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April 10, 2026
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"Matthias Beckh analyzes these hyperbolic lattice towers... [and] demonstrates how... Shukhov was already parameterizing his structures as part of the design... Modern methods... provide... Beckh with the tools to place Shukhov's achievements in a historical context and validate their considerable contribution to the history of . He also...demonstrate[s] their relevance to modern structures. ...Beckh was part of the first research project into Shukhov's structures ...The research project ...included in-depth studies of building history ...and detailed investigations into the way the structures were built. Later investigations were intended to provide ...knowledge about the load assumptions... also... relevant to modern structures."
"Until now, the form and geometry of the hyperbolic lattice structures have only been investigated to a limited extent."
"Shukhov is credited with the construction of some 200 towers using this method ..."
"Abu-Sitta and Davenport... investigated the effects of dynamic earthquake loading. ...[I]nduced dynamic stresses were related to equivalent membrane stresses from static loads, resulting in... a simplified earthquake analysis procedure."
"This is an interesting paradox: you get the best local buckling resistance because the beams are straight and the best overall buckling resistance because the surface is double curved."
"We leave it to the political arithmetician to compute how much money will be saved to a country, by its spending two thirds less of fuel; how much labor saved in cutting and carriage of it; how much more land may be cleared by cultivation; how great the profit by the additional quantity of work done, in those trades particularly that do not exercise the body so much, but that the workfolks are obliged to run frequently to the fire to warm themselves; and to physicians to say, how much healthier thick-built towns and cities will be, now half suffocated with sulphury smoke, when so much less of that smoke shall be made, and the air breathed by the inhabitants be consequently so much purer."
"It is to be observed, that the entering air will not be warm at first lighting the fire, but heats gradually as the fire increases."
"[T]he builder of chimneys has been left to grope his way in the dark without assistant; and in almost every instance his attempts to improve upon the practice of his predecessors, have been unsuccessful; so that the inhabitants of these countries, with justice, complain that the inconveniencies felt in new houses from this cause, usually are more than sufficient to counterbalance all the elegancies that modern refinement has introduced into the dwellings..."
"[T]he flame and smoke will ascend and strike the top... which will thereby receive a considerable heat. The smoke, finding no passage upwards, turns over the top of the air-box, and descends between it and the back plate to the holes in the bottom plate, heating, as it passes, both plates of the air-box, and the said back plate; the front plate, bottom and side plates are also all heated at the same time. The smoke proceeds in the passage that leads it under and behind the false back, and so rises into the chimney."
"5. The German stove is like a box, one side wanting. It is composed of five iron plates, screwed together, and fixed so as that you may put the fuel into it from another room, or from the outside of the house. It is a kind of oven reversed, its mouth being without, and body within, the room that is to be warmed by it. This invention certainly warms a room very speedily and thoroughly with little fuel; no quantity of cold air comes in at any crevice, because there is no discharge of air which it might supply, there being no passage into the stove from the room. ...Its inconveniences are, that people have not even so much sight or use of the fire as in the Holland stoves, and are, moreover, obliged to breathe the same unchanged air continually, mixed with the breath and perspiration from one another's bodies, which is very disagreeable to those who have not been accustomed to it."
"The air of the room, warmed behind the back plate, and by the sides, front, and top plates, becoming specifically lighter than the other air in the room, is obliged to rise; but the closure over the fire place hindering it from going up the chimney, it is forced out into the room, rises by the mantel-piece to the ceiling, and spreads all over the top of the room, whence being crowded down gradually by the stream of newly-warmed air that follows and rises above it, the whole room becomes in a short time equally warmed."
"[T]he causes which produce smoke in rooms... may be all reduced to one of the three following general classes: 1. A faulty construction of the tube, vent, or chimney itself; 2. To some fault in the other parts of the building, and a wrong position of the chimney with respect to these; or, 3. To an improper situation of the house with respect to external objects."
"1. The first of these methods has generally the conveniency of two warm seats, one in each corner; but they are sometimes too hot to abide in, and, at other times, incommoded with the smoke; there is likewise good room for the cook to move, to hang on pots, &c. Their inconveniences are, that they almost always smoke, if the door be not left open; that they require a large funnel, and a large funnel carries off a great quantity of air, which occasions what is called a strong draft to the chimney, without which strong draft the smoke would come out of some part or other of so large an opening, so that the door can seldom be shut; and the cold air so nips the backs and heels of those that sit before the fire, that they have no comfort till either screens or settles are provided (at a considerable expense) to keep it off, which both cumber the room, and darken the fire-side. A moderate quantity of wood on the fire, in so large a hearth, seems but little; and, in so strong and cold a draft, warms but little; so that people are continually laying on more. In short, it is next to impossible to warm a room with such a fire place; and I suppose our ancestors never thought of warming rooms to sit in; all they purposed was, to have a place to make a fire in, by which they might warm themselves when cold."
"[M]any of the diseases proceeding from colds, as fevers, pleurisies, &c., fatal to very great numbers of people, may be ascribed to strong-drawing chimneys, whereby, in severe weather, a man is scorched before, while he is froze behind."
"3. Fire sends out its rays of heat, as well as rays of light, equally every way; but the greatest sensible heat is over the fire, where there is, besides the rays of heat shot upwards, a continual rising stream of hot air, heated by the rays shot round on every side."
"2. Heat may be separated from the smoke as well as from the light, by means of a plate of iron, which will suffer heat to pass through it without the others."
"[C]onsider the fire-places heretofore in use, viz. 1. The large open fire-places used in the days of our fathers, and still generally in the country, and in kitchens. 2. The newer-fashioned fire-places, with low breasts and narrow hearths. 3. Fire-places with hollow backs, hearths and jambs of iron, (described by M. Gauger, in his tract entitled La Méchanique de Feu,) for warming the air as it comes into the room. 4. The Holland stoves, with iron doors opening into the room. 5. The German stoves, which have no opening in the room where they are used, but the fire is put in from some other room, or from without. 6. Iron pots, with open charcoal fires, placed in the middle of a room."
"2. Most of these old-fashioned chimneys in towns and cities have been, of late years, reduced to the second sort mentioned, by building jambs within them, narrowing the hearth, and making a low arch or breast. It is strange, methinks, that though chimneys have been so long in use, their construction should be so little understood till lately, that no workman pretended to make one which should always carry off all smoke, but a chimney-cloth was looked upon as essential to a chimney. This improvement, however, by small openings and low breasts, has been made in our days; and success in the first experiments has brought it into general use in cities, so that almost all new chimneys are now made of that sort, and much fewer bricks will make a stack of chimneys now than formerly. An improvement so lately made may give us room to believe, that still farther improvements may be found to remedy the inconveniences yet remaining. For these new chimneys, though they keep rooms generally free from smoke, and, the opening being contracted, will allow the [house] door to be shut, yet, the funnel still requiring a considerable quantity of air, it rushes in at every crevice so strongly, as to make a continual whistling or howling; and it is very uncomfortable, as well as dangerous, to sit against any such crevice. Many colds are caught from this cause only, it being safer to sit in the open street; for then the pores do all close together, and the air does not strike so sharply against any particular part of the body."
"3. To remedy this, the Sieur Gauger gives, in his book, entitled La Méchanique de Feu, published in 1709, seven different constructions of the third sort of chimneys mentioned above, in which there are hollow cavities made by iron plates in the back, jambs, and hearths, through which plates the heat passing warms the air in those cavities, which is continually coming into the room fresh and warm. The invention was very ingenious, and had many conveniences; the room was warmed in all parts, by the air flowing into it through the heated cavities; cold air was prevented rushing through the crevices, the funnel being sufficiently supplied by those cavities; much less fuel would serve, &c. But the first expense, which was very great, the intricacy of the design, and the difficulty of the execution, especially in old chimneys, discouraged the propagation of the invention; so that there are, I suppose, very few such chimneys now in use. The upright heat, too, was almost all lost in these, as in the common chimneys."
"4. The Holland iron stove, which has a flue proceeding from the top, and a small iron door opening into the room, comes next to be considered. Its conveniences are, that it makes a room all over warm; for, the chimney being wholly closed except the flue of the stove, very little air is required to supply that, and therefore not much rushes in at crevices, or at the door when it is opened. Little fuel serves, the heat being almost all saved; for it rays out almost equally from the four sides, the bottom, and the top, into the room , and presently warms the air around it, which, being rarefied, rises to the ceiling, and its place is supplied by the lower air of the room, which flows gradually towards the stove, and is there warmed, and rises in its turn, so that there is a continual circulation till all the air in the room is warmed. The air, too, is gradually changed, by the stove-door's being in the room, through which part of it is continually passing, and that makes these stoves wholesomer, or at least pleasanter than the German stoves... But... There is no sight of the fire... When the room is warm, people, not seeing the fire, are apt to forget supplying it with fuel... The change of air is not carried on quite quick enough; so that, if any smoke or ill smell happens in the room, it is a long time before it is discharged. For these reasons the Holland stove has not obtained much among the English (who love the sight of the fire) unless in some workshops..."
"6. Charcoal fires in pots are used chiefly in the shops of handicraftsmen. They warm a room (that is kept close, and has no chimney to carry off the warmed air,) very speedily and uniformly; but, there being no draft to change the air, the sulphurous fumes from the coals (be they ever so well kindled before they are brought in, there will be some,) mix with it, render it disagreeable, hurtful to some constitutions, and some times, when the door is long kept shut, produce fatal consequences."
"To avoid the several inconveniences, and at the same time retain all the advantages of other fire-places, was contrived the PENNSYLVANIAN FIRE-PLACE, now to be described."
"At the same time, the air, warmed under the bottom plate and in the air-box, rises and comes out of the holes in the side plates, very swiftly, if the door of the room be shut, and joins its current with the stream before mentioned, rising from the side, back, and top plates."
"The air that enters the room through the air-box is fresh, though warm; and, computing the swiftness of its motion with the areas of the holes, it is found that near ten barrels of fresh air are hourly introduced by the air-box; and by this means the air in the room is continually changed, and kept at the same time sweet and warm."
"Its advantages above the common fire-places are, 1. That your whole room is equally warmed, so that people need not crowd so close round the fire, but may sit near the window, and have the benefit of the light for reading, writing, needlework, &c. They may sit with comfort in any part of the room... 2. If you sit near the fire, you have not that cold draft of uncomfortable air nipping your back and heels, as when before common fires, by which many catch cold, being scorched before, and... froze behind. 3. If you sit against a crevice, there is not that sharp draft of cold air playing on you, as in rooms where there are fires in the common way; by which many catch cold, whence proceed coughs, catarrhs, tooth-aches, fevers, pleurisies, and many other diseases. 4. In case of sickness, they make most excellent nursing-rooms; as they constantly supply a sufficiency of fresh air, so warmed at the same time as to be no way inconvenient or dangerous. A small one does well in a chamber; and, the chimneys being fitted for it, it may be removed from one room to another, as occasion requires, and fixed in half an hour. The equal temper, too, and warmth of the air of the room, is thought to be particularly advantageous in some distempers... 5. In common chimneys, the strongest heat from the fire, which is upwards, goes directly up the chimney, and is lost; and there is such a strong draft into the chimney, that not only the upright heat, but also the back, sides, and downward heats are carried up the chimney by that draft of air; and the warmth given before the fire, by the rays that strike out towards the room, is continually driven back, crowded into the chimney, and carried up by the same draft of air. But here the upright heat strikes and heats the top plate, which warms the air above it, and that comes into the room. The heat likewise, which the fire communicates to the sides, back, bottom, and air-box, is all brought into the room; for you will find a constant current of warm air coming out of the chimney corner into the room. Hold a candle just under the mantel-piece, or breast of your chimney, and you will see the flame bent outwards; by laying a piece of smoking paper on the hearth, on either side, you may see how the current of air moves, and where it tends, for it will turn and carry the smoke with it. 6. Thus, as very little of the heat is lost, when this fire-place is used, much less wood will serve you, which is a considerable advantage where wood is dear. 7. When you burn candles near this fire-place, you will find that the flame burns quite upright, and does not blare and run the tallow down, by drawing towards the chimney, as against common fires. 8. This fire-place cures most smoky chimneys, and thereby preserves both the eyes and furniture. 9. It prevents the fouling of chimneys; much of the lint and dust that contributes to foul a chimney being, by the low arch, obliged to pass through the flame, where it is consumed. Then, less wood being burnt, there is less smoke made. Again, the shutter, or trap-bellows, soon blowing the wood into a flame, the same wood does not yield so much smoke as if burnt in a common chimney; for, as soon as flame begins, smoke in proportion ceases. 10. And, if a chimney should be foul, it is much less likely to take fire. If it should take fire, it is easily stifled and extinguished. 11. A fire may be very speedily made in this fire-place by the help of the shutter, or trap-bellows... 12. A fire may be soon extinguished by closing it with the shutter before, and turning the register behind, which will stifle it, and the brands will remain ready to rekindle. 13. The room being once warm, the warmth may be retained in it all night. 14. And lastly, the fire is so secured at night, that not one spark can fly out into the room to do damage."
"With all these conveniences, you do not lose the pleasing sight nor use of the fire, as in the Dutch stoves, but may boil the tea-kettle, warm the flat irons, heat heaters, keep warm a dish of victuals by setting it on the top, &c."
"In the mean time, very little is done by these chimneys towards warming the room; for the air round the fire-place, which is warmed by the direct rays from the fire, does not continue in the room, but is continually crowded and gathered into the chimney by the current of cold air coming behind it, and so is presently carried off."
"[I]n any chimney, the air over the fire is rarefied by the heat, becomes lighter, and therefore immediately rises in the funnel, and goes out; the other air in the room (flowing towards the chimney) supplies its place, is rarefied in its turn, and rises likewise; the place of the air thus carried out of the room, is supplied by fresh air coming in through doors and windows, or, if they be shut, through every crevice with violence, as may be seen by holding a candle to a key-hole."
"2. Air rarefied and distended by heat is specifically lighter than it was before, and will rise in other air of greater density. As wood, oil, or any other matter specifically lighter than water, if placed at the bottom of a vessel of water will rise till it comes to the top; so rarefied air will rise in common air, till it either comes to air of equal weight, or is by cold reduced to its former density."
"If the room be so tight as that all the crevices together will not supply so much air as is continually carried off, then, in a little time, the current up the funnel must flag, and the smoke, being no longer driven up, must come into the room."
"[A]ny new proposal for saving the wood, and for lessening the charge and augmenting the benefit of fire, by some particular method of making and managing it, may at least be thought worth consideration."
"In an edition of the author's writings on electrical and philosophical subjects, published in London in the year 1769, the following note is appended to this tract. "Soon after the foregoing piece was published, some persons in England, in imitation of Mr. Franklin's invention, made what they call Pennsylvanian Fire-places, with improvements; the principal of which pretended improvements is, a contraction of the passages in the air-box, originally designed for admitting a quantity of fresh air, and warming it as it entered the room. The contracting [of] these passages gains indeed more room for the grate, but in a great measure defeats their intention. For, if the passages in the air-box do not greatly exceed in dimensions the amount of all the crevices by which cold air can enter the room, they will not considerably prevent, as they were intended, the entry of cold air through the crevices.""
"1. Air is rarefied by heat, and condensed by cold, that is, the same quantity of air takes up more space when warm than when cold. This may be shown... Take any clear glass bottle (a stript of the straw is best), place it before the fire, and, as the air within is warmed and rarefied, part of it will be driven out of the bottle; turn it up, place its mouth in a vessel of water, and remove it from the fire; then, as the air within cools and contracts, you will see the water rise in the neck of the bottle, supplying the place of just so much air as was driven out. Hold a large hot coal near the side of the bottle, and, as the air within feels the heat, it will again distend and force out the water. Or, fill a bladder not quite full of air, tie the neck tight, and lay it before a fire as near as may be without scorching the bladder; as the air within heats, you will perceive it to swell and fill the bladder, till it becomes tight, as if full blown; remove it to a cool place, and you will see it fall gradually, till it becomes as lank as at first."
"1. Fire... throws out light, heat, and smoke (or fume.) The [first] two... move in right lines, and with great swiftness; the latter is but just separated from the fuel, and then moves only as it is carried by the stream of rarefied air; and without a continual accession and recession of air, to carry off the smoky fumes, they would remain crowded about the fire, and stifle it."
"In both these sorts of fire-places, the greatest part of the heat from the fire is lost; for, as fire naturally darts heat every way, the back, the two jambs, and the hearth drink up almost all that is given them, very little being reflected from bodies so dark, porous, and unpolished; and the upright heat, which is by far the greatest, flies directly up the chimney. Thus five sixths at least of the heat (and consequently of the fuel) is wasted, and contributes nothing towards warming the room."
"The earth is every where surrounded with a great body of air, that is called the atmosphere. This air is a thin elastic fluid, possessing some qualities peculiar to itself, but subjected in general to the same physical laws with other fluids; and of consequence it hath a constant tendency to preserve an exact equilibrium in all its parts; so that if at any time the weight of it at one place is diminished, the heavier air rushes from all sides towards that point, till the equilibrium be again restored."
"This difficulty may be in part removed, by supposing... that the heated metal sends off in rays... even when it is not heated red hot; but still, as it never can be admitted that the heat, absorbed by the metal and afterwards thrown off by it in rays, is increased by this operation, nothing can be gained by it; and as much must necessarily be lost... to the air in contact with it, which... always makes its way up the Chimney, and flies off into the atmosphere, the loss of heat attending the use of it is too evident..."
"[T]he quantity of radiant heat thrown into the room is diminished;—and it is easy to show that almost the whole of that absorbed by the metal is ultimately carried up the Chimney by the air, which, coming into contact with this hot metal, is heated and rarefied by it, and... goes off with the smoke; and as no current of air ever sets from any part of the opening of a Fire-place into the room, it is impossible to conceive how the heat existing in the metal composing any part of the apparatus of the Fire-place, and situated within its cavity, can come, or be brought into the room."
"There is, however, in Chimney Fire-places... one essential part, the grate, which cannot well be made of any thing else but iron..."
"The best materials... are fire-stone, and common bricks and mortar. Both... are, fortunately, very cheap..."
"As the object... is to bring radiant heat into the room... that material is best for the construction of a Fire-place which reflects the most, or which absorbs the least of it; for that heat which is absorbed cannot be reflected. ...[W]e have only to find out ...what bodies acquire least heat when exposed to the direct rays of a clear fire ...And hence it appears that iron, and ...metals off all kinds, which ...grow very hot when exposed to the rays ...are to be reckoned among the very worst materials ...to employ in the construction of Fire-places."
"When bricks are used they should be covered with a thin coating of plaster, which, when it is become perfectly dry, should be white-washed. The fire-stone should likewise be white-washed... and every part of the fire-place, which is not exposed to being foiled and made black by the smoke, should be kept as white and clean as possible. As white reflects more heat, as well as more light than any other colour, it ought always to be preferred for the inside of a Chimney Fire-place; and black, which reflects neither light nor heat, should be most avoided."
"If it should be necessary to diminish the opening of a large Chimney in order to prevent its smoking, it is much more simple, œconomical, and better in all respects, to do this with marble, fire-stone, or even with bricks and mortar, than to make use of iron, which... is the very worst material... for that purpose; and as to registers, they not only are... unnecessary, where the throat of a Chimney is properly constructed, and of proper dimensions, but in that case would do mach harm. If they act It all, it must be by opposing their flat surfaces to the current of rising smoke in a manner which cannot fail to embarrass and impede its motion. But... the passage of the smoke through the throat of a Chimney ought to be facilitated as much as possible in order that it may be enabled to pass by a small aperture."
"Chimnies so often smoke when too large a quantity of fresh coals is put upon the fire. So many coals should never be put on the fire at once as to prevent the free passage of the flame between them. In short, a fire should never be smothered; and when proper attention is paid to the quantity of coals put on, there will be very little use for the poker; and this circumstance will contribute very much to cleanliness, and to the preservation of furniture."
"When the fire burns bright, much radiant heat will be sent off from it; but when it is smothered up, very little will be generated... and the combustion being very incomplete, a great part of the inflammable matter of the fuel being merely rarefied and driven up the Chimney without being inflamed, the fuel will be wasted... And hence it appears of how much importance it is, whether.. with a view to economy... cleanliness, comfort, and elegance, to pay due attention to the management of a Chimney Fire."
"Now as the rays which are thrown off from burning fuel have this property in common with light, that they generate heat only when and where they are stopped or absorbed, and also in being capable of being reflected without generating heat at the surfaces of various bodies, the knowledge of these properties will enable us to take measures, with the utmost certainty, for producing the effect required... bringing as much radiant heat as possible into the room. This must be done, first, by causing as many as possible of the rays, as they are sent off from the fire in straight lines, to come directly into the room; which can only be effected by bringing the fire as far forward as possible, and leaving the opening of the Fire-place as wide and as high as can be done without inconvenience; and secondly, by making the sides and back of the fire-place of such form, and constructing them of such materials, as to cause the direct rays from the fire, which strike against them, to be sent into the room by reflection in the greatest abundance."
"There is, however, one method by which combined heat... may be made to assist in warming a room... by making it pass through something analogous to a German stove, placed in the Chimney above the fire."
"What proportion does the radiant heat bear to the combined heat? ...[T]he quantity of heat which goes off combined with the smoke, vapour, and heated air is much more considerable, perhaps three or four times greater... And yet, small as the quantity is of... radiant heat, it is the only part... ever employed... in heating a room. The whole of the combined heat escapes by the Chimney, and is totally lost; and... no part of it could ever be brought into a room from an open Fire-place, without bringing along... the smoke..."
"[A]s it is the radiant heat alone which can be employed in heating a room, it becomes an object of much importance to determine how the greatest quantity of it may be generated... and how the greatest proportion possible of that generated may be brought into the room."
"[T]he best form for the vertical sides of a Fire-place, or the covings... is that of an upright plane, making an angle with the plane of the back of the Fire-place, of about 135 degrees.—According to the present construction of Chimnies this angle is 90 degrees... a right angle; but as... the two sides or covings of the Fire-place are parallel to each other, it is evident that they are very ill contrived for throwing into the room by reflection the rays..."