Heated Air as a motive power

Source: Minutes of the Proceedings of the Institution of Civil Engineers, Vol 12, N° 886, p. 312
Date: Feb 15, 1853
Title: On the Use of Heated Air as a Motive Power
Author: Benjamin Cheverton

Early hot air engines

The principle of employing heated air as a motive power is very old ; but it appears to have been first used in a really efficient form by the Messrs. Stirling, of Scotland, in the year 1827. Messrs. Parkinson and Crosley also brought forward an air engine in 1827, in which the arrangements were very similar to those of the Messrs. Stirling, although not so well devised for economising heat ; but they introduced the principle of using air of greater density than that of the atmosphere, and so obtained an engine of greater power in the same compass.

In both these projects, the same vessel became alternately the heater and the condenser, according as the air was made, by the action of a plunger, to occupy the hot, or the cold end ; and thus the necessity of forcing a continual supply of cold air into the heater was avoided.

But in the year 1833, Lieut. Ericsson, whilst a resident in this country (England), brought forward his caloric engine, in which, reverting to the steam engine type, he made the heater and condenser distinct vessels, with permanent functions. This arrangement was necessarily accompanied with what may be termed a force pump ; but which is called by the inventor the "supply cylinder". As under the temperature employed, the expansion of the injected air is only double, this force pump becomes a formidable affair, requiring its cubic contents to be half that of the working cylinder.

If the heated air were allowed to escape freely, there would be a loss of heat ; it therefore occurred to the Messrs. Stirling to employ it in heating the incoming air ; and it is important to notice, that this principle was acted upon by them from the first, and that the means they employed to carry it into effect consisted of metallic laminae, and also wire gauze, through the interstices of which the hot and cold air passed alternately - the contrivance being analogous to the subsequently introduced, medical respirator of Julius Jeffreys.

Ericsson brought forward the same principle ; but his arrangements were somewhat different, inasmuch as his abstracters and transmitters of heat consisted of a series of tubes in pairs, the one being enclosed within the other. In 1840, Messrs. Stirling took out a second patent for improvements on their engine ; but they referred only to matters of detail, and were of no great importance.
In 1845, the invention was explained to the Members of this Institution, and was the subject of an interesting discussion.

In 1851, Lieut. Ericsson also a second time patented his caloric engine, with improvements, the principal one consisting in the adoption, in the "regenerator", of the means already employed by Messrs. Stirling, for abstracting and transferring heat from and to the hot and cold currents of air.

Though the respective engines of these gentlemen are, in their latest forms, characterised by the same principles, and essentially by the employment of the same means, yet they are widely different in their construction and arrangements, on account of one party employing a force pump to inject air from the cold vessel to the hot one, and the other dispensing with it, by displacing the air from the cold and sending it to the hot part of the same vessel; but in both inventions, the air, during this transfer, percolates through the interstices of a metallic mass, alternately receiving and imparting heat in its passage.

The regenerator and perpetual motion

Both parties also rest the efficiency of their engines on the repeated use of caloric; they contend, that in recovering from the ejected hot air, the caloric which gave it superior tension, and employing it in heating the injected air, "it is made to operate over and over again".

Mr. Ericsson aspires to embody a new principle in motive mechanics, no less, to use his own words, than "that the production of mechanical force by heat is unaccompanied by the loss of heat", except such as arises from radiation, or other practically unavoidable waste.

It is to this point, chiefly, that attention must be directed, for if this is a correct statement of the merits of the "caloric engine", it is impossible to overestimate the importance of the invention, in comparison with which all past discoveries in motive mechanics are utterly insignificant.

This new principle must be submitted to the test of general laws, and if it will not bear this scrutiny, such advantages as the new engine may possess over the steam engine (if such shall be proved), might be referred to circumstances of a practical nature, which it may be worth while to ascertain and discuss.

Caloric, in the mechanical view of the subject, is known simply as a force. Now, a force whose action does not imply, to the same extent, its extinction, in reference to the body to which it primarily belonged ; or a force which, admitted to become for an instant extinct in one body, by transmission to another, is the next moment capable of becoming self-recruited, are assumptions inconsistent with all natural phenomena, and involve a manifest impossibility. Yet the "caloric engine" is chargeable with this absurdity, so far as it is founded on the principle "that the production of mechanical force is unaccompanied by the loss of heat", and that "caloric can operate over and over again".

In truth, it amounts to nothing less than affirming the principle of perpetual motion, affirming that power can be gratuitously exerted, that it can be continued indefinitely in action, without exhaustion, affirming, in short, that Newton's third law of motion is untrue, and that action and reaction are not equal and opposite.

The entire science of motion is implicated in this law of action and reaction, which certainly it is not necessary now to defend ; but it is not a law of motion only, it is a universal law of Nature. All observations and experience prove, that qualities and quantities of all kinds, of a communicable nature, are in the very act, lost by one body, in proportion as they are received by the other.

Take caloric, for instance, in its other aspect, as simply a heating quality, and only as one body loses temperature is it able to impart it to another. But caloric, doubtless, is in all its aspects a manifestation of force, and unquestionably, as a mechanical agent, of a dynamic force, and therefore is directly amenable to the third law of motion. It is force, in the disguise of molecular action - it is atomic force, not yet converted into mechanical force - it is, in respect to either ponderable, or imponderable matter, a speciality of condition, appealing to the feeling of heat for its perception, but susceptible of being changed into another speciality, recognised by a sense of force, or power.

As mechanical motion, which is the motion of masses in their entirety, can be and to be made useful, usually is transformed into molecular actions, such as those involved in heat and electricity, and in the rupture of cohesive force, so, through the medium of combustion, these transformations can be reversed, by first liberating molecular forces, and then fixing them in the entire movement of a mass, so as to be rendered available as a mechanical power.

Now that peculiar molecular activity, which, by some mysterious process, creates the feeling of heat, is not susceptible of an increasing degree of intensity, except when the body is under the restraint of limits to its volume.

Remove these, as can be done in an elastic fluid, and any further accession of caloric is no longer apparent, under the form of an increasing temperature, or of an increasing degree of repulsive force ; but it makes itself visible in an increased range of this force, that is to say, the tension remaining constant, a dynamic force is generated, at the expense of this caloric, as its exciting cause.

Thus mechanical force is developed simultaneously with a loss of heat, in entire conformity with the law of action and reaction. The usual phrase is, that heat becomes latent.

The order and character, then, of these phenomena justify the inference, that what is at one time heat, is at another time modified into mechanical action, they being reciprocally convertible quantities, and in truth, the change of either into the other is matter of experiment. It follows, then, that sensible caloric is an indication, not of the presence, but of the abeyance of mechanical action, not of its actual, but of its potential existence, and that a working force can appear, only as heat disappears.

This is an important truth, although veiled somewhat by refinement of conception and nicety of distinction, for which there is a want of an adequate terminology. This truth, so directly in opposition to the idea of caloric operating over and over again, is, however, apt to be overlooked, on account of the general familiarity with a display of heat, simultaneously and in intimate connection with the development of steam force.

It thus appears, on a superficial view, that heat operates as a force, and at the same time exists as heat ; whereas, heat appertaining even to steam in the cylinder, is not really acting, although ever ready to act in the production of elastic force, and ever vanishing in the process.

This sensible heat of the working steam is, it is true, the necessary condition for maintaining the constant state of its tension, but it is not the efficient cause of force — it is not that which creates repulsion between the particles of steam, otherwise it would at all times be the direct measure of that repulsion, which it is not — it is only an accompanying quantity of caloric, which when called upon by the permitted expansion of steam to do real work, is absorbed, becomes latent, and disappears.
If this were not the true representation of the fact, caloric could be heat and force also, at the same time.

This is the popular idea, and science perhaps has not been exempt from it, but if it were so, there would be no impracticability in the project of making it operate over and over again, and the creation of power, in the absolute sense of the words, would be within the capability of man.

Heat cannot be used "over and over again"

There is a difficulty, however, which requires explanation, for it may be said in reply, that in the low pressure steam engine, all the heat that is contained in the steam, as it comes from the boiler, is to be found in the water of the condenser, although it has in the interim, generated power ; that the only question is, how to get it wholly back to the boiler, as it already is done partially, by the boiler being supplied with this heated water, and that the analogous problem is solved, when the motive medium is air, by the invention of the "regenerator".

Undoubtedly in respect to the materiality of caloric, if it be material, it is transferred intact to the condenser, yet in its passage it may have parted with force, which it cannot communicate again.

It will be admitted, also, that in the aspect of temperature, the quantity of caloric, as estimated jointly with the quantity of water, will measure the same before and after the condensation of steam ; but the change takes place, not in the quantity, but in the intensity of heat.

It is in the declination from a higher to a lower degree of temperature, it is in the aspect of a vis viva force in caloric, that mechanical action is developed ; in proof of which, if it be required again to raise the motive body to the higher temperature, recourse must be had, either to a further consumption of means, or to the employment, in the case of air, of the same amount of mechanical force in compression, as had been previously developed.

This explanation of the difficulty, may not, however, be satisfactory to a mathematician of the old school, who has been conversant only with that aspect of power, in which it is estimated by the product of force and velocity, and has not been accustomed to view it in the more practical light of mechanical efficiency.

He would be inclined to say, that just as a mass, or force with a given velocity, is equal to a less mass, or force with a proportional greater velocity, so a body of water (that of condensation) raised a given number of degrees of temperature, is equivalent to a less body of water absorbing, in like ratio, a greater number of degrees of temperature. Thus no loss is found and yet power is developed.

The answer is this ; as the efficiency of causes is known only by their effects, so they must be measured by their effects ; and if by the same action of a cause, two classes of effects are produced, and if by the same variations in the action of the cause for both classes, it is discovered, that in one, the results, in the matter of cause and effect, are always equal to each other, and in the other class, that they are unequal, there must be two distinct and different measures enunciated, expressive of these facts.

Now by the application of only one measure, to the operations of such a power, it may appear, that the cause is fully accounted for in the effect ; that reaction is equal to action, and yet a surplus fact, not of the same, but of a different kind, remains unexplained. The loss is seen to be balanced by the gain, yet extra results are acquired, and so the incautious reasoner, inattentive to the inviolable character of general laws, is led to conclude, that this acquisition has been effected, free of all cost.

This apparent anomaly, or exception to the law of action and reaction, arises from the recognition of only one class of effects, when there are really two, and it disappears by the application of a second measure, supplementary to the first, and appropriate to the nature of the second class of effects.

This comhination of measures, by embracing the whole of the case, subjects and reconciles it to the law in question. If the motive force be caloric, and if concurrently with a change from a higher to a lower degree of temperature, mechanical power is acquired, the inference is inevitable, that the latter is produced at the expense of the former; although by a measure, which takes no notice of this change, but recognises quantity only, there will not appear to be any loss.

The idea of making heat generate mechanical power, and yet lose nothing itself, cannot be sound, as it must be ever ready to produce more power ad infinitum a course of action, which if it were possible to prevail, as an ordinance of nature in her general operations, would soon bring the world to an end.
This erroneous assumption is based on overlooking the change in the intensity of caloric, and of taking as the sole index of its action, the unaltered amount of its quantity.

The same diversity as to distinct classes of effects, and as to their appropriate measures, occurs in mechanics, and was the occasion of much controversy, among the mathematicians of the last century, as to the true measure of force. Both parties were partially right, although they differed materially in expression, for whether force be measured by time, or by space, they are both true measures under different conditions, although the physical circumstances be the same.

It was reserved, however, for practical men to show, that the selection of the measure is not a matter of arbitrary choice, but that there is an appropriateness in the one, or the other, founded on the reality and utility of things. They forced into recognition the importance of another modification of power, besides that of momentum, or quantity of motion, and thus the names by which it is known, bear witness to its practical origin, such as "mechanical power", "work", "duty", "labouring force", etc.
To them, also, practical science is indebted for a clearer idea of this aspect of power, by their having excluded from its definition and measure, the idea of velocity, or the element of time.

Now the products of force by time, and of force by space, although taken in reference to the same physical action, yield different conclusions, as to the relation between power and its effects ; the difference being in the ratio of the simple velocity, to the square of the velocity, according as momentum, or mechanical action be contemplated as the effect. And so there will appear to be a discrepancy, as in the case of caloric, in regard to the law of action and reaction ; there will appear to be an equality, a deficiency, or an access, according as one, or the other formula is applied, and according to the mode in which it is applied to the admeasurement of causes and effects.

But the third law of motion admits no exception, if adequate reaction cannot be discovered by one rule, it may be by the other, which will thus be proved to be the true measure, for that particular aspect of the case, to be the one appropriate to the nature of the change under review. The same law applies to caloric and its transformation, in the same manner as it does to motion and its transmission ; there can be no gain without a loss, either in kind, in degree, or in something equivalent in the way of conversion.

In short, heat, as indicated by its station on the scale of temperature, is as different physically, from heat measured by the number of its degrees, as momentum and working force are mechanically dissimilar; and as the former can be transformed into the latter, so by a greater transformation the molecular activity of caloric can be converted into mechanical power; but in no case can there be a development, or acquisition of any kind, without a corresponding loss ; and yet as in the one case, so in the other, if the measure is not correspondent with the things measured, the loss may not appear commensurate with the gain, nay, it may appear, that no loss at all has been sustained, or a total loss without any gain.

Theoretical explanation

These views admit of an easy illustration, by considering what takes place in the collision of two suspended balls, one of which is hard and the other inelastic, as of clay, for instance. Let the hard ball strike the other with a given velocity ; then by the rule which measures the momentum of bodies, namely, by the product of the mass, or force by the simple velocity, it will impart to the clay ball, precisely that quantity of motion which itself loses in the impact.

Thus action and reaction are equal and opposite, and limited to this particular view of the case, the cause is seen to be equal, but not more than adequate to the effect ; yet it is undeniable, that as thus estimated, the whole of the action is not accounted for. The quantity of motion in both balls, is the same as existed in the acting one ; although it is changed from a smaller mass with a greater velocity, to a larger mass with a less velocity ; just as in the case of steam, when after being employed in the production of motive power, the quantity of caloric, as estimated jointly by temperature and the mass of water, continues the same, although it is changed from a higher to a lower degree of the one, hut from a less to a greater amount of the other.

And yet, as in the case of steam, so in the collision of the balls, a certain amount of work has been done, although this mode of viewing and measuring the action does not in either instance ascertain it. In the latter case the work consists in the indentation made in the clay, or to put it in a more measurable form, in the driving in of a peg. Here, then, in the transmission of motion from one body to another, arises a surplus fact, an extra result ; and as much like an absolute gain, as the analogous mechanical action of the caloric engine is assumed to be, during the transmission of heat from one body to another, and apparently as equally destitute of any special cause, in which a corresponding loss can be traced.
The truth is, the supposed gratuitous acquisition belongs to another class of effects, different in kind, and although ignored because it cannot be measured as momentum, is equally entitled to be considered a part of the action, which bodies exert on each other in collision.

It is that part with which practical men are conversant, consisting of "work," and into which, generally, it is their object to transform all species of force ; it has a measure of its own, in which time is excluded and space alone is considered. Now measured by this rule, causes and effects will be found to be mutually equivalents, as well under this aspect of causation as under the other ; for the work done on the peg, in overcoming resistance through a certain space, will be equal to the product of the force and space in the raising, or falling of the ball. So also, in any variation of the experiment, the spaces will vary in like simple proportions ; and in other cases, in which time must needs be introduced, in order to form an equivalent expression for the measure, the effect will vary as the squares of the velocities.

Thus the law of action and reaction can in all cases be satisfied, provided a due discrimination is exercised, in regard to the character of the phenomenon, both in the cause and effect, and that the measure adapted to each kind, or class of motion, is appropriately, and not promiscuously, employed for each.

In some cases, even three classes of motion may be conceived simultaneously to exist, in the same action ; thus the falling ball may impart momentum to the other, drive in a peg, and shatter the end of it ; for the last effect, however, it may be difficult to find a common and appropriate measure.

In short the most erroneous assumptions will not fail to be entertained, leading, as in the case of the caloric engine, to the idea of an effect without a cause, if the value of the entire action of a cause be estimated by only a portion of it ; especially as in so doing, the measure employed must of a necessity be of a kind, appropriate only to the part recognised.

It is scarcely a less error, if indeed it be not substantially the same, although it is one into which mathematicians of the last century fell, to take cognizance of only one class of effects, and insist on its measure, as being the only true and appropriate one.

In opposition to all reasoning on the subject, an appeal in defence of the caloric engine may be made to its performances, and especially to the experiment which has been much insisted on, of the continued working of the engine, for some time after the fire has been withdrawn. Now on the alleged principle of its construction, it may fairly be argued, that it ought to perform a greater feat than this.

If it be assumed, that the work to be done, be such as to afford, whatever the velocity, a constant resistance ; then the friction and the radiation of heat being also constant quantities, the effect of the slightest excess of heat, beyond that lost by radiation, ought to be a progressive accumulation of force, until the engine knocked itself to pieces, by the rapidity of its movements. Indeed, a governor to such an engine, if the assumed principle were correct, should rather regulate its motion, by bringing into play an increasing resistance, than by the usual method of diminishing the power.

Any force, extraneously imparted to the engine, the caloric being assumed to operate over and over again, would necessarily maintain the velocity unimpaired ; whilst a slight addition of heat, would constitute an accelerating power, urging it on to its destruction. Still the doing of work by the engine, after the withdrawal of the fire, in a case where there is no large storage of power, as in the boiler of a steam engine, is a some what paradoxical fact and requires explanation.

To utilize, to the greatest extent, a motive force generated by heat, the body should be brought down to the lowest temperature at command, through its own expansive action ; for it is only in the reduction of temperature that force is elicited ; so that all sensible caloric, remaining in the body, higher than this point, involves a loss of power. In the issue of steam from a non expansive high-pressure steam engine, both heat and elastic force escape to a considerable amount unemployed, and power is of course wasted.

The true role of a regenerator

Now the caloric engine is analogous to a non expansive high-pressure steam engine, and consequently would be an exceedingly wasteful machine, if it were not furnished with some appliance, to recover either the heat, or the force of the escaping air. But these two factors, the heat and the force, do not imply a double loss, they being in truth, as before explained, convertible quantities ; for if the body were allowed to expand, sensible heat would be absorbed and utilized, and conversely, if the heat were otherwise absorbed and utilized, it would be an equivalent for the expansive force of the escaping air.

This, then, is the office of the "regenerator," for expansion is not a practical expedient in this engine, because, among other reasons, of the low tension of the motive force. The "regenerator" is not what its name imports, nor is it exclusively a condenser, but it recovers unappropriated force, by absorbing unutilized caloric. It is this recovered sensible heat, which otherwise would have been wholly wasted, that is made to operate, not over again, but through another opportunity afforded it, in conjunction with fresh supplies of caloric, to generate force.

The great efficiency of this office of the "regenerator", is due to the process being conducted per gradum, instead of per saltum as in ordinary condensation ; by which means, much of the sensible heat is recovered at a higher temperature, than could be otherwise effected ; a construction, for which Captain Ericsson is indebted, both for principle and practical means, to the Messrs. Stirling.

Now because of the difference in latent heat, and the very high temperature of the caloric engine, the sensible heat of the escaping air, bears a much larger proportion to the efficient, or force generating caloric, than in the case of steam.

Hence the loss of power, by the waste of the sensible heat, would be enormous ; and therefore the recovery of it by means of the "regenerator" constitutes a considerable power, relatively to that of the engine, and is sufficient, aided by the inertia of the parts, to keep it in work with a decreasing speed, corresponding to a decreasing temperature, for a considerable time, even after the fire is withdrawn ; especially as the "regenerator" more effectually answers its purpose, under these circumstances, than in the ordinary working of the engine, on account of the greater exhaustion of its innate force, in the decreasing temperature of the air.
Thus this paradox receives an easy solution, without resorting to the questionable hypothesis of a regeneration of force.

That Ericsson's engine may be an efficient one is not disputed, but its merits must rest on common ground with those of the steam engine. The great question is, whether an economy of fuel can be effected, and this is not an improbable claim.

Some thirty years since when engaged on a project of this kind, the Author calculated, that an air-engine would be more efficient with a given quantity of caloric than a steam engine, in the proportion of 1.24 to 1.0 ; but doubtless a calculation founded purely on theoretical data, would give in this, and in all cases of gases and vapours, the ratio of equality ; for every investigation leads to the conclusion, that the effect of caloric, is independent at least of the chemical, if not also of the physical constitution of bodies.

Economy of fuel or economy of caloric

But economy of fuel is a different question from the economy of caloric ; it is altogether a practical matter, and can only bo determined by experiment; for this, and indeed most other points of practice, are too intractable to come within the grasp of the most powerful calculus.

The economy of fuel, as a distinct subject from that of caloric already in possession, has scarcely met with the attention it deserves, except in Cornwall, and there only in regard to one particular view of it, the management of the furnace. It was observed, during the experiments of Mr. Perkins on high pressure steam, that whilst he was intent on economising caloric, by carrying the pressure to an extraordinary degree, he allowed the upper part of his chimney to become red hot.

But without entering on the subject of the construction and management of furnaces, there is a theoretical point connected with it, which deserves attention, as being relevant to the question under discussion.

Let the possibility be admitted for a moment, of the whole of the caloric developed by combustion in the furnace, being absorbed by the water in the boiler ; still it will follow, from what has been already stated, as to mechanical power resulting, solely, from a difference in the intensity of caloric, that a large amount of fuel would be wasted ; for between the temperature of the furnace and that of the water, even in Mr. Perkins' "generators", there is a great interval, within the range of which, no means are taken to elicit power.

By going higher up towards the fountain of power, it may not be impracticable to appropriate it between variations of temperature, where, for want of a proper motive agent, it is now lost, simply because it is neglected.

Air, a better candidate than steam

The experiments of Mr. Perkins were therefore made in the right direction, although unwittingly, for he had another object in view. But it is to be greatly doubted, whether water is so constituted as to render it a suitable body to receive very high degrees of temperature, with the requisite facility.

Considerations, not now to be entered on, connected with the state of repulsion that is then manifested ; the comparative immobility of water under great pressure, as interposing an obstacle to the rapid communication of heat ; the many important points of a practical kind, involved in the action of steam, under very high pressure, all seem to disqualify water for being a motive agent, at a higher temperature than is usually adopted. But the use of air, in a highly-heated state, is not encompassed with these difficulties, although it may have others peculiar to itself.

The experiments both of Captain Ericsson and of the Messrs. Stirling testify, that it can be conveniently heated up to more than double the temperature of steam ; and in this there is not of course involved any dangerous pressure, which may indeed be just what the operator chooses to make it, or may find easy to manage.

The arrangements for the production of the hot-air blasts at the iron works, prove also, that heat at a very high temperature, probably approaching 1000°, can be communicated to air with all necessary rapidity ; but to make it available, in this state, for the development of power, would be a very difficult practical problem.

If these considerations be based on sound premises, and if it shall hereafter be found, that a saving of fuel does result from the employment of hot air as a motive power, such saving must be principally attributed to the passing of the air through a doubly greater range of temperature, than in the case of steam, during which, at every moment of gradation, intensity of caloric changes into force.

On the other hand, the immense surfaces which are, in practice, exposed to the radiation of heat, by the cylinders being so very large, in proportion to the power of the engine, must entail a great loss of heat ; so that after all, the final result must be left to be determined by experiment, and if the saving of fuel be not found very decidedly in favour of heated air, steam power will continue to be preferred, on account of the superior compactness of the engine.