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Lift the bonnet of most petrol cars and you will find an engine that repeats four steps over and over: draw in fuel and air, squeeze it, burn it, push the exhaust out. That sequence is called the Otto cycle after Nicolaus Otto, the German engineer who was the first to build an engine on it. This post covers what he built, what his patent actually says, and the physics that explains why compression matters.
Who was Nicolaus Otto?
According to Britannica's biography, Otto was born on 10 June 1832 in Holzhausen, Nassau, and died on 26 January 1891 in Cologne. He built his first engine in 1861. In 1864 he formed a partnership with the industrialist Eugen Langen, and their improved engine won a gold medal at the Paris Exposition of 1867. In 1876 Otto built an internal-combustion engine using the four-stroke cycle.
Britannica is careful about credit. The four-stroke cycle had been patented in 1862 by the French engineer Alphonse Beau de Rochas, but Otto was the first to build an engine on the principle, which is why it carries his name. His engine was reliable, efficient and fairly quiet, and more than 30,000 were built in the following ten years. In 1886 Otto's patent was revoked when Beau de Rochas's earlier patent came to light.
What does Otto's patent describe?
Otto's United States patent No. 194,047, dated 14 August 1877 and assigned from the Gas-Motoren Fabrik Deutz, describes the engine in his own words. Reading it in order gives you the four strokes:
Intake. On the outstroke the piston draws in air, then a mixture of coal gas (or petroleum vapour) and air.
Compression. The flywheel's momentum drives the piston back, compressing the charge into the space at the end of the cylinder.
Power. The charge is ignited and the expanding gas drives the piston outward.
Exhaust. On the next return stroke the products of combustion are pushed out through a valve.
The patent says the valve slide makes one to-and-fro movement "while the piston makes two double strokes". That is the four-stroke idea in one line: one power stroke for every two turns of the crankshaft. Otto also explains that compressing the charge inside the working cylinder lets him "dispense with any such additional compressing mechanism".
Interestingly, the patent spends most of its words on something else: layering the charge so that it burns gradually rather than exploding, which Otto believed reduced shocks and wasted heat.
Why does compression make an engine more efficient?
Physics textbooks model the Otto cycle as two adiabatic strokes (compression and power) joined by heating and cooling at constant volume. The efficiency of this idealised air cycle depends only on the compression ratio r, the ratio of the largest to the smallest cylinder volume:
η = 1 − 1/r^(γ−1)
where γ is the ratio of specific heats, about 1.4 for air. It follows from the adiabatic relation TV^(γ−1) = constant, which you meet in the thermodynamics chapter of Class 11 physics.
Worked example. These are idealised textbook values, not figures for Otto's 1876 engine.
With r = 4: 4^0.4 = e^(0.4 × ln 4) = e^(0.555) ≈ 1.74, so η = 1 − 1/1.74 ≈ 1 − 0.574 = 0.426, or about 43%.
With r = 8: 8^0.4 = e^(0.4 × ln 8) = e^(0.832) ≈ 2.30, so η = 1 − 1/2.30 ≈ 0.565, or about 56%.
Doubling the compression ratio raises the ideal efficiency from about 43% to about 56%. Real engines reach much less because of friction, heat loss and incomplete burning, and petrol engines cannot raise r without limit, because the mixture may ignite too early.
Common mistakes:
Using γ instead of γ − 1 as the power.
Treating r as a pressure ratio. It is a volume ratio.
Applying the Carnot formula 1 − T₂/T₁ with the wrong temperatures. The Otto result and the Carnot limit are different things; our guide to heat engines and the Carnot cycle shows how they compare.
How did Otto's engine lead to others?
The 1877 patent describes an engine running on coal gas or petroleum vapour. The same four-stroke sequence was later adapted for vehicles. Rudolf Diesel took a different route, compressing air alone so hard that the fuel ignited without a spark; our post on Rudolf Diesel and the compression ignition engine tells that story.
What can a student take from Otto's way of working?
Building it counts. Others had described the cycle; Otto made one that worked reliably, and that is what spread.
Credit is not the same as priority. The 1886 ruling is a reminder that ideas often have more than one parent. Read the history before you decide who did what.
Read the primary source. The patent reveals what Otto himself thought was important, which was not the same as what textbooks later stressed.
If the adiabatic steps in the derivation feel shaky, the Fermi Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revise adiabatic processes before coming back to the cycle.
Try it now: calculate the ideal efficiency for r = 10 and see how much you gain over r = 8.
