These thoughts are prompted by the appearance of a range of Caledonian Railway locomotives for train simulators.
The story begins with William Stroudley, who had been in charge of locomotives at workshops of the poverty-stricken Highland Railway at Inverness for four years, when in 1870, at the early age of 37, he moved to the prestigious job of Locomotive Superintendent at the Brighton works of the London, Brighton and South Coast Railway (LBSC), taking with him his workshop manager, Dugald Drummond. Between them, they established a solid tradition of locomotive design which continued until the 1920s, with locomotives which remained in service until almost the very end of steam in Britain.
On arriving at Brighton, Stroudley initiated a programme of standardisation, based on a limited number of locomotive types with components common to the different classes. These included the famous A1‑type Terrier 0‑6‑0 tank locomotives for lightly laid lines, the G‑type 2‑2‑2 single driver express passenger locomotives, the C‑type 0‑6‑0 tender locomotives for freight, the D1‑type 0‑4‑2 tank locomotives for short distance passenger services, and the E1‑type 0‑6‑0 tank locomotives for freight.
The single driver locomotives soon proved to be unsuitable for the heavier express trains—there is a steep climb out of Victoria—and because Stroudley did not like bogies, he constructed a series of 0-4-2 tender locomotives, starting with a tender engine version of the D1, with successive enlargements of the type, of which the best known was the famous B1 ‘Gladstone’ class.
The 0-4-2 design was a dead end, no other railway using this type in any significant numbers. When, in 1875, Drummond moved took over responsibility for the locomotives of the North British Railway, he designed what was probably the first modern 4-4-0 tender locomotive type with inside cylinders, the ‘Abbotsford’ class, which entered service in 1876. These were the first of a breed that would continue to be developed for another forty years. In 1882, Drummond moved to the Caledonian Railway and enlarged and improved locomotives of the same general type, the ‘60’class, were brought into service on that railway. Drummond resigned from the Caledonian in 1890, and his successors, Lambie, and McIntosh, continued this line of development. McIntosh’s contribution was to fit the locomotives with a much larger boiler, and this was the famous 721 ‘Dunalastair’ class. The type went through four successive enlargements, the final version being the superheated ‘Dunalastair IV’, followed by yet another version by the successor to McIntosh, Pickersgill, who took over in 1914. The Pickersgill locomotives were constructed between 1916 and 1922, and although their performance was disappointing, all remained in service until 1959.
Most of the Dunalastairs, however, were not built for the Caledonian but for the Belgian State Railways, which put over 400 of the type into service between 1899 and 1912.
Tender freight locomotive design followed a parallel path, with successively larger 0-6-0 types being introduced in response to the need for greater power.
There was a similar development with tank engines. The 0-4-2 type D was stretched to create an 0-4-4 design and these went through a number of phases, the last of the Caledonian design entering service in 1925, in LMS days. They were still to be seen on Glasgow suburban routes in the late 1950s and there were normally a few at Beattock on standby for banking work.
Drummond himself took over at the London and South Western Railway in 1895 and again proceeded to equip the railway with locomotives of similar types to those he had provided for the Caledonian: 4-4-0 tender locomotives for express passenger services, of which the best known were the T9 for the main line and the S11, a small wheeled version for hilly routes in the west, an 0-6-0 tender locomotive for freight, and an 0-4-4 tank engine, the M7, for local passenger services. As on the Caledonian, the designs were successively enlarged, culminating in the D15 4-4-0, a class of ten locomotives introduced in 1912. All of these types were extraordinarily long-lived, no doubt because of their efficiency, ease of maintenance and very sturdy construction.
Stretching the design
The basic Drummond inside-cylinder 4-4-0 design had its limits. Trains became heavier and 4-4-0 locomotives were no longer adequate. On the Caledonian, the type was stretched to a 4-6-0 type, including the famous ‘Cardean’ class. These were elegant but disappointing in performance. The Caledonian never had a effective 4-6-0, though it could certainly have done with one. The Pickersgill 4-6-0s were elegant but feeble and spent their lives shuffling around the Glasgow area.
Drummond, on the London and South Western, put various types of 4-6-0 into service, some with four cylinders. The styling which suited the small 4-4-0 types looked monstrous on the huge 4-6-0 classes. Their performance was dismal. This was at a time when Churchward had produced the highly competent Saint and Star classes, following a long series of experiments leading to a range of designs which continued into production until the 1950s, since the same basic types were adopted for construction by the London Midland and Scottish Railway and by British Railways. The brilliant young Drummond had clearly got stuck in a rut, being well past retirement age when he started on his 4-6-0 designs; put plainly, Drummond just did not know how to design a 4-6-0 and at that time the type was still fairly novel.
The South Western at least did better than the Caledonian. When Drummond retired in 1912, he was succeeded by his works manager, Robert Urie, who produced a range of simple, sturdy and competent 4-6-0 designs with two outside cylinders: the H15 mixed traffic type, the S15 freight class and the N15 express passenger class. Their performance was not as good as it might have been due to the design of the valves, but after the grouping, the Southern Railway’s Chief Mechanical Engineer, Maunsell, applied the Swindon practice for valve design to the N15 (the ‘King Arthur’ class) and S15 types, to produce two classes of outstanding locomotives which remained in front line service almost to the end of steam; in preservation, the S15 class has proved to be remarkably competent at handling passenger trains.
As so often with the history of steam locomotive design, there are principles which apply to engineering generally.
lördag 7 juli 2018
onsdag 12 april 2017
Which is Britain's favourite steam locomotive class?
Which is Britain's favourite type of steam locomotive? Flying Scotsman is clearly the most famous, but as a sole survivor of the A3 Pacifics, it is out of the running.
The Gresley A4 Pacifics have an obvious appeal, and fortunately it is still possible to see several of them lined up together, but with their streamlined casings they do not conform to the pattern of the archetypal steam locomotive. The same applies to the unrebuilt Bulleid Pacifics, the appearance of which was a successful attempt to get away from that archetype at a time when it was commercially necessary to update the image of steam.
Surprisingly, LMS Class 5s, with the most survivors of any class, have more of a following than in the days of steam, when they were commonplace, neglected and ignored. Looking at the type in their present-day immaculate condition, however, their elegance and perfectly balanced appearance is evident.
Then there are the Great Western classes, which survived in large numbers thanks to the good fortune of having been sent to Barry. Here of course the obvious candidates are the Kings and the Castles. The former are imposing but the design pushed the GWR's four-cylinder 4-6-0 formula to the limit and they originated in a desire for publicity as much as for the needs of the traffic; the huge boiler sits uncomfortably and the inside/outside framed (and initially troublesome) bogie is an oddity which was the result of having too much to squeeze in. Which of course leaves the Castles, another class which has survived in large numbers. The single chimney variant is as nearly visually flawless as any practical machine can be. To judge by the number of Youtube videos of simulations which bring Castles to such improbable routes as the West Highland, and the West Coast Main Line north of Carlisle, one wonders if the type is not now at the top of the list.
The Gresley A4 Pacifics have an obvious appeal, and fortunately it is still possible to see several of them lined up together, but with their streamlined casings they do not conform to the pattern of the archetypal steam locomotive. The same applies to the unrebuilt Bulleid Pacifics, the appearance of which was a successful attempt to get away from that archetype at a time when it was commercially necessary to update the image of steam.
Surprisingly, LMS Class 5s, with the most survivors of any class, have more of a following than in the days of steam, when they were commonplace, neglected and ignored. Looking at the type in their present-day immaculate condition, however, their elegance and perfectly balanced appearance is evident.
Then there are the Great Western classes, which survived in large numbers thanks to the good fortune of having been sent to Barry. Here of course the obvious candidates are the Kings and the Castles. The former are imposing but the design pushed the GWR's four-cylinder 4-6-0 formula to the limit and they originated in a desire for publicity as much as for the needs of the traffic; the huge boiler sits uncomfortably and the inside/outside framed (and initially troublesome) bogie is an oddity which was the result of having too much to squeeze in. Which of course leaves the Castles, another class which has survived in large numbers. The single chimney variant is as nearly visually flawless as any practical machine can be. To judge by the number of Youtube videos of simulations which bring Castles to such improbable routes as the West Highland, and the West Coast Main Line north of Carlisle, one wonders if the type is not now at the top of the list.
söndag 26 mars 2017
Professor W A Tuplin
Professor W A Tuplin (1902-1975) was an engineering academic and specialist in the design of gears. He worked for the vehicle manufacturer David Brown, eventually becoming Chief Engineer before being appointed Professor of Applied Mechanics at Sheffield University until he retired in 1968.
In addition to contributions to journals, Tuplin was the author of many books about steam locomotives, including Midland Steam, Midland Steam, The Steam Locomotive, Great Western Power, Great Western Saints and Sinners and North Eastern Steam, Great Northern Steam, Great Central Steam, Tuplin's large output meant that he was widely read amongst the interested public, but he was not a locomotive engineer. His sometimes controversial opinions brought him into conflict with practising engineers such as E S Cox and Ell, who was responsible for the redesign of the King and Castle classes in the early 1950s. Consequently, his views need to be read with caution, if not taken with a pinch of salt.
However, and subject to that caveat, it is instructive to read Tuplin's comments on particular classes, including some which have been selected as prototypes for replicas. Even the best machines have their weaknesses, and some of the selected replica types are referred to in his writings. Those who are engaged in these projects could usefully comb through Tuplin's observations. It seems pointless to perpetuate faults in brand new locomotives when small modifications could get rid of the defects without affecting their appearance. Some of the proposed replicas might be of designs which would be best left as memories rather than re-created at full size in new metal.
In addition to contributions to journals, Tuplin was the author of many books about steam locomotives, including Midland Steam, Midland Steam, The Steam Locomotive, Great Western Power, Great Western Saints and Sinners and North Eastern Steam, Great Northern Steam, Great Central Steam, Tuplin's large output meant that he was widely read amongst the interested public, but he was not a locomotive engineer. His sometimes controversial opinions brought him into conflict with practising engineers such as E S Cox and Ell, who was responsible for the redesign of the King and Castle classes in the early 1950s. Consequently, his views need to be read with caution, if not taken with a pinch of salt.
However, and subject to that caveat, it is instructive to read Tuplin's comments on particular classes, including some which have been selected as prototypes for replicas. Even the best machines have their weaknesses, and some of the selected replica types are referred to in his writings. Those who are engaged in these projects could usefully comb through Tuplin's observations. It seems pointless to perpetuate faults in brand new locomotives when small modifications could get rid of the defects without affecting their appearance. Some of the proposed replicas might be of designs which would be best left as memories rather than re-created at full size in new metal.
onsdag 22 mars 2017
Big Green Machine
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One night in August 2007 this was heading a construction train in connection with the installation of a new bridge on the Swiss railways at Thayngen. The steam engine proved popular for permanent way and works trains especially at night because it is practically silent when stationary and less obtrusive when working, which was appreciated especially by local residents.
This was not the whole story either, because unlike a diesel, which is constantly idling even when stationary, no fuel is used while in standby mode. When all the sums are done, it turns out that the greater thermal efficiency of the diesel is negated by the cost of processing the fuel to make it suitable for use in an internal combustion engine, and in these standby losses. Hence it has been found that on the Swiss and Austrian mountain railways where both steam and diesel locomotives run on the same diesel fuel, the former use less as they consume nothing when stationary or running downhill.
The locomotive was rebuilt from a German Kriegslok constructed in 1944 and intended for no more than a few months' service. The work was carried out by the Swiss engineering company Dampflokomotiv- und Maschinenfabrik DLM AG of Winterthür. Improvements were incorporated to provide for quick startup and efficiencies around 50% higher than the best that was being achieved when steam locomotives were last used regularly in the 1950s.
Steam locomotives are in many ways ideal for rail traction, where demand for power is intermittent, for example, when starting, accelerating, and on uphill stretches of route. Because the boiler acts as an energy reservoir, the conversion of the chemical energy in the fuel to mechanical energy is separated off from the use of that energy to provide traction. In an internal combustion engine, on the other hand, the engine where the conversion of fuel to mechanical energy takes place has to be sufficiently large to provide for the maximum power demand. And being external combustion devices, steam locomotives are not particularly fussy about the fuel that is used. The use of waste materials is relatively simple and thus the machines can be carbon-neutral.
Steam locomotives are in principle simple, with direct drive from the cylinders to the wheels. By contrast, internal combustion engines used for rail traction require a complex and expensive electrical or hydraulic transmission system, with consequential high manufacturing and maintenance costs and energy losses. Given a reasonably long production run, the cost of steam locomotives should be less than 40% of the equivalent diesel electric.
Unfortunately, there were no takers for the technology, which still has to recapture its credibility amongst conservative railway managers who dismiss it as obsolete. It is unfortunate, however, that the obvious advantages when used, as here, for maintenance trains, have not been recognised.
tisdag 21 mars 2017
The strange case of the Lord Nelsons
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The Lord Nelson class should have been an immediate success. Under Maunsell's leadership, the Southern Railway had a first-rate design team with a good record of producing successful new designs and improving existing ones. The prototype was thoroughly tested before series production was put in hand in 1928. The picture shows 854 Howard of Effingham at Waterloo; the locomotive must have been almost brand new, and smoke deflectors had not yet been fitted.
Yet they were disappointing, and despite efforts to improve them, only really came near their potential when Bulleid took over from Maunsell as CME of the Southern Railway in the late 1930s. Then came the war, and afterwards there were so many Bulleid Pacifics that with only 16 locomotives in the class there was little opportunity for them to show their potential. They had very long fireboxes and the rear half of the grate was level, and for that reason they were difficult to fire. Four sets of valve gear for the four cylinders was necessary as the cranks were set at 135 degrees to give a more even beat, but it sounds like an unnecessary complication. The prototype, 850 Lord Nelson, was preserved, and has been restored for main line operation.
One wonders why the design did not closely follow the GWR Castles? The Southern Railway's design team included Holcroft, who had been at Swindon from 1906 until he moved to the South Eastern and Chatham at Ashford in 1914, and would have been familiar with the extended testing and development work which produced the Star class, the predecessors of the Castles.
Background to the design
Extracted from J. Inst. Locomotive Engineers Volume 38 (1948)
In December 1924, Maunsell wrote to the CMEs of the other British railways to ascertain the maximum axle load permitted on their lines. Hughes had submitted three designs on the LMS where the driving axles carried a load of 20 tons which, at the time, was the extreme load permitted on the LMS. Gresley stated that the highest axle load in use on the LNER was 20 tons 16 cwt., and Collett, from Swindon, said that 20 tons was the maximum built to at the time, but new engineering work would permit loads up to 22 tons. Maunsell investigated every channel both at home and abroad to see whether such an engine of the power required could be built within the weight laid down by the Civil Engineer.
The original scheme for an engine which ultimately led to the construction of the Lord Nelson had an axle load of 21 tons 10 cwt., which was 17 cwt. in excess of the 20 tons 13 cwt. of the final Lord Nelson. The cab was rather a departure from the usual Southern Railway cab, being more in keeping with the old North Eastern. To enable the weight to be reduced, the boiler barrel was shortened by approximately 10 in., and this enabled the King Arthur tubes to be used as the distance between the tubeplates was identical.
The improvement made by the alteration to Engine No. 449, particularly with regard to the saving in coal, was so marked that it was decided to incorporate the arrangement in the new "Lord Nelson" class. The arrangement provides a more uniform torque and more regular effect on the firebox draught than is customary and enables the engine to be worked more heavily without fear of 'breaking up" the fire.
The revolving and reciprocating parts were kept light by using high tensile steel, Vibrac, and the balance weight in the wheels was reduced in consequence: this produced a much lighter hammer blow and influenced the Civil Engineer in accepting an axle loading up to 21 tons.
The boiler was large, and a new feature for engines built at Eastleigh was the provision of a Belpaire firebox. The superheater was the Maunsell type with air relief valves. The boiler has probably the widest type Belpaire firebox that could be used within the limitation of the SR loading gauge, consistent with a clear view from the cab; also the longest firebox it is possible for a fireman to conveniently fire. The grate is virtually in two sections, the rear portion being horizontal as a landing and the forward portion sloped. This caused a definite break in the fire and on occasion led to indifferent steaming when inexperienced firemen are used to fire the locomotives.
The Lord Nelson boiler was originally fitted with steel and copper water stays in the firebox. Copper stays were used on the firebox side for the top six rows and the outer end rows only, the remaining stays being of steel. The steel stays were afterwards replaced by Monel stays and this was probably the first application of Monel stays as standard practice to locomotive fireboxes in Britain. The stays are fitted with steel nuts on the inside of the inner firebox.
To enable the engine to be built to the weight allowed by the Civil Engineer, great care was exercised, both in design and actual building. Certain parts normally left as forged or cast were machined to keep within the weight. So much care was exercised that the engine was actually well within the weight when completed, so the remainder of the class did not receive similar treatment. After the balancing of the engine had been calculated at Eastleigh, the figures were submitted to Professor Dalby, who agreed that the engine balance as shown would be very satisfactory in running. Cocks notes that the Southern was unlike the other members of the Big Four: in its intensive passenger services, its electrification and its quest for punctuality. On the rebuilt E and D classes he noted that these shared the large N class piston valves.
...contact with German engineers (in 1930) had an important sequel. They were full of enthusiasm for the solid-headed piston valve with plain rings which had come into use in Germany, and they brought over drawings. This led to their general introduction on the Southern Railway. A snag was struck, however, when these valves were applied to " Schools " class engines working on the Eastern Section.. Certain trains to Cannon Street or Charing Cross have to make a stop at No. 7 platform, London Bridge, which is on a curve and has an up gradient of 1 in 100. To make matters worse, there are catchpoints immediately in the rear of long trains, so that setting back more than a few yards is prohibited. Great difficulty began to be found with the Schools " class in starting their trains and an investigation was made. These engines, in common with the Nelson " class had a lead of ¼ in., but as the solid heads of the valves had a small clearance in the liners, some pre-admission in excess of lead steam started as far back as the first ring, when it passed the port edge. The amount of steam leak was insignificant when on the move, but on starting a heavy load enough leakage occurred to cause a negative turning moment and so seriously affect the tractive effort.
The remedy adopted for this state of affairs was to reduce the lead and transfer the point of cut-off from the edge of the head to the first ring, turning down the diameter of the head in advance of the ring to expose the side of the ring to steam.. This reduction in diameter of the head can only be small in amount, otherwise the reduced bearing surface of the ring in its groove leads to excessive groove wear.
While this alteration ameliorated conditions at starting in the case of the " Schools " class, it was applied also to the " Nelson " class in accordance with the policy of standardisation of parts. In my opinion this was most unfortunate and quite uncalled for from the performance aspect, and I attribute to this the blight which seemed to descend on the " Nelsons " after their earlier brilliance. The alteration did not matter so much to the " Schools," which are customarily worked at a 25 per cent, cut-off and part regulator, but the Western working of the " Nelsons " with full regulator and short cut-off was another matter altogether. Not only was the area of opening to steam restricted by the projecting edge of the head beyond, the first ring but lead steam was reduced as well, so that port opening was much smaller than before, with the same travel. This state of affairs remained until the front end was modified by Mr. Bulleid in recent years.
söndag 19 mars 2017
Hydrogen power blind alley?
Alstom's hydrogen powered train, the iLint,
based on fuel cell technology, is now undergoing tests. The train is expected to enter service in passenger-carrying trials on the Buxtehude–Bremervörde–Bremerhaven–Cuxhaven (Germany) route at the beginning of 2018. It is zero emission and promoted as a
solution for lines which are not likely to be electrified. The exhaust
is pure water vapour.
However, whether hydrogen is zero emission or not depends on how the electricity used to make the hydrogen is generated. There are also energy-efficiency questions which need to be considered. There is an immediate loss, the size of which depends on how the electricity used to make the hydrogen is generated. There is a further loss when energy is converted into hydrogen and back again into electricity in the vehicle, and then there are the usual losses associated with the drive train and control systems.
Nor is that the end of the energy losses. There are also losses associated with the transport of the hydrogen, which is not a portable fuel. It has to be compressed and put in tanks. It will liquify only at extremely low temperatures. What is the overall thermal efficiency when all of this is taken into account? There is a discussion of the subject here, in relation to automotive applications of hydrogen fuel cells.
Then there is the platinum issue. Fuel cells require expensive platinum catalysts. Alternatives are not even on the horizon. Platinum mines are not environmentally friendly. Taking one thing with another, this is nothing like as clean as it appears on the surface.
A good benchmark for cost, energy efficiency and performance would be a locomotive-hauled train using refurbished vehicles in push-pull mode. The fuel cell powered train must cost at least £4 million, and probably much more, not to mention the development costs which must be recouped. In comparison, a small steam locomotive such as the DLM design, which has an efficiency around 12%, would cost not more than £2 million per unit, given a minimum production run of twenty. The locomotive, which can run on anything that will burn but realistically can use diesel oil or biomass waste as fuel, easily satisfies current emission regulations. The use of refurbished vehicles gets rid of the bulk of amortisation charges.
As well as being less expensive, such a solution would be far more capable and flexible than a fixed formation passenger unit of any kind.
When running on biowaste, steam locomotives are a zero-net-carbon technology. What a pity that Alstom did not devote its engineering resources to a simpler and less costly technology. Is this a case of not being able to see the wood for the trees?
However, whether hydrogen is zero emission or not depends on how the electricity used to make the hydrogen is generated. There are also energy-efficiency questions which need to be considered. There is an immediate loss, the size of which depends on how the electricity used to make the hydrogen is generated. There is a further loss when energy is converted into hydrogen and back again into electricity in the vehicle, and then there are the usual losses associated with the drive train and control systems.
Nor is that the end of the energy losses. There are also losses associated with the transport of the hydrogen, which is not a portable fuel. It has to be compressed and put in tanks. It will liquify only at extremely low temperatures. What is the overall thermal efficiency when all of this is taken into account? There is a discussion of the subject here, in relation to automotive applications of hydrogen fuel cells.
Then there is the platinum issue. Fuel cells require expensive platinum catalysts. Alternatives are not even on the horizon. Platinum mines are not environmentally friendly. Taking one thing with another, this is nothing like as clean as it appears on the surface.
A good benchmark for cost, energy efficiency and performance would be a locomotive-hauled train using refurbished vehicles in push-pull mode. The fuel cell powered train must cost at least £4 million, and probably much more, not to mention the development costs which must be recouped. In comparison, a small steam locomotive such as the DLM design, which has an efficiency around 12%, would cost not more than £2 million per unit, given a minimum production run of twenty. The locomotive, which can run on anything that will burn but realistically can use diesel oil or biomass waste as fuel, easily satisfies current emission regulations. The use of refurbished vehicles gets rid of the bulk of amortisation charges.
As well as being less expensive, such a solution would be far more capable and flexible than a fixed formation passenger unit of any kind.
When running on biowaste, steam locomotives are a zero-net-carbon technology. What a pity that Alstom did not devote its engineering resources to a simpler and less costly technology. Is this a case of not being able to see the wood for the trees?
lördag 18 mars 2017
Gas laws
Engines - whether driven by steam or internal combustion, make use of the properties of gases. These were well-known by the time steam power was coming into widespread use at the end of the eighteenth century.
The first of the gas laws to be discovered was Boyle's Law, published in 1662, which states that for a given mass of gas at a constant temperature, the volume is inversely proportionate to its pressure.
The second was Charles' Law, or the law of volumes, discovered in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature (minus 273 degrees Centigrade), assuming the system is closed - ie that nothing can get in or out of the containing vessel.
The third gas law was Gay-Lussac's Law, the Pressure Law, discovered in 1809. It states that, for a given mass of a gas at a constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.
Adiabatic processes
The term "adiabatic process" is used to describe what happens when the volume of a gas is allowed or forced to change without any heat being added or removed. An example is when the air in a bicycle pump heats up when pumping. The energy from the pumping action heats up the air in the pump. The same effect in reverse is observed when a compressed gas is allowed to expand suddenly, for example, when it is released from a gas cylinder: it cools.
This is the key to understanding what happens when a hot gas under pressure is allowed to expand, for example in the cylinder of an engine. The gas cools, and useful work is done as heat energy is lost, being converted into mechanical energy. The process was analysed by the 28 year old French military engineer Nicolas Carnot. His army career having stagnated, Carnot befriended the scientist Nicolas Clément and attended lectures on physics and chemistry. He became interested in steam engines and what could be done to improve their performance. This led him to the investigations that became his "Reflections on the Motive Power of Fire", (Réflexions sur la Puissance Motrice du Feu) published in 1824, in which he described what became known as the Carnot Cycle. Not only is it one of the core concepts in the theory of engines of all kinds, it is also the basis of the Second Law of Thermodynamics.
The first of the gas laws to be discovered was Boyle's Law, published in 1662, which states that for a given mass of gas at a constant temperature, the volume is inversely proportionate to its pressure.
The second was Charles' Law, or the law of volumes, discovered in 1787 by Jacques Charles. It states that, for a given mass of an ideal gas at constant pressure, the volume is directly proportional to its absolute temperature (minus 273 degrees Centigrade), assuming the system is closed - ie that nothing can get in or out of the containing vessel.
The third gas law was Gay-Lussac's Law, the Pressure Law, discovered in 1809. It states that, for a given mass of a gas at a constant volume of an ideal gas, the pressure exerted on the sides of its container is directly proportional to its absolute temperature.
Adiabatic processes
The term "adiabatic process" is used to describe what happens when the volume of a gas is allowed or forced to change without any heat being added or removed. An example is when the air in a bicycle pump heats up when pumping. The energy from the pumping action heats up the air in the pump. The same effect in reverse is observed when a compressed gas is allowed to expand suddenly, for example, when it is released from a gas cylinder: it cools.
This is the key to understanding what happens when a hot gas under pressure is allowed to expand, for example in the cylinder of an engine. The gas cools, and useful work is done as heat energy is lost, being converted into mechanical energy. The process was analysed by the 28 year old French military engineer Nicolas Carnot. His army career having stagnated, Carnot befriended the scientist Nicolas Clément and attended lectures on physics and chemistry. He became interested in steam engines and what could be done to improve their performance. This led him to the investigations that became his "Reflections on the Motive Power of Fire", (Réflexions sur la Puissance Motrice du Feu) published in 1824, in which he described what became known as the Carnot Cycle. Not only is it one of the core concepts in the theory of engines of all kinds, it is also the basis of the Second Law of Thermodynamics.
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