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A. Evan Lewis


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 * Hero's Steam Engine
 * Video of Hero engines
 * Summary
 * Can it lift weights
 * Gearbox
 * How does it work?
 * Grandfather's Engine
 * Speed
 * My Hero Engines
 * Pivot Designs
 * Other models
 * Bigger Boiler
 * Testing Boiler
 * Copper Rotor
 * New Spherical Rotor
 * Jet Size
 * How Much Power
 * Efficiency
 * Theoretical Power
 * Levers & Gauges
 * Operating the Engine
 * Hero Describes his Engine
 * Hero's Dancing Figures
 * Was it used?
   Myth
 * Did he invent it?
 * Why was it named the Aeolipile?
 * Why did they make it
 * Ancient Greek Knowledge
 * Greeks use of gears
 * Knowledge of gasses
 * When did Hero Live
 * Hero's appearance-
   Myth
 * Was he Greek?
   Myth
 * Hero or Heron?
 * Where did he work
 * What manuscripts exist
 * Appendices A-F Calculations:
 * A: Watts to lift weight
 * B: Theoretical Jet Thrust
 * C: Watts to boil water
 * D: Inertia and time to spin
 * E: Boiler shape and volume
 * F: Area for heat conduction
 * G: Material strength of copper boiler
 * References
 * Links to the authors other sites:
 * Gear Train Calculator-RideTheGearTrain
 * YouTube: Building the Hero Engine
 * YouTube: History of steam engines
 * Privacy Policy, Copyright, EULA
 * Contact Us

Hero’s steam engine


Hero engines in action

A 4 minute video of different engines in action lifting weights


CORRECTION: There is a typing error in one of the captions in the video: Hero's
engine Version 3 produces 0.055 Watts rather than 0.55 Watts. I will not replace
the video on YouTube because it would delete all the comments and visitor count.
FYI: Version 4 ran at 5400 RPM without a load, but dropped to 3500 RPM while
lifting a weight with a winding spool 25mm in circumference. When a larger 80mm
spool was used in this video it slowed down to 660 RPM, but was still able to
lift a similar weight.

Was Hero’s steam engine actually used



SUMMARY

A model of Hero's steam engine was built capable of rotating at 5,400
revolutions per minute (the highest speed ever reported). To demonstate that it
could perform useful work it was connected to a gearbox to reduce revolutions
per minute to 122 RPM or less. This was used to lift a weight on a small crane
and it lifted 200 to 300 grams to a height of 500 mm in about 15-18 seconds.
From that it was calculated that it produced about 0.1 Watts of power. This is
considerably less than the power output calculated from the theory of thrust
produced by steam jets, which was up to 9 Watts (Appendix B). This proved that
it could do work, but whether it would be considered useful work is another
story.The efficiency of converting heat to mechanical work was calculated from
theory to be 1% but in practice was as low as 0.0128%.

Efficiency may not matter if there is an unlimited supply of fuel, such as wood,
to produce the fire necessary to generate steam. On the other hand, if it takes
more labor to collect the fire wood than it saves in providing mechanical
energy, perhaps it was not economic. It could however have been the beginning of
the development of more efficient steam engines. Some engineers disagree (w)
saying that they did not have the knowledge (thermodynamics, fluid dynamics,
gear design, and boilers) to develop it further, but that is debatable. Trial
and error goes a long way.

The Hero engine is now considered the first steam engine in recorded history.
This web page looks at the technology and knowledge which the Greeks possessed.
It can be argued that they were in a position to invent a turbine or piston
driven steam engine. Hero's writings illustrate that he knew how to use
expanding air or steam to do work. He was also aware of the use of pistons as
pumps (described by Archimedes about 300 years earlier), and Hero even described
a piston operated hypodermic syringe for medical uses. They also described a
geared winch with a worm gear as the first stage. Hero's wind organ used a
wind-mill to move a beam with a piston at the other end, just like a beam
engine. The piston pumped air into an organ to make it play. They even had some
basic understanding of the behaviour of gases and proposed the existence of
atoms.

The question still remains, why didn't the Greeks or other scientists and
engineers put these facts together and develop more advanced steam engines (x).
That did not happen until 1700 years later when development of the steam engine
was key to the industrial revolution? The most common reason given is that the
majority of the population in the ancient world were slaves, so engineers saw no
reason to develop labor-saving devices. There is some evidence that they thought
the development of labor saving devices may cause the slaves to revolt. What
might they do with their muscles if they were not working?

There are several myths about Hero and his steam engine and they are addressed
here. There are many references, URL links, diagrams, photos, and quotes from
translations of Hero's original books in Greek. There are also appendicies
containing extensive theoretical calculations.

Could Hero’s engine do any work at all?

The answer came after five years of work perfecting a Hero’s engine.

Yes, I was able to prove that it could lift a weight on a small crane.


Many people have said that it produces so little torque that simply placing your
finger on the ball will stop it spinning. They considered it a useless toy. In a
machine with a rotating shaft, like the Hero engine, torque is the force that it
can exert at a given radius from the axle (given in pound.feet or
Newton.meters).

Power can be calculated by multiplying the speed of rotation (revolutions per
minute or RPM) by torque. The fact that the Hero engine can spin at a very high
rate, means that it could be geared down to produce more torque. If it is geared
down to produce slower rotation the torque increase as the rate of rotation
decreases, but the power remains the same.

The worm drive gearbox

I made a worm gear that turns one time for every 44 turns of the input shaft. By
reducing RPM by a factor of 44 we increase torque by a factor of 44 and this
gives it enough torque to operate a crane and lift a weight (power stays the
same).

The worm gear consists of a thread (20mm diameter with 1.5mm pitch) meshing with
a gear wheel which has 44 teeth. For every turn of the thread it advances by one
tooth, so it takes 44 turns of the shaft to make the gear wheel turn once. This
type of gear reduction should produce relatively little friction.

This engine was built using a small engineers lathe and during its production a
series of YouTube videos were produced, including a very simple method for
making the worm drive gear (See YouTube.com/evanecent/playlists and find the
playlist about lathes or use the embedded videos shown at the end of this page.)


Click to enlarge the photo
A gearbox was constructed using a worm drive similar to those described by Hero
and others in the Ancient world. It is driven by a bronze thread 20mm diameter
with 1.5mm pitch. This meshes with a gear wheel with 44 teeth, giving a gear
reduction of 44:1. The construction method is remarkably simple and is shown in
one of the short YouTube videos at the end of this page (Season 2 Episodes 1 and
2).


How did Hero’s steam engine work?

The moving part was a spinning sphere with jets placed on its equator pointing
along the equator. Steam rushing out of the jets created a force that made the
sphere spin. It wasn’t until 1690 AD that Sir Isaac Newton proposed the three
laws of motion that we still use today. The third law states that “Every
action produces a reaction equal in force and opposite in direction”. In this
case the force that causes the steam to rush out of the jets causes an equal and
opposite force on the jet itself and that makes the sphere turn. This is the
same way that rockets, jet engines and other aircraft engines work.

Hero was the first to write about windmills and he may have thought that the
escaping steam was pushing on its surroundings like wind pushing the sails on a
windmill, causing the motion of the sphere relative to its surroundings. Hero
also described a device with dancing figures on a stage that rotated using the
same principal as his steam engine, except that it was driven by air which
expanded when heated by a fire (below). Hero used this explanation: “the air,
growing hot, will pass through … the smaller tubes [jets]; when, meeting with
resistance from the sides of the altar, it will cause the tube and the dancing
figures to revolve.”


My Grandfather’s Hero’s Engine

I became interested in Hero’s steam engine when I inherited a model of the
‘aeolipile’ from my Grandfather, Hugh Sargeant Barrett, who was a stationary
steam engine engineer. He made this model by using a large copper kettle as a
boiler (3.5 liters) to produce steam which was conducted up vertical pipes.
These pipes supported a copper sphere (which had been the float in a toilet
cistern) supported between two pointed pivots. I saw this operating as a child
but now it was badly dented and the base had blown out of the kettle when it had
been allowed to run dry.


The Hero's engine when I inherited it from my mother and her father had been
quite badly damaged. It was restored to working order.


Rather than try to repair my grandfather's engine I decided to build my own
version. But eventually, with the help of a local radiator repair man, Graeme
Galyer, we took it apart. There was a polished round copper plate covering the
hole where the spout of the kettle had been.

When it fell off we found it was an old English penny with the image of George
the Fifth on it. He reigned from 1910 when Hugh was 32 years old. To continue
the tradition, the newer versions now have coins in them as well. We soldered
the joints back together again and it worked. We couldn't get inside the sphere
to knock the dents out and restore some resemblance to a sphere so we had to
push the dents out with a rod inserted through holes in the sphere.

Click to enlarge the photo
Hugh Barrett's Hero engine had a polished copper plate covering the hole where
the spout of the kettle had been.


Click to enlarge the photo
When the copper plate fell off, we found that it was a penny with an image of
George the fifth of UK.


How was the speed (RPM) measured?

My grandfather's engine ran at 2400 RPM. But the ball was badly balanced and
when I allowed it to run faster (using compressed air instead of steam at a
public display) it shook itself to bits and the ball went bouncing at speed
across a field. It was easily repaired but clearly we needed to make one that
was well balanced and perhaps it would run even faster.

Modern turbines can exceed 30,000 RPM. The absolute maximum speed (if the jets
of Hero's engine were able to reach the speed of sound) was calculated to be
60,000 RPM (Appendix B in subsection Maximum possible RPM). But as the jets
approach the speed of sound their thrust diminishes towards zero. This means
that the jets might be able to approach the speed of sound (mach 1), but can
never reach it. In reality Hero's engine only reached 5,400 RPM with jet
velocity of about one eleventh of the speed of sound in steam, and actual air
speed of 122 km/h or 73 MPH.

Revolutions per minute were calculated from a video recording by measuring how
far a jet moved in one frame which is 1/30th second. The result was 2400 RPM.
Video was recorded with an Apple iPhone 6 plus and the frame rate can be changed
in 'Settings > Camera > Video' to 30 or 60 frames per second and slow motion
recording is 240 frames per second. This can be useful for assessing speed of
rotation by counting how many frames it takes to complete a single rotation
(typically 3 to 6). Reflector tape on the sphere helps.



Analysis of the sound track (a sample is shown below) using Audacity.app showed
a clear cyclic pattern at 4800 from the two jets confirming the speed as 2400
RPM.



A laser counter also confirmed the speed but often produced quite erratic
readings even using a black disc with a strip of white reflector tape.



Later, when a small crane was connected to my Hero's engine, the speed could be
calculated from the rate the weight was rising on the crane, but this gave RPM
under load, which is slower than the unloaded speed.


My Hero’s Engines
The design of my Versions 2 and 3 of the Hero engine

Version 1 was my Grandfather’s engine. For safety reasons my Hero engines,
referred to as versions 2 and 3 used a small elliptical boiler. Version 2 was
built with ball bearing races, but because they had to be sealed to prevent
steam from escaping they created too much friction and it would not run. So I
scrapped that idea and rebuilt it with plain phosphor-bronze bearings. But they
too seemed to create too much friction.

Click to enlarge the photo
My first Hero's engines with ball bearings or plain bronze bearings did not
work. The first working version had simple pivots and this was referred to as
version 2. It was built in the old style with copper and copper alloys: mostly
bronze and a little brass.


Click to enlarge the photo
Since my grandfather had unintentionally given us a clue to the date of
manufacture (after 1910), I deliberately incorporated a dated New Zealand coin
in my Hero's engine filler cap. This shows Queen Elizabeth II.


So I looked back at my grandfather's engine and the Greek drawings and found
that they used small pivots with much less surface area and thus reduced
friction. So all susequent versions were built with pivots and they worked. This
convinced me that the Greeks actually built these machines and knew exactly what
they were doing, and so did my grandfather.

Click to enlarge the photo
Hero's engine version 3 with simple pivots at each end of the shaft and a one
liter elliptoidal boiler.


Experiments with various pivot designs

The two pivots I used initially were conical pins that were stationary, inserted
into cone shaped recesses on the ends of the rotating shaft. One of these pivots
has steam entering through a hole in the center of the stationary pin and moving
into the cone shaped recess with a hole in the center. As an added safety
feature these joints were surrounded by a metal ring or sleeve so that if the
joint came apart the shaft would be retained in the ring. This actually occurred
several times.

From the pivot the steam moved into the rotating shaft, into the ball and out
through the jets. The pivot on the opposite end of the shaft does not have to
provide steam but is mounted on a screw that can be tightened. This increases
pressure on both pivots and reduces the steam that tends to escape around the
pivot. This allows the steam pressure to increase which tends to produce
increasing speed. But as the screw is tightened the friction increases and the
rotation slows down. It is difficult to get the perfect balance between these
opposing factors. Also if the rotating shaft was not in perfect alignment with
the axis of the pivot it would leak steam.

I looked back at my grandfather’s engine and realized that his pivot was not a
perfect cone but slightly rounded like part of a small sphere about 6mm in
diameter. I had thought this had been roughly machined, but then realized that
the shape may have been by design and I changed mine to match. A sphere fitted
into a cone shaped recess will seal with minimal surface area touching and this
minimizes friction. It also meant that alignment was not critical. On the other
a hand, a cone seated in a cone can create an enormous amount of friction
especially if the angle of the cone is shallow. On lathes and other tools we
make use of this fact with Morse tapers which have a cone angle of about 1.5
degrees and can lock in so tightly that they can hold a drill chuck while
drilling holes in steel.

Click to enlarge the photo
The pivots found in my grandfather's engine. The left pivot has a hole in the
center for the steam to enter the rotor and it is slightly rounded. The right
pivot is on a thread so that the distance between the two pivots can be adjusted
and this alters the pressure applied to the left pivot.

In the top left image there is a tiny pulley mounted over the pivot on the
sphere. My grandfather must have tried to drive something with it. Driving a
large pulley would have provided a good reduction in RPM. Unfortunately I don't
have any records of what he did with it.


Origanally I used a cone with a surface at 30 degrees to the axis (using a
center drill). This design worked quite well and it ran at speeds up to 3,300
RPM. A speed of 5,400 RPM was recorded with no load on version 4 which was
balanced more precisely. Despite improved balance it still rattled and by
watching the steam escape from the pivot I could see it was pulsating in time
with the rattle. This was caused by the shaft oscillating backwards and forwards
along it's axis. If the adjustable pivot was tightened the rattle stopped but
the sphere slowed down due to increased friction. It was very difficult to get
the tension between the pivots perfect. They needed to be a bit loose to allow
it to pick up speed, but at high speed it was possible to tighten the pivots so
that less steam escaped and the pressure increased causing the speed to increase
further. With bigger jets it was necessary to minimize steam loss but if the
pressure applied to the pivots was increaased the friction actually made it stop
spinning.

It took another careful examination of my grandfather's Hero engine to realize
that the angle he used was shallower at about 45 degrees. I thought the
shallower the better, so I tried the tip of a drill which has an angle of 88
degrees from the axis. The pivots jumped out with this angle. Finally I followed
my grandfather's design exactly: ball shaped sationary pivot on both ends,
seated in a cone shaped recess in the rotating shaft cut at an angle of 45
degrees. This gave the best results. The steam escaping through the pivot
actually provides a cushion of pressurized steam for it to float on.
Consequently steam loss cannot be completely stopped. But to reduce steam loss I
placed the pivots inside sleeves so that the steam had to escape through a small
gap between the pivot and the sleeve (see the diagram).

All the modern designs I have seen appear to allow the steam to enter through
one pivot while using the other to adjust the amount of pressure applied between
the pivots, as described above. If steam was allowed to enter through both
pivots it would allow both to ride on a cushion of steam and may help to
minimize friction. Will this be version 5?


Click to enlarge the photo
Pivots used in Hero Engine version 4. The shaft through the rotating ball is
shown at top left. It is made of stainless steel with bronze inserts in the
ends. Each of the inserts has a cone shaped recess for the pivots to fit into.

In the bottom left image there is a stainless steel screw with a spherical tip.
This does not have a hole for steam entry, but the screw can be wound in by the
operator to increase the pressure applied to both pivots.

The image at botton right is the pivot with a hole in the center for steam to
pass from here into the rotating shaft shown above. This pivot was originally
cone shaped but has been rounded off to reduce the amount of surface area that
is in contact with the cone shaped recess. The base of this pivot has parallel
sides that fit neatly into a parallel sided recess in the shaft. Any steam
leaking from the pivot has to get through this small gap to escape.

The sleeve around the outside of this pivot is a safety feature. If the pivots
adjustment is too loose the shaft can jump off the pivot but is retained by this
sleeve.



Click to enlarge the photo
This schematic sketch is not an engineering drawing but treats the shaft as
though it is glass so that you can see the recesses cut for the pivots.


Who else has built a Hero's Engine?

Simply searching Google and YouTube will reveal many versions of Hero’s
engine. Many are simplified designs which do not require a separate boiler.
Instead water is placed in the sphere (or cylinder) and heat applied directly to
the sphere causing the water to boil and escape from the jets. To prevent water
from escaping from the jets the sphere is allowed to spin on a vertical axis
instead of a horizontal one.

One very skilled model builder , John Bentley (v), built a Hero’s engine that
looks just like the original diagram. He used a plain sleeve bearing instead of
a pivot on the side that steam was entering, but used a screw pivot on the
opposite side. The pressure of the steam pushed the shaft onto the pivot. He is
the only other model builder who has reported the speed at which the engine
operated. His engine achieved 1500 RPM with a steam pressure of 1.8 pounds per
square inch (psi) steam pressure and jets that were 1/32 inch or 0.89 mm in
diameter.


Click to enlarge the photo
This beautiful reproduction of Hero's engine following the appearance of these
machines in the ancient or medieval literature was built by expert model maker
John Bentley. He may be the only other person who has reported the steam
pressure, jet size and RPM achieved by a Hero's engine.


Size and design of the boiler

Versions 2 and 3 of my Hero Engine had a one liter boiler in the shape of a
rotated ellipse which looked nice. So that I would not have to interfere with
its integrity I suspended it inside a hexagonal brass cage with stainless steel
nodes.

Click to enlarge the photo
A close-up photo of the elliptical boiler used in versions 2 and 3 of the Hero's
engine.



Click to enlarge the photo
One of the 12 stainless steel nodes used to create a hexaagonal cage where the
boiler could be suspended. Grub screws have been placed in the underside to
secure the horizontal rods.


Click to enlarge the photo
The process of spinning copper from a flat sheet into the shape of a bowl
resulted in some nice copper bowls as gifts, but even after softening the copper
by annealing I could not form a pair of hemispheres that could be joined
together to make a sphere. The copper buckled. I was using a wooden pattern and
it probably would have been more successful with a steel pattern but that would
have required a large chunk of steel.


Although this worked, the engine quickly ran out of steam pressure. It ran
really well on compressed air. The elliptical boiler was one liter and my
grandfather’s kettle boiler held 3.5 liters and was able to produce much more
steam, capable of supplying large jets of 2mm.

I increased the surface area for conducting heat by passing 17 copper tubes
vertically through the boiler. They were attached with Silfos brand rods
containing 5% to 15% silver. Hot gases from the propane burner pass through
these tubes heating the water rapidly. This produced steam faster than the old
boiler without tubes. It also made the boiler very strong.

For safety reasons, rather than making a large boiler I decided to make a new
small boiler with increased surface area to conduct heat more rapidly into the
water and thus produce steam more rapidly. In Hero’s time the same could have
been achieved just by making a slightly bigger boiler with an equally large
surface area and using a large fire, but it may not have been as safe,
especially with a flat top. This point must be emphasised because the use of the
more modern idea of boiler tubes and a propane burner could be critized. The
actual method used to produce the steam is felt to be of seconday importance to
demonstrating the function and performance of the rotor. I'm sure the Greeks
could produce as much steam as they needed, but probably could not handle high
steam pressures which exceed 100 psi in modern boilers.

Increasing the diameter of a cylindrical boiler with a flat bottom from 200mm (8
inches) to 350mm (14 inches) is all that would be required (Appendix F) to give
the same surface area as my 200mm boiler with tubes, but my lathe cannot handle
that size. If the boiler was in the shape of half a sphere like the cauldron in
the drawings, the diameter could be reduced even more. The area of a flat disc
is Pi.r squared while the area of of half a sphere is 2.Pi.r squared. The radius
or diameter can be cut in half by using the cauldron design instead of a flat
bottom! Rather than 350mm, a diameter of 175mm (6.9 inches) would give the same
surface area for heating the water. Surprisingly this is a smaller diameter than
the almost flat bottomed boiler I used. If I build version 5, I might consider
this option but I had problems trying to spin anealed copper into a hemisphere
on a wooden pattern (see my Youtube videos on spinning copper below).

Click to enlarge the photo
The new boiler with 17 vertical copper tubes to increase the surface area
without using a large tank. The dome in the center is a water trap to try to
prevent water from entering the system along with the steam.


Testing the boiler

I only planned to operate the boiler at 15 pounds per square inch (psi) which is
roughly equal to atmospheric pressure or one bar (actually 14.7 psi). However it
is usual to test a boiler at about 4 times the operating pressure to give a good
safety margin. I closed off all the vents, filled it with water and placed it in
a bucket of water. Then I pumped it up to 125 psi which is 8.3 times the
operating pressure. The tubes, which I brazed into the tank with silver solder,
made it very rigid and it tolerated the pressure well. It included a dome shaped
water trap similar to those used on the top of locomotives to prevent boiling
water from going straight up the steam pipe. This can be a problem in small
boilers where the water level is close to the steam outlet.

Since water is nearly non-compressible it does not store any energy when
pressure is applied. Consequeently if the tank suddenly ruptured it would not
cause a large explosion during testing. Air and steam are compressible and store
a lot of energy and have the potential to cause a large explosion if the boiler
ruptured. This explains why it is important to test the boiler under high
pressure while full of water. I also immersed it in a bucket of water so that
the energy of any rupture would be absorbed by the surrounding water.

Click to enlarge the photo
For pressure testing the new boiler it was filled with water, and immersed in
water, before pumping the pressure up to 125 psi.


The spinning rotor made for Versions 2 and 3 of Hero’s steam engine

The new high efficiency boiler was used with the original spinning rotor. I made
the rotor used in versions 2 and 3 by spinning a flat copper disc in the lathe
and pressing it onto a wooden mold or pattern until the copper was transformed
into the shape of a bowl. (Several ornamental bowls were produced in the
process.) Two bowls were joined together with a lip of copper holding them
together and then they were soldered together. I had difficulty spinning the
copper into a complete hemisphere so that a sphere could be produced, so I made
this “flying saucer” shape instead. It should work just as well as a sphere.
But it was mounted on a piece of copper pipe as an axle or shaft. Unfortunately
this became slightly bent and at high speed it vibrated and caused the gear
wheel to jump out of its thread.

Click to enlarge the photo
A close-up photo of the elliptical spinner of Hero's engine version 3 showing
the way the copper edge of one bowl was wrapped over the second bowl before
using lead/tin solder to join them.


Click to enlarge the photo
The elliptical spinner after the joint was soldered.



Click to enlarge the photo
Hero's engine version 3 after the improved boiler and crane had been added.


Version 4 of Hero’s steam engine with a new spinner


I purchased a light 120mm diameter stainless steel ball from China and made a
rigid shaft out of solid stainless steel. I bored 10mm holes from each end of
the 16 mm shaft to conduct steam and reduce the weight. (The thinly gold plated
inexpensive spheres are used by the Chinese to produce a calming effect and
perhaps see the future.)


Click to enlarge the photo
Version 4 with its gold plated sphere and improved boiler.


Speed calculated from the sound track

Version 4 ran very smoothly with two 1 mm jets and reached a speed of 3500 RPM
while lifting a load of 300 grams to a height of 500mm in about 15 seconds
producing 0.1 Watts of mechanical energy. Without any load the speed increased
to 5400 RPM measured by analyzing the sound track which showed 10,800 cycles per
second as the two jets passed by. This was the highest speed and highest power
output recorded.

Click to enlarge the photo
This sound track extracted from a video recording shows very clear oscillations
as each jet passes by, confirming that it was spinning at a record speed of 5400
RPM - a record breaking speed.



The boiler pressure was maintained so well that the pressure relief valve opened
at 15 psi to release surplus steam pressure. This seems to be close to the upper
limit of the speed that these machines can produce at this pressure, although
bigger jets and even more steam production would, no doubt, produce more power.



Varying the size of the jets

My grandfather’s engine had jets made from welding tips. The holes where the
steam escaped were about 2 mm in diameter. My versions 2 and 3 used grease
nipples with the ball bearings removed which made jets 2.25mm diameter. These
produced a lot of thrust when a pressure of 14 psi was applied but they used so
much steam that the pressure from the small boiler dropped rapidly and the water
ran out quickly.

In version 3 with the better boiler I did more experiments with smaller jets. I
found that the nozzles used in 3D printers have the same 6mm threads as the
grease nipples and by buying several of these I could drill them out to various
jet sizes. The smallest size was 1/32 inch or 0.89mm. The engines ran well with
this size and the steam pressure remained very high and when it reached 15 psi
the pressure relief valve opened. The high pressure produced the highest RPM
despite the small size of the jets. The next size was 1mm and that worked well
too. 1.4mm worked, but ran at a slightly lower pressure and lower RPM.

Many modern versions of Hero's engine have used spheres with jets placed on the
tips of long arms. This is not a good idea because the arms moving through air
at high speed suffer from air resistance. Since the sphere rotating does not
have to displace air as it moves its air resistance is minimal and the jets
should be placed near its surface. The rotor does not have to be a complete
sphere but a cylinder or disk shape, ellipsoid or other shapes generated by
rotation around the axis will work just as well because they do not displace air
as they rotate. This is the advantage of using a sphere instead of pipes. Did
the Greeks understand this concept too? They may have discovered by trial and
error that this design gave the highest speeds.


How much power did Hero’s engine produce?

Well that is the burning question. We know that power output is proportional to
the speed of rotation (Appendix B) so high speeds are desirable but must be
geared down. Versions 3 and 4 were connected to the worm-drive gearbox which
rotated a spool. String wound around the spool, was threaded over a pulley at
the top of a crane and then to a plastic bottle containing water. (A second
pulley was added half way up the crane to prevent the tension on the string from
pulling the gear wheel out of its position in the worm gear thread.) The
following power calculations are shown in Appendix A.

Version 3 with 0.89mm jets was able to lift 200 ml of water weighing 200 grams
to a height of 500 mm in 18 seconds. The calculated power production was 0.055
Watts.

Version 4 lifted 300 grams 500mm in 15 seconds with a power of 0.1 Watts.

The circumference of the spool was 25mm and this rate of lift corresponds to
3000 RPM which is the same as I measured using a laser counter. Analysis of the
sound track shows that version 4 was spinning at 5400 RPM with no load.

The circumference of the spool was increased from 25mm to 80mm and the height of
the lift was increased from 500mm to 1170mm. Testing was started with 100 g of
water in the bottle. It completed the lift in about 15 seconds which corresponds
with power output of 0.078 Watts, just slightly less than earlier tests and the
speed of lift corresponded with 2500 RPM which was a bit slower.

Click to enlarge the photo
Version 4 with the crane set up to measure how fast it could lift a bottle
containing a known weight of water. The ruler is 0.5m long and the rate of rise
is timed.


Calculations reveal that the best power output was about 0.1 Watts. The fact
remains that the engine did do some real work. The theoretical power which was
calculated before the engine was built (Table 1 below) was 1.725 Watts which is
17 times more. It should have been able to lift this weight in about one second.
The rate of lift was actually determined by the speed of rotation and gear
ratios. Alternatively it should have been able to lift a weight 17 times heavier
(3,400 grams), but heavier weights tended to slow it down, which results in less
power output, and as a result of this cycle it ultimately stopped turning.


Efficiency

Efficiency of an engine is the amount of mechanical energy produced, divided by
the amount of heat energy required to run it. This calculation produced low
percentage efficiency for the Hero engines, but is this important? Is it even
relevant if there is an unlimited supply of energy? After all, they only need to
use a big boiler and put more wood on the fire until it produces enough steam to
make the engine run. So efficiency may be irrelevant to its practical
application, but it is of interest to compare it with modern machines.

When filled with 800 cc water it took 6 minutes to raise the temperature from
16C to boiling at 100C at atmospheric pressure. This works out to about 781
Watts being absorbed by the boiler (not including heat being lost into the air
due to inefficiency of the boiler). This would suggest that the efficiency of
the engine in converting thermal energy into mechanical energy is only 0.1 /781
x 100 = 0.0128% or less. For comparison relatively modern steam locomotives were
7 to 11% efficient, petrol engines 30%, diesel 40% and gas turbines 37%
efficient.

Roy Brander published an interesting graph (y) on his web site in 1995 showing
that the efficiency of steam engines doubled every 60 years over a period of 300
years starting in 1700. This was compared with the doubling of silicon chip
technology about every 2 years in modern times. If we add the efficiency of the
Hero's steam engine with an efficiency of about 0.0128% and compare it with
Newcomen's engine of 0.2% there really is not such a huge difference, except
that there was a gap of almost 1700 years. The improvement is about 16 fold
which is 5 doubling times and 5x60 = 300 years, rather than 1700 years that
slipped by.



Exponential improvement in steam engine efficiency over 300 years. The vertical
axis is the log of efficiency, resulting in an almost straight line. The
exception was a significant improvement introduced by James Watt.
Graph reproduced with permission from Roy Brander (y). The data was derived from
the work of Grant Walker at the University of Calgary.



It is possible that more work on the engine may have improved the efficiency
further. According to my theoretical calculations the thrust from the jets
should not increase after they reach choke velocity and that should occur at 10
psi. However in practice the rotor did spin faster at higher pressures so it
appears that my calculations may not be correct. Others have suggested it might
take up to 25 psi. It is therefore possible that if it operated at a higher
steam pressure it could become more efficient, but I think the Greeks may not
have been able to produce steam boilers producing pressures much higher than 15
psi. The production of boilers that could handle higher pressures was a limiting
factor in early steam engine designs in the 18th century, and explosions did
occur (see my video in the history of steam engines below.)


How was the theoretical power of a Hero engine calculated?

In order to calculate the power it was necessary to calculate the torque from
the thrust produced by steam escaping from each of the two jets (Appendix B).
The maximum velocity of gas traveling through a jet cannot exceed the speed of
sound at the temperature and pressure within the jets (377 m/s). Although I
expected the steam pressure required to reach the speed of sound would be very
high, I was surprised to find that my calculations suggested it would occur at
about 10 psi. That is one of the reasons why I designed the machine to work at
10-15 psi.

If we assume that the steam does reach the speed of sound it makes it relatively
easy to calculate what mass is being ejected through the jets every second.
Newtons third law then allows us to calculate the thrust. Multiplying the thrust
by the radius of the sphere gives the torque produced. Multiplying torque by the
speed of rotation in revolutions per second gives us the power being produced in
Watts. From the mass being ejected through the nozzles it is also possible to
calculate how much water is consumed per second and how long 500ml of water
would last. All of these numbers vary with the size of the jets being used. The
theoretical calculations are shown in the following table.

In these calculations the efficiency is always 1.5%. The fact that it does not
vary in this table is not a coincidence. The power output is determined by the
thrust produced by the jets and that is calculated fom the weight of steam being
ejected per second. Consequently the amount of water used is propotional to the
thrust. The amount of energy needed to heat that water is also proportional to
the thrust. When efficiency is calculated by dividing power output by power used
by the boiler the ratio is always the same.

However, in this table it was assumed that the speed of rotation was always 3000
RPM. If the speed were doubled with the same thrust and torque, the power output
would be doubled and efficiency would increase to 3%. In trials the speed
reached 5,400 RPM which is almost double 3000, but it dropped back to 3000 RPM
under load.

Practical experience with these models showed that friction in the bearings was
a major factor. This and air resistance of the rotating jets probably explain
the difference between theoretical and practical calculations of efficiency, viz
0.0128% compared with 1.5%. If improvements could be made in these areas, it may
have had a similar efficiency to Newcomen's first engines at 0.2%.

With regard to air resistance, it is possible to make an aeolipile using long
arms and the ball can even be omitted as can be seen in several examples online.
However, these long arms moving through the air, and displacing air, create air
resistance. A sphere, on the other hand, is not constantly displacing air and
would reduce air resistance, so it appears that the Greeks had already developed
the optimal design and we should build these engines with the shortest arms
possibe. It can also be seen that minimizing the surface area of the bearings by
using small tapered pivots is also critical in reducing friction and improving
efficiency of Hero's engine. It is interesting that steam escaping through these
pivots appears to cause the pivots to float of a cusion of steam which is
probably ideal for reducing friction but the loss of steam decreases efficiency
too.



Table 1: Theoretical results for different jet sizes with 2 jets spinning at
3000 RPM (Appendix B)


Jet diameter Thrust Power produced Water used 500cc water lasts Power used*
Efficiency mm Newtons Watts grams/second minutes Watts* % 2.25 0.475 16.0 2.52
3.3 1063 1.5 1.5 0.259 8.72 1.376 6 580 1.5 1.0 0.090 3.03 0.48 17.5 202.5 1.5
0.89 0.0512 1.725 0.272 30 114.8 1.5

* The amount of energy required to boil water is 422 Joules per gram.



However, the results actually obtained by measuring how fast it could lift a
weight were much lower. The reason is not entirely clear. Energy loss through
friction in the bearings and due to air resistance would play a role. It was
also observed that the RPM kept increasing as the pressure increased from 10 to
15 psi. This would suggest that the upper limit of thrust had not been reached.
These calculations assumed that the speed of rotation was the same for all jet
sizes, but in practice we find that the increased thrust of larger jets does
result in higher RPM, if steam can be provided at a high rate. This increase in
RPM would result in proportionately increased power output and efficiency. Steam
production was a limiting factor with this model and this might have been
resolved by using a much larger boiler. For safety reasons tubes were added to
the boiler to increase the surface area rather than increasing its size
significantly and this increased its strength (It was tested to 125 psi). But it
would be interesting to make version 5 with a big boiler and heat source and
running at higher pressure eg 25 psi.


Valves Levers and Gauges

My design includes a pressure gauge that shows 0-15 psi and a pressure relief
valve which opens to release steam if the pressure goes over 15 psi. In this
version I made a single 'stop-cock' valve that could direct the steam up to the
rotor, out to an exhaust vent, or close it off completely. Unfortunately it
buckled when heated for soldering and was replaced with two commercially
available valves, one for the exhaust vent and one to open the pipe to the
spinning rotor.


How was the gearbox and crane operated?

The original gearbox was designed to rotate so that the output shaft could be
tilted down to an angle of 45 degrees to drive an Archimedes screw intended to
demonstrate pumping power (above). However, it was modified later to operate a
small crane instead, as it would be easier to test varying loads. This required
a mechanism for engaging and disengaging the gear by lowering the gear wheel
into the thread or raising it out of the thread. This was achieved by mounting
the gear carrier frame on a shaft so that it could be tilted by a cam on the
back of the unit. Whenever the gear wheel was moved it could be locked into
position by a long lever that clamped the shaft.

A strip of copper bar above the gear wheel has a brake pad on its under-side so
that if the gear is raised up high it presses on the pad and prevents the spool
from turning, and prevents the weight from dropping.

Under this mechanism there is a small white wheel with a brass handle on it.
This is the right hand pivot that the main shaft rotates upon. The tip was
originally cone shaped but changed to a spherical shape. It is threaded
(actually a stainless steel screw) and can be screwed in and out by turning the
white knob as seen in the photo with the operator turning the knob. The spring
creates friction and stops it from unwinding on its own. The spool for winding
the string on the crane has a circumference of 25 mm.


Click to enlarge the photo
A front view of the gearbox on version 4.



Click to enlarge the photo
The plan view of the gearbox and gear engagement mechanism with parts labeled.



Click to enlarge the photo
The Hero engine with the crane actually lifting a bottle containing 100 grams of
water. The small winch spool has a circumference of 25mm.



Click to enlarge the photo
The gear engagement mechanism after removal from the Hero's engine.



Click to enlarge the photo
The gear engagement mechanism removed from the Hero's engine. The blue lever is
mounted on the head of a screw which clamps against the shaft, locking the gear
engagement into any position.



Click to enlarge the photo
Underside of the gear engagement mechanism removed from the Hero's engine. The
cam at the bottom right is operated by the silver lever and raises the arm by
pressing against the copper bar.



Click to enlarge the photo
The thread of the worm drive after removal of the gear engagement mechanism from
the Hero's engine.



Click to enlarge the photo
Back view of the rotor mechanism. The white knob is for adjusting the pressure
applied to the pivots.



Click to enlarge the photo
The gear mechanism with the gear engaged in the screw thread. The shaft through
the gear wheel turns the winch spool to wind in the string and lift the weight.



Click to enlarge the photo
The worm gear in this image is disengaged and in the braking position.



How did Hero describe his steam engine or aeolipile?

From the English translation by Woodcroft (a).

PLACE a cauldron over a fire: a ball shall revolve on a pivot. A fire is lighted
under a cauldron, A B, (fig. 50), containing water, and covered at the mouth by
the lid C D; with this the bent tube E F G communicates, the extremity of the
tube being fitted into a hollow ball, H K. Opposite to the extremity G place a
pivot, L M, resting on the lid C D; and let the ball contain two bent pipes,
communicating with it at the opposite extremities of a diameter, and bent in
opposite directions, the bends being at right angles and across the lines F G, L
M. As the cauldron gets hot it will be found that the steam, entering the ball
through E F G, passes out through the bent tubes towards the lid, and causes the
ball to revolve, as in the case of the dancing figures.


Click to enlarge the photo
This etching of Hero's steam engine is not from his original manuscript which
has been lost. It was probably produced in the middle ages. It shows steam
forced out of the jets causing the sphere to rotate. It is heated by a fire.
Letters on the diagram match those in Hero's written description.



Click to enlarge the photo
Another etching of Hero's steam engine also probably dates back to the middle
ages.



Click to enlarge the photo
A third, more elaborate, etching of Hero's steam engine. The shape of the pivot
is clearly shown. It is heated by a fire and in this case there is an image of a
man holding the fire under the cauldron which is supported by pedistals in the
image of lions.



What were Hero’s dancing figures?

Number 70 in Hero’s list of designs in Pneumatica was called “Figures made
to dance by fire on an alter”. This worked on the same principal as Hero’s
steam engine, but instead of using steam he used air escaping from a chamber as
it heated up and expanded. The jets were mounted on the floor of a rotating
stage with figures of people dancing mounted on it. Unfortunately in this
drawing, most likely from a later manuscript, the jets appear to be pointing
straight up or straight down. They should remain in the same plane as the stage
floor and tangential to the edge of the floor. Here is Hero's description taken
from the English translation (a,o).

WHEN a fire is kindled on an altar, figures shall be seen to dance: for the
altars must be transparent, either of glass or horn. Through the hearth of the
altar (fig. 70), a tube is let down turning on a pivot towards the base of the
altar, and, above, on a small pipe which is attached to the hearth.
Communicating with, and attached to, this tube are smaller tubes lying at right
angles to each other, and bent at the extremities in opposite directions. A
wheel or platform on which the dancing figures stand, is also fastened to the
tube. When the sacrifice is kindled, the air, growing hot, will pass through the
pipe into the tube, and be forced out of this into the smaller tubes; when,
meeting with resistance from the sides of the altar, it will cause the tube and
the dancing figures to revolve.


Click to enlarge the photo
A woodcut etching of Hero's dancing figures. This works on the same principal as
Hero's steam engine but uses heated air (instead of steam) escaping from jets at
the edges of the dance floor to make it rotate. The jets appear to be drawn at
the wrong angles.They should be in the same plane as the dance floor at a
tangent to the floor. (From Wikipedia.)



Was Hero’s steam engine actually used to do any useful work?

We consider engines today to be machines providing mechanical power to relieve
mankind from manual work. But that was not the intention of the people who
developed the aeolipile. They considered it a scientific experiment. It has been
claimed that Hero’s engine was used to perform useful work, but these turn out
to be incorrect. This is of particular interest because if Hero’s machine had
been recognized as a useful engine it could have been developed and may have led
to more powerful engines resulting in an industrial revolution 2000 years ago.
Instead it seems to have been treated as a novelty or curiosity for centuries.

It was astonishing to read in the Wikipedia article a quote from Mokyre (g)

“Among the devices credited to Hero are the aeolipile, a working steam engine
used to open temple doors”


and another quote from Wood (h)


Two exhaust nozzles...were used to direct the steam with high velocity and
rotate the sphere...By attaching ropes to the axial shaft Hero used the
developed power to perform tasks such as opening temple doors”.


These quotes are clearly a confounding of two of Hero’s devices, as the
Wikipedia article pointed out. Pneumatica (a) did include a machine which opened
temple doors but it did not use Hero’s steam engine or aeolipile. This is how
the temple doors were opened:

In the temple there was an alter where a fire could be lit. As it burned it
heated air in the chamber under the alter. The door hinges were connected to
poles in a chamber underneath the temple and the increasing air pressure from
the alter was transferred by a tube into the chamber where it was connected to
an enclosed vessel full of water. The pressure caused the water to be pushed out
of the vessel into another open vessel or bucket which was connected to ropes
wrapped around the poles. The bucket falling caused the poles to rotate and the
doors to open. When the fire went out, the cooling caused the whole process to
be reversed and the doors closed.

Click on the animated GIF below. It was found on a web site by Lahanas (n) but
the original source for several of the images he used appears to have been lost
as broken links. He said it is an animated image by P. Hausladen, RS Vöhringen
from Neu Ulm in Germany. I have revised the GIF as described in the caption.



Click to view the GIF on its own
An animation showing Hero's mechanism for opening temple doors when a fire was
lit on an alter. It has been modified by using color with red to indicate that
the air was being heated by a fire. It shows that as the air expanded, the air
pressure increased, forcing water out of the reservoir into a bucket. As the
weight of the bucket increased it opened the temple doors. It is also modified
to show the temple doors closing automatically when the fire goes out. From
Lahanas (n). This mechanism has been confused with Hero's engine.



It has also been frequently claimed that Hero’s engine was used by Taqī
Ad-DÄ«n in 1551 to turn meat on a spit (k). But this is also incorrect. The
device he described used steam jets directed at vanes placed on the periphery of
a wheel (m). This is known as an impact steam turbine. (The device for adjusting
the height of cooking vessels over a file was known as a jack and the steam
driven spit was called a steam jack. The life of Taqī Ad-Dīn is described by
Sevim Tekeli (l) and mentions that he was born in Damascus in 1521.)

The question of whether the Hero engine could perform any useful work remained
unanswered until today.


Did Hero actually invent the Aeolipile steam engine?

Woodcroft (a) states in his introduction to the Greek translation that Hero says
his books are a compilation of information from other philosophers with the
addition of some of his own ideas, but he does not specify which ideas are his
own. In the case of the aeolipile steam engine he referred to previous writings
by a Roman author, Marcus Vitruvius Pollio (referred to as Vetruvius), who
described a machine like the aeolipile in De Architectura (f) about 100 years
earlier (He lived about 80 BCE to 15 CE). However, Vitruvius did not give
sufficient detail or drawings to confirm that he was writing about the same
device but he did state its name. He did not mention any moving parts and he
seems to be describing a simple steam boiler:

Aeolipilae are hollow brazen vessels, which have an opening or mouth of small
size, by means of which they can be filled with water. Prior to the water being
heated over the fire, but little wind is emitted. As soon, however, as the water
begins to boil, a violent wind issues forth (f).

It seems clear that he was simply describing steam escaping from a spherical
vessel and recognising that it produced a significant "wind". But there is no
mention of it producing any movement. I do not think he was describing Hero's
engine as we know it. Incidentally, the mention of a "brazen vessel" would
suggest brass, but brass was not defined as a specific alloy at the time. Any
mixture of metals that include copper could be referred to as brass. Modern
brass is an alloy of copper and zinc whereas bronze is an alloy of copper and
tin.

Hero frequently refers to the work of the Ctesibius (285-222 BCE), sometimes
spelled Ktesibios or Tesibius, and for many years it was thought that Hero was
his student in Alexandria. However it is now thought that Hero was alive almost
300 years later in 63 CE.


Why was Hero’s steam engine called an Aeolipile?

The word Aeolipile means the “Ball of Aeolus” and Aeolus (in Greek
Αἴολος) was the Greek god of wind and air. Pila is the Roman word for
ball. It is sometimes spelled aeolipyle or eolipile.


Why did the Greeks build the steam engine?

Vetruvius (f) described the aeolipile as a

“scientific invention [used to] discover a devine truth lurking in the laws of
the heavens… Thus from this slight and very short experiment we may understand
and judge the mighty and wonderful laws of the heavens and the nature of
winds.”

It seems clear that he was describing a scientific experiment rather than
inventing a machine or engine.


Did the Greeks have the technology to utilize the power from Hero’s Engine?

Interestingly they did. The Greeks not only knew about the use of gears and
pulleys but could also carry out all kinds of metal work. An Australian engineer
Chris Ramsay (r) noted the presence of solder in x-rays of the Antikythera
computer (u), and has produced a fascinating series of YouTube videos showing
how they might have built this device, including joining it together with an
alloy of tin and lead, known today as solder (modern solder also contains
antimony).

The Greeks even had lathes. About 100 years before Hero the Roman engineer,
Vetruvius, described a lathe. This consisted of a string wrapped around a shaft
so that as the string was pulled alternately up and down it caused the shaft to
rotate alternately clockwise and anti-clockwise. It was pedal operated with a
foot pedal pulling the string down against a spring loaded lever that pulled the
string back up. A tool was supported on a platform to cut material from the
surface of any material (metal or wood) attached to the rotating shaft. A
translation of the description by Vesuvius follows:

Machine for the finishing of metal or wooden objects giving form on a surface by
their rotation with matter removal. The upper end of the rope wrapping the
object was attached to a flexible yet stable horizontal rod, and the lowest end
was attached to a foot powered axle. The finished metal or wooden object rotated
counter-clockwise with pressing of the foot pedal by the craftsman, and then
clockwise by the restoring force of the rod. The cutting tool, based on the
front horizontal bar, was applied over the rotating piece.

The image below is a photo taken by Augusta Stylianou of a model made by
students and described by Lahanas, in References (o) to (u), as from an "Ancient
Greek Technology" exhibition at the Evagoras & Kathleen Lanitis Centre in Carob
Mill Limassol, [showing] Replicas and Reconstruction by Prof. Kostas Kotsanas
and his students.

A BBC documentary recently showed a similar technique which they think was used
4000 years ago in Dartmore to make wooden ear rings which clearly have turning
marks on them. The Greek lathe reminds me of the tiny lathe my grandfather used
in his car shed with a dirt floor. It used the pedal mechanism of a modified
Singer sewing machine which could spin the work constantly in one direction. His
sheds contained several old Edison cylinder phonographs which were themselves
like lathes with leadscrews.


Click to enlarge the photo
This model of a pedal operated lathe, thought to be used by ancient Greeks, was
made by students of Professor Kostas Kotsanas, photographed by Augusta
Stylianou, and used in a web site by Lahanas. The pedal pulls a string which is
wrapped around the shaft, causing the work to rotate clockwise when the pedal is
pressed. When the pedal is released the string is pulled up by the spring
quality of the bar at the top, causing the shaft to rotate in the
counterclockwise direction. So it alternately rotates clockwise and
counterclockwise.



Another invention described by Hero was the Wind Organ. This included a piston
pump driven by a windmill. The piston pump had already been attributed to
Aristotle who died in 212 BCE nearly 300 years before Hero. Hero also described
an hypodermic syringe for medical use. He was very familiar with the concept of
pistons and could have been very close to inventing a steam engine using
pistons.


Click to enlarge the photo
Hero's wind organ consists of a small windmill driving a piston pump connected
to a pipe organ. With this knowledge of steam and pistons he was tantelizingly
close to inventing a piston operated steam engine.



In fact scholars in Mediteranian and Arabic states throughout the middle ages
studied the Greek scientific literature, including Hero, and it is surprising
that no-one put these ideas together. It is thought that the reason is, not the
lack of knowledge, but a belief that such things were not needed. In fact it was
felt to be dangerous to introduce labor-saving machines when most of the
population were slaves who could revolt if set free from labor.


Did the Greeks know about gears and pulleys?

Emphatically yes! The best example is the Antikythera which is considered to be
the first known analogue computer. It was used to very accurately predict the
movement of all the bodies in the known universe at the time and could predict
eclipses of the sun and moon. It was found in a ship wreck in 1901 and x-ray’s
reveal that it is made up of dozens of intricate intermeshing gear wheels and
levers, much more complicated than a mechanical watch or clock. The engineering
skill in building this device is very impressive and involved soldering as well
as gear making. It has been argued (w) that they did not have the advantages of
modern gear design to reduce friction and handle heavy loads, and yet they did
have a design for lifting heavy weights with gears. Perhaps we tend to be a bit
arrogant but engineers say it is doubtful that this design with triangular gears
rather than the involute curves of modern gears could handle heavy loads.

The astronomy and mathematical knowledge required to build the Antikyther is
equally complex and may date back to work done by the Babelonians. It’s
mechanism has been found to work on dates from 205 BCE and that is thought to be
the date of manufacture as well (s). Interestingly that coincides with the life
of Archimedes who was killed when the Romans invaded Syracuse in 212 BCE, and he
may be the inventor of the Antikythera. It is thought that he did design other
similar objects. However he did not personally write about any of his work.

Hero also described an odometer in his book Dioptra (n) for measuring the
distance that a cart traveled by road and this utilized worm gears. It was also
described by Vetruvius and may have been invented by Archimedes. The Roman mile
was 5000 feet. (The British changed their definition of a mile to 5280 feet so
that it could be divided into furlongs which was their preferred measurement of
land.) Interestingly a wheel 4 feet in diameter revolving 400 times measured
5026.5 feet which was considered to be close enough to a Roman mile. The wheel
had a peg that tripped a pegged gear wheel to move by one peg each time the
wheel rotated. The gear wheel was attached to a worm gear mechanism which drove
another shaft, which drove three more worm gears and shafts in series. The
final, geared down shaft rotated a horizontal disc with many holes containing
stones. When the disk rotated and one of these holes lined up with a stationary
hole, a stone dropped through the hole into a container. At the end of the
journey the number of miles traveled was equal to the number of stones in the
container.


Click to enlarge the photo
A sketch of an odometer following the design of Hero and others. It could
measure how many miles the cart had traveled. (From Lahanas (n)).



Click to enlarge the photo
Another sketch of Hero's odometer showing four worm gears in series (From
Lahanas (n).



Another device called the Baroulkos (q) designed for lifting heavy weights was
described by Hero and has been reviewed in an article in Scientific American
(p). It was operated by a crank which turned a worm gear, which then turned a
series of four pairs of gear wheels to reduce the speed of rotation and this
increase torque. The last gear was connected to a spool and rope to lift the
weight. This, or a similar device, could have easily been connected to a
Hero’s steam engine. In fact, my design with a worm gear parallels the design
of the Baroulkos and odometers.



Click to enlarge the photo
A mechanical gear reduction winch known as a Baroulkos with 4 sets of gears with
two gear wheels in each stage and driven by a worm gear. (From Lahanas(n)).



What did Hero know about gases?

Heros two-volume work Pneumatica was all about devices and inventions based on
behaviour of gasses, air and steam. The English translation of Hero’s
Treastise on pneumatics (a) gives a wonderful description of how air can be
compressed. Considering that it was nearly 2000 years before Boyle developed his
gas law describing the relationship between pressure, volume and temperature and
the modern understanding of atoms and molecules, this text is amazing. There was
a controversy in the time of Hero about whether vacuum really exists. At the
time they thought of air, earth fire and water as the primary elements of
nature. There was a group who thought that all matter consisted of tiny
indivisible particles which they called atoms. Hero apparently agreed with these
'atomists'.


Now the air, as those who have treated of physics are agreed, is composed of
particles minute and light, and for the most part invisible. If, then, we pour
water into an apparently empty vessel, air will leave the vessel proportioned in
quantity to the water which enters it. This may be seen from the following
experiment. Let the vessel which seems to be empty be inverted, and, being
carefully kept upright, pressed down into water ; the water will not enter it
even though it, it be entirely immersed : so that it is manifest that the air,
being matter, and having itself filled all the space in the vessel, does not
allow the water to enter. Now, if we bore [a hole in] the bottom of the vessel,
the water will enter through the mouth, but the air will escape through the
hole… Hence it must be assumed that the air is matter. The air when set in
motion becomes wind, (for wind is nothing else but air in motion), and if, when
the bottom of the vessel has been pierced and the water is entering, we place
the hand over the hole, we shall feel the wind escaping from the vessel ; and
this is nothing else but the air which is being driven out by the water. It is
not then to be supposed that there exists in nature a distinct and continuous
vacuum, but that it is distributed in small measures through air and liquid and
all other bodies. …The particles of the air are in contact with each other,
yet they do not fit closely in every part, but void spaces are left between
them, as in the sand on the sea shore: the grains of sand must be imagined to
correspond to the particles of air, and the air between the grains of sand to
the void spaces between the particles of air. Hence, when any force is applied
to it, the air is compressed, and, contrary to its nature, falls into the vacant
spaces from the pressure exerted on its particles: but when the force is
withdrawn, the air returns again to its former position from the elasticity of
its particles,… bodies will have a rapid motion through a vacuum, where there
is nothing to obstruct or repel them, until they are in contact. Thus, if a
light vessel with a narrow mouth be taken and applied to the lips, and the air
be sucked out and discharged, the vessel will be suspended from the lips, the
vacuum drawing the flesh towards it that the exhausted space may he filled. It
is manifest from this that there was a continuous vacuum in the vessel.


When did Hero of Alexandria live?

At the time of the translation of Hero’s two books called ’Pneumatica’ by
Bennet Woodcroft in 1851 it was not known when he lived. It was thought that he
had been a pupil of Ctesibius of Alexandria which would place him in about 150
BC to 270 BC and these dates are sometimes quoted even today. But Hero’s most
important work on geometry ‘Mechanica’ was lost until 1896 and according to
Encyclopedia Britanica it wasn’t until 1949 that it was revealed by Boas that
Hero reported in his book ‘Dioptra’ an eclipse of the moon on March 13th 63
CE (most modern texts say 62 CE).

It is now assumed that he was alive at the time of that eclipse and might been
born about 10-20 CE and would have died about 70-100 CE, but it is possible that
he lived some time later. Hero was interested in the local time recorded for an
eclipse in Alexandria and Rome so that he could describe how to calculate the
distance between the two cities based on spherical geometry. The actual data was
less important than the method he was describing, and Sidoli (c) quotes Hero as
saying:

“Now, let the same lunar eclipse have been observed at Alexandria and Rome. If
one is found in the records, we will use that, or, if not, it will be possible
for us to state our own observations because lunar eclipses occur at 5- and
6-month intervals.”


What did Hero look like?

No-one really knows. The drawing universally used to depict Hero was in fact
created by a German artist in the 1700’s. It appears to be purely an artists
impression of what a Greek philosopher should look like (t,n). Claims that his
parents moved from Greece to Egypt in 10CE is pure conjecture based on
historical events which occurred about the time of his estimated date of birth.


Click to enlarge the photo
A drawing that has been used since the 1700s to show what Hero might have looked
like Actually there is no description of him in the literature.



Was Hero actually Greek?

Hero or ‘Heron of Alexandria’ is considered a philosopher and polymath which
means he was skilled in many different fields of study, but today we would
probably call him an engineer or scientist. He lived in Alexandria on the
northern coast of Egypt, but Alexandria at the time was under Roman rule after
being annexed by the Romans. Roman influence in Egypt dates back to 3500 CBE.

Hero wrote in Greek and is therefore described as Greek, but since most of the
previous literature had been written in Greek he would have to be able to read
and write in Greek. That doesn’t necessarily mean that he was of Greek ethnic
origins. Woodcroft in 1851 pointed out that there was no mention of his origins
in the literature and no description of his appearance. Greek was commonly
spoken in Rome. Today English is the language used in most scientific literature
but just because a scientist publishes in English does not mean that he is from
England. Similarly Latin used to be the common language for academics, but does
not have anything to do with ethnic origins.


Why is he called either Hero or Heron of Alexandria?

Paul Smith provided the explanation on another YouTube channel. The word can be
spelled either way, depending on how it is used in a sentence. Quote: "Both
spellings and pronunciations are accepted in English. I believe this confusion
has to do with case endings in Hellenistic Greek grammar between the nominative
and accusative case. Depending on the place or role of the name in the sentence
e.g. subject ,object of the verb, possessor or owner (genitive case ending), or
object of a preposition (dative case ending) determines the ending of the name."

Where did Hero work?

It is thought that he would have studied and later taught in the Mouseion
(Museum) associated with the Temple of Serapis or the Serapion which was the
Temple of the nine Muses (d). The Muses were Greek godesses, the nine daughters
of Zeus, who promoted nine branches of the arts, but are now considered to
support all learning and study. This temple was actually more like a modern
university campus (e) and included the Great Library of Alexandria which
contained huge numbers of scrolls and documents of the ancient world.
Unfortunately the library was later destroyed by fire. It is thought that
Hero’s many books were actually collections of lecture notes that he used for
teaching. Alexandria is a city on the Mediteranean coast of Egypt founded in 331
BCE by Alexander the Great when it was taken over by Rome. It is particularly
famous as the place where Pharos resided, for the Great Library of Alexandria
and an ancient lighthouse.


What copies of Hero’s manuscripts still exist today?

Hero wrote at least a dozen major works and the aeolipile was the 50th of 78
devices or inventions mentioned in his treatisse 'Pneumatica'. Copies of
Hero’s works were the most important scientific books read throughout the
middle ages. About a 100 copies of Pneumatica are known to exist in various
translations but the oldest was produced in about the 13th century. It is known
as Codex Gr.516 and is held in the Bibliotheca Marciana in Venice (i).

The first full version produced by a printing press was the Latin translation by
Frederico Commandino in 1575 and soon after that there was a version printed in
Italian by Bernadino Baldi in 1579 (i). A paraphrased version of the beginning
of Pneumatica had been printed in Venice in 1501 by Valla (i).

When Woodcroft (a) prepared his English translation he had many versions in
Latin and Italian to compare with the copy of a Greek manuscript. Each of these
included drawings and in his translation he used the best drawings available or
drew his own. So although it is said to be an English translation of the
original Greek manuscript, he actually only had a copy of the original produced
by hand and it included obvious copying errors. He had to suplement it with
information and drawings reproduced in many different translations and copies.

Some of Heros works include:
 * Pneumatica on gases
 * Dioptra including optical instruments and surveying the land and stars
 * Mensurae on measurement
 * Mechanica on mechanical devices
 * Belopoieca on engines of war
 * Catoptrica on propogation of light and laws of reflection
 * Geometrics on geometry
 * Stereometrica on geometry
 * Geodaesia
 * Definitiones
 * Metrica was three books of geometric rules and formulas
 * Liber Geeponicus (similar to Metrica)


References

URL links can be clicked to find the reference online in most cases.


a. Woodcroft (1851) (Hero's Steam Engine is item 50)
The Pneumatics of Hero of Alexandria from the Original Greek - Translated by
Woodcroft. Gutenberg.org or
https://web.archive.org/web/20080514090439/http://www.history.rochester.edu/steam/hero/index.html

b. Boas (1949):
"Hero's Pneumatica: A Study of its Transmission and Influence, Isis 40, no. 1
(1949) 38-48. https://www.historyofinformation.com/detail.php?id=10

c. Sidoli (2005):
https://individual.utoronto.ca/acephalous/Sidoli_2005.pdf

d. Anon.
https://www.ancient.eu/alexandria/

e. Anon.
https://www.ancient-origins.net/ancient-technology/hero-alexandria-and-his-magical-jugs-001852

f. Vitruvius
"De Architectura", Chapter VI (paragraph 2) from Ten Books on Architecture by
Vitruvius (1st century BC), published 17 June 2008.

g. Mokyr, Joel (2001).
Twenty-five centuries of technological change. London: Routledge. p. 11.
ISBN 0-415-26931-8. “Among the devices credited to Hero are the aeolipile, a
working steam engine used to open temple doors”. Quoted in
https://en.wikipedia.org/wiki/Hero_of_Alexandria

h. Wood, Chris M.; McDonald, D. Gordon (1997).
"History of propulsion devices and turbo machines". Global Warming. Cambridge,
England: Cambridge University Press. p. 3. ISBN 0-521-49532-6. “Two exhaust
nozzles...were used to direct the steam with high velocity and rotate the
sphere...By attaching ropes to the axial shaft Hero used the developed power to
perform tasks such as opening temple doors”
Quoted in https://en.wikipedia.org/wiki/Hero_of_Alexandria

i. Anon.
https://www.historyofinformation.com/detail.php?id=10

j. Black, John 21 March 2014.
https://www.ancient-origins.net/ancient-technology/ancient-invention-steam-engine-hero-alexandria-001467

k. Anon.
https://en.wikipedia.org/wiki/History_of_the_steam_engine quotes Tekeli, Sevim
(2008) below.

l. Tekeli, Sevim (2008).
"Taqī Al‐Dīn". Encyclopaedia of the History of Science, Technology, and
Medicine in Non-Western Cultures. Springer, Dordrecht. pp. 2080–2081.
doi:10.1007/978-1-4020-4425-0_9065. ISBN 978-1-4020-4559-2.

m. Anon.
https://en.wikipedia.org/wiki/Taqi_ad-Din_Muhammad_ibn_Ma%27ruf

n. Michael Lahanas

http://www.hellenicaworld.com/Greece/Technology/en/HeronAlexandria.html

o. Michael Lahanas

http://www.hellenicaworld.com/Greece/Technology/en/InventionsA.html

p. André Wegener Sleeswyk
"Vitruvius' Odometer", Scientific American 245(4) October, 1981, pp. 188-200

q. Michael Lahanas (The Baroulkas)
http://www.hellenicaworld.com/Greece/Technology/en/AncientGreekTechnology012.html

r. Chris Ramsay
http://www.ClickSpringProjects.com

s. Anon.
“The World's Oldest Computer Just Got Older”
https://www.engineering.com/DesignerEdge/DesignerEdgeArticles/ArticleID/9113/The-Worlds-Oldest-Computer-Just-Got-Older.aspx?ENGCOM=

t. Anon.
https://en.wikipedia.org/wiki/Hero_of_Alexandria

u. Michael Lahanas (Antikythera)
http://www.hellenicaworld.com/Greece/Museum/NationalMuseumAthens/en/NationalArchaeologicalMuseumAthens.html

v. John R. Bentley 2007
https://modelengines.info/aeolipile/

w. Achilleas Vortselas
https://www.quora.com/How-would-the-world-today-be-different-if-the-aeolipile-device-steam-engine-invented-in-60-AD-had-been-developed-further

x. Matt Rigsby
https://www.quora.com/Has-the-aeolipile-ever-been-put-to-practical-use

y. Roy Brander (2007)
www.cuug.ab.ca/branderr/eeepc/017_coal.html
Steam efficiency graph showing doubling every 60 years.


References used for calculations in the appendices

1. Critical Pressure
www.physicsforums.com/threads/at-what-pressure-does-steam-exiting-a-nozzle-reach-mach-1.843944/#post-5293979

2. Choked Flow
https://en.wikipedia.org/wiki/Choked_flow

3. Equations for mass flow through nozzles
http://www.engineeringtoolbox.com/nozzles-d_1041.html

4. Properties of steam
http://help.syscad.net/index.php/Water_and_Steam_Properties#Introduction

5. Velocity of air coming out of a nozzle and choked flow.
https://www.physicsforums.com/showthread.php?t=694656

6. Calculation of Thrust from a jet in an aeolipile
https://www.physicsforums.com/threads/need-help-with-project-similar-to-a-sprinkler.744967/

7. Pipe flow calculations
http://www.pipeflowcalculations.com/airflow/

8. Thrust Calculations by NASA
https://www.grc.nasa.gov/www/k-12/airplane/thrsteq.html

9. Physical properties of gases
https://browkinnari.files.wordpress.com/2015/07/handbook-of-physical-properties-of-liquids-and-gases-pure-substances-and-mixtures.pdf

10. Calculation of material strength required for a Pressure vessel (Boiler)
https://en.wikipedia.org/wiki/Pressure_vessel#Scaling_of_stress_in_walls_of_vessel

11. Yield Strength and Ultimate tensile strength of copper
https://en.wikipedia.org/wiki/Ultimate_tensile_strength

12. Design, safe operation, maintenance and servicing of boilers in New Zealand
https://worksafe.govt.nz/topic-and-industry/machinery/working-safely-with-boilers/).




Privacy Policy, Copyright Policy and End User License Agreement (EULA)

This is an agreement between the user and the web site developer (`The
Developer` who is identified below).


The Web Site

Operating under the domain name `HeroSteamEngine.com` is a web page and is
intended to be used freely by anyone. It is referred to here as the `site`.


Free Site - No Fees:

The site can be used by any user free of charge. However, if it is used by any
commercial entity or activity that generates income it would be appreciated if a
donation could be made. The Developer has a Patreon page for contributions.


Limited Liability:

The developer cannot be held liable for any errors, inaccurate or omissions from
the Site.


Copyright:

If text, tables or images on this site are reproduced in any form, credit should
be given to "Evan Lewis, developer of HeroSteamEngine.com" or similar text. An
email notification to 'The Developer' would be appreciated if such material is
used or a link provided to this site.


Privacy Policy:
No Cookies and No Log-in

• This site does not record any personal details, personal information or
financial information about the user.
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recorded and cannot be passed on to third parties.
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If so the counter does not record it as a visitor to the site. The IP address is
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• Advertising may be included in this site and the user is referred to the
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Purpose of the EULA:

This is a binding legal agreement between The Developer and the online user.
It also describes the privacy policy, liability waiver and copyright notice.


Contact Information:

The phrase `The Developer` refers to Anthony Evan Lewis PhD, MD who can be
contacted at AEDLewis at gmail dot com.
He is a New Zealand Citizen and was physically located in New Zealand when this
software was written and uploaded.
Any legal issues must be addresses in New Zealand courts unless alternative
arrangements are mutually agreed by all parties involved.




Video: History of the development of steam engines
(one hour presentation with videos, animated graphics and photos)





Video: Using an engineer's lathe

In these short YouTube videos I am using the engineer's lathe to make all the
parts for the Hero Steam Engine. It includes several special techniques such as
spinning copper into a bowl shape from a flat sheet, and making the gear wheel
for the worm drive gear box. The methods apply to any engineering lathe. The
model I am using is a 1955 Boxford Model A Mark 1.




Season 1 Part 1: Introduction to the tutorial How to use a Boxford engineers
lathe



Season 1 Part 2: The knobs and levers on a Boxford lathe 1953



Season 1 Part 3: Setup Options for the Boxford Lathe



Season 1 Part 4: Planning the project to build a Hero's Steam Engine



Season 1 Part 5: Parting and Facing using a Boxford lathe



Season 1 Part 6: Facing the end to the correct length



Season 1 Part 7: Use of a four-jaw chuck and dial gauge on a Boxford lathe.



Season 1 Part 8: Drilling and tapping a hole at 120º with 4 jaw chuck on the
Boxford lathe



Season 1 Part 9: The boiler, valve, filler cap and rotor of the Hero steam
engine




Season 2 Episode 1: An easy method for making gear wheels and worm gears




Season 2 Episode 2: Cutting a thread




Season 2 Episode 3: Overhauling the lathe head and back gear




Season 2 Episode 4: Re-assembly of the lathe head




Season 2 Episode 5: How to set up a reversing switch for a single phase motor




Season 2 Episode 6: Basics of gear train calculations.
(See notes for a simplified method)




Season 3 Episode 1: Installing a milling attachment on an engineers lathe



Season 3 Episode 2:Making a simple indexing wheel from a circular saw blade



Season 3 Episode 3: Turning a taper by the tailstock offset method to make a
Morse taper.



Season 3 Episode 4: Making a dedicated tool post for cutting off (parting) on an
engineers lathe.



Season 3 Episode 5: Repairing a BOSTAR quick-change tool post.



Season 3 Episode 6: Dismantling, lubricating and re-assembling the Three-jaw,
self-centering chuck.



Season 3 Episode 7: Softening copper by annealing prior to spinning on a lathe.



Season 3 Episode 8: Flaring a copper sheet before brazing tubes into the boiler.



Season 3 Episode 9: The Hero's steam engine lifting a weight
(The same video shown at the top of this page).









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Contact me by email


AEDLewis@gmail.com AEDLewis@gmail.com


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