WesWorld

4-stroke Petrol engines operate on the Otto Cycle as shown on the Pressure-Volume graph above.
Stage 1->2 Compression
Stage 2->3 Heat addition
Stage 3->4 Expansion
Stage 4->1 Heat rejection

The volume enclosed can be found. This gives the Mean Effective Pressure (MEP) which is used as a yardstick for comparison between different engines.

MEP = (4 x Pi x Torque) / (Displacement x 10^-3)

Where displacement is in litres, MEP in Pa and torque in Nm. A suitable modifier can be incorporating into the equations for the heathens who still use cubic inches.

It is not usually common to find torque values so this is replaced by power/engine speed. Engine speed is usually given in rpm and so needs to be multipied by 60/(2 x Pi). This gives;

MEP = (8 x Pi^2 x Power) / (0.06 x Displacement x Engine Speed)

MEP = (960 x Power) / (Displacement x Engine Speed)

Note Power in hp not kW for kW use 1290 and answer in bar

From this it is possible to work out historical MEP values and then use these to get a value for any engine you want to invent.

The Merlin for example goes from MEP of 12.2 to an eventual 31.2bar

There are further limitations on engines related to volumetric effeciency and strength issues.

The bore of the cylinder has a maximum size of about 160mm. Much greater than this and there are problems in spreading out the charge to burn evenly. You'd need different valves (e.g. sleeves) to operate more efficiently.

The speed of the piston is limited by the stress placed on the piston rings to about 15m/s. To find the engine speed for a given stroke(in m);

(15 x 60) / (2 x stroke) = engine speed

It'll typically be between 2500 and 4000rom

To find the displacement of an engine decide on the bore, stroke and no. of cylinders

Displacement = (Pi x bore^2 x stroke x No. of cylinders) / 4

Quoted

Originally posted by Red Admiral
the heathens who still use cubic inches.

...people use some other measurement ?

Actually cu. in. rarely matters here, we deal in cu. yards For a truely archaic measure, we use chains, as in 80 chains to the mile.

Back to the subject, interesting post. Graphing the MEP in relation to date would seem to establish a basis for hypothetical engine's performance.

For cu in of displacement instead of 960 multiplier use 58600 instead.

I'll work out some MEP values and plot them against date.

Some acquired BMEP values.

A plot of BMEP against date shows an increasing trend but there is a lot of variation. Generally a lower BMEP will result in a more reliable engine.

For comparison with the above, my bike engine (lowest of all the low powered things) has a BMEP of 11.5bar

Very nice RA, thank you. Now all I have to do is digest it

I thought I'd include this list as well. It's obviously not complete, but while learning to use planebuilder I found the question of engine dimensions to be valid, and wound up trying to piece together information from that notoriously reliable source... the internet.

HP (TO vs. Max vs. at what altitude) and year (i.e. reliable production vs. prior) were often hard, and often only one weight, usually of the main or later model was available.

Historical Engines
1929: 625hp Gnome-Rhone Mistral Major 14k radial

1930: 650hp /1,387 lb V-1710-115 Allison prototype. 2.45' h x 3.05'wide.
1930:

1931: Jumo 210 19.7L development started.

1932: 775hp / 1,162lb R-18303 Twin Wasp, 31.63L, 4.2'dia.
1932: 760hp / 1,036lb, Hispano-Suiza 36L 12Y, 3.1 ft high x 2.5 ft. wide x 5.7 ft long.
1932: DB600 development started.

1933: 750hp / ?lb Pegasus III
1933: 1,025hp / ?lb Gnome-Rhone Mistral Major 14kfrs
1933: 770hp Gnome-Rhone Mistral 7k

1934: 670hp / 981lb Jumo 210A 19.7L est. 3.4 ft high x 2.3 ft. wide x 4.9 ft. long.

1935: Historical date Standard Oil developed 100 octane fuel.
1935: 750hp / 1,036lb, M-100 variant of Hispano-Suiza 12Y
1935: PV-12, Merlin prototype
1935: 867hp / 1,687lb Jumo 211 prototype 35L 3.5 ft high x 2.7 ft. wide x 7.2 ft. long.
1935: 867hp / 1,036lb, Hispano-Suiza 12Y-21 100 octane 36L, , 3.1 ft high x 2.5 ft. wide x 5.7 ft long.
1935: RR Kestrel VI

1936: 810hp / 1001lb Wright Cyclone GR-1820-G2, 29.88L, 4.5' dia.
1936: 890hp / 1001lb Wright Cyclone GR-1820-F52, 29.88L, 4.5' dia.
1936: 719hp / 981lb Jumo 210G 21L 3.4 ft high x 2.3 ft. wide x 4.9 ft. long.
1936: 850hp / 1,036lb, Hispano-Suiza 36L 12Y-31, 3.1 ft high x 2.5 ft. wide x 5.7 ft long.
1936: 950hp / 1,300lb Gnome-Rhone Mistral Major 14N, 38.7L, 4.3' dia.

1937: 1,050hp/ 1,310(?)lb P&W R-1830-66 Twin Wasp, 31.63L, 4.2' dia.
1937: 600hp / 883lb SIHI-G Wasp, 21.9L, 4.3' dia.
1937: 800hp / 1,015lb SIE-G Hornet, 27.7L, 4.6' dia.
1937: 700hp / 1,070lb S2A4-G Twin Wasp Junior, 3.7' dia.
1937: 1,000hp / 1,265lb SB-G Twin Wasp, 31.63L , 4' dia.
1937: 1,065hp / 1,180lb Pegasus XVIII, 28.7L, 4.6' dia.
1937: 955hp Dagger VII , unreliable.
1937: 1,000hp /1,387 lb V-1710-115 Allison prototype. 2.45' h x 3.05' wide.
1937: 1,085hp / 1,687lb Jumo 211A 35L 3.5 ft high x 2.7 ft. wide x 7.2 ft. long.
1937: 970hp / 1,300lb Gnome-Rhone Mistral Major 14N, 38.7L, 4.3' dia.

1938 : 1,350hp / 2502lb = 36.8hp/L Napier prototype, H block.
1938 : 2,050hp / 2502lb = 55.9hp/L Napier prototype, H block.
1938: 1,030hp/ 1,320lb Merlin II, 27L, unreliable.
1938: 1,183hp / 1,455lb Jumo 211B 35L 3.5 ft high x 2.7 ft. wide x 7.2 ft. long.
1938: 900hp / 1,036lb, Hispano-Suiza 36L 12Y-45

1938 : BF109V14 : DB601A 1100

1939: 1000hp Dagger VIII, air-cooled H, unreliable.
1939: 1,130hp/ 1,320lb Merlin X, 27L, reliable.
1939: 995hp/1,065lb Bristol Mercury XV, 24.9L, 4' 3.5"dia.
1939: 1,290hp/ 1,930lb Bristol Hercules I, 38.7L, 4'4" dia.
1939: 1,375hp/ 1,930lb Bristol Hercules II, 38.7L, 4'4" dia.
1939: FW 190 v1, 1550hp BMW 139
1939: FW 190 v1, 1550hp BMW 801
1939: Gnome-Rhone 14R, 1291hp
1939: 1030hp /1,300lb Gnome-Rhone Mistral Major 14N, 38.7L, 4.3' dia.
1939: Gnome-Rhone 14R, start 1578hp MAX


1940: 1,030hp/ 1,320lb Merlin II, 27L, reliable.
1940: USN 2-stage supercharger.
1940: 2,200hp / 2,502lb = 59.9hp/L Napier 3.84' h x 3.33'wide.
1940: 1,500hp/ 1520hp Hispano-Suiza 12Z-17, 36L,
1940: 1,084hp/1,036 lb. Hispano-Suiza 12Y-51, 36L, 3.1 ft high x 2.5 ft. wide x 5.7 ft long.
1940 : 1,200hp/1,467 P&W R-1830-76 Twin Wasp, 31.63L, 4.2'dia.
1940 : 1,000hp Wright R-1820-G205A Cyclone
1940 1,100hp / 1,365lb, M-105, 35L,
1940: 1,500hp/ 1,930lb Bristol Hercules XI, 38.7L, 4'4" dia.
1940: Gnome-Rhone 14N, 1100hp
1940: DB601E start

1941: 1,730hp / 2,707lb BMW 801-C, 41.8L, 4.2'dia.
1941: Japanese 2-stage supercharger.
1941 : Nakajima Sakae 21, 1,130hp
1941: 1,250hp /1,595 lb V-1710-115 Allison prototype. 28L, 2.45' h x 3.05'wide.
1941: 1,322hp / 1,587lb Jumo 211F 35L 3.5 ft high x 2.7 ft. wide x 7.2 ft. long.

1941: Bf109E-4/N DB601N 1,200hp
1941: FW 190A-1, 1560 BMW 801C-1
1941: FW 190A-2, 1600 BMW 801C-2

1942: 1,180hp / 1,365lb, VK-105PF , 35L
1942: 1,650hp / 1,685lb, VK-107A, 35L
1942: 2,520hp/ 2,695lb Bristol Centaurus VII, 53.6L, 4'7.3" dia.

edit: squares