Managing the power

When operated at a lower load than it was intended for, a Newcomen steam engine gave off sharp shocks. To address this problem, Newcomen either decreased the volume of water offered for injection into the vessel or alternatively, for the same result, shut the injection cock earlier. Of course, this is a waste of the uncondensed steam that was thrown away.

In essence, Watt had contrived three solutions for this issue. The first two on the following list were difficult to find when looking at Watt & Boulton's steam engines, which was fortunate for them. Before Watt revealed them in his friend Robison's book on steam engines in 1828, Watt and Boulton were silent for nearly 50 years.

  1. The regulation valve, which admits steam above the piston, opens to a limited extent and remains open for the duration of the stroke.
  2. Having the regulation valve open from the start of the stroke and closing it entirely once the piston has only partially descended
  3. a throttle valve to only allow in as much steam as is necessary to produce the required amount of power

 Solution two was used particularly in what is now known as the expansive steam engine.

The expansive engine

Watt's single action engine

As early as 1769 Watt mentions to Dr. Small a method by which he could double the steam's effect to the detriment of enlarging a vessel too much. [2]. Too much probably means that the costs for a larger vessel are not justified by the improvement of the efficiency, i.e. the lower consumption of coal. Boulton & Watt were initially charging on the savings achieved with their steam engines compared to the coal consumption of a Newcomen steam engine of comparable water lifting capacity. Their interest was not to sell oversized engines but to optimize the profit stream from license income over the lifetime of a machine or the patent lifetime, respectively.

Watt's business acumen is revealed when he describes a new business strategy. Alterations made by him to the steam engine allow for scalable power output. Boulton & Watt could erect in a mine, that at the moment only needs the power to pump water from 10 fathoms (18m), an oversized steam engine, the power output of which was throttled by allowing steam expansion. The tradeoff was improved efficiency. In case years later the mine is sunk to 50 fathoms (91m) The power could be adapted and the mine would need to burn only 5 times the coal they had to burn when the pumps lifted water from 10 fathoms. So the efficiency could be kept at the same level. If finally, the mine had to be sunk to 100 fathoms (183m) the mine would need to burn 4 times the coal than at 50 fathoms, i.e. now the efficiency dropped to half of the efficiency at 50 fathoms. [3] The advantage of this business model for Boulton & Watt was that they did not have to change the steam engine when more power was needed but had better efficiency in the beginning. So this strategy was based on long time investment. 

Watt would fill the cylinder only to a fourth of its stroke and then cut off the steam inlet valve.  Watt calls the process expansion. From the sources I have analyzed so far it is not clear if the expansion is based on steam entering the vessel at a slightly higher pressure and letting the steam do the work to push the piston by expanding until it reaches atmospheric pressure or if the piston does the work to "suck" on the steam until the full stroke is finished. The latter expansion is nowadays called forced expansion [4].

Boulton obviously did not want that the operators (fire men) of the steam engine would play around with this aspect of the steam engine. He, therefore, describes that this mechanism could be installed inside the vessel/piston [5] so that its existence is hidden.

Watt describes 30 years later that it was used only with cylinders where steam was also admitted on the side of the piston that was usually charged with the atmospheric pressure [6]. Probably this steam had a slightly higher pressure than the atmospheric pressure.

The first engine with steam expansion was built around August 1777. The performance was not very satisfactory, and its movement was jerky and violent [7]. Despite some modifications, it would appear that Watt lost interest in the expansive engine but Boulton still favored this approach [8]. He applied the expansion principle with double engines and wrote in reference to the "Wheel Maid whim engine": "I never saw an engine take so little steam as this in my life & you may be assured that where a fly [wheel] can apply'd so as to go 300 or 400 ft per minute, the expansive principle in practice will come up to theory" [9]. The principle of expansive action was given up in 1784 when a new valve gear was introduced that prohibited the early closing of the steam valve. [10]

The expansion principle was implemented in an engine at Soho and a few other places around 1776, and at Shadwell Water Works in 1778. Then, in 1782, it was detailed in a patent among a number of new developments in steam engines.

The steam valve is controlled by plug pins in a plug frame. They are set to open the steam valve fully at the start of the down stroke. The steam valve then closes when the piston has descended a predetermined distance, such as a quarter, third, or half of the cylinder's length. If necessary, the timing can be changed by adjusting the plug pins within a minute. The engine's inertia causes the piston to be pushed further downward, which forces the steam to expand.

The accelerating force is constantly changing as a result of the pressure on the piston. As a result, the motion will no longer be uniform. The load resistance, however, might well be greater than the pressure when the piston is close to the bottom. Making the outer arch head portions spiral-shaped rather than circular could help counteract this.

After Watt had erected many atmospheric engines to his plan with success, he afterwards adopted another arrangement of the parts, in which the steam for the supply of the working cylinder does not pass through the steam case but instead enters from the steampipe, through a valve, immediately into the top of the cylinder. Although the steam case has a connection to the boiler, it only receives enough steam to maintain heat and avoid condensation of the steam inside the cylinder. Messrs. Boulton and Watt started then manufacturing the steam casings out of wrought iron plates around 1778. They chose a gap of 1½ inches as the distance between the inner side of the steam case and the outside of the working cylinder.

The adjacent drawing was taken from an engine erected at Hull, in 1779 and was at the time the standard engine for pumping water. In a working cylinder E, a piston J divides the working cylinder E into a top compartment above the piston J and a bottom compartment below the piston J. The top of the cylinder E is closed by a cover, which is screwed to the top flange of the cylinder itself rather than the top flange of the steam case. A pipe a, which appears in the drawing as a circle, delivers the steam from the boiler to a regulating or throttle valve b. Through a top fluid communication c in the top of the working cylinder E, the steam, after having passed the throttle valve b, is allowed to continuously enter the top compartment of the working cylinder E. A steam pipe d descends from the throttle valve B to the bottom of the cylinder arrangement. An equilibrium valve e at the steam pipe's base regulates the flow of steam via a bottom fluid connection f into the bottom compartment of working cylinder E. When the piston J is about to ascend, the equilibrium valve e opens, and when piston J is about to descend, the equilibrium valve e closes. An exhaust valve i functions in the opposite manner. When the equilibrium valve e is closed, the exhaust valve i opens, allowing the steam in the lower compartment of the working cylinder E to escape through an evaporation pipe g to an external condenser.

A cycle begins with a returning stroke. A working gear closes the exhaust valve i and opens the equilibrium valve e. A partial vacuum from the previous cycle is kept in the eduction pipe g and the condenser by the closed exhaust valve i. As a result of the open equilibrium valve e, steam enters the bottom compartment of the cylinder through the steam pipe d and the bottom fluid communication f. Given that the cross section of the piston rod reduces the area of the piston top exposed to steam, the area of the piston bottom is somewhat larger than on the piston top. As a result, there is a differential in pressure between the top compartment and the bottom compartment, which increases a counterweight's pulling force for completing a returning stroke.

The working gear closes the equilibrium valve e when the piston reaches a specific height, such as one-fourth of the way up. This is the beginning of the expansion phase. The steam in the bottom compartment expands until the end of the returning stroke.

The returning stroke is followed by a working stroke. When the working gear opens the exhaust valve i, the steam in the bottom compartment of the working cylinder extends by its own elasticity and the pressure difference, through the exhaust valve i, into the eduction pipe g, and finally into the condenser, where a partial vacuum was preserved from the previous cycle. The steam cools and condenses there after being met by a jet of cold water. Thus the condenser's vacuum is maintained, if not increased, because the condensed steam occupies less space than originally. More and more steam is forced into the condenser by the pressure differential between it and the working cylinder's bottom compartment. As a result, the steam that is in the upper compartment at atmospheric pressure is no longer opposed to a counterforce and pushes down the piston J. The piston continues to descend until it is close to the bottom of the cylinder. The working gear then closes the exhaust valve i and opens the equilibrium valve e thus starting a new cycle with a new returning stroke.





Watt measured the pressure inside the working cylinder at various positions of the piston. Dr Robinson developed a calculation method that was using hyperbolic logarithm.

Analysis of atmospheric engine with forced expansion

PV diagram Atmospheric steam engine with 2:1 ratio forced expansion


For a demonstration of the calculation of the increase of efficiency of an atmospheric steam engine with forced expansion I chose an expansion ratio of 1:2, i.e. the steam inlet valve is closed when the piston is halfway up, or in other words, when the volume of the cylinder is filled with one part of steam and the steam is expanded to twice this volume.

PV diagram number 2 indicates the moment when the inlet valve is closed and no more steam is admitted into the cylinder. Between numbers 2 and 2* the piston is still moved upwards by the inertia of the flywheel. The flywheel is adding work to the system (and thereby is slowed down a bit). Volume and pressure of the steam are changing, so it is either an adiabatic process or an isothermal process (or something in between). According to the definition an adiabatic process is without exchange of heat and an isothermal process is with exchange of heat otherwise the temperature could not be kept at the same level. As the steam vessel is at substantially at the same temperature, especially when a heat jacket is applied, there may be substantial heat transfer, at least f the steam that is close to the vessel walls. As the volume is changing there might be sufficient turbulence for heat transfer from the outer layers of the steam to the inner layers. When we look at the curves for an adiabatic process (green dashed line) and an isothermal process (dashed red line) we see that for temperature and pressure range they are quite close. 

Let's therefore assume first that the forced expansion is an isothermal process.

Reaching the end of the stroke (number 3*), or a little bit before to smoothen the inversion of the stroke, the air pump sucks steam from the cylinder into the external condenser and starts the condensation, and creates energy. The energy created between the end of stroke 3* and where the stroke would have ended 3 without forced expansion is the energy that is created in addition to an atmospheric steam engine without force expansion. As long as this energy is higher than the energy the flywheel had to "lend" for the force expansion the efficiency is higher than without forced expansion




What is an adiabatic process?

A process is called adiabatic when no heat is exchanged over system boundaries. In particular, this is the case when an expansion or contraction of a gas occurs so quickly that there is not sufficient time during the compression or expansion for the gas to exchange heat across system boundaries, for example to cylinder walls. The change dU in internal energy U is only done by work W.

For example, for an internal combustion engine running at 6000rpm, the compression phase takes one hundred of a second. This is not enough time to transfer heat in a substantial amount to the piston and the cylinder walls. On the other extreme, the rise or fall of air masses is also considered adiabatic, even if it takes hours. Heat is exchanged only at the boundaries where an air mass is in contact with a colder or warmer air mass. This contact surface is neglectable to the spatial extension of an air mass that extends hundreds of kilometers horizontally and some km vertically. It may take days before the air masses have exchanged heat and thus have completely mixed.

The state variables for for pressure P and volume V of a gas submitted to a reversible adiabatic process follow the formula:  

or for the transistion from a first state 1 to a second state 2 the formula can be rewritten:

If we are interested to know the  pressure P2 when a volume V1 of a pressure P1 is expanded to a volume V2 we can rearrange the formula to:

For a expansion ratio r = V1/V2 we finally arrive at :

In theory, the so-called adiabatic index γ for ideal monatomic gases (noble gases) is 1.666; for diatomic gases (nitrogen, oxygen …) 1.4 and for triatomic gases, such as superheated steam 1.333. For nonideal gases,  the adiabatic index is often renamed to κ and has to be determined experimentally. The adiabatic index is also a dependent on the temperature.


adiabatic index
steam, superheated [10]1.300
steam, dry saturated [10]1.135
steam, wet [10]1.113




For our example with an adiabatic expansion of r = 2 the atmospheric pressure inside the vessel is reduced to 0.455 kPa when assuming dry saturated steam and to 0.462 kPa when assuming wet steam.

The expansion, however, produced a less favorable pressure profile for the descending piston. One possible solution to counteract this effect is to design the connecting machinery in such a manner that the chain at the large lever's outer end will consistently apply the same amount of force to raise the pump rods. Typically, the chains that joined the piston rods to the arch head of the beam ran around the circumference of a circle. To produce a constant force when lifting the water, the piston's force on the lever and pump rods can be adjusted by forming these segments into suitable spiral parts. [20] This compensation was the subject of Mr. Watt's third patent, issued on March 12, 1802, for certain improvements upon steam-engines and certain new pieces of mechanism to be added thereto.


[1] Robison, page 126

[2] Boulton Papers, Watt to Dr. Small 28 May 1769 cited in H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 120.

[3] Boulton & Watt Colln.: Letter Books. Watt to Meason, 24 April 1777; cited in H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 120.


[5] Boulton & Watt Colln.: Letter Books. Boulton to Watt, 16 May 1777; cited in H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 120.


[7] H.W. Dickenson & R. Jenkins, James Watt and the Steam Engine, republished edition 1981, page 122.

[8] Ibid.

[9] Ibid, page 126.

[10] Ibid.

[20] John Farey, page 340.