The equation for the induced drag coefficient is typically presented in textbooks this way:

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c_di = c_l²/(pi)AR e, where

c_l is the lift coefficient of the wing, pi is the Greek letter symbolizing the ratio of a circle’s circumference to its diameter, AR is the aspect ratio and e is the span efficiency factor.

The lift coefficient c_l is the lift force exerted by the wing, which must equal the airplane’s weight W, divided by the dynamic pressure and the wing area A,

c_l = W/0.5 (rho) v² A, where rho is the mass density of the air and v is the airspeed.

Taking the area of the smaller wing to be A, that of the larger wing is 2A. Therefore the lift coefficient of the large wing will be half that of the smaller wing.

Aspect ratio AR is the ratio of the square of the wingspan to its area

AR = b²/A

so the aspect ratio of the larger wing is half that of the smaller wing.

[We’ll disregard the span efficiency factor e and simply assume that its value is always 1.]

The induced drag coefficients of the two wings are, for the smaller wing, cl2/(pi) AR , and for the larger wing (0.5 c_l)²/(pi) 0.5 AR or or one-half the induced drag coefficient of the smaller wing with the higher aspect ratio. If we accept this as the final word, reducing aspect ratio should give better induced drag.

Now if I and many others had bothered to carry my calculations this far, it would have raised suspicion. Unfortunately, I hadn’t – a friend had to enlighten me.

You see, when we convert the coefficient to an actual force, here is what happens:

D_i = c_di 0.5 (rho) v² A

Plugging in values to this formula makes it clear that doubling wing area cuts the induced drag coefficient in half, while the area of the wing doubles; one-half times two equals 1, so at equal span, changing aspect ratio neither increases nor decreases induced drag.

Using the formula for the actual drag force directly would have saved us time and confusion.

Di = W²/0.5 (pi)(rho)v² b²

Here it’s obvious that if span is constant, the induced drag can’t change. Wing area and aspect ratio don’t appear in the equation.

Note that there is nothing wrong with the equation for the coefficient - it is physically and mathematically valid - but many students (and not a few teachers) have been misled in interpreting it. They see AR in the denominator, and that’s it. If they had calculated it through for our two cases, they would have noticed the paradox of lower AR giving a lower induced drag coefficient and would have become curious. I’m sorry to admit that I didn’t do that calculation until a friend asserted the irrelevance of aspect ratio.

It is span, more precisely span loading W/b, that governs induced drag: a lower span loading results in lower induced drag.

It would be better if, for textbooks, the authors should set aside their preference for dimensionless coefficients and concentrate on dimensional numbers.

My thanks to Hernan A. Posnansky, who set me straight about this.

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Jean-Edouard Andreau (1890-1953) was a St. Cyr-trained military engineer and self-taught aerodynamicist whose unfortunately brief life included many accomplishments. He is best remembered in the automotive industry for originating the unit-body construction of the justly famous Citroën “Traction Avant” Model 11, whose derivatives remained in production for decades. He had a continuing interest in the aerodynamic efficiency of automobiles, and designed vehicles whose drag coefficients raise eyebrows even today.

Late in life he seems to have developed an interest in wind power, and in typical fashion he strayed well off the beaten path in his wind-turbine work. In the late 40’s he was granted three British and one US patents for a wind power system that completely eliminated any rigid mechanical coupling between the wind turbine and the power generation equipment. In the Andreau system, the hollow blades of the wind turbine double as centrifugal inducers, aspirating air from the hollow hub and expelling it at their tips. The hub in turn is rotatably sealed to a hollow tower that doubles as an air duct. The internal airflow thus induced drives a small pneumatic turbine installed at or in the base of the tower.

This eliminates the need for machinery at the top of the tower, which in turn can lead to significant savings in support structure weight and cost or allow a taller tower supporting a larger-diameter rotor for a given cost. This in turn should lead to a lower cost for each kilowatt-hour “harvested” from the wind, all else being equal. There is a corresponding reduction in the amount of maintenance work that must be performed at tower top, reducing the risk to maintenance workers and the number of manhours expended in skilled labor.

A further advantage is that, since there is no kinematic connection between the wind turbine and the output turbine shaft, the former can operate at its best speed for the existing wind conditions while the latter is governed for best output characteristics—e.g. grid-synchronous electrical output.

Unfortunately, Andreau died before the prototype, built by a British firm, could be tested. Testing was undertaken—first in England and later in Algeria—but the results were disappointing and were apparently not pursued. They are documented only in one paper in the United Nations conference proceedings on New Sources of Energy (Delafond1961). So far as I can determine, none of Andreau’s own writings about this work have been published, with the exception of his patent applications.

As time permits, therefore, I have been building a mathematical model of this type of plant with a view to determining the bounds of achievable efficiency and quantifying the plant’s self-regulating property. This in turn should allow a valid comparison of the economic performance of the Andreau system to that of more conventional wind powerplants.

General Considerations about Wind Energy

Unlike the water flows exploited by hydropower plants, the wind is an exceedingly variable resource over which the user has absolutely no control. At any given moment, a certain amount of power is available at the wind turbine disk. Any part of that power that is not used—whether because there is no load to receive it and no means of storing it or because the turbine or the attached power conversion and conditioning equipment cannot handle it—goes to waste. If the costs of two wind turbine plants of the same height and diameter are assumed equal, then the plant that can harvest useful power from the wider range of wind speeds will be the more economical of the two. The margin of superiority will of course be a function of the site’s characteristic wind speed distribution—a narrower margin for sites with steady winds, a wider one for more variable conditions.

For small, individual wind plants the cut-in speed—the wind speed at which the plant begins to produce power—is important because the turbine may be the primary, or even the only power source available. For a commercial plant the cut-off speed is far more important, as the power available in the wind is proportional to the cube of the wind speed, so wind speeds above the turbine’s acceptance band represent substantial amounts of lost energy, even if they occur only seldom.

It follows that there is more to the economy of a wind turbine plant than the design point coefficient of performance; the acceptance range is much more important, because the coefficient of performance of the plant when the wind speed is outside its acceptance range is effectively zero, however scintillating it may be at design point.

Clearly, a high cutoff speed is desirable; equally clearly, most wind turbines don’t have it. The reason is simple and obvious: high speeds mean high stresses, both on the turbine itself and on all components connected to it. What is more, if the turbine should for any reason lose its mechanical load-say, by the failure of a field-current source for a mechanically connected generator or by stripping a clutch or an elastic coupling-there is a danger that it will “run away” and fly to bits before it can be brought back under control. For this reason, designers tend to take multiple precautions against excessive turbine speed, incorporating mechanical and/or aerodynamic brakes and sometimes even using a sub-optimal blade angle distribution to ensure self-braking during overspeed. If a turbine configuration were available that could not be disconnected from its load and that would be inherently self-braking, it would be safe to allow it to operate at somewhat higher speeds than current designs-and even a small widening of the speed range, as we have seen, means a large potential harvest of otherwise wasted energy from a gusty site.

The Andreau turbine seemed to have these desirable characteristics—hence my interest. But first, let us answer the question that is on everybody’s mind.

Efficiency

It is safe to assume that the collector efficiency of the Andreau turbine—the efficiency with which it transfers power from the wind to the rotor—is going to fall in the same band as that of any competitor; it is, after all, subject to the same physical law. At the delivery end of the system, the efficiency of the turbogenerator set which converts the induced, internal air flow into electrical output likewise needs no discussion as cold-air turbines are well documented.

What we are concerned with here is what I call the pneumatic efficiency. This is the efficiency with which the turbine converts power into internal airflow, which is the mechanism by which it transmits power to the power turbine. The value of this efficiency is 78.9% at the volume flow that gives maximum power output (.577 Qmax), as calculated in the attached worksheet. This result assumes that the exit flow is tangent to the blade tip trajectory. This is not a very impressive figure when compared with the 90%+ figure that can be easily achieved with mechanical power transmission. It is even less impressive when one considers that it is an induced loss that does not take into account parasitic losses through skin friction, turbulence due to flow turning and so forth. What is more, it must be multiplied by the efficiency of the turbogenerator set, which must naturally be less than 100%, to get a power-transmission efficiency figure that allows direct comparison with more conventional means. The result, counting parasitic losses, could be as low as 50%. What is more, because the pneumatic loss is inherent in this method of transmitting power, no significant improvement can be expected.

It must therefore be concluded that an Andreau system will always be less efficient at its design point than a turbine using a conventional power transmission system, all else being equal. Why, then, bother with this system?

Stability and Safety

Referring again to the worksheet, we see that the characteristics of the system change with the orientation of the tip nozzles, through which the internal airflow leaves the blades.

For every wind turbine speed, there is a maximum volume flow Qmax that can pass the internal flow system; this is the value that occurs if there is no impediment to the flow, i.e. if the power turbine is bypassed or feathered and braked.

When the flow escapes opposite the direction of motion of the blade tips, total power withdrawn from the rotor by the internal flow system rises with volume flow until half the maximum volume flow is reached; any further increase in volume flow produces a lower total power demand, but output power continues to rise until .577 Qmax. This means that the turbine will tend to overspeed beyond the half-Qmax point and needs some regulating mechanism to allow it to operate at its point of maximum power output at 57.7% of maximum volume flow. The regulating mechanism would preferably act on the power turbine, changing its blockage factor to control internal flow. Interaction with the wind turbine should help a little: as speed increases, so does Qmax, and the current Q becomes a smaller fraction of Qmax, giving a higher power demand on the wind turbine. This will help stabilize the system against the effects, for instance, of small changes in load on the power turbine but cannot be expected to stabilize the system without help.

When the flow escapes radially, the behavior of the system changes radically. The optimum value of volume flow remains the same, but pneumatic efficiency at that point declines to 33.3%. More significantly, the power demand on the wind turbine continues to rise with volume flow, instead of declining past .5 Qmax as with anti-spinward exit. This means that bypassing the turbine has a braking effect rather than an overspeeding effect, so the system is inherently stable for all possible values of Q and Qmax with the exit flow radial.

Proposed control scheme

This suggests a very simple way to make an Andreau system unconditionally safe: provide a simple mechanism -perhaps a flyweight arrangement-to reorient the tip nozzles from tangential to radial when a given speed is reached by the wind turbine. Thus any tendency to overspeed causes a fundamental change in the turbine’s operating characteristics that strongly damps any further excursion. Ideally, the nozzles would return to their more efficient operating position once the condition that threatened overspeeding disappeared.

Conclusion

Clearly, the Andreau system has an important market open to it, namely wind turbines that operate unattended in remote sites with a wide range of wind speeds. Communications repeater stations in mountainous areas come to mind, as do scientific sensor packages that have to operate for extended periods. Some sites would favor this type of installation even if there were people present at all times - Antarctica for instance. In cold, windy areas the variable nozzle orientation arrangement might be dispensed with, for fear that it might freeze in the tangential orientation. In this version the exit flow would always be radial, and there would be no moving parts at tower top except the turbine itself, which would never stop completely unless the wind did. Any danger of freezing would thereby be avoided, at some sacrifice in efficiency which might not matter in an area where wind speeds were consistently high.

The aim is to provide a catalog of technical means for moving when the State desires you to stay put, for showing up where it doesn’t want you, and for crossing lines that the State draws on perfectly innocent countryside.

There are exceptions to that general description, including a brief chapter on the Right of Locomotion and means to distance oneself legally from seizable assets, particularly real estate and vehicles.

CONTENTS

Engines and Fuels. 1

Fuels. 1

Fossil fuels. 1

Synthetic and “Bio” Fuels. 2

Gaseous and synthetic fuels. 4

Liquid fuels from coal 6

The Electric Revolution.. 6

Engines. 8

Types. 8

Automotive Engines. 9

Rotary-Piston Engines. 10

Compound Engines. 11

External combustion engines. 14

Other Power Sources. 16

Wind power 16

Land.. 18

Off-road vehicles. 18

The Landmaster. 18

The Gama Goat 19

Motorcycles. 20

Amphibious vehicles. 21

The Amphibious Jeep. 22

Amphibious Conversions. 23

Cars running on rails. 27

Bicycles. 27

Horseback. 28

Foot 28

Water. 29

Boats and Barges. 29

Classic sailing yacht. 29

Motor vessels and motor/sailors. 32

Hovercraft & Airboats. 34

Submersibles and submersible amphibians. 36

Bottom-Crawlers and Amphibians. 40

Tourist Sub. 44

Canoes and Kayaks. 45

Air. 47

VTOL/STOL. 48

Helicopters, Autogyros. 48

Rotodynes. 51

Fan-in-Wing Configurations. 54

VTOL machines using ducted fans. 57

Extreme STOL. 58

Custer Channel Wing. 60

MARVEL. 60

The Flying Pancakes. 61

Marine Aircraft, Free-wings, WIGs. 61

Amphibians. 62

Free Wing or Controlwing. 64

Wing-in-ground effect 65

Flying Car 65

Tailless. 66

Lighter than Air: Balloons and Airships. 66

Desiderata. 67

A Home Base. 68

RVs. 68

Motor Coaches. 68

Articulated. 70

Trailer or Semi-Trailer 70

Shipping Containers. 71

Water-Based Options. 73

Barge. 73

Yacht 74

Anchoring. 75

Ken Neumeyer and Sailing the Farm... 77

Control Systems. 78

Stability. 80

Free Flight: Personal Leased Air Transportation.. 81

A typical trip scenario, freedom fashion: 83

Putting Legal Distance Between You and Your Property. 86

The Right of Locomotion.. 87

Licensing. 87

What is it Worth?.. 89

Author Biography  90

From the Foreword: "Ours is an age of paradox and hypocrisy: never before in history has the freedom to emigrate and to travel been so vigorously proclaimed, and never before has travel been so restricted and supervised."
"...entire cultural groups–the so-called Gypsies or Travelers–make it their business to go where they like, when they like, no matter what governments may have to say about it. We applaud them and wish them continued success, but their use of the existing infrastructure does not concern us here; instead, we want to discuss means and methods that bypass the usual ones, and which the traveler or migrant can provide for himself."
"Our topic here, then, is alternative means of travel and emigration, that is, means which mitigate or avoid entirely the restrictions placed on the usual means of travel. These means can also be livelihoods, as moving passengers and goods quickly from and to places not served, or served inadequately and with restrictions, is within their specifications."
Contents include discussion of fuels, and of the various vehicles used to travel in or over land, sea and air. A discussion of the means to distance oneself legally from seizable assets, and also of the Right to Locomotion, are also included.

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Schooling and Education

Private schools through Grade 3, then public through Grade 6. Swiss boarding schools for the next three years, then back to the States. Phillips Academy (Andover), class of 1972. Earned academic credit by examination and by attending night classes when in the US Army. After discharge, matriculated at the University of California San Diego (Mechanical Engineering, minors in Mathematics and Linguistics). Exhausted my veteran’s educational benefits before completing the too-lengthy academic program.

Took and passed the Engineer-in-Training examination in an attempt to get engineering work without a bachelor’s degree - foiled by the requirement to have six years of documented work in the field BEFORE taking the Professional Engineer exam in any particular field.

Employment

One year as a civil engineering intern in France after graduation from PA.

Odd jobs, then enlistment in the US Army. Intelligence training and assignments in the US, followed by Counterintelligence Agent training, the Intermediate German course and assignment to Belgium and Germany, where I made good use of my native-quality French, decent German skills, and got rare exposure to the Russian language, which I had studied for two years at PA. Did some part-time translation work while in the military, following up on work that I completed for my father when he became ill.

While attending UCSD after leaving the Army, did translation work for agencies on the West Coast and worked other part-time jobs. Entered the active U.S. Army Reserve, both to make extra money and to stay in touch with intelligence work. After exhausting my veteran’s benefits, began working for a DoD and DoE contractor in its security office. Later, after the interruption caused by the Gulf War, worked as a freelance field editor in the area of industrial gas turbines and co-generation.

After moving to the Philippines, I returned to translation work, which I had practiced part-time in the Army and earlier. My specialties are patents and other technical works, though in fact I’ve translated just about anything over the years.

Interests

Developed my early interest in aviation in Switzerland, where I learned to build flying models of balsa wood. Engines were expensive, so most of my flying was with gliders, which made me particularly interested in efficient flying machines in general. Took flying lessons while in the active Army and stopped just short of solo to take up another expensive hobby - skydiving. After moving to the Philippines, I got interested in ground effect machines - air cushion and wing-in-ground-effect vehicles.

Later, during my enlistment in the active Army, I read John McPhee’s The Deltoid Pumpkin Seed, which stimulated my interest in lighter than air (LTA) flight - balloons and airships - and inflatable structures. That merged with my interest in parachutes, since they are structures inflated by ram air. After leaving active duty and moving to southern California I joined the Association of Balloon and Airship Constructors and began a forty-year association with its founder, George E. Wright Jr. Later I contributed to, still later edited and even later published the Association’s quarterly journal Aerostation.

LTA became the means by which I became interested in ducted propulsors. George’s and my work Ducted Fan Design, Volume 1 first appeared in 1997. It has been revised twice since, and needs further revision to take big changes in ducted fan applications into account.

I also helped found an organization called TWITT - The Wing Is The Thing - dedicated to tailless and all-wing airplanes, and I edited its newletter until issue twenty-something. That organization, alas, is now dormant.

I became an explicit libertarian at the age of 15, when a speaker at PA introduced us to the term and defined it. I wish I could remember his name, because he changed my thinking from a vague notion that things were not as they should be to being focused accurately on what was wrong and why, and how to fix it. My initial orientation was in favor of limited government, but over the decades since I have continued to lose any belief in the ability of government to do good, and the ability of citizens to limit its power. In effect, I have become an anarchist, although that term brings up an image of a short swarthy fellow with a spherical black-powder bomb, which doesn’t fit me very well. In fact, I have become an anti-revolutionary, based on the observation that disorder always favors the emergence of an authoritarian régime. Accordingly, my emphasis for some years has been on means for liberty-minded people to avoid interaction with government and be invisible to it, to the extent possible.

I’ve been interested in firearms since childhood, and one of the few drawbacks of my move to the Philippines was having to leave my guns behind. Other exotic and intricate mechanisms also interest me: cameras, typewriters and mechanical typesetting equipment, sewing and knitting machines, unusual engine configurations. I have a camera collection and a large file of documents regarding free-piston engines, for example.

Cryptography is another interest. I discovered in the unclassified library at Fort Huachuca a typescript of a translation by American cryptographer Helen F. Gaines of General Luigi Sacco’s Manual of Cryptography. Nearly fifty years later, I published it as an alternative to the generic Aegean Park Press translation.

Family

I was divorced from my first wife, whom I had met in the Army, in the early 1980s. In 1996, I married my second (and final) wife and began organizing my affairs to move to the Philippines to live with her. I moved here permanently in 1998. I adopted her son, and we have had two daughters together.

Projects

I’ve noted that disorder leads to the creation of strong-man régimes. Accordingly, my emphasis for some years has been on means for liberty-minded people to avoid interaction with government and be invisible to it, to the extent possible.

This includes mobility while exercising the right of locomotion (i.e. without obtaining a license from government) - I recently published Personal Mobility in an age of restrictions, through Amazon.

Secure communication these days relies primarily on the encryption of digital communications and their disguise through steganography, but I rely on the greater expertise of others for that. I do retain an interest in microdots and am working on a manual about those. Spread-spectrum radio communication also interests me.

Producing useful goods that the government wishes to deny us is important, and I am working on means for producing those goods on a small scale. Therapeutic drugs and supplements are an emphasis, as I am quite sure that our numbers are to be reduced by limiting access to those while stuffing us with statins and “vaccines.” But so too are labor-saving materials like effective cleaners, and comfort items like refrigerants, all of which are being put out of our reach.

Earning a livelihood independently of the corporate goldfish bowl system is vital, and I am always on the lookout for ways that I and others can do it.

Recently I have noticed that technical reports prepared under government auspices have gradually been disappearing from public databases, and so are becoming unavailable. There doesn’t seem to be any system for this, as the topics that I am aware of are completely harmless - homing pigeons, for example. Another project, then, is trying to document the missing material and to obtain copies whenever possible, reprinting them if they appear useful.

As soon as I began my search, I was overwhelmed by the range of applications of this technique, and I became even more intrigued. Fluidics has applications in both digital and analog devices, and finds its best field of application in areas where there is a continuous flow of fluid (usually air) that can be used for computation or control. Early applications or proposed applications were industrial (most plants have compressed air and/or hydraulic fluid under pressure continuously available), including counters and proximity sensors, space travel (a clever guidance system for an orbital lifeboat, running off the oxygen flow used for life support), navigation and guidance (Garner, Hewes and Hill worked for NASA).

The definitions used in this field have changed since 1960, when the Army’s Harry Diamond Laboratories published their first reports. Fluerics is now the term for mechanisms using only moving fluids - in other words, containing no moving mechanical parts. Fluidics now includes moving parts. This mainly allows displays, switches and interfaces between fluidic and conventional hydraulic and pneumatic circuits to be taken into account.

I’ve been accumulating books and technical reports ever since, always looking for one source that had general coverage and was accessible to the broadest possible class of readers.

As soon as I had a copy of this treatise, meant to promote Bendix’s advanced fluidic components and assemblies, I saw it was what I had been looking for.

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Enter the book, Spurious Correlations, by then Harvard student Tyler Vigen (tylervigen.com) (Hachette Books, 2015), to provide an entertaining collection of correlations - some of them very close - that nevertheless could not have any causal relationship. My favorite so far is Earnings per share of Domino’s Pizza Group vs. Economic loss due to Cybercrime, with a Pearson correlation coefficient of 98%.

It might be worth providing yourself with a copy of this little book, if only to brandish it the next time somebody says “it must be true, that correlation is almost perfect.” Unfortunately, its price in the used-book market ranges from $30 on up, much higher than the $2.50 that I spent for it in a used-book store here in the Philippines.

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Notes is a new space on Substack for us to share links, short posts, quotes, photos, and more. I plan to use it for things that don’t fit in the newsletter, like work-in-progress or quick questions.

Go to Notes

How to join

Head to substack.com/notes or find the “Notes” tab in the Substack app. As a subscriber to Polymath, you’ll automatically see my notes. Feel free to like, reply, or share them around!

You can also share notes of your own. I hope this becomes a space where every reader of Polymath can share thoughts, ideas, and interesting quotes from the things we're reading on Substack and beyond.

Why Substack Notes

Fellow writers and readers are spending time in Notes for a variety of reasons.

Ted Gioia sees Notes as a forum for dialogue.

The idea behind Notes is simple. Millions of people now participate in Substack as writers and readers—but much of this is built on long articles and essays. We now have a forum for dialoguing and sharing shorter posts.

Chris Ryan is drawn to Substack as an alternative for legacy social media.

One of my main reasons for joining Substack was to wean myself off exploitative social media platforms. I’m hoping this is going to help move us along on that journey!

Sherman Alexie wants to create a kind and creative new space in Notes.

I’m going to focus on being positive, with my own thoughts and photos and by linking to songs, stories, poems from around the web and from other Substacks.

If you encounter any issues, you can always refer to the Notes FAQ for assistance. Looking forward to seeing you there!

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ABAC was founded in southern California, originally as a special interest group within the Experimental Aircraft Association. The founder and charter members intended for the Association to focus on the technological and engineering aspects of lighter-than-air (LTA) flight. Technical information was to be made available through Aerostation, through Technical Notes, through the Association’s library of technical documents and through periodic conferences.

Buoyed by the presence of capable volunteer LTA enthusiasts, by the roughly decennial revival of interest in LTA worldwide, by southern California being a center for aviation and by the fact that many eminent names from the heroic period of airship development were still alive, and willing to help, ABAC’s membership and Aerostation’s subscription base expanded rapidly, to the point that the Association experimented with bimonthly publication in 1976. In its early years, Aerostation documented many projects that will not show up in the aviation literature - privately funded projects that succeeded or failed quietly. The early years also brought in the core of the Association’s technical library. Many old US Navy “poopie baggers” (airshipmen) had retained copies of manuals for the airship types that they had flown (in defiance of regulations), while others had technical documents that had since disappeared from their official archives. They donated these to the association, with the result that ABAC sold photocopies of Navy documents to the US Navy when these proved impossible to retrieve from government archives.

As time passed, interest in lighter-than-air flight became more diffuse. The association’s technical document collection filled many orders (some of them even from the organizations that had produced the documents in the first place), while contributors to the Journal became fewer and more widespread geographically. Then, too, the eager volunteers diminished in number to four, three, two and finally the undersigned.

As of 1996, Aerostation began combined publication with a New Zealand based magazine called Gasbag (later Airshipworld).

Aerostation ceased publication with Volume 26, Number 4, December 2003, leaving 26 volumes that need to be re-published to make them available again to technical libraries and to individual researchers. The first three volumes are out, and the rest will follow. Most of the rest are scanned, though some missing issues are being obtained as loans from private collections.

An index of Aerostation has been prepared by Kent O’Grady, and is included in The LTA Index published by Atlantis Productions, which also indexes five other LTA publications.

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At this writing (2023), attacks have tapered off due to naval operations by various governments and the occasional use of armed teams on board ships traveling through the dangerous zone. This will not last. In time the teams will be withdrawn for reasons of cost, countries will find better uses for their navies, and small crews with poor or no aft lookout will miss the approach of small pirate vessels, and the cycle will resume. This is because countermeasures are expensive, and are often inhibited by restrictions placed on firearms on board commercial vessels (yet another instance of "gun control" favoring criminals).

Inspired by Nevil Shute's novel Most Secret, I think I have a cheap and "passable" remedy.

This is the use of flamethrowers to defend vessels.

The advantages are that the “projectile” is a thickened hydrocarbon fuel, most likely diesel fuel, which I believe commercial vessels carry to fuel small engines such as ship’s service generators (the propulsion engines run on heavier fuel). The thickener by itself is neither flammable nor explosive and can safely be stored for a long time. The thickener can be mixed with fuel during use with the right machinery, so a large quantity of thickened fuel (napalm) need not be stored; the unused diesel fuel is still available for all uses. A flamethrower installed in a commercial vessel does not suffer the limitations of space and weight experienced by an individual soldier or by a tank.

The installation could consist of two projectors, one on each wing of the bridge, each able to engage boats on one side of the ship. Such an installation would have only two blind spots – directly behind the stern and directly ahead of the bow.  Due to the small crew size, both projectors would be operated from inside the bridge by a single crewman. They would  be  aimed using stereographic video cameras and a computer program able to determine the firing parameters of the projector that is able to engage; the crewman’s job will be to designate a target, select the throw weight (how much napalm is fired with each pulse) and whether the stream is ignited or not. The projectors will be traversed and elevated automatically, and will fire, not a steady stream, but a pre-selected weight of napalm, which will be projected through a nozzle by a piston most likely driven by compressed air. An igniter near the muzzle will ignite the fuel. Depending on the desired effect, the fuel stream can be ignited at its beginning, its middle or its end. Igniting the start of the stream will create a brilliant gout of flame, but lighting the opposite end will do more damage because most of the fuel will reach the target before it catches fire. The firing of a calibrated weight of napalm through a long nozzle should ensure that the ballistic characteristics of the stream are consistent and predictable. That makes it possible to fire it accurately, ensuring maximum damage for a minimum use of fuel.

Each projector will be fed with fuel automatically drawn from its reservoir and mechanically mixed with thickener just prior to insertion into the projector. The fuel will be fed into the firing chamber (the piston having been drawn back by a spring after the previous shot, and held by a sear while a new charge of compressed air is fed in behind it). Once there is a firing solution, the projector is aimed and the operator selects FIRE, the sear will be withdrawn and the air allowed to expand, driving the fuel before it. At the pre-selected time during the firing, the fuel is ignited.

Flamethrowers are known to have three problems:  range, capacity and the reliability and availability of ignition. They are typically provided with either cartridge type pyrotechnic igniters, which allow a fixed number of shots, or a flame source using an auxiliary fuel, typically gasoline or flammable gas.

Capacity is taken care of by the ship’s ability to carry essentially any amount of fuel and thickener. The use of pulses of fixed amounts of fuel should allow any reasonable range to be reached. That leaves ignition. The fuel itself is not mixed with air inside the nozzle, and thickeners traditionally do not include oxidizers (though one thickener included nitrocellulose). Including oxidizers in the thickener could make it less storable, and if that were so might disqualify it. So the trick is to blow a flame – auxiliary fuel + air – into the napalm while on its way out of the nozzle. Having to carry an auxiliary fuel is not desirable, both from a logistical and a safety standpoint. My thought is to have an ejector at the end of the nozzle which injects air into the fuel stream and a high-power electrical discharge to ignite the oxidized fraction of the napalm. It will probably be necessary to have a valve in the injector to allow air in only when needed for ignition. Letting it in all the time may disperse the napalm.

Tactics

If the crew becomes aware of an attack before the pirates start to board, the captain or deck officer will cause the ship to swerve to keep the pirate boat in sight and disrupt the attack. The trained crewman will use his video aiming gear to designate the pirate boat. The projector that is able to engage will be loaded automatically and trained.

If the ship is being boarded before the crew are aware of the attack, the same procedure is followed except that it is the top of the boarding ladder that is taken under fire. If pirates are not already on deck, a warning stream may be fired over the top of the ladder.

As hinted at earlier, a nonlethal use of this weapon is possible. A charge of fuel can be fired without igniting it. When pirates find that their boat is coated in sticky, flammable mixture, they may decide that they have pressing business elsewhere. If they press the attack, the next stream can be ignited.

After testing, it may be determined that only one size of charge is needed, eliminating the variable throw weight and making the projector cheaper and more reliable.

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The report has been in the Association of Balloon and Airship Constructors' collection since the 1970s, and was scanned in the 1990s, but only recent improvements in digital image processing software have made it possible to make easily-readable copies of the masters, which were electrostatic photocopies of the original blueline prints (Don was stuck with retracing some of the drawings when doing his research).

What is not included is a set of 15 11 inch by 17 inch drawings. These can’t be included because of the format restrictions of Amazon and Lulu. Sadly, these were stored separately from the original master, for unknown reasons, and there they were attacked by rodents. I am piecing them back together, and plan to have them scanned, and to restore the missing parts digitally to the extent possible. Once that is done, they will be offered for free download from my Web site.

CONTENTS:

Girder Report
Appendix I Column Theory of Girders.
Appendix II Analysis of Significant Data Available to the Goodyear-Zeppelin Corporation prior to the Contract.
Appendix III Application of the Theory of Appendix I to the Design of Triangular Girders.
Appendix IV Design and Testing of New Boom Sections.
Appendix V Design and Testing of Girder Trussing.
Appendix VI Construction and Tests of Girders.
Appendix VII Methods of Comparison of Airship Girders.
Appendix VIII Fatigue Tests of Airship Girders.

Girder Drawings - See Drawing Index (there are 68 drawings).

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Connected with this report are fifteen 11 x 17 inch drawings, which are not in the published report because they do not fit Amazon’s or Lulu’s publishing format. They were stored separately, and were damaged there by rodents. They’ve been restored to the extend possible and will be scanned. The scans will be offered free of charge on ABAC’s Web site. Their availability will be announced here.

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It is a collection of articles by experts in their respective fields for use by amateurs intending to build and test model rockets. It is one of a pair of books, the other being Brinley's Rocket Manual for Amateurs. Of the two, this is the more advanced, as it covers the construction of liquid fueled rockets, which Brinley does not, and discusses theory in greater depth. Nevertheless, it would be a great contribution to the success of the next generation of rocketeers if Brinley’s literary successor would reprint his book, which is still in copyright.

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The author: Makes minimum use of nondimensional coefficients, and takes great care to define them, and to show their function, their use in the industry and their physical meaning. Contrast this with a typical exposition of the “momentum method,” in which the reader is lost in C sub this and C sub that after the first page. Uses the technique of dimensional analysis in explaining the operation of propellers. Explains all the theoretical treatments relevant to the task at hand, shows their relation to one another and gives examples contrasting the procedure and the solutions obtainable with each theory. Each chapter has relevant references listed at the end.In the helicopter section, makes use of propeller theory and gives a clear exposition of the special problems of helicopters. Here again, instead of spending pages expounding the details of theory, he states the results, explains their limitations, and again offers examples. And if that were not enough, he covers numerical procedures for solving problems, which means that this sixty-year-old book is a good basis for digital computer programs or MathCAD worksheets solving the relevant problems. In fact, the computation forms published in the book can easily be converted to spreadsheets.It is true that the book is not a comprehensive or encyclopedic treatment of helicopters. The problem of vibration is not covered, for example. Thus, this text will be useful in preliminary design, but a more detailed text will be needed for more advanced work.

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Among my bizarre technical interests is ships and boats made using Portland Cement rather than the conventional steel, fiberglas or wood. These concrete vessels come in three types:

• ferrocement, which is PC mortar reinforced with layers of metal mesh, generally used for smaller vessels such as yachts

• reinforced concrete, which is concrete reinforced with heavy-gauge steel reinforcing bars, just like conventional buildings

• prestressed concrete, which is used for highly-stressed floating concrete structures such as offshore petroleum storage facilities.

The first type was experimented with starting in the 19th century, and revived after World War 2 by Nervi. It later caught the imagination of yachtsmen (and aspirant yachtsmen) all over the world. Many FC yachts were produced, ranging in quality from detestable to superb. Because of the wide range of quality, they are difficult to insure, but they are liked by serious yachtsmen, especially those voyaging far from home.

The second type was used to build commercial vessels during both World Wars, but as the ships proved heavier than their steel competitors they tended to be retired once peace returned. Interest in them is revived occasionally, in applications requiring durable marine structures that require minimal maintenance.

The third is in use for highly-loaded offshore structures…and proposed for use in a submarine as explained in the text.

This book is compiled from a course that covers the second an third type, though ferrocement is mentioned in the historical paper that opens the collection.

CONTENTS

Morgan, Rowland G.: History of and Experience with Concrete Ships, Harris, Alan: Prestressed Concrete Ships Considerations for Design, Paulling, J. R.: Lecture Notes on Ship Structural Loads for Concrete Ships and Vessels, Hansen, Hans Richard and Waagaard, Knut: Some Recommendations for Design Loads and Design Criteria for Concrete Vessels, Lin, T. Y. and Chow, Philip Y.: Economics and Problem Areas of Structural and Constructional Options for large Prestressed Concrete Ships and Vessels, Webster, W. C.: Basic Naval Architecture Considerations for Concrete Ships and Vessels, Mast, Robert F.: The ARCO LPG Terminal Vessel, Muller, Jean: Structural Considerations and Configurations II, Haynes, Harvey H.: Structural Considerations and Configurations III Implosion Criteria and Behavior Considerations for Concrete Deep Submergence Vessels, Gerwick, Ben C. Jr.: Materials for Concrete Ships Durability and Corrosion Protection Coatings, Gerwick, Ben C. Jr.: State of the Art Report Durability of Concrete Structures Under Water, Physical Constants of Crandalon* Materials, Adhesive Engineering Company: Technical Bulletin AE207/2: Concresive* 1050-15, Campbell, Roger: Classification of Concrete Vessels, Smith, David Albert: Feasibility Study for a Concrete Submarine, Inomata, Shunji: Japanese Rule on Prestressed Concrete Barges, Jansky, Charles and Mascaro, Francisco: Owner and Operator Requirements and Applications for Concrete Ships, Gerwick, Ben C. Jr.: Construction Considerations II: Assembly and Launching of Concrete Ships, Yee, Alfred A.: Design Considerations and Configurations: The Yee Concept, Closner, John J. and Marchaj, Tadeusz: Prestressed Concrete for Primary Storage of LNG & LPG on Ships or Barges and as a Secondary Barrier, Turner, F. H.: Optimizing the Size of Concrete Hulls

Hope something interests you…

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In summary, the government has no rightful power, morally or at Common Law, to restrict the right of individual citizens to move around, by any means. This is not unique to mobility – it also applies to any activity that we need to sustain us: our livelihood (no right to limit access to professions or trades), our access to medical treatment, our access to food, our right to own property, our freedom to communicate with others, and so on. It makes good logical sense – we have an undisputed right to life; how then can government limit our access to the things needed for living?

It has no right, but does it anyway, by the process of licensing.

Licensing

The definition of this activity takes many forms, but the most common one is that a license is permission from government to carry out an act that would otherwise be unlawful.

A simple example is a parade license: without it, the participants in the parade would be arrested for obstructing traffic and violating any number of other municipal ordinances.

But there is another, converse aspect. Licensing, sometimes called licensure in this context, is a means of making unlawful an activity that an individual could by right pursue peacefully otherwise. This is the aspect that we see when we consider “driver’s” licenses, pilot’s licenses, maritime licenses, radio licenses and any other license that limits an individual’s right to do what would otherwise be a lawful activity for him.

One case:

This case outlines the right very clearly: Thompson vs. Smith, 154 SE 579

“The Right of the Citizen to travel upon the public highways and to transport his property thereon, either by horse drawn carriage or by automobile, is not a mere privilege which a city can prohibit or permit at will, but a common Right which he has under the right to life, liberty, and the pursuit of happiness.”

Simple, and obvious. Government cannot restrict my right to move around, because I must earn my keep, purchase food, and so on, and limiting or eliminating these activities ultimately curtails my right to life.

And there is the simple procedure followed by several legislatures (California for example), that of simply declaring the use of a motor vehicle a privilege. Each of those statutes will have to be opposed and destroyed in court, at great cost. If the bureaucrat says “oh well, the privilege of driving doesn’t prevent you from being a passenger in a motor vehicle, so you see, you can still get around.” But that means that one class of persons has the right to drive a motor vehicle, and another class does not. If the drivers were not drivers by right, then all that government has to say is stop, and we are right back to where we started, with everybody on foot. Therefore everybody has the right, or nobody does. In fact, everybody does, because everybody has the right to life.

So all I have to do is turn in my driver’s license, carry around a copy of this court decision, and never have to visit the Department of Motor Vehicles again.

Not quite. Apparently, once an individual has sought a license to do a certain thing, he has (usually without knowing it) surrendered his right to do that thing to the government agent issuing the license. Once I obtained a license to drive a car, I surrendered my right to do that, and it became a privilege. If that privilege is refused in the future, I apparently can’t simply toss the license and demand my right of locomotion back. This seems to be the case, despite the obvious argument against it (namely, that removing my mobility ultimately curtails my right to life).

I have to assume that there is an “un-licensing” procedure that can be followed to get out of this trap, but I don’t know what it is. I once met a fellow who drove around in a car with no license plates, without a license himself, and earned his keep, if you can call it that, by suing the government organisms that stopped him, arrested him and otherwise impeded him. It was a full-time job. He must have developed such a procedure, and made it stick in court, but I never learned what it was.

Worse, it appears that if you are in control of a vehicle that is registered with government, you are automatically obligated to be licensed by government. At least, this is what I infer from the research that I have done, bearing in mind that I am not a lawyer.

So the best procedure is of course not to seek a license in the first place.  Second best is to arrange things so that you are never challenged to produce your license, or prove that you don’t require one. That is hard to do when using the road – you are simply too accessible to agents of the state. It is easier on the water, and very easy in the air, provided… well, this book is all about the “provided.”

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In 1974, Rohr Chairman Burt Raynes resolved to move Rohr into the light airplane market. Challenging the marketing base of the Wichita giants would be an extraordinary step in itself. In order to succeed, Rohr had to offer a product so undeniably superior to its competition that prospective buyers and dealers could not resist it. Raynes summoned Walt Mooney and told him to come up with a quantum leap in light aircraft technology. It must have better performance, greater safety, accessibility and comfort, greater economy and lower production cost than any competitor. It must also, in Mr. Raynes’ own words, “drive Cessna nuts!” Walt was given an adequate budget and promised the services of any Rohr employee he needed. Within budget and on time, Mooney et al. built three airframes (two flying prototypes and a static test article) and two scale models (1/10 and 1/2) for water landing/takeoff feasibility tests(!). By the time the project ended (for reasons having nothing to do with the merits of the airplane) one prototype had accumulated 23 hours in the air.

Walt took full advantage of Burt Raynes’ license to grab the best people Rohr had to offer. The key players on the project team were:

· Walt Mooney—Designer and Project Manager

· Bill Chana—Engineer and Project Administrator

· Mike Voydisch—Propeller and Duct Design

· Don Westergren—Test Pilot

· Bob Fronius—Shop Foreman

At first glance, the Rohr Two-175 looked like an exercise in novelty for its own sake. It was a low wing Delta of stressed skin, fiber-reinforced plastic (FRP) construction, propelled by a buried pusher engine driving a shrouded propeller. Its nose-wheel fairing doubled as a “rhino rudder.”

Both the wing and the vertical tail folded for transport and storage. Seating was side-by-side; access to the cockpit was through huge polycarbonate panels that opened in gullwing fashion. The single stick was mounted centrally, accessible to both pilot and co-pilot. The landing gear was fixed and rigid ... no springs. Oh, yes. The vertical tail was attached to the top of the propeller shroud. It was very hard to find a single conventional feature in the aircraft.

In context, the bizarre features listed above seem not only sensible but ingenious. Take the Delta wing: the whole machine was intended to fit a standard Federal Housing Administration single-car garage, which dictated a 20-foot maximum span. Keeping the wing loading and structural loads within reason led to a deep root chord and sharp taper, and voilà! A Delta with folding outer panels. The vertical tail alternatives were a fuselage-mounted tail which would have to be huge to compensate for the shorter moment arm, or a small-area, high aspect ratio tail mounted on the prop shroud. The second choice reduced wetted area, so that’s what Two-175 got... with its own hinge so it would fit that low-ceilinged FHA automobile hangar.

But why composite construction? Surely that was a big technical risk in 1974. The point of that choice of manufacturing technique was to reduce the parts count and the number of manufacturing operations, which it did. The combination of adhesive bonding and molding major sub-assemblies in one piece kept parts count down to a minute fraction of that of a two-seat metal airplane, even counting each ply of the laminate as a separate piece.Wing cores for the prototype were cut by the hot-wire method familiar to builders of modern FRP homebuilt airplanes, but a faster and more elegant method had been worked out for production. The wing would be built in clamshell molds. First, foam “sugar” would be placed in the mold. Live steam would then be injected to expand the polystyrene beads to the mold contour. The mold would be opened, the core temporarily withdrawn, and “B” stage fiberglass prepreg would be laid up on the inside surfaces of the mold. The core would then be reinserted and the mold would be closed, compressing the core slightly and ensuring even pressure on the laminate. Heat would then be applied in the usual manner to cure the assembly. The use of prepreg would avoid the weight gain problem of a wet layup and would prevent the laminate from becoming resin-starved. The process as a whole is simple, repeatable and cheap.

Polycarbonate is both stronger and harder than Plexiglass, both very desirable features considering the huge “glass” area in the cockpit, but the conventional wisdom said it couldn’t be molded. Bob Fronius and his team worked out a way and molded three sets.

The landing gear needed only to be long enough for the plane to rotate without dragging its tail; prop clearance was not a problem. So why not have a fixed, unsprung gear, with the mains faired directly into the bottom wing surface and the fin-like nosegear fairing attached to the steerable nosewheel strut? Conventional wisdom said it wouldn’t work. It did.

Deltas need high static thrust for takeoff, when their high induced drag puts them at a disadvantage vis-a-vis conventional planes. Getting the necessary thrust with reasonable horsepower and prop diameter called for a shrouded prop turning at 4400 rpm, faster than any conventional reciprocating airplane engine’s output. Fate intervened: Lycoming had two special high speed engines which had been built for a contract that didn’t quite pan out. Lycoming let Rohr have them cheap. These gave 150 horsepower at 4400 rpm. They had special cam profiles, but were otherwise conventional. That stroke of luck left the problem of cooling a buried aircooled engine for long periods at zero forward speed. A generously-sized dorsal scoop and an exhaust-driven ejector nozzle did the trick. In typical 108 degree F weather at the test site, the engine never overheated. The cooling system was in fact a bit too effective, and the inlet area would likely have been reduced or louvers added if the program had continued. A short extension shaft drove a four-bladed propeller. Mike Voydisch’s prop, shroud and six-bladed stator gave a 1280 fpm climb with a single pilot aboard. Stator and blade profiles and pitch distributions were critical, and adding the stator made a big difference in rate of climb.

The wing and fuselage underbody formed a “chassis” which was the major structure of the airplane. The rest (except for the duct and tail) was a fairing. Plugs for non-structural panels were carved out of body clay, Detroit style. Even the engine mount, though otherwise conventional, attached to the structural “pan” instead of the firewall bulkhead. Fatigue tests on the FRP structure showed that a structure that could resist a specified static load had an indefinite life under alternating loads. NASA spent a lot of money some years later to find out the same thing. A few details of wing design: the outboard leading-edge droop/extension (Walt Mooney called it a “dog tooth") was added to correct a pitch-up tendency at high angles of attack. NASA might call this feature a “fixed vortex flap.” The airfoil section was a symmetrical French curve special laid out by Walt according to exacting scientific criteria: if it looks right, use it. There was no spar, and the structural joint between the center-section and the outboard panel was made up of two FRP piano hinges adhesive-bonded to the stressed skin of the wing. The FRP hinges were developed for the Two-175 because of questions about the reliability of adhesive bonds to metal. Torsional loads were transmitted by trunconic bosses molded into the root of the outboard panel near the leading and trailing edges; these fit neatly into recesses in the center-section. Folding the wing was a matter of removing the lower hinge pin.

Don Westergren, the project’s test pilot, noted that despite the machine’s unorthodox layout it had a very normal feel. He got used to the machine quickly and felt comfortable with it, despite the fact that the wing was completely outside his field of vision, requiring the use of the instrument panel as an attitude reference. Only in landing did the Delta’s special character demand special techniques: approaches must be flown at constant attitude and the machine allowed to flare itself in ground effect; hauling back on the stick C-150 style would have “buried” the tail. Don had a chance to test engine-out performance somewhat earlier than intended when a driveshaft coupling failed shortly after takeoff. Don 180’d and put the plane down on the runway without damage. The pivot point of the nose-wheel fairing/rudder had to be moved forward early on.

Otherwise the tests were uneventful and there was little down-time for modifications. Early in the program somebody realized that the plane was capable of floating on its sealed, foam-filled wing. Tests with scale models showed that the airplane could take-off and land on water with the help of hydro-skis. This opened up the possibility of snow landings as well. With retractable skis, the Two-175 would certainly have had the cleanest seaplane configuration ever seen.

So what happened? Rohr got into financial trouble with other projects and the Two was a victim of the ensuing corporate belt-tightening. Reusable equipment was salvaged from the airframes and they were destroyed, as was every speck of technical documentation. The plane lives on only in Mooney’s collection of color slides, a few 3-views and the memories of the team who built and flew them. Even today, that team is very close-mouthed about their work. The surviving members of the development team (Walt Mooney and Mike Voydisch have died) occasionally meet to reminisce, but the Press are not invited...

[Later: this is now a very open secret. Books have been written, a Web site set up, videos posted on YouTube. But at the time the article was writen the people who had worked on the "71X" were only willing to talk to a small aviation group dedicated to tailless aircraft (The Wing is The Thing - TWITT) and have their reminiscences published in a newsletter with a circulation of fewer than fifty copies.]

Chapter outline:

1.    Units – customary and scientific – and how we recommend using them

2.    Basic propulsion physics

The world has gradually gravitated to two systems of units – the US Customary or FPS (foot-pound-second) system, and the Système International (SI) or “metric” system whose fundamental units are the meter, kilogram and second. They don’t convert directly into one another, because the US system is based on Length, Force and Time (LFT) while the SI system is based on Length, Mass and Time (LMT).  Thus force in US customary is measured in pounds, while the SI unit of force, Newtons, is equal to kilogram-meters per second squared, following Newton’s familiar formula that equates force to mass times acceleration F=m·a. The same formula can be used in the US system, of course, and the result is expressed in slug-feet per second squared, the slug being the unit of mass in the US system.

And that should be all we have to say about it, except that a quick look around will show us that other units are in common use that don’t belong fully to either the customary or SI systems, or use some variation of their fundamental units. A quick look at the instrument panel of an aircraft will show you that its speed is displayed in knots, or nautical miles per hour. There is a valid reason for this. A nautical mile is equal to one minute of arc (1/60 of a degree) on a great circle of the earth (the equator or any meridian), so navigation based on nautical miles is easier and more intuitive, and requires fewer unit conversions. In the USA, power is customarily expressed in SAE horsepower instead of in foot-pounds per second, which would use the fundamental units of the customary system. In the metric world, power is now being expressed in watts, which uses the fundamental units of the SI system, but older literature uses the “metric” horsepower.

All this can easily lead to confusion and error, so we have compiled a table of units, conversions and dimensions which appears <insert>.

To avoid the errors that these different units can cause, we recommend starting your calculation by converting to units using the fundamental units of whatever system you are using, completing the calculation within that system, and then converting if necessary to the “usual” units at the end. For example, you may start with an airplane that needs to go X knots using an engine of Y horsepower. You convert these respectively to meters/second or feet/second, and to foot-pounds/second or watts, perform the calculation, then convert back into the “usual’ units at the end of the calculation.

Before we can understand the advantages and drawbacks of a ducted fan, we need to know how air-breathing propulsion systems in general do their job.

Force and Momentum

Basically, any air-breathing propulsion system produces a force called thrust, by adding momentum to a portion of the air surrounding it. This is not true of rockets, which add momentum only to fluid (or reaction mass) that they carry internally and expel to the rear, but it is true of propellers, propfans, turbojets, turbofans, thrust augmentors and so on. This brings us to our first physical relation, that between force (thrust) and momentum. But what is momentum?

Momentum is the product of mass and velocity. Mass is often confused with weight, particularly because scales typically (and misleadingly) give readings in pounds (a unit of force) or kilograms (a unit of mass). An object's mass is a measure of the quantity of matter the object contains, while its weight is the force that object exerts in a given gravity field. The constant that relates mass to weight is the acceleration of gravity, g, which is 9.8 m/s² or 32 ft/s² at sea level on Earth. Thus we multiply mass in kilograms times 9.8 to get the force in newtons (N) exerted by that mass, while we divide pounds (a unit of force) by 32 to get the mass in slugs.

For example, my mass is about seventy-three kilograms. My weight on Earth is 73 kilos (kilograms-force) as measured on a bathroom scale. The scale is really measuring a force of 73 x 9.8 = 715.4 Newtons, but it has been calibrated to read in kilograms at sea level on Earth. Now pretend that I have persuaded SpaceX to move me and the scale to the surface of the Moon, where the same scale now registers a force of about 120 newtons, making it read about twelve kilos. My mass (the quantity of matter in my body) is unchanged (assuming that I didn't eat too much rich food on the trip up), but the Moon's weaker gravity is causing it to exert a smaller force (weight). More importantly, my momentum, while loping at four meters per second across the lunar surface, is just the same as if I were sprinting at the same speed through Central Park. Because momentum is the product of mass (kilograms) and speed (meters/second), it is measured in units of kilogram-meters per second. The FPS unit is slug-feet per second.

Now for that important physical relation: Force equals rate of change of momentum.

Where Thrust Comes From

Specifically, the thrust of our propulsion system is achieved by steadily increasing the momentum of the air that it leaves behind. It does this by adding a fixed increment of velocity (called Δv “delta vee”) to a steadily increasing mass of air. The rate at which that affected air mass increases is simply the rate of mass flow  (“em dot”) through the propulsion system, that is the number of kilograms of air going through the system in each second. Δv is the difference between the air velocity far upstream of the prop and its velocity far downstream of the prop. For our purposes, then, “force equals rate of change of momentum” translates to “thrust equals mass flow rate times total velocity change.” In other words,

where v₅ is the speed of the air far downstream of the propulsor, and v₀ is the speed of the air far ahead of it.[1]

Thrust is a force, so we measure it in units of (kilogram-meters per second) per second, or Newtons in the SI system. The FPS force unit is, of course, the pound.

Power Required to Generate Thrust

So far, we haven't said anything about how much power we will need to get the desired change in momentum. It's time for our second important physical relation:

Power equals rate of change of energy.

The energy that we are interested in is the kinetic energy of the air that passes through the propulsion system. The kinetic energy of an object is one half its mass times the square of its velocity (meaning the velocity multiplied by itself).

The factor one-half is mathematically necessary but has no physical meaning. Notice that, because KE is proportional to velocity squared, doubling velocity requires a fourfold increase in the kinetic energy. Energy is measured in units of Newton-meters or Joules in the SI system, pound-feet in FPS units.

The rate of change of kinetic energy in the air is therefore the mass flow rate times the difference between the squares of the initial and final air velocities.

This is the power we need to produce thrust. It is measured in Newton-meters per second or Joules per second. This metric unit of power is called the Watt. The FPS unit is foot-pounds per second, but horsepower (1 hp = 550 ft-lb/s) is often used.

(Note here that a higher initial velocity v₀ requires more power to achieve the same thrust.)

Maximizing Thrust per Horsepower

We want to design our propulsion system to get the thrust we need (to balance the drag of the aircraft at design speed) for the lowest possible power. To help us figure out how to do this, let's rewrite the thrust and power equations in terms of the initial velocity v₀ (usually equal to the true airspeed of the aircraft), the velocity change Δv and the mass flow rate .

 (Thrust)

         (Power)

But we know from rearranging the thrust equation that  and , so

    (Power)

The first thing we notice is that we can keep thrust constant by adjusting Δv and m dot reciprocally; in other words, if we double Δv we can chop m dot  in half, and vice versa. Now let's look at the effects that changing  and Δv have on the power required to produce thrust.

Suppose that we decide to double Δv. This means we must cut m dot in half to keep thrust the same. Now look at the power equation: the first term on the right hasn't changed (we've multiplied it by two and divided it by two), but the parentheses contain Δv, which has doubled. By doubling Δv and halving m dot we've kept the same thrust, but increased the power required to achieve that thrust. If we do the opposite, namely halve Δv and double m dot, the first term is again unaffected, but we reduce the second term in the power equation.

This is the result we want. So the general rule is; to reduce power required, reduce Δv (and increase mass flow to get the same thrust). It would be nice, though, if we had a more definite relation between Δv and P. Looking at our two equations again, we notice that the second and third factors in the power equation are the same as the expression for thrust.

Substituting T for m dot Δv in the power equation gives:

Multiplying the factors gives:

        (Power)

This is (almost) exactly what we've been looking for! The quantity (thrust times airspeed) is a constant for each design problem; only Δv is adjustable by the designer. The curve of power required vs Δv is a straight line beginning at Tv₀ for Δv equals zero, and rising with a slope equal to the thrust. The quantity Tv₀ is the ideal power; it's the very lowest power for which you can get that thrust at that inlet speed. Thrust by itself tells you how much power required goes up for each unit increase in Δv; the higher the thrust, the more it costs you to increase Δv. For instance, if the thrust is 1000 Newtons and airspeed is 100 meters per second, ideal power is 100,000 Watts, or 100 kilowatts, and a one meter per second increase in Δv will cost you 1000 additional Watts.

As we'll see later, we can't usually influence Δv directly through design; we influence it indirectly, by making design decisions that affect mass flow through our propulsion system. It would be nice, then, to relate power required to mass flow rather than to Δv. With just a little more algebra, we can do this.

Rearranging the thrust equation gives us

Substituting  for Δv in the power equation gives

(Power)

To show the trend in power required with increasing mass flow, we have prepared a plot in which T and v₀ are set equal to 1 (making the ideal power also 1) and mass flow varies arbitrarily from 1 to 10. Note that as power required approaches the ideal, the gains from increasing mass flow diminish. Doubling the mass flow drops required power from 1.5 to 1.25 times the ideal power, an improvement of .25; but we have to multiply mass flow by 10 to get another .20 reduction in power required.

[1] The subscripts will start to make sense later, when we start on duct design theory

Characterization

A fuel is known by:

-          its physical state: solid, liquid or gaseous

-          its source – coal, petroleum or biological

-          its heating value: LHV or HHV

The LHV or lower heating value is based on the assumption that the water vapor produced when the fuel is burned does not condense. The higher heating value (HHV) assumes that it does, and adds the heat of condensation of the water vapor produced by combustion to the total amount of heat produced. For vehicles, the LHV is most commonly used, since there are few if any applications where the heat of condensation of the water vapor can be recovered.

Heating value is a key contributor to the range and payload ratio of vehicles using the fuel. If you use a fuel with a lower heating value – say, alcohol - you must carry more of it to develop a certain amount of heat energy, so there is less weight available for carrying payload, all else being equal.

-          its melting point, evaporation temperature, flash point, vapor pressure and other characteristics bearing mostly on its safety, but also, in the case of gasoline and other fuels for spark-ignition engines, on its ability to ignite reliably in the engine.

-          characteristics, such as viscosity, which affect its handling in a power plant, and in an engine’s injection or carburation system.

-          characteristics affecting its behavior during combustion: octane number and cetane number for example

Fossil fuels

The fossil fuels are coal and its by-products, and petroleum with its many distillates and derivatives.

Coal consists of a solid component which is mostly carbon, but also includes solid hydrocarbons, and “volatiles” which consist of lighter hydrocarbons. Different types of coal contain these in different proportions. It also has a non-combustible mineral content called, appropriately, “ash.”

Petroleum is a complex mixture of hydrocarbons, linear and cyclic, with many different molecular weights and distillation temperatures, ranging from gases to light naphtha – the essence of lighter fuel – to heavy tars. The proportions of these various components can be modified during refining by “cracking” or dissociation of component molecules. This was originally instituted to get more gasoline out of a barrel of crude petroleum than could be obtained from straight distillation.

The fuels made from petroleum are:

Liquids: bunker fuel, diesel fuel, jet fuel, kerosene, gasoline, naphtha

Gases: natural gas, butane, propane, Liquefied Petroleum Gas (a mixture of butane, propane and minor constituents)

Synthetic and “Bio” Fuels

Biodiesel has been in the news, so we will start with it. This is fuel derived from vegetable (and sometimes animal) oil and fats, intended to replace diesel fuel and jet fuel derived from petroleum. Although it is used successfully to replace petroleum-derived diesel fuel, it is very different chemically from petroleum fuels. It consists in fact of glycerides – a common form of fat – in the feedstock, in which the tri-hydroxyl alcohol glycerol has been replaced with a one-hydroxyl alcohol, usually methanol but in some cases ethanol. The process is referred to as trans-esterification and was primarily a laboratory analytical method before being used to make biodiesel. The waste product from biodiesel production – glycerine – has many uses, including the use of certain yeast species for producing ethanol from it.

Because the biodiesel production process can be implemented on a small scale, small entrepreneurs have taken to buying used fats and vegetable oils from food processors and restaurants and processing them into biodiesel. Often, this is for their own use, but an increasing number are conforming to widely accepted standards so as to sell it to other users. This makes biodiesel of interest to people seeking freedom, because it will always be possible to either make it yourself or obtain it from other individuals.

Another source of biodiesel is also being explored, namely microalgae and other aquatic microorganisms which contain a high percentage of fats in their bodies. There is immense potential in this approach, as it lends itself to mass production, potentially on the same scale as petroleum. It is not suitable for small-scale, amateur operations, since keeping the algae culture pure, subjecting them to just the right amount of sunlight, CO₂ and other nutrients, separating algae from the culture medium and breaking the cells to recover the fats are capital-intensive operations.

Alcohol has been used as a fuel, mostly for gasoline engines, but reportedly also for diesel engines. The alcohol in question is usually ethanol, but methanol and even butanol can also be used. The technical issues mostly relate to the materials that fuel system seals are made of, and to adjustments in the induction system. Alcohol has a higher octane number (better resistance to end-gas detonation) than most gasolines, and therefore allows a higher compression ratio in the engine that uses it. The higher alcohols – butanol for example - have an even greater anti-knock effect. Butanol also has nearly the same heat content as gasoline. This is just as well, as ethanol has a lower heating value (LHV and HHV) than gasoline, and the increased efficiency obtained from the higher compression ratio partly compensates for that. Butanol can also be used in diesel engines, though usually as an additive to biodiesel.

Ethanol can be made in the conventional way - by fermenting any sugary liquid using yeast – and then distilled and rectified. This can be implemented at small scale, though even a small-scale rectifying column is more bulky than, say, a biodiesel plant. The remaining beer, after distillation, is a good animal feed. Alcohol can also be made by breaking down polysaccharides into simple sugars and then fermenting and distilling them. The polysaccharide usually used is cellulose from plants and trees. This method was implemented during both World Wars due to the severe shortage of ethanol, but currently most ethanol comes from petroleum processing or from food crops like alcohol or beets. Another production method uses crude glycerine (from e.g. biodiesel or soap production). The second and third methods are more attractive, because they use waste products instead of primary products like grain or fruit that are more valuable as food.

Methanol can be obtained by distilling wood waste in a closed vessel and then refining the condensed liquid produced.

Butanol can be obtained from petroleum, but also from fermentations which also produce other substances, such as acetone which has its own uses. Recently, an amateur group meeting on line was working to perfect this process. Primary problem is the high dilution of the feedstock, which leads to low concentrations of the product. Members of the group were looking at membranes to selectively extract the product while the fermentation continues.

Gaseous and synthetic fuels

These are combined into the same section because one type of gaseous fuel is a precursor to synthetic liquid fuels.

Gaseous fuels come in two flavors: fuels that occur naturally as gases, and gases that are generated from solid fuels or from petroleum by cracking or distillation or from other “process” sources.

Natural gas is a mixture of methane, carbon dioxide and other components that is found in connection with petroleum deposits. Originally flared (burned) at the well, it is now sometimes collected and distributed through the same kind of pipeline networks as the old “city gas” made by gasifying coal. It has become a popular fuel, where available, for power plants, particularly those using gas turbines, but it is also used to power large diesel generators converted to use it. It is very clean burning, and its sale is profitable because it is essentially a by-product of petroleum exploitation, so most of the costs are chargeable to liquid fuels.

Other petroleum-based gases are the result of refining petroleum; these are liquefied petroleum gas (LPG), a mixture of propane and butane in varying proportions, with a small quantity of a number of other hydrocarbons and impurities.

Other gases, based on petroleum, on coal or on wood (or other biologicals) are created either by pyrolysis or by retorting (essentially, heating the fuel source in a sealed chamber until its volatile components escape). The former is the source of the old “city gas” produced from coal, while the latter produces “coke oven gas” which contains the volatile components of coal that is being converted to coke.

Gas fuels can be produced on a small scale, using “gasifiers” or “gazogènes.” These are machines in which a solid fuel – typically coal, charcoal or wood - is partly burned, so as to leave a combustible gas behind. Some processing – filtration and cooling - is required to make it safe to use in an engine, but gazogènes were used extensively during both world wars when petroleum products were denied to civilians. The gazogènes used were typically attached to the vehicle, though some were fixed and exhausted into a balloon later carried on the roof of the vehicle. The resulting gas was a mixture of carbon monoxide, carbon dioxide and nitrogen, of which only the first component was combustible [“water gas” also contained hydrogen]. Processing to remove the CO₂ and N improves the thermal value of the gas, but gas straight from the gazogène will work.

Generally, an engine using a gas as its fuel will have a lower power output than the same engine burning liquid fuel, due to lower volumetric efficiency. On the other hand, engines running on petroleum-based gases tend to run more smoothly, require fewer oil changes and go longer without overhaul. Engines running on manufactured gases depend on the efficiency of the filter used between the gas storage reservoir and the engine. In cars running on a gazogène that they carried with them (as opposed to stored gas), frequent cleanings were said to be necessary.

Refined gas-generator gas, called syngas, is also used for making synthetic liquid fuels, using various processes including the Fischer-Tropsch method which dates to before WW2.

Another source of gaseous fuels is methane produced by bacterial processes from organic waste. This too can be done on a small scale, and there is extensive literature on how to do it. This gas, too, starts as a low-heating-value gas containing non-combustible components, and methods for separating the methane from the other constituents are useful in improving the thermal value of the gas.

Hydrogen is another fuel gas that can be derived from many sources. It is being extensively studied, primarily in terms of its use in fuel batteries, where an overall energy conversion efficiency of as much as 90% is possible. The major problem with hydrogen is that, in gaseous form, it has a very low energy density per unit volume, and must be carefully protected from contact with oxidizers, with which it can form a combustible or even explosive mixture. Some progress is being made in storing it in solid form as metal hydrides and using other substances as well.

The Electric Revolution

The use of electric motors for propulsion in cars and in aircraft has been featured very prominently in the news lately. It is the most recent manifestation of a trend that is over a hundred years old. The use of storage batteries for power goes back to early urban delivery vehicles, and culminated in the justly famous "milk floats" used in the British Isles. The use of electricity for power transmission is almost equally old; its best-known use is in Diesel/electric locomotives that pull passenger and freight trains. It is also used in some vessels, most notably Diesel-powered submarines, where the motors are driven by current generated by Diesel generators on the surface, and by storage batteries when the submarine is submerged. Some surface vessels also use Diesel/electric power.

Most of the media attention is on battery-driven propulsion, and the expectation has been created that soon we will be completely independent of liquid fuels, at least when it comes to propelling vehicles. This fits the no-more-petroleum dogma of the anti-technology Left, but is contrary to fact. The best storage batteries currently in use deliver 250 to 300 watt-hours of stored energy per kilogram, and some storage battery technologies hope to raise that to 500 watt-hours per kilogram. Petroleum fuel stores around 12,000 watt-hours per kilogram. That forty-fold difference is somewhat reduced by the fact that the petroleum fuel has to be burned in a heat engine to produce electricity (although hydrocarbon fuel cells are under development), at an efficiency unlikely to get much above 40%. Still, that leaves the liquid fuel with a twenty-plus advantage over storage batteries. We are told glibly that if storage batteries can improve by a factor of two, we won't need petroleum, but that is a long way from the truth.

It is true that storage batteries are not the final word in electrochemical conversion. Research into flow batteries, essentially suspended since the early 1970s, is again in progress and may produce an effective increase in specific energy storage greater than two. And of course there are fuel cells, which essentially provide a "battery" that can be refueled like an engine. The problems with fuel cells are known. Liquid-fueled cells exist but have very low power densities or require a "reformer" to release the hydrogen that the cell ultimately uses. The high-performance cells run directly on hydrogen and oxygen, with all the fascinating problems of storing and handling the hydrogen, though some progress is being made in safely storing it.

Another means of storing electricity that has been developed and commercialized fairly recently is super- or ultra-capacitors. These have the advantage of discharging and being recharged very quickly, and the disadvantage that, like any other capacitor, the voltage across them decreases during discharge and rises during charging. Various hybrid (battery + ultracap) storage means have been considered to solve this problem – generating a flurry of patent applications.

For the moment the work on long-range vehicles focuses on hybrids - machines with internal-combustion engines (piston engines or gas turbines) driving generators, producing electrical current for one or more electric motors that convert electricity into mechanical power. In other words, the emphasis is on electrical power transmission. Short-range vehicles, including one prospective passenger plane with a claimed range of 500 miles or so, are being built with high-performance storage batteries only.

The motors in use for hybrid and electric cars are primarily induction and permanent magnet motors, though brushless DC motors are used in smaller vehicles such as electric scooters or motorcycles. The main drawback of the brushless motors seems to be that the circuitry that performs the commutation (replacing the brushes and commutator of conventional DC motors) has to pass the entire load current of the motor, limiting the motor's total power output. Conventional AC synchronous motors are also used, coupled with circuitry to vary frequency to control their speed. As hardware gets cheaper, brushless DC motors should become more prevalent.

For our purpose, the current emphasis on electrical propulsion means that automotive components will be available from scrapped cars, at prices that should be affordable. That is the economic advantage. The other advantage is stealth - a hybrid can be run for brief periods on electric power alone, very quietly. In fact, some current electric vehicles have noisemakers to make them safer for pedestrians to be around.

I am curious, and never happier than when I acquire new knowledge and skills. Years ago I set up a weblog with the same name to share the results of my curiosity with others, but I have never been able to bring the ‘blog to the attention of others. As a result, it has been visited by few enough people to be counted on my hands.

First step - transfer my ‘blog posts. Then add more.

What might you find? My primary interest, in all the fields that have attracted me over the years, is access - individual access to knowledge, to skills, to inspiration, all intended to promote freedom and autonomy. Some samples are in the existing ‘blog posts, and more are being worked on.

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