because the land surface has such a relatively low SHC and doesn't hold so much heat. The low SHC causes the ground surface to heat up fast in summer so ambient air temperature becomes high, but in winter, temperatures plummet.

 

Sea breezes.

 

The difference in SHC of sea versus land is responsible for how sea breezes change direction between day and night. In the daytime, land heats up quicker than the sea and air moves towards land to replace air that rises as it increases in temperature. This is because the air becomes less dense as it expands and therefore more buoyant, just like a helium or hot air balloon rises upwards (that's how your fireplace and chimney work also). During the night the opposite happens: Land cools down quicker than the sea, so rising air over the sea causes air movement away from the land.

 

What material has the highest specific heat capacity?

 

Hydrogen has a SHC of 14,307 kJ/kg K, over three times that of water.

On the Engineering Toolbox site. Specific heat capacity of various materials. 

 

https://www.engineeringtoolbox.com/specific-heat-capacity...

Why Are Such High Voltages Used for Electricity Transmission?

 And why do we use AC?

Public domain image by FelixMittermeier on Pixabay.com

 

To understand the absolute basics of electricity, you might like to read my electricity 101 guide on the Medium.com website first, which is more detailed and has diagrams. This post on Facebook is a summary of that article.

 

Electricity 101: A Complete Beginner's Guide at this link:

https://medium.com/.../how-to-understand-electricity...

 

Volts and amps 

 

If we call the voltage in a circuit V (measured in volts) and the current I (measured in amps), the power P in watts used by a connected electrical load is simply calculated by multiplying the voltage by the current. I.e:

 

P = VI

 

Amps are denoted by the symbol A, volts by V and power in watts by W.

 

Question. A toaster takes 4 amps (4 A) at 230 V. How much power does it use?

Answer. Power P = VI = 230 x 4 = 920 watts (920 W)

 

Electrical resistance 

 

Electric cables and loads also have a property called resistance, analogous to the resistance in a water hose. When a hose is reduced in diameter or made longer (or someone steps on it), resistance to flow increases. Resistance to electricity flow in electrical cables, or any conductor for that matter (something that carries electricity) results in power dissipation as heat when electricity flows through the cables. (That's why we use thicker cables whose copper cores have greater cross sectional area (CSA) to carry heavier current, because it reduces resistance).
If we denote the resistance of a cable or electrical load by R and the current again by I, then the power dissipation in the cable is given by:

P = I²R

 

So we square the current (multiply it by itself) and multiply by the resistance to calculate the power dissipation. Resistance is measured in ohms.

 

Question. An incandescent lightbulb has a resistance of 100 ohms. A current of 200 milliamp (200 mA or 0.2 A) passes through it. How much power does it use?

Answer. P = I²R = 0.2 x 0.2 x 100 = 4 W

 

So current flowing through a resistance produces heat. This isn't of any advantage unless it's a desired effect. Devices such as electric heaters, toasters, elements in kettles, immersion elements and electric blankets make use of the property of resistance to create heat which is useful. Incandescent light bulbs also use an electric current to make a filament white hot. However in this case it's the light produced that's of benefit and the heat is just a wasteful by-product (95% of the energy used is converted to heat).

 

Resistance of electrical cables

 

We saw above that the power dissipated in a resistance is P = I²R. It doesn't matter whether the resistance is that of an electrical device, the resistance of a cable or an electrical component called a resistor (You might have seen these if you've opened a device with electronics inside. They look like cylinders with coloured stripes).

When Eirgrid or ESB Networks transmit power, they want to reduce power losses in cables, i.e. reduce P = I²R). This power loss is known as copper loss (although transmission cables are primarily aluminium to reduce weight). To reduce P, we need to make I and/or R smaller. R can be reduced by sizing cables accordingly. Making them thicker reduces R, but obviously there are practical limits because of cost and weight. A more sensible option is to reduce I, the current. Because of the squared term in the equation, the effect of reducing current is exponential. So for instance if current is made 10 times smaller, for the same resistance R, power loss is reduced to one hundredth of what it was previously. So this is exactly the technique used by transmission networks: Step up voltage by a factor of 100 or more and reduce current proportionately. 

 

So what are transformers for ?

 

Devices called transformers, which are the electrical analog of a mechanical gearbox, convert low voltage high current to higher voltage lower current. (They also do the reverse). This is easy to do when alternating current or AC is used. The lower current then reduces the power loss in cables over distance. It also reduces voltage drop because drop is proportional to current. the third advantage is lower current allows lighter gauge cables to be used, reducing cost and weight on supporting pylons or poles. Very high voltages are used for transmission countrywide and voltage is then reduced or stepped-down to a more practical level at substations. It's then further reduced by additional transformers (often pole mounted) before electricity is delivered to consumers' premises. The transmission line from Moneypoint Power Station on the Shannon Estuary that runs to the substation at Dunnstown near Carnalway operates at 400,000 volts or 400 kV.

 

See this guide for an explanation of the difference between AC and direct current DC

 

https://medium.com/.../whats-the-difference-between-ac...)

 

Also this Wikipedia article about the late 19th century War of the Currents which was a series of events surrounding the introduction of Edison's DC and George Westinghouse's competing AC electric transmission systems. Guess which won out?

https://en.wikipedia.org/wiki/War_of_the_currents