Type a line (two-stroke D 470 mm S 1880 mm 108 r/min pmi 17.5 bar 6 cyl) or fill in the fields: the line and the fields stay in step.
Enter the engine type, two-stroke or four-stroke, the bore D and the stroke from the engine documents, the speed, the number of cylinders and the mean indicated pressure (pmi), and the calculator gives the indicated power of one cylinder and of the engine in kW, PS and hp. From a known power it finds the mean effective pressure or the pmi, from the indicated and the brake power the mechanical efficiency, and from the pmi of each cylinder the cylinder balance. It shows the working with your numbers, and gives a line you can copy or add to a request.
The calculator holds no engine sizes or powers: the bore and the stroke come from the documents of your engine. There are no limits for the cylinder balance and no figures for the mechanical efficiency here; compare the result with the engine maker’s guidance. The pmi can also come from an indicator diagram: its area divided by its length, times the spring scale.
Pi = pmi x A x L x n / k. A two-stroke engine with D 470 mm, S 1880 mm, 108 r/min and pmi 17.5 bar: piston area A = pi x 0.47^2 / 4 = 0.17349 m2, n = 1.8 r/s, Pi = 1750 kPa x 0.17349 x 1.88 x 1.8 = 1027 kW per cylinder; 6 cylinders give 6165 kW.
A two-stroke engine completes a working cycle in one revolution, k = 1; a four-stroke engine takes two revolutions, k = 2, so at the same pmi, sizes and speed it gives half the power. A four-stroke engine with D 310 mm, S 390 mm, 740 r/min and pmi 21 bar: 381 kW per cylinder, 3050 kW for 8 cylinders.
The mechanical efficiency is Pe / Pi: 9100 / 9800 = 92.9 %. From the pmi of each cylinder the calculator finds the mean and the deviation of each cylinder from it: at 18.2 17.6 18.5 17.9 18.1 18.4 bar the mean is 18.12 bar, cylinder 2 is 2.85 % below it and cylinder 3 2.12 % above. The limits come from the engine maker.
| Quantity | Relation | Note |
|---|---|---|
| Piston area | A = pi x D^2 / 4 | m2, with the bore D in m |
| Indicated power of a cylinder | Pi = pmi x A x L x n / k | kW with pmi in kPa, L in m and n in r/s |
| k | 1 two-stroke; 2 four-stroke | revolutions per working cycle of a cylinder |
| Engine power | sum of the cylinders, or mean pmi x z | z the number of cylinders |
| Pressure from a power | p = P x k / (A x L x n x z) | from Pi the pmi, from Pe the pme |
| Brake power from pme | Pe = pme x A x L x n x z / k | the same formula with the mean effective pressure |
| Mechanical efficiency | Pe / Pi = pme / pmi | for one engine at one speed |
| Cylinder deviation | (pmi / mean - 1) x 100 % | no limit is set here |
| Indicator diagram | pmi = area / length x spring scale | scale in bar per mm; divide by a scale in mm per bar |
| Units | 1 bar = 100 kPa; 1 MPa = 1000 kPa | 1 PS = 0.7354988 kW; 1 hp = 0.7456999 kW |
pmi in kPa x area in m2 x stroke in m x revolutions per second gives kW with no constant; 1 bar = 100 kPa. The power in PS and hp uses the factors 0.7354988 kW and 0.7456999 kW. The engine power from the cylinder pmi is the sum of the cylinders; with one pmi value it is that value times the number of cylinders.
The relation Pi = pmi x A x L x n / k, with k = 1 for a two-stroke and k = 2 for a four-stroke engine, is the standard indicated power formula of the piston engine: it is given in reference articles on the mean effective pressure and in marine engine training material, also as P L A N k / 4500 for kgf/cm2, cm2 and power strokes per minute. The mechanical efficiency as the brake power divided by the indicated power, and the difference between them as the friction power, are the definitions of the same engine testing material. The pmi from an indicator diagram as its area divided by its length, times the spring scale, is described in marine engine training material and in planimeter descriptions. Comparing the pmi of the cylinders to even out their load is described in training material on power measurement on ships; these sources give no general limit. The PS and hp factors are those of the national standards conversion tables and reference data.
For one cylinder Pi = pmi x A x L x n / k: the mean indicated pressure times the piston area, the stroke and the speed, divided by k, the revolutions per working cycle. With pmi in kPa, A in m2, L in m and n in revolutions per second the result is in kW. A two-stroke engine with D 470 mm, S 1880 mm, 108 r/min and pmi 17.5 bar: A = pi x 0.47^2 / 4 = 0.17349 m2, n = 108 / 60 = 1.8 r/s, Pi = 1750 x 0.17349 x 1.88 x 1.8 / 1 = 1027 kW per cylinder, and 6165 kW for 6 cylinders.
k is the number of revolutions for one working cycle of a cylinder. A two-stroke engine fires each cylinder once per revolution, so k = 1; a four-stroke engine fires each cylinder once every two revolutions, so k = 2 and the speed is halved in the formula. A four-stroke engine with D 310 mm, S 390 mm, 740 r/min and pmi 21 bar: A = 0.075477 m2, n = 12.333 r/s, Pi = 2100 x 0.075477 x 0.39 x 12.333 / 2 = 381 kW per cylinder, and 3050 kW for 8 cylinders. The calculator asks for the engine type when the line does not give it.
By turning the same formula round: p = P x k / (A x L x n x z). From the brake power it gives the mean effective pressure (pme), from the indicated power the mean indicated pressure (pmi). A brake power of 7000 kW on the two-stroke engine above, 6 cylinders: pme = 7000 x 1 / (0.17349 x 1.88 x 1.8 x 6) = 1987 kPa, or 19.87 bar. The calculator refuses a result above 40 bar and asks to check the figures.
As the brake power divided by the indicated power, Pe / Pi, when both are given: entered as powers, or worked out from pme and pmi for the same engine at the same speed, where Pe / Pi = pme / pmi. Pi 9800 kW and Pe 9100 kW give 9100 / 9800 = 0.9286, or 92.9 %. The difference is the power lost to friction and to the driven auxiliaries. The calculator gives no typical figure, and a brake power above the indicated power is shown as not possible.
Enter the pmi of each cylinder, such as pmi per cylinder 18.2 17.6 18.5 17.9 18.1 18.4 bar. The calculator takes the mean, 18.12 bar here, and gives each cylinder’s deviation from it: (pmi / mean - 1) x 100 %, so cylinder 2 at 17.6 bar is -2.85 % and cylinder 3 at 18.5 bar is +2.12 %; the spread from the highest to the lowest is 4.97 % of the mean. With the engine data each cylinder gets its own power and the engine the sum. No limit is set: compare the deviations with the engine maker’s guidance.
The area of the diagram (by planimeter) divided by its length gives the mean height; the mean height divided by the spring scale in mm per bar, or multiplied by the scale in bar per mm, gives pmi. A diagram of 1620 mm2 and 60 mm with a spring of 1.5 mm/bar: 1620 / 60 = 27 mm, 27 / 1.5 = 18 bar. Write area 1620 mm2 length 60 mm spring 1.5 mm/bar in the line, with the engine data for the power.
The engine type (two-stroke or four-stroke), the bore D and the stroke in mm or m from the engine documents, the speed in r/min, the number of cylinders, and the pmi in bar, MPa or kPa, one value or one per cylinder in one unit; or a pme; or an indicated or brake power in kW, MW, PS or hp. Powers are given in kW, PS and hp. The calculator takes a bore of 50 to 1200 mm, a stroke of 50 to 4000 mm, 10 to 4000 r/min, up to 24 cylinders and pressures up to 40 bar.
The calculator gives the indicated power, the mechanical efficiency and the cylinder balance. When engine parts are needed, for the cylinders, the fuel injection equipment or the indicator cocks, send the line from the calculator with the engine details and a photograph of the nameplate, and Vessel Core checks the details before an offer goes back.
