Diesel engines

In the Maginot Line, the works are equipped with generators driven by spark-ignition engines (primarily Diesel). We thus found useful to create treating document of the technical part of the diesel engines 4 a times.

Plan of the document

- presentation of a cylinder of diesel engine,

- principle of the Diesel at 4 times,

- elements of calculations and calculations,

- application to an engine SMIM of the Line Maginot (work of Fressinea - SFAM-),

- appendices.


We made this study in memory of our father (Gaston Cima), specialist in the diesel engines in the Air force, then professor of thermodynamics to the IUT of Town of Avray. Bernard and Raymond Cima.

It is after having followed the courses of my father (then others) that I supported a thesis of doctorate on the diesel engines, in 1982, at the Pierre University and Marie Curie of Paris. Bernard Cima.

Presentation of a cylinder

Diagram of cylinder

The spark-ignition engine is born at the end of the XIX° century. Two figures are detached at a few years from interval: the French Beautiful of Rochas (1815-1893 patent in 1862) and the Diesel German (1858-1913 patent in 1893). The internal combustion engine was born.

Basic technology is common to both types: the shirt (*), tube closed at an end by the cylinder head (*), comprises a piston (*) mobile which moves between the PMB (Dead bottom centre) and the PMH (Not high dead). Openings bored in the cylinder head comprise obturators, the valves (*), putting on the shirt in communication with the surrounding air. Another opening is used as support with the body which will cause the explosion: the candle (petrol engine) or the injector (*) (diesel engine with gas oil).

Alphonse BEAUTIFUL (1815-1893)

Civil statue

Born in Dignes in 1815, Beau is the son of Alexandre BEAUTIFUL and Lucrèce JACQUES of ROCHAS (old dignoise family).

His/her father, notorious Bonapartist, controller with the Direct taxation, are deposed of his official functions after the abdication of Napoleon. He then has some problems to make live his family and in 1823, the maternal uncle of Alphonse Beau (the knight Henri-Justin de Rochas), to deal with the education of his nephew, under the condition which he carries the two names, governor and maternal: Beautiful of Rochas.

After a life full with bounces, Beau of Rochas dies in Vincennes in 1893.

Professional life

At sixteen years it gains the first price of mathematics of the Royal College of Orleans. Then, Civil engineer, it makes in turn research and of the policy.

On January 16, 1862, Beau of Rochas deposits, near the Company of Industrial Protection, the patent n°52-593 in which he proposes an internal combustion engine at four times:

- aspiration during a whole travel of the piston

- compression during the following race of return

- ignition at the dead point and relaxation during the third race

- repression of waste gases, out of the cylinder, with the last return of piston.

Beautiful of Rochas specifies that the ignition of gas clashing, beforehand compressed, can be caused by a spark or be spontaneous by auto-ignition.

It thus has just described the operation of the future petrol engines (first case of ignition) but not completely that of the diesel engines (second case of ignition) because of the concept of - beforehand compressed gas clashing (see our document on Diesel).

Beautiful of Rochas will never make build such engines. And it is only in 1876 qu ' a German engineer, Nicolas OTTO (1832-1891), carries out the first 4 times with gasoline.

DIESEL Rudolf (1858-1913)

Civil statue

Born in Paris, in 1858, it is wire of a modest couple which leaves France at the time of the war of 1870.

It makes its studies at the polytechnic school of Munich and in fate with the title of engineer.

Rudolph Diesel disappears in full crossing from the English Channel, in 1913, in not yet elucidated circumstances.

Professional life

Engineer in various fields, in 1893 it deposits a patent of internal combustion engine at four times (like that of Beautiful of Rochas), with the difference - important close flammable substance (for this patent it is heavy oil, residue of distillation of oil) which produces the explosion is injected when the air and already compressed by the piston. Moreover this injection the self-ignition of the substance causes, without requiring ignition system.

In 1897, it builds a functional prototype and takes part in creation, in Bar the Duke (Meuse), of - French company of the diesel engines with internal combustion.

In 1900, with the World Fair of Paris, Rudolf Diesel makes turn its engine to the groundnut oil. But as the gas oil is less expensive, this fuel remains anecdotic. This does not prevent Rudolf Diesel from declaring, in 1911, that its engine, thanks to plant oils, will be one day able to strongly contribute to the development of the agriculture of the countries which will use it. He predicts whereas the use of plant oils as carburizing for engines as that of oil will become soon as important. Prophetic declaration?

However, due to difficulties of injections, the output of the engines as good as is not wished and it is the French Lucien Inchauspé (1867-1930) who, by inventing the injection pump in 1924, in fact an engine which will become a few years later very powerful.

The Maginot Line benefits from this increase in output and the petrol engines initially planned for the first forts to be built are replaced by diesel engines.

SMIM 4 cylinders of Holy Agnes (SFAM)


For an engine, if we want to calculate:

- Pressures, volumes and temperatures corresponding to the various points of the cycle,

- The work and the quantity of heat released at the time of the cycle, which will lead to the calculation of the mechanical power at exit of engine,

we need certain data and some pre necessary pointed out below.

Data: manufacturer

The manufacturer of the engine gives, in general, the total cubic capacity (C), the number of cylinders (N) and the volumetric report/ratio (ε), relationship between the maximum volume of the cylinder and his minimum volume. (ε = V1/V2). From these 3 values one draws:

Unit cubic capacity (useful by cylinder) Vu_ = V1 - V2 = C/N

V1 = ε. Vu_/(ε - 1)

V2 = Vu_/(ε - 1)

Data: ambient air

Admission: One defines the pressure and the temperature of the air which enters the cylinder. For an engine - atmospheric the pressure of admission (p1) is equal to the atmospheric pressure (around 100.000 Pa) and for an engine - overfed this pressure depends on turbo or the pump of overfeeding.

Exhaust: it is almost always done with the free air thus the pressure of exhaust is equal to the atmospheric pressure.

Always for this air, one defines 2 thermodynamic sizes:

it constant mass (or of Meyer) R = CP - Cv which is the difference of the specific heat (*) applied to transformations with constant pressure (CP) and constant volume (Cv). For the air R = 287 J/kg/K

it isentropic coefficient γ = CP/Cv = 1,4 for the air.

Before launching out in the numerical values on the various points of the cycle it could seem necessary to measure 2 masses: mass of air entering the cylinder and the mass of gas taking part in the transformations. The difference deserves to stop there one moment.

At the end of the exhaust, the piston is with the PMH but there remains a small volume between him and the cylinder head. Are the gases flarings contained in this volume ejected towards outside or remain in the combustion chamber? In the first case, allowed volume will be equal to (V1) whereas in the second case it is equal to (Vu_). The nuance can appear weak but it influences the calculation of the energy contribution of the gas oil.

For a petrol engine one considers that there remain unburnt gases at the end of the exhaust. But for a diesel, the phenomenon of - sweeping makes that in end admission it does not have there any more but of the air. One is thus led to consider, for a diesel engine, that the mass of entering air is equal to the gas mass taking part in the transformations: m = (p1. V1)/(R.T1) according to the law of Mariotte (*).

Data: fuel

The gas oil (gas oil) is extracted from oil and contains mainly hexadecane (C16H34). For calculations one needs:

- report/ratio (mass of entering air/fuel mass injected) leading to a stoechiometric combustion (*) of the fuel. Here this report/ratio is close to 15.

- calorific value (*) of the fuel, NCV = 44.000.000 J/kg.

Recall on the standardized units employed

They are the following ones:

Mass (m) in kg (kilogramme)

Pressures (p) out of Pa (Pascal)

Volumes (V) in m3 (meter-cubic)

Temperatures (T) in K (Kelvin); for example Centigrade 15° = 15 + 273 = 288 K

Formulas to be applied

Cycle Diesel

Precise details on the thermodynamic transformations

In the diagram, one sees appearing three types of curves:

- Vertical Curve (with telling volume) called isochoric,

- Horizontal Curve (with constant pressure) called isobar,

- Round Curve (arc of exponential) called isentropic or adiabatic.

With each curve a type of calculation corresponds.

Pressure, volume and temperature at each point of the cycle

Between items 1 and 2

Adiabatic compression. It is governed by the law: p1. V1 γ = p2. V2 γ.

As p1 is known, V1, V2 and γ one can calculate p2.

Then, by application of p2. V2 = Mr. R.T2 (law of Mariotte), one finds T2.

Between items 2 and 3

Isobar combustion. As the pressure remains constant p3 = p2

The energy contribution due to the combustion of the gas oil gives a quantity of heat Q 2-3 = mc. NCV (gas oil X mass calorific value).

For an isobar transformation, this term Q 2-3 is equal to [(Mr. R. γ/(γ - 1)] (T3 - T2) what makes it possible to calculate T3 then V3 (with the law of Mariotte).

Between items 3 and 4

Adiabatic pressure drop. One finds the same law as for the transformation 1-2. And as V4 = V1 one can calculate p4 and T4.

Between items 4 and 1

Isochoric relaxation. No calculation is necessary since one falls down on the item 1 which one knows already the characteristics.

Work and quantity of heat

Seek the energies implemented during the cycle

Between items 1 and 2

Mechanical work (to be provided to the piston so that it compresses gas) is equal to W 1-2 = [(Mr. R)/(γ - 1)] (T2 - T1)

Calculation is easy since all the terms are known. This work is positive. It is expressed in Joule (J).

The quantity of exchanged heat, Q 1-2 is equal to 0 (by definition of an adiabat).

Between items 2 and 3

Mechanical work provided by gas, which involves the displacement of the piston, is equal W 2-3 = - Mr. R (T3 - T2). This work is negative.

The quantity of heat was already above defined; it is equal to the energy contribution of the gas oil.

Between items 3 and 4

As for phase 1-2, W 3-4 = [(Mr. R)/(γ - 1)] (T4 - T3). This work is negative. There still Q 3-4 = 0.

Between items 4 and 1

Mechanical work is null and Q 4-1 = [(Mr. R)/(γ - 1)] (T1 - T4). This quantity of heat is negative.

Assessment of the cycle

Work: a cycle - engine must give a negative sum of W. The absolute value of this sum |Σ W| corresponds to the driving work of the cycle. The first principle of thermodynamics specifies that Σ W + Σ Q = 0

Power: the engine turns at a rotational frequency NR (tr/min); a cycle corresponding to 2 turns, the duration of a cycle (in seconds) is thus equal to Δt = 120/NR. the power being, by definition, the report/ratio of work at the duration, one a: P = |Σ W|. NR/120 (P in Watt)

To obtain the total power of the engine, it is finally necessary to multiply the preceding result by the number of cylinders.

And afterwards?

It does not remain any more that to program a calculator, with these formulas, to give him the characteristics relating to the studied engine, and one obtains the numerical values corresponding to the various points of the cycle of this engine.

Principle. 4 times of a diesel engine

Animation of the image?

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It is noted that there is more than 4 - time by cycle. In fact, 4 times mean 4 successive displacements of the piston with: time of admission, time of compression, ignition cycle and relaxation (engine), time of exhaust.

Application to engines SMIM of Fressinea (SFAM)

SMIM of Fressinea

Engines SMIM (Company of the Engines for Industry and the Navy) SR 14 n° 8124 and 8126 of the work of Infantry of Fressinéa (SFAM). Certain values were found in the files of the Genius (Vincennes), others come from various general documents on the diesel engines.


Data of the manufacturer

Diesel engine 2 cylinders

Diameter of the piston: D = 140mm

Race: C = 180mm

Rotational frequency in normal circumstances: 750 tr/min

Nominal nominal output = 24 CV (17,7kW)

Personal data

One will take as assumption that, in a strengthened work, on the level of the Factory the temperature is close to 20°C (15° elsewhere) either T1 = 20 + 273 = 293K and pressure slightly higher than the atmospheric pressure (overpressure is desired in preparation for attack by poison gas and to evacuate the foul air) or p1 = 102000Pa. For the air one will use the usual constants: R = 287 J/kg/K and γ = 1,4

Preliminary calculations

Unit cubic capacity: Vu_ = Π. D 2. C/4 = 2770884,5mm3 is 0,00277m3

With a volumetric report/ratio ε = 12 one finds: V1 = 0,00305m3 and V2 = 0,00025m3

Mass gas during the cycle: my = p1. V1/(R.T1) = 0,0037kg

Report/ratio my/mc = 15 one deduce mc = 0,0037/15 = 0,000247kg

Points of the cycle

The application of the formulas obtained in the theoretical study gives:

Point 1

p1 = 102000Pa; V1 = 0,00305m3; T1 = 293K

Point 2

p2 = 3307150Pa; V2 = 0,00025m3; T2 = 779 K

Point 3

p3 = 3307150Pa; V3 = 0,00115m3; T3 = 3570K

Point 4

p4 = 844133Pa; V4 = 0,00305m3; T4 = 2424K



W 1-2 = 1290J

W 2-3 = -2963J

W 3-4 = -3042J

W 4-1 = 0J

Assessment: ΣW = 1290 - 2963 - 3042 = - 4715J

Quantities of heat

Q 1-2 = 0J

Q 2-3 = 10374J

Q 3-4 = 0J

Q 4-1 = 5657J

Assessment: ΣQ = 10374 - 5657 = 4717J


The first principle of thermodynamics specifies that energy interns of a closed cycle is null. One should thus have the same absolute value for ΣW and ΣQ, which is almost the case.


The engine turns to 750 tr/min. A cycle (2 turns) thus corresponds to Δt = 120/NR = 120/750 = 0,16 S

The power (for 1 cylinder) is thus, in theory, of: P = |ΣW| /Δt = 4715/0,16 = 29469W

The total power of the engine is thus of 2 X 29469 = 58938W (or 58,9 kw)


It was seen that the manufacturer gives 24 CV is 17,7kW. Would the estimates above be thus optimistic?

In fact of many differences exist between the theoretical cycle, on which calculations are based, and the real cycle. Why?

Theoretical cycle. One supposed:

- Opening and instantaneous closing of the valves and without pressure loss (pressure decrease at the time of the passage on the level of the valve).

- Opening or closing of the valves with the PMH or the PMB.

- Injection (and thus combustion) instantaneous, with the PMH.

- Compression and adiabatic pressure drop.

- R and γ constant.

Cycle real

- There are pressure losses to the passage of the valves, losses partially compensated by increasing the duration of the phases of opening and closing (advances opening admission, delay closing admission and idem for the exhaust).

- The injection and combustion last 1,5 to 3 milliseconds. During this time the displacement of the piston is not negligible, especially for fast engines.

- Compression and the relaxation are not isentropic (adiabats) but polytropic involving a heat transfer (Q1-2 and Q3-4 are not equal to zero).

- Finally R and γ are not constants (but their variation is however very weak).

And then?

Under these conditions it is not astonishing to note that the theoretical results are optimistic compared to reality. To correct them one introduces one then - coefficient of form (close to 0,5) and, especially, one does not forget to take into account the power absorptive by the auxiliaries (pumps, compressor, frictions etc) leaving only one useful output estimated at 60% (0,6 times) of the total power.


58,9 X 0,5 X 0,6 = 17,7kW. The account is good and brings back these results to closest to the actual values, measured on testing ground.

Teachware on the phases of a Diesel cycle 4 times

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injection - explosion

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Gaston Cima, specialist in the diesel engines

March 1939. Cima Gaston (on the right) poses in Rochefort, his BS Mécanicien Plane out of pocket.

Civil statue

Born in Sainte Maxime in 1917, he marries Josette Fornari in 1942 with whom he has two wire: Raymond and Bernard Cima. He dies in Menton, in 2008.

Professional life

Its professional life, as well military as civil, is centered on the engines; and particularly the diesel engines.

Volunteer in 1937 in the Air force, it specializes in the engines at the school of Rochefort and obtains to its Patent Higher Mechanic Plane on March 31, 1939.

Sergeant, in 1939 and 1940 he is chief of the level rolling of the group of hunting 1/6.

Adjudant, in 1949 it is monitor of training course of specialization Diesel, training course organized with the CIOA with Arzew (Algeria) by the Navy, for the Air force!

Duquesne cruiser on which most of the training course is carried out. The Cima adjudant is in the center of the photograph.

Does Cima Gaston animate this training course by chance? Indeed, at the end of the training course the Captain Maggiar returns account to the Rear-admiral ordering the Navy in Oran:

For lack of qualified personnel of sufficient number, the conferences were generally made by the Adjudant CIMA who, being first mechanic BS made at the CIOA, was, at once, considered as monitor.

Then, in note, it specifies that the training course being finished:

To date nothing came to confirm that it was well to this end that this graded had been indicated for Arzew!

However the sign of vessel adds:

The Adjudant CIMA, monitor of the training course, appeared remarkable organizer and excel instructor.

And one entrusts to him the management of a new training course (the second and the last of this type, organized by the CIOA), at the conclusion which the Captain Maggiar still writes, on October 12, 1949:

This graded was perfect instructor and organizer out of par. It carried out hand of Master all the questions of relation and discipline and set up a true professed course.

At all events, the Adjudant joined the ZDA 902 and the fort of Revère (SFAM) where it is affected.

In 1953 he proposes a course on the diesel engine. Its hierarchy transmits.

The reward which it seems to obtain, if supposed reward there is, is a change on the theatre of the operations of Indo-China! Also, in 1962 it leaves the army for State education where it starts a second career. Its course on the Diesel (as well as others), it is as professor of thermodynamics to the aeronautical College, then with the IUT of Town of Avray, that he will teach it with his students. It takes its retirement with Menton.

Its principal medals, in addition to those of war, are: the Medal of Aeronautics and the Military decoration.

Roll of internal combustion engine.

The engineer

The engineer.

Knowledge necessary to conclude calculations of thermodynamic.

Calculations, for a Diesel.

Precise details over 4 times of the diesel engine.

Application of the theory to engines SMIM of Fressinea (SFAM).

To test its knowledge on the phases of a diesel engine 4 times.

Specialist in the diesel engines.

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Cylinder head



here it is the energy released in the form of heat by the reaction of combustion of the gas oil by oxygen.

The specific heat (or mass heat capacity) is the quantity of energy to bring to raise of a degree the temperature of the unit of mass of a substance. For gases one distinguishes the capacities with constant volume (Cv) and the capacities with constant pressure (CP).

Stoechiometric combustion: complete and total combustion of the fuel, not leaving any carbon residue.

Law of Mariotte: p.V = m.r.T; the product of the pressure by volume is equal to the mass multiplied by the mass constant, multiplied by the temperature. It is the law which connects the 3 sizes characteristic of a gas: pressure - volume - temperature.

See its position on the image

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The piston is at the point died high (PMH). The 2 valves are open. One is in phase of sweeping. The fresh air entering expels the foul air towards the exit.

The piston starts to go down. The exhaust valve is closed. It is the real beginning of the admission.

The piston continues its descent. The cylinder fills little by little of air.

The piston reaches the dead bottom centre (PMB). The direction of displacement is reversed.

The piston goes up slightly. The inlet valve is closed. It is the end of the admission and the real beginning of compression.

The piston goes up and the pressure increases in the cylinder.

The piston reaches almost the PMH. The pressure is to the maximum, the injector is actuated and sends gas oil under high pressure. It is the injection followed by the explosion.

The explosion has just taken place. The piston passes to the PMH, its direction is reversed and it begins a second descent, propelled by gases. It is the beginning of the relaxation.

The piston continues its descent and the pressure inside the cylinder decreases.

The piston reaches almost the PMB. The exhaust valve opens. It is the end of the relaxation and the real beginning of the exhaust.

The piston again changed direction to the PMB. While going up, by the exhaust valve it evacuates the gases flarings.

The piston continues its increase. The gases waste are evacuated.

The piston reaches almost the PMH. The inlet valve opens in its turn allowing the surrounding air - to clean the combustion chamber. It is the beginning of sweeping. Shortly after one finds the phase n° 1 and one cycle starts again.

Maginot line - Diesel engines; Document carried out by B Cima. B-E-R Cima ©2008

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