The Steam Engine Rome Didn't Use
About 2,000 years ago, in Alexandria, a Greek-speaking city in the Roman Empire, an engineer named Hero wrote down how to make a metal ball spin by itself. Boil water in a sealed pot, pipe the steam into a hollow ball, and let the steam escape through two bent nozzles. The ball whirls around.
That ball is a steam engine. It came more than 1,600 years before steam engines started pumping water out of English coal mines and helped launch the Industrial Revolution. For all those centuries, the spinning ball changed almost nothing.
Make your guess. Why didn't Hero's steam engine change the world?
- The Roman government banned it to protect workers' jobs
- Hero's design was lost and forgotten until the 1700s
- The world around the sphere wasn't ready for an engine yet
Show answer
C. The world around the sphere wasn't ready for an engine yet
The world wasn't ready. No law banned steam, and the design wasn't lost: copies of Hero's book survived, and a Latin translation was printed in 1575. The sphere was missing almost everything else an engine needs, and finding those missing pieces is what this page is about.
Start with the sphere itself. How fast can you make it spin?
Fire up the sphere
Your goal: get the sphere past 3,000 turns a minute using the heat and the nozzle size. Keep an eye on the pressure gauge.
More heat makes more steam, and more steam spins the ball faster. A narrower nozzle helps too, up to a point. Past that point the pressure inside gets too high, and steam hisses out of the joint where the ball turns.
But nothing pushes on the ball from outside. Steam simply leaves through the nozzles. So what is actually pushing the ball around?
Push back, go forward
Let go of a blown-up balloon and it zooms off. Air rushes out of the neck one way, and the balloon shoots the other way. Each nozzle on Hero's sphere does the same thing with steam.
To throw the steam backward, the nozzle has to push on the steam. The steam pushes back on the nozzle just as hard, in the opposite direction. That pairing of pushes is Newton's third law: every push comes with an equal push back, called action and reaction. Rockets and jet engines fly the same way.
With the same fire under the pot, why does a narrower nozzle spin the sphere faster?
- A narrow nozzle makes more steam
- The same steam has to squeeze through a smaller hole, so the steam leaves faster and pushes harder
- A narrow nozzle makes the sphere lighter
Show answer
B. The same steam has to squeeze through a smaller hole, so the steam leaves faster and pushes harder
The fire sets how much steam is made each second. Through a smaller hole, that steam must leave faster, and faster steam carries more push. The cost is pressure: squeezing steam through a tiny hole takes a harder shove from inside the ball, and the joint leaks.
So Hero had a working steam engine. Why not build a big one and put it to work?
A toy, not a motor
Look under "Numbers for nerds" in the sphere widget: the sphere turns only a fraction of a percent of the fire's heat into spinning. The ball whirls fast but pushes gently. Hook the ball to a millstone, and the ball would simply stop.
Hero himself doesn't say what the sphere was for. His book, the Pneumatics, lists it among 78 devices: temple doors that open by themselves, singing toy birds, a coin-operated water dispenser. He compares the sphere's spin to his "dancing figures" on an altar. Some writers call the sphere a temple wonder and others a teaching demonstration. No one knows for sure.
Light a fire under a covered pot of water. The steam runs up a bent pipe into a hollow ball that sits on a pivot. Two bent tubes on the ball, pointing opposite ways, let the steam out, and the ball turns.
Hero's recipe, item 50 of the Pneumatics, in our words
A better nozzle wouldn't have fixed the sphere. What else was missing?
Four missing ingredients
An invention needs more than a clever idea. The world around the idea has to be ready too. Hero's world was short of four ingredients:
- Cheap fuel. Wood and charcoal were cut and carried by hand. An engine that burns fuel all day only pays when fuel costs almost nothing.
- Materials that hold pressure. The sphere was thin metal with soldered joints. You saw the problem in the widget: raise the pressure and the joints leak.
- A real need. Muscle was cheap: workers, many of them enslaved, plus oxen, mules and water wheels.
- The right ideas. Nobody yet knew that the air presses on everything, about 10 tonnes on every square metre. That was discovered in the 1640s.
One Roman story hints at the third ingredient. The writer Suetonius tells of an engineer who offered the emperor Vespasian a cheap machine for hauling huge columns. Vespasian paid the engineer for the idea but turned the machine down: he had to let the common people earn a living. Historians still argue about how much cheap labour really held back machines.
A myth to skip: "The ancients had no pistons or valves"
They did. In the same book, Hero describes a fire pump with two bronze cylinders, bored smooth on a lathe to fit pistons, and flap valves to keep the water flowing one way. Roman fire pumps of this kind really existed.
So the parts were there. What nobody had done was join steam, a piston and the push of the air into one machine.
Once the push of the air was understood, all four ingredients came together in one place within 70 years. Where?
Coal, water and air
In England around 1700, coal mines had a problem. The deeper the miners dug, the more groundwater flooded in, and pumps turned by horses struggled to keep up. A mine full of water is a mine full of coal no one can reach.
In 1712, Thomas Newcomen, an ironworker from Dartmouth, and his partner John Calley set up an engine at a coal mine near Dudley Castle. All four ingredients were there. The fuel was coal, dug right at the mine. The need was urgent. And the engine relied on the newly understood push of the air, so the engine never needed high pressure or perfect metal.
Newcomen's trick: fill a cylinder with steam, then spray in cold water. The steam turns back into a few drops of water, leaving almost nothing below the piston. The air above pushes the piston down, and a giant rocking beam lifts water out of the mine.
Your goal: pump the mine dry with Newcomen's engine, and count the coal. Then switch to Watt's engine and pump the mine again.
Newcomen's engine was hungry: every cold spray chilled the cylinder, and the next load of steam was mostly wasted warming the metal back up. At a coal mine, nobody cared much. By the time Newcomen died in 1729, more than 100 of his engines were at work across Europe.
Away from the coal mines, fuel cost real money. Could an engine work without chilling its own cylinder?
Watt keeps it hot
In 1765, James Watt, an instrument maker in Glasgow, was repairing a model Newcomen engine when he saw the fix: cool the steam in a separate box, a condenser, so the cylinder stays hot. Built with his partner Matthew Boulton from 1776, Watt's engine used about 75% less fuel than a Newcomen engine of the same size.
Watt needed a better ingredient too: cylinders that fit their pistons closely. In 1774, the ironmaster John Wilkinson found a way to bore big iron cylinders far more accurately. By the 1780s, Watt's engines could also turn wheels, and steam moved from the mines into mills and factories.
Notice the order: the engines came first, and the science of heat came later. How does the push of steam turn into numbers?
How it really works
In 1824, the French engineer Sadi Carnot wrote a short book asking how much work any engine could ever get from heat. His question started the science of heat and work, thermodynamics.
Every push from a jet comes from the same rule. Each second, the nozzle throws out a mass of steam \(\dot m\) at speed \(v\), and the push back on the nozzle is:
Show the full working (try it yourself first)
- Steam made each second. Boiling water takes about \(L = 2.26\) million joules for every kilogram. A fire that puts \(P\) watts into the pot makes steam at a rate of
\[ \dot m = \frac{P}{L} \]2. How fast the steam leaves. Steam of density \(\rho\) squeezing through nozzles of total area \(A\) must leave at
\[ v = \frac{\dot m}{\rho A} \]3. The push. Each second the nozzle gives momentum \(\dot m v\) to the steam, so the steam gives the same push back:
\[ F = \dot m\,v = \frac{\dot m^2}{\rho A} \]Halve the nozzle area and, with the same fire, the push doubles.
- The price of a narrow nozzle. Speeding the steam up to \(v\) takes a pressure inside the ball of about
\[ \Delta p \approx \tfrac12 \rho v^2 \]So a jet twice as fast needs four times the pressure, and the joint starts to leak.
- The spin settles. The sphere speeds up until the jets' turning force is used up by friction in the pivot and drag from the air. Most of the fire's heat simply leaves with the warm steam, so well under 1% becomes spinning.
- Newcomen's push. The air presses with about \(p = 101{,}000\) pascals. On a piston half a metre across (area about \(0.2\ \text{m}^2\)), the push is
\[ F = pA \approx 101{,}000 \times 0.2 \approx 20{,}000\ \text{N} \]about the weight of two tonnes, with no high-pressure steam at all.
- Carnot's limit. No engine working between a hot temperature \(T_h\) and a cold one \(T_c\) (in kelvin) can turn more than this fraction of its heat into work:
\[ \eta_{\max} = 1 - \frac{T_c}{T_h} \]For steam at 373 K cooled by water at 288 K, the limit is about 23%. Estimates for Newcomen's engine are around 1% or less.
Steam waited 1,600 years for its ingredients. Is that just ancient history, or do modern inventions get stuck the same way?
Too early, again
Electric cars
Around 1900, about a third of the vehicles on American roads were electric. Electric cars were quiet, clean and easy to start. Then cheap Texas oil arrived, Ford's Model T sold for $650 in 1912 against $1,750 for an electric roadster, and an electric starter got rid of the gas car's hand crank. By 1935, electric cars had all but disappeared.
Today the story has flipped. Light lithium-ion batteries got far cheaper, chargers spread, and in 2025 about one new car in four sold worldwide was electric.
Video calls
In 1964, AT&T showed its Picturephone at the New York World's Fair. A three-minute call between public video rooms cost $16 or more, and the rooms hosted just 71 calls in their first six months. AT&T ended the service in 1973.
More than fifty years later, cameras sat in every phone, internet lines were fast, and the pandemic of 2020 sent work and school home. Zoom went from about 10 million daily meeting participants in December 2019 to more than 200 million in March 2020.
Your goal: for each invention, pick an era and make your call: does the invention take off for good? Then see which ingredients were ready.
Every flop on the board is missing at least one ingredient. The electric car of 1900 had most of them, but its batteries, its range and the electricity outside cities were only "partly" there, so a better-equipped rival won.
Hero, the electric car makers of 1900 and the Picturephone engineers weren't wrong. Each had the right idea at the wrong time. So what should an inventor do with an idea the world isn't ready for?
Why you keep trying
Keep trying, and keep watching the ingredients. Newcomen built on Thomas Savery's steam pump of 1698 and on Denis Papin's piston of 1690, and Watt started by repairing Newcomen's engine. Today's electric cars stand on a century of battery work. None of those early "failures" was wasted.
Now you can explain the spinning ball. Steam thrown backward out of a nozzle pushes the nozzle forward: action and reaction. The sphere worked, but Hero's world lacked cheap fuel, strong metal, a pressing need and the knowledge that air pushes. When a flooded coal mine brought all four together, Newcomen's engine took off, and Watt's condenser made engines cheap enough to run almost anywhere.
Where to go next
A spinning ball opens a lot of doors. Here are the questions worth chasing next:
- What is heat, really, and why can no engine turn all of its heat into work?
- How does a jet engine use the same push as Hero's sphere, only millions of times stronger?
- Why do most power stations still boil water to make electricity?
- Which inventions today are waiting for one missing ingredient?
- What other clever machines did the ancient world build and then forget?
What to learn next: Newton's third law and momentum first, then thermodynamics: heat, work and Carnot's limit. Both are part of AP Physics and most high school physics courses. After that, search for "steam turbine" to see how Hero's jets came back in modern power stations, "Antikythera mechanism" for another ancient machine far ahead of its time, and "diffusion of innovations" for how new ideas spread.
To see Newcomen's engine in motion, watch Branch Education's animated explanation:
Ask Phy
- Why does a narrower nozzle push harder with the same fire? Walk me through F = ṁv.
- How did Watt's separate condenser save so much coal? Explain it with heat and temperature.
- Use the four ingredients from this page to judge an invention I'm thinking of.
Sources
- The Pneumatics of Hero of Alexandria (B. Woodcroft, ed., 1851), Project Gutenberg — No. 50, the steam sphere; no. 27, the fire pump with pistons and valves; the list of temple gadgets.
- Aeolipile (Wikipedia) — Vitruvius's earlier aeolipile; no known practical use in ancient times.
- Hero of Alexandria (Wikipedia) — Dating by the eclipse of 62 AD, and how uncertain it is.
- Suetonius, Life of Vespasian, section 18 (LacusCurtius) — The engineer and the columns.
- K. Greene, Technological innovation and economic progress in the ancient world: M. I. Finley re-considered, Economic History Review 53 (2000) — The debate over slavery and ancient technology.
- Newcomen atmospheric engine (Wikipedia) — How the engine works, about 12 strokes a minute, Savery and Papin.
- Thomas Newcomen, Scientist of the Day (Linda Hall Library) — The 1712 engine near Dudley Castle, with John Calley.
- The Newcomen engine and its role in Britain's industrial revolution (National Museums Scotland) — At least 100 engines in use by 1729.
- Watt steam engine (Wikipedia) — The condenser (1765), Wilkinson's boring (1774), about 75% less fuel.
- Reflections on the Motive Power of Fire (Wikipedia) — Carnot's 1824 book.
- The History of the Electric Car (US Department of Energy) — A third of vehicles around 1900; $650 against $1,750; gone by 1935.
- Global EV Outlook 2026: Executive summary (IEA) — One in four new cars sold in 2025 was electric.
- Picturephone (Engineering and Technology History Wiki) — The 1964 fair, prices, 71 calls, three pairs of wires, the end in 1973.
- A Message to Our Users (Zoom, April 1, 2020) — About 10 million daily meeting participants in December 2019; over 200 million in March 2020.