The physics of organ blowing
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  The physics of organ blowing  

 

Colin Pykett

 

"To most human beings, wind is an irritation" 

Mokokoma Mokhonoana

 

Posted: 7 September 2020

Revised: 18 September 2020

Copyright © C E Pykett

 

Abstract. Raising the wind in pipe organs by human muscle power was universal until the industrial revolution got underway, though the subject has not been extensively studied. Yet by the mid-nineteenth century, at least two millennia of development had resulted in highly evolved bellows systems which were capable of providing stable and copious wind to the largest instruments such as Schulze's monumental organ at Doncaster. However there remains a problem today in that the physics of organ blowing is not apparently tackled anywhere in the public domain literature. Consequently one struggles to find answers to quite basic questions such as the wind pressures and volumetric air flow rates which human blowers could achieve, and the time for which they could maintain the effort. The upshot is that it is easy to overlook useful information which some of the most apparently bizarre and fanciful images of organ blowers at work can reveal until we have looked at the physics of the humble bellows. Similarly, the physics can enable some of the ancient texts relating to organs to be interpreted more intelligently. Another example relates to claims that some instruments built in the nineteenth century used wind pressures exceeding 20 inches (508 mm) of water raised by manpower alone, which might seem extraordinary given that most church organs made do with about 3 inches. Yet without understanding the physics of bellows it is impossible to verify such assertions. These and similar uncertainties obviously assume importance in the context of organ historiography, which looks at codified history to judge whether it is sensible, but resolving them is not an entirely trivial undertaking. Therefore this article attempts to augment the story of organ blowing by outlining the physics which governs how bellows and their blowers were perforce constrained to operate in times past.

 

Contents

(click on the headings below to access the desired section)

 

Introduction

 

The value of the iconography

 

Calculation of wind pressures

Horizontal bellows

 

Hinged bellows with rectangular top board

 

Hinged bellows with triangular top board

Blowing power considerations

 

Volumetric air flow rates

 

Levers

 

Concluding remarks

 

Notes and references

 


Introduction

 

By the latter half of the nineteenth century the industrial revolution was changing the way organs were made, and a major feature concerned how the wind was raised. Until then human organ blowers had been as universal as the organists themselves, and it was not until high pressure water mains became available (the pressure being raised by steam engines often housed in epic Victorian pumping stations not unlike mini-cathedrals) that people could be replaced with novel hydraulic motors. Steam power was also sometimes used to blow organs directly. Town gas and oil blowing engines also appeared around the same time, and subsequently mains electricity was harnessed to do the job. Even so, these new sources of power were at first uncommon outside cities and sizeable towns, thus many organs still required muscle power until well into the twentieth century. This was not confined to small instruments in country churches; even the large organ at Notre Dame in Paris was not converted to electric blowing until the 1920s, prior to which it had relied on a motley collection of humankind of both genders for its wind. 

 

Thus organ blowing has a history as long as that of the instrument itself, and it would be wrong to assume that winding systems relying on manpower were necessarily crude and unrefined. On the contrary, centuries of development had resulted in experienced blowers working highly evolved bellows systems which were capable of providing stable wind to the pipes for as long as they could sustain the effort. Organ blowing has nevertheless attracted less attention from historians than other aspects of the craft. Elvin's book [1] is an exception and therefore essential reading, but although of riveting interest it is little more than a qualitative description of the scene. Moreover the majority of it deals with mechanically powered blowing rather than manual methods. Hopkins and Rimbault [2] dug deeper by focusing on the practical design details of manual blowing systems up to about 1850 which could produce copious and stable wind supplies to the largest organs such as Schulze's monumental instrument at Doncaster.  However Hopkins's closest encounter with physics led him to quote a vital number, the reservoir mass loading per square foot required to produce a pressure of an inch of water, which was wrong.  The correct value and the means of deriving it are given later.  More recently the Doncaster organ has also been studied by Mander [3]. Although many other authors have also addressed the subject, if only in passing, they mostly rely on a few sources such as these. Hence there remains a problem in that the basic physics of organ blowing is not apparently tackled anywhere in the public domain literature. Consequently one struggles to find answers to questions such as the maximum wind pressure and volume flow rate which a human blower can achieve, and the time for which they can be maintained. 

As a result one searches largely in vain for reliable numbers to put into discussions about organ blowing. But why should this matter, particularly insofar as it affects the history of the subject? One answer concerns the iconography which has come down to us. It might evoke surprise that even the most apparently bizarre and fanciful images of organ blowers at work can sometimes reveal useful information once we have looked at the physics of the humble bellows. Another answer is that the physics might enable us to better interpret ancient texts such as that relating to the tenth-century organ at Winchester by questioning whether any conceivable instrument would really have required 70 perspiring men to blow only 400 pipes. Then there are the statements which have worked their way into organ folklore such as those relating to Hill's high pressure Tuba stop at Birmingham Town Hall, said to have worked on 15 inches of water in 1840 [4]. Or the reeds on 22 inch pressure in Willis's organ at St George's Hall Liverpool having to be blown by hand in 1867 while the rest of the instrument apparently relied on steam [1]. Could pressures as high as these have been raised by manpower alone, bearing in mind that a contemporary church organ would typically have made do with 3 inches? In fact, what is the maximum wind pressure that can be raised by muscle power? Or is this apparently simple question meaningless in that there might not be a limit at all, within reason? These and similar uncertainties obviously assume importance in the context of organ historiography, which looks at codified history to judge whether it is sensible, but answering them is not an entirely trivial undertaking. Therefore this article attempts to augment the story of organ blowing by outlining the physics which governs how the bellows and their blowers were perforce constrained to operate in times past.

 

 

The value of the iconography

 

Although the ancient iconography relating to organ blowing is often scorned, sometimes even by scholars who apparently just want to raise a titter, it is worth examining carefully before dismissing it as entirely fanciful. Anyone who sat down and carved, sculpted or drew pictures of organs in past centuries presumably had sober reasons for doing it rather than just idling away their time. It is also probably reasonable to assume that they would most likely have reflected in their art some idea of the main features of what they saw, regardless of how much they knew of the subject. For instance, if they depicted two blowers rather than one, it is worth asking what this might imply quantitatively about the wind pressure and air flow rate required by the organ in question. But one needs a tool chest which includes collateral information in the form of organ blowing physics before one can do this. Hence this article.

 

 

Figure 1. Organ depicted on the obelisk of Theodosius

 

Figure 1 is the well known nineteenth century sketch [5] of an organ originally carved on the fourth century obelisk of Theodosius in Constantinople. Although the sounding portion of the instrument might be fanciful [6], the wind raising apparatus is of more interest here. It shows a large diagonal bellows, hinged at one end, delivering air to the pipes with the pressure resulting from two people standing on the top board. The fact that two were necessary suggests that the pressure raised by just one was insufficient, so it had to be doubled. In turn, this might only have been discovered once the instrument was complete. If this were true it would not be surprising, since it is shown later that typical pressures arising from this type of blowing mechanism (a large bellows loaded with a heavy weight) might seem surprisingly small to the uninitiated. The drawing is also plausible in detail in that the pressure resulted in the leatherwork bulging outwards, suggesting that no reinforcing ribs were used. Moreover the bellows is divided into segments, perhaps to prevent a single lap of leather between the top and bottom boards being excessively strained by the overall force due to the pressure within [7]. The positions of the blowers, standing close together towards the centre of the board, might also be relevant in that the pressure would have varied had they stood closer to the fulcrum or the outer edge. This would have affected the tuning of the pipes and possibly their onset of speech in terms of their attack transients. It is unclear whether the bellows board was rectangular or tapered in plan, though the former is perhaps more likely given that it had to accommodate two people. Because the weight of the blowers always acts vertically downwards the wind pressure would have increased as the bellows deflated, following the cosine of the angle included between the top and bottom boards, and thus sending the pipes sharp. However, since this angle as shown is less than 15 degrees the variation would probably have been insignificant in practice (when fully deflated the angle would be zero and its cosine therefore equal to one; when inflated, the cosine of 15 degrees equals 0.97 - nearly the same). Since there is no reservoir more than one bellows would have been necessary to keep the organ in wind, with the blowers stepping between one and another. Each bellows would have emptied into the common wind trunk via a non-return clack valve while the inactive one simultaneously reinflated from the atmosphere (through a second similar valve), perhaps under the action of some form of spring [8]. Some skill would have been necessary to prevent excessive pressure fluctuations, but this has always been part and parcel of the blower's art over the centuries and a reason why experienced blowers were sought after.

 

Thus a useful amount of credible information can be extracted from this illustration. Drawing on the physics outlined in this article, it is reasonable to conclude that it probably depicts an organ with flue pipes working at a relatively low pressure. It also shows that bellows had already developed over 1600 years ago some way beyond the primitive animal skin bag still used in bagpipes today, and therefore organs were probably benefitting from their parallel use by blacksmiths and the like. 

 

Another well known image is quite different in the type of organ represented. Taken from the ninth century Utrecht Psalter [9], it depicts what is generally thought to be an hydraulus or water-organ in which the wind pressure was defined and stabilised by cisterns in which water was displaced by the air pressure (Figure 2). The hydraulic system itself does not concern us here but some features of the image are of more interest in terms of organ building physics.

 

 

Figure 2. Organ depicted in the Utrecht Psalter

 

In view of this, the dismissive views of most commentators are disappointing. Sumner, the mid-twentieth century authority, described it thus [10]:

 

"One of the players seems to be admonishing, with an angry fore-finger, the undernourished, kyphotic organ-blowers. The other, with acromegalic hands is apparently stopping leaks in the sound-board. The shapes and sizes of the pipes are misleading. The points of interest are the uprights and cross-pieces which may have held up a curtain or cover for the pipes and the holes which are probably intended to hold a second set of pipes. Almost the only real value of the picture is that it represents a hydraulus, and that there are two players".

 

Although Sumner had a physics degree he did not linger long in that profession, and it shows in his prose above. To his mind the image conveyed little more than the fact that there were two players, so the number of blowers was therefore of no interest to him. Why he considered the possible presence of a curtain to be so significant is curious. More surprising still is that he missed the important point that the blowers were operating levers. The lever is an invention dating back thousands of years and, together with the wheel, it is one of the most significant in the history of engineering. It can amplify or attenuate the force applied to it, simultaneously attenuating or amplifying (respectively) the distance over which the force operates. It is therefore a transformer which transmits the same power from input to output while varying the mechanical impedance to match the source and load. It stretches credulity to posit that the draughtsman responsible for the image conjured up the levers from his imagination, so we have to take their appearance seriously. Levers were part of the high technology of the day whose function and purpose were unlikely to have been widely understood by an uneducated peasantry or even many artisans and scholars. Also important is the length of the levers which on the face of it imply a considerable mechanical advantage, meaning that the force applied to the bellows or blowing cylinders of the organ was much greater than that which the blowers themselves could exert. In turn this means that, unlike the organ in Figure 1, the pipes of the instrument probably operated at a relatively high pressure. However, amplifying the blowing force with a lever also means that the volume of air delivered per blowing stroke would have been attenuated by the same factor, and this shortfall would have meant that the necessary air flow rate might have had to be made up by multiplying the number of blowers. Therefore, what we see in this imperfectly rendered image is an organ with a relatively small number of pipes blown at high pressure by several blowers so that it would, presumably, command attention by sounding loud. Going further, one might hypothesise that the pipes were high pressure reed pipes with a fierce and penetrating tone, perhaps similar to those of bagpipes, which would also account for their unusually small scales (narrowness relative to their lengths). Later sections of this article will put some numbers into these arguments which might be useful to those with the inclination to take them further.

 

Hopefully enough has now been said to show that these and similar images, which often appear bizarre at first sight, actually form a good starting point from which to explore the physics of bellows and manpowered blowing systems in more detail.

 

 

Calculation of wind pressures

 

This section of the article shows how to calculate the wind pressures arising from different types of bellows. The results can be used for several purposes, one of which is to assist in deciding whether the old images of organs which have come down to us are credible. Another is to determine whether there is an upper limit to the pressure which can be raised manually, and if so, what that limit is.

 

Horizontal bellows

 

Initially we shall derive an expression for the pressure resulting from a mass placed on the top board of the simplest type of bellows sketched in Figure 3. This, the horizontal bellows, is commonly used as an air reservoir rather than as the feeder bellows which are worked directly by the blower. In this case the organ blower operates the feeders, forcing air into the reservoir. The reservoir performs the dual function of defining the wind pressure on which an organ works by suitably choosing the mass, as well as smoothing out the pressure fluctuations from the feeders. It consists of two parallel horizontal boards made airtight by means of some flexible material such as leather which encloses the air in the space between them. The mass M is placed on the top board, chosen to define the desired pressure p inside the bellows. The arrangement shown is somewhat impractical since the top board as depicted is not prevented from wobbling around, but for now this will be ignored. The problem is solved in organs by various detailed means, but to address these at this point would divert attention from the thrust of the article.

 

 

Figure 3. Horizontal bellows

 

The mass exerts a downward force on the top board given by Mg where g is the acceleration due to gravity. This follows from Newton's second law of motion which states that force equals mass times acceleration. Since pressure is defined as force per unit area (e.g. pounds-force per square inch, Newtons per square metre, etc), we have to divide the force by the horizontal area (wl) of the top board, where w is its width and l its length. The pressure p is then given by:

 

p = Mg/wl     (1)

 

But because pressure is measured using a water manometer in organ building, we now have to find the equivalent height of a water column which counterbalances the pressure (p) inside the bellows. So we first calculate the mass of the column, which equals its volume times its density. And as we want to derive forces (not masses) here, the weight of the column (W) then equals its mass times the acceleration due to gravity g. Thus:

W = volume times density times g = hA.r.g     (2)

 

where h is the height of the water column, A its area, and r (supposed to be rho but not all browsers display it!) the density of water. Since pressure is force (i.e. the weight) per unit area we next have to divide by the area to get:

 

p = hrg     (3)

 

Equations (1) and (3) both express the same thing, the pressure inside the bellows, so we can now equate them to get:

 

hrg = Mg/wl 

 

in which g cancels out, and the equivalent water manometer height balancing the bellows pressure p therefore becomes:

 

h = M/rwl     (4)

 

This is an important and useful equation in organ building, but before going further it is emphasised that it refers only to this type of horizontal bellows. The other types of bellows discussed later generate different pressures. Also, compatible units must be used throughout. For example, you must not accidentally mix Imperial and metric units without first converting one to the other as required. To illustrate this, let us work through a practical example to find the reservoir loading mass per unit area required to produce a pressure of 1 inch (25.4mm) water gauge, which is something actually useful to an organ builder and to those trying to make head or tail of the ancient organ iconography. Without apologising for the repetition, note the care taken with units in the following.

 

Since we are considering mass loading per unit area, let the product wl equal one square metre. Water density (r) is 1000 kg per cubic metre, and h is 0.0254 metres. These numbers are all expressed in compatible units, so from equation (4) the required bellows loading mass M per inch of water equals hr or 25.4 kg/m2 (5.2 lb/ft2 in Imperial units).

 

Another example concerns the wind pressure created by loading a reservoir of given dimensions with a given mass. In this case reservoir length (l) is chosen as 6 feet, reservoir width (w) is 4 feet 6 inches, and the total mass (M) sitting on top of the reservoir is 12 stones. In Imperial units the density of water is 62.4 lb/ft3. Bearing in mind the importance of keeping the units compatible, let us reduce all length measurements to inches and masses to pounds. Then:

l = 72 in
w = 54 in
M = 168 lb
r = 0.036 lb/in

 

Hence, using equation (4), the resulting wind pressure is 1.2 inches of water. This is a very low pressure and one which would seldom be satisfactory except for the smallest chamber organs. Several remarks are now necessary. Firstly the reservoir dimensions typify those for small organs with up to about 15 speaking stops whose pipes require a more usual wind pressure around 3 inches. Secondly the figure for mass equates to that of a typical adult. Therefore the conclusion is that very considerable loading on top of a sizeable reservoir is required to generate even modest wind pressures, which is the point made earlier when discussing the image at Figure 1. Organ builders will be well aware of this though others might not. In this example 3 inches pressure could only be raised by increasing the reservoir loading by a factor of 2.5 to around 30 stones (191 kg). Even more would be necessary if the bellows area was larger. It could well explain why two blowers were drawn in the image at Figure 1, suggesting that this detail is credible and important. However we shall now examine bellows of two different designs which can generate usefully higher wind pressures than a horizontal bellows for the same mass loading.

 

Hinged bellows with rectangular top board

 

 

Figure 4. Hinged bellows with rectangular top board

 

Two types of hinged bellows are discussed in this article, but the names describing them can be confusing elsewhere in the literature (e.g. diagonal, wedge, cuneiform, etc). So the names used here might be less than succinct but they should reduce uncertainty as to what is under discussion. The first hinged type consists of a bellows having a diagonal side aspect with a rectangular top board. Figure 4 should make this clear as well as specifying the dimensions involved. Such bellows have been commonly used as feeders for many centuries, though it is important to recall that they can also supply pipes with steady wind directly without needing a reservoir at all. For a small organ this can be done by an arrangement with two bellows each loaded with weights to get the desired wind pressure. A single organ blower then alternately raises the top board of each bellows, using an attached lever if necessary, while the other bellows slowly discharges into the pipework under the influence of its weight. Extending the scheme for larger instruments by using more bellows could be done, but the blower would then have to work harder by running up and down the line of bellows. Employing multiple blowers in such a system was not always successful in terms of maintaining a steady wind supply, as chaos could ensue unless the several blowers were unusually experienced in their art.

 

Calculating the pressure raised by this type of bellows requires a little high school calculus, and to restrict the length of this article the necessary mathematics is available in a supplementary PDF download obtainable here. There it is shown that the pressure p resulting from the applied force F is given by:

 

p = 2F/wl     (5)

 

If the force is due to the weight of a blower standing at the right hand edge of the top board, the force F = Mg where M is the blower's mass and g the acceleration due to gravity. If he stands elsewhere on the board the pressure will change owing to the leverage effect introduced by the hinge.

 

Note that the pressure is, usefully, twice that produced by the same force applied to the top board of a horizontal bellows without a hinge (see equation 1). This is because the force is effectively amplified by the leverage effect of the hinge and it therefore results in an increased pressure overall. However the volume of air supplied at each stroke by this type of bellows is only half that of the simpler horizontal bellows. (These figures for the pressure increase and volume reduction are approximate because practical bellows would use folded leather sides which affect both internal pressure and volume). This means that more bellows and blowers would be required to get the same air flow if the other dimensions remain the same.

 

Hinged bellows with triangular top board

 

 

Figure 5. Hinged bellows with triangular top board

 

This type of bellows is sketched in Figure 5 and, like that which used a rectangular top board discussed above, it was sometimes used as a feeder bellows either supplying the pipes directly or by first charging a reservoir. This or other shapes having a tapered top board were also commonly used for domestic purposes. In this example the top board is an isosceles triangle rather than the rectangle discussed earlier. Also as before, the force is assumed to be exerted by the blower at the edge of the top board remote from the hinge and it is denoted by F

 

Calculating the pressure raised by this type of bellows again requires calculus, and the mathematics is available in a supplementary PDF download obtainable here. There it is shown that the pressure p resulting from the applied force F is given by:

 

p = 3F/wl     (6)

 

Thus the pressure is now three times that which would be produced by the same force applied to the top board of a horizontal bellows without a hinge, and 50% more than for the previous case of a bellows with a hinged rectangular top board. The latter effect is because the applied force results in an additional pressure increase since the area of the top board has been reduced. However the volume of air supplied at each stroke by this type of bellows is also correspondingly reduced by the same factor of three that the pressure has increased relative to a horizontal bellows. (These figures for the pressure increase and volume reduction are approximate because practical bellows would use folded leather sides which affect both internal pressure and volume). This means that more bellows and blowers would be required to get the same air flow if the other dimensions remain the same.

 

 

Blowing power considerations

 

The amount of mechanical power needed to operate bellows is important because humans are obviously power-limited, especially in situations where they must continue to deliver the power for relatively long periods as when blowing an organ. Power is well defined in physics as the rate of doing work, and work is the product of force and distance. So let us analyse the power involved in a typical organ blowing scenario. It does not matter which type of bellows we consider at this point.

 

Consider a blower standing on the top board of a bellows. Thus his entire body weight will be the force which expels the air. If the bellows (and thus the blower) descends a distance d, the work done (force times distance) equals Mgd where M is the blower's body mass and g the acceleration due to gravity. The blower has done work even though he has only passively stood still while his body descends with the bellows, because the work was done previously when he had to climb onto the bellows board and thus raise his body mass against gravity through the distance d. That gave him the gravitational potential energy needed to subsequently squeeze air out of the bellows. The number of such climbs he can do in a given time interval is limited by his continuous muscle power. In other words, his power output limits the number of bellows strokes a blower can make in a given time.

 

Since we have just seen that the work done in emptying one bellows' worth of wind equals Mgd, the corresponding power (rate of doing work) is the product of Mg and the rate of change of height as the bellows descends. Thus the power W required to operate the bellows is given by:

 

W = Mgv     (7)

 

where v is the speed of descent (rate of change of height) of the bellows measured at the point where the blower is standing.

 

If t is the time taken to empty the bellows, t = d/v.

 

Thus, substituting for speed using equation (7) we get:

 

t = dMg/W     (8)

 

It is of interest to find the shortest allowable time in which a bellows can be emptied by a blower dissipating a power W as this will determine the maximum number of blowing strokes he can make in a given time interval. From this, further useful information can then be derived such as the maximum air volume flow rate he can generate from a given type of bellows. To get the emptying time we shall consider a practical example. We first need to assume an approximate figure for the power (W) a typical blower can sustain. Over a period of a few minutes a healthy young adult can generate a mechanical power output of around 350 watts, which approaches half a horsepower. This is about the same as that consumed by a small vacuum cleaner motor. However, on the basis of the historical evidence organ blowers tended to be drawn from the less physically fit or elderly members of the public, or they were children. Moreover, an organ would often have needed blowing for periods somewhat longer than a few minutes, which would barely service a short hymn. So a more conservative quasi-continuous power expectation of around 200 watts from a human blower seems more appropriate to the organ blowing scenario.

 

Using this figure together with other typical values, let:

 

M = blower's body mass = 73 kg (11st 7lb)

d = bellows descent at the point where the blower stands = 0.3 metres (about one foot)

W = maximum continuous muscle power available from the blower = 200 watts

g = 9.81 m/s

 

Putting these into equation (8) then gives the bellows emptying time as 1.07 seconds. Note the interesting fact that this result is independent of the type of bellows under consideration (horizontal, diagonal, etc). It was derived purely from considerations of work and power which apply universally - they are independent of the scenario. Moreover, since the value of W (200 watts) is a typical maximum value, our bellows which descends through 0.3 metres must empty in a minimum of 1.07 seconds given a blower of average body mass and muscle power. If the emptying time were to be smaller than this, the blower would have to exert more than 200 watts in repeatedly replenishing the bellows quickly enough. As it is, and since the blower is working flat out at his maximum continuous power dissipation of 200 watts, these figures for d and t are therefore limiting ones which could not realistically be improved very much. Another way of looking at it is to imagine the blower stepping alternately from one bellows to another every 1.07 seconds to keep the organ in wind, each step being 0.3 metres (about a foot) in height. The blower would have to keep this up continuously for as long as the organist required. It is the same as asking the blower to climb a staircase with an indefinite number of treads and an (excessive) riser height of 0.3 metres while pausing for 1.07 seconds on each one. Thus if a hymn lasted for four minutes, the blower would effectively have had to climb a flight of such stairs with 224 treads in this time, equivalent to a total climb of 67.3 metres (221 feet) or around seven times the height of a typical house. This well exceeds the celebrated climb of 199 steps up to Whitby Abbey in England! Figures such as these show how hard an organ blower had to work in the days before mechanised blowing came along. Anyone today (including myself) who has tried to blow even a small village organ for anything beyond a minute or two will probably confirm this. It is a salutary experience.

 

The foregoing has considered the input power to a bellows derived from a blower. It can also be useful to relate the output power delivered by the bellows to the product of pressure and the volume of air expelled, since this product has the fundamental dimensions of power (ML2T-3 where M, L and T represent mass, length and time respectively). For the three types of bellows considered in this article, the product remains constant for bellows supplied with the same blowing power and having the same linear size in terms of their length, width and height, even though their air deliveries in terms of pressure and volume vary.

 

 

Volumetric air flow rates

 

The air volumes and flow rates delivered by the three types of bellows discussed above are considered here, having already been hinted at in the previous section dealing with wind pressures. The values are approximate, because without going into an unjustified amount of detail it is only possible to compare the internal volumes of various types of bellows when attempting to estimate their relative air flow rates. It is nevertheless a reasonable approach, since emptying a bellows of given volume causes the corresponding number of gas molecules to be expelled, and they obviously must go into the wind trunking of the organ.

 

For the horizontal bellows sketched in Figure 3 the volume of air delivered each time it empties is wld where w is the width of the bellows, l is its length and d is its vertical descent as it collapses.

 

The diagonal bellows with a rectangular top board (Figure 4) has only half the vertical cross-sectional area of the horizontal bellows because it has triangular rather than rectangular sides. Therefore the volume of air it delivers for each blowing stroke is half that of the horizontal bellows having the same dimensions.

 

The diagonal bellows with a triangular top board (Figure 5) delivers still less air because the board area is only half that of a bellows with a rectangular top. However in this case it is less easy to estimate the volume of air it delivers purely by inspection of the diagram but it is reduced yet again, by a factor of three relative to the horizontal bellows.

 

These three types of bellows deliver wind at successively higher pressures in the ratio 1 : 2 : 3 (respectively) as discussed previously if they all have the same dimensions (w, l and d) and are subjected to the same blowing force, whereas their internal volumes get smaller following the reciprocal ratios 1 : 1/2 : 1/3 respectively. These figures are sufficient to explain why more bellows and blowers might be required to get the same air flow if one needs to select a bellows design giving a higher pressure while its dimensions must remain the same. The constraint on dimensions will often be important because of the floor footprint involved: enough has been said in the article to show that organ bellows are frequently very large objects which consume a lot of space in the building housing the organ.

 

In the previous section dealing with power, equation ( 8) gave the time taken to empty a bellows for a blower possessing the muscle power W. No assumptions were made about the type of bellows other than that its top board descended through a distance d. Therefore the air flow rate resulting from the blower's exertions can be derived for a given bellows of known internal volume thus: for a volume V (e.g. the product wld for a horizontal bellows) discharged in a time t seconds (from equation 8), the flow rate is simply V/t volume units per second. In particular, if the power W is assigned the limiting value of 200 watts discussed above, the maximum volumetric air flow rate which a single blower can sustain can be calculated for the chosen bellows, together with the corresponding pressure obtained from equations (1), ( 5) or ( 6) as appropriate.

 

Repeating what was said in the section dealing with power, it can be useful to relate power to the product of pressure and the volume of air expelled, since this product has the same dimensions as power (ML2T-3 where M, L and T represent mass, length and time respectively). For the three types of bellows considered in this article, this product remains constant for bellows of the same linear size in terms of their length, width and height.

 

 

Levers

 

A brief commentary on the importance of levers was included when discussing the organ pictured in the Utrecht Psalter (Figure 2) so it will not be repeated here. Nor will the theory of levers be summarised as it is widely available elsewhere. For the present we shall restrict the treatment to the simple fact that a lever enables a higher wind pressure to be obtained from a given bellows.

 

Without using a lever with a mechanical advantage greater than one, the maximum blowing force which a blower can exert on a bellows is limited to his own weight. For example, if pressing down on the top board of a bellows with his hands, the blower cannot do so with a force greater than this otherwise he would lift himself off the ground. However a lever enables the force applied to the bellows to be multiplied as much as necessary, within practical limits. This is important when high wind pressures are required. We have already seen that pressures are perhaps surprisingly low from bellows of typical size when the blowing force is limited to the blower's weight. An example was given earlier of a horizontal bellows with a top board measuring 6 feet by 4 feet 6 inches (1.83 by 1.37 metres) supporting a total weight of 12 stones (76.2 kg). This generated a wind pressure of only 1.2 inches of water (30.5 mm), far too low to be of use for any but the smallest organs. Yet the 22 inch pressure needed by certain reed stops on Willis's organ in St George's Hall, Liverpool was reputedly provided solely by manpower in 1867 [1]. With bellows of the size just mentioned, this could be done by introducing a lever with a mechanical advantage of 18.3 (= 22/1.2), which borders on the unfeasible however. But it could be reduced and thereby made more practical by decreasing the bellows area, which would increase the pressure. It could be reduced still further by using some form of diagonal bellows which generate pressures higher than those from a horizontal bellows having the same external dimensions. For example, merely using a diagonal bellows having a triangular top board would increase the pressure by a factor of three, resulting in a reduction in the mechanical advantage required to about 6. This is now a decidedly practical proposition. The upshot is that quite high pressures can indeed be obtained from human blowers by using a lever combined with suitably designed bellows, and that is why levers appear so often in old illustrations of organs.

 

The downside of amplifying the blowing force using a lever is that the amplitude of movement of the lever at the bellows is reduced by the same factor. Thus the volumetric air flow will also be reduced, meaning that more bellows and blowers might be required to compensate for this effect. It is a point worth bearing in mind when analysing some ancient images of organs, which sometimes seem to have more blowers than one would expect given the relatively small number of pipes visible in the pictures. Before dismissing such images as fanciful it might be worth considering whether the pipes were blown at high pressure, implying the need for more blowers to generate the necessary air flow rate. The validity of this approach would be strengthened if levers were also visible, as they are for the Utrecht Psalter organ pictured at Figure 2.

 

 

Concluding remarks

 

This article has presented the basic physics of three types of bellows: the horizontal form commonly used as a wind reservoir, and two varieties of diagonal feeder bellows. The pressures and volumetric air flow rates for each have been discussed and related to the muscle power available from the blower. The importance of levers was highlighted, showing how they would have enabled wind pressures exceeding 20 inches (508 mm) of water to be raised by manpower alone when used in conjunction with enlightened bellows designs. By considering examples, it has been shown that it is easy to overlook useful information which some of the most apparently bizarre and fanciful images of organ blowers at work can reveal until we have studied the physics of the humble bellows.

 

 

Notes and references

 

1. "Organ blowing: its history and development", Laurence Elvin, self-published, 1971.

2. "The Organ", E J Hopkins & E F Rimbault, 2nd edition, London, 1870.

3. "Feasibility Study into the Restoration of the 1862 Schulze Organ in St George's Parish Church, Doncaster", G McMahon, N P Mander Ltd, London, 1997.

4. "Birmingham Town Hall Organ", Nicholas Thistlethwaite, Birmingham City Council, 1984.

5. E de Coussemaker, Annales Archéologiques 11.277, Paris, 1845.

6. Although it is tempting to think that the eight pipes of the organ on the Constantinople obelisk might have sounded a diatonic octave, their speaking lengths as drawn would not have spanned anything like the necessary 2:1 pitch range. Therefore one might dismiss this aspect of the drawing as whimsical, or alternatively, perhaps allow that the pipe mouths out of sight were not horizontal but lay on a curve.

7. While these details relating to the bellows of the Constantinople organ are indeed plausible, it is possible they have been anachronistically emphasised to reflect later practices by the draughtsman (E de Coussemaker).

8. The inactive bellows in a dual-bellows system might also have been reinflated by means other than a spring. Other ancient images show arrangements based on a rope connected to both bellows passing over a pulley fixed above the level of the blower's head, with he treading on them alternately. 

 

9. Although the source of the image shown above at Figure 2 is commonly said (as in this article)  to be the ninth century Utrecht Psalter, this is not in fact the case.  It is a line drawing made from a picture in the later twelfth century Eadwine or Canterbury Psalter which is nevertheless an obvious copy of the earlier one, though some details differ.  However the salient features of the Utrecht organ are retained in the Canterbury image insofar as this article is concerned.

10. "The Organ", W H Sumner, 3rd edition, Macdonald & Co, 1962, London.