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Thermal calculus of a Spark Igniton Engine
Rated Power 66 kW
Rated Speed 5750 rpm
No. of cylinders i = 4 no.
Initial parameters
T0 = 293 K initial temperature
p0 = 1,02 initial pressure
Tr = 1000 K residual gases temperature
pr = 1,2 pressure of residual gases
= 0,9 excess air coefficient
= 10,2 compression ratio
Parameters of the change of gas process
There are chosen :
pa= 0,85 pressure at the end of admission
T = 25 C pre-heating of the mixturep = 1,1 afterburner coefficient
By calculus, there are determined the following coefficients:
Residual gases coefficient
0,05
The temperature at the end of admission
347,85 K
Filling coefficient
0,82
Compression parameters
It is chosen 1,36
The pressure at the end of the compression
20,00
The temperature at the end of the compression
802,58 K
=+
=
=+ +
1 + =
=
1
1 + =
= =
= =
=
=
10
=
N m
10
N m 10
10
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Combustion parameters
There are chosen c= 0,854 kg composition of gasoline
h= 0,142 kg composition of gasoline
o= 0,004 kg composition of gasoline
43500 kJ/kg lower heating value
0,008772 kcal/kg molar mass of gasoline
= 0,85 coefficient of heat usage
= 4,2 coefficient of increasing the pressure
0,8 coefficient of correction of the pressure
The minimum mass of necessary air used to burn 1 kilo of fuel:
0,508
Necessary amount of air for burning the fuel:
0,457
Quantity of fresh mixture for 1 kilo of fuel:
0,466
Theoretical coefficient of molar variation of fresh mixture for
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The specific heat released at incomplete burning of the fuel:
37400
The temperature at the end of the burning results from:
92496,50
The pressure at the end of burning process:
79,03
63,23
The increase of pressure coefficient:
3,95
Stroke parameters
It is chosen: 1,28
The pressure at the end of stroke:
4,04
The temperature at the end of stroke
1537 K
The main parameters of the engine
There are chosen: 0,96 the rounding coefficient of the diagram
0,8 mechanical efficiency
The average pressure of the theoretical cycle:
11,25
10,80
The indicated efficiency of the engine:
0,34
= = 61000 10 = 43500 61000 10 0.9 =
+ 1
+ =
=
=
= 18.83 10 1.08 2945
807.32= 10
= = 0.8 73,93 10 =
=
=
=
=
= 10
=
=
==
=
1
1 1
1
1
1 1
1
= 10
= =
=
=
10
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The average effective pressure:
8,637
The effective efficiency of the engine:
0,270
Effective specific fuel consumption:
0,307 = 298
Basic dimensions of the engine
It is chosen the bore/stroke ratio: 0,99
It is determined the displacement of a cylinder:
0,40 l
There are determined the bore and the stroke:
0,801 dm = 80,1 mm
79,251922 mm
The average piston speed:
15,19 m/s
The engine total displacement:
1,59 l
The power litre engine:
41,39
= = 10
= =
= 3600
=
=
=
=120000
=
= 4
=
= =
= 30 =
= =
=
=
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The indicated diagram:
The volume at the end of intake stroke:
0,44
The volume at the end of compression stroke:
0,043
Ignition advance angle:
30 RAC= 0,5236 rad
The exhaust opening advance angle:
60 RAC= 1,0472 rad
The ratio between the radius of the crank and the length of the connecting rod:
0,27027
6,648 mm
24,00
15,80
2,45
Mass of one piston
The mass of one piston is calculated as following:
The volume of one cylinder has been calculated previously, and it is
Vh = 0,4 l = 400 cm^3
Piston stroke is
S= 79,251922
=
1=
=
=
=
=
=
=
=
=
2 1
+
4 1 2
=
= 1.15 1.25 = 1.2=
=
2 1
4
1 2 =
=
1
2 + =
1
3,7=
10
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As material for the piston, it is chosen aluminium with density
rho= 2,70 g/cm^3
Piston height is app. And the bore is
Hp= 0,04 m D= 0,08 m
The space displaced by the piston is calculated as:
Ap= 0,0050265 m^2 Ap*Hp= 0,0001992 m^3 = 199,1818 cm^3
,where Ap-piston head area, Hp-piston height
So, by substracting the lack of material that is inside the piston, we'll have the piston displacement
Pd= 119,509083 cm^3
And for having the mass of one piston, all we have to do is to multiply with the density of Al
Mp= 322,674524 g = 0,322675 kg
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Data for diagrams
D= 0,080052 m p0= 102000
S= 0,079252 m pa= 85000
Ap= 0,005033 m2 pr= 120000
pz= 7903375,02
n= 5750 rot/min
0,2703
0,8053026 160 kg/m2
0,4529827 90 kg/m2
0,855634 170 kg/m2
0,6744409 kg/m2
0,22145821 kg/m2
0,58384436 kg/m2
R=D/ 0,04003 m
R=D/ 0,040 m
602,139 rad/s
Va= 0,44
Vc= 0,0433 mc= 1,36
Vz= 0,0433
Vt= md= 1,28
=
= 0,275 =
=
30 =
==
=
= + =
= 0.725 =
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Xp Vx px vx ax Fg Fj F
[grd] [m] [l] [N/m2] [m/s] [m/s2] [N] [N] [N]
0 0,00000 0,0433352 102000 0 18434,598 0 -12433,0468 -12433,05
10 0,00076 0,0471779 85000 5,2990907 17977,582 -85,5634 -12124,8165 -12210,38
20 0,00302 0,0585158 85000 10,33666 16641,7633 -85,5634 -11223,8858 -11309,45
30 0,00665 0,0767934 85000 14,871257 14529,1853 -85,5634 -9799,07675 -9884,64
40 0,01148 0,1011318 85000 18,699495 11798,1922 -85,5634 -7957,18335 -8042,74750 0,01730 0,1303947 85000 21,67015 8647,26194 -85,5634 -5832,0671 -5917,63
60 0,02383 0,1632706 85000 23,692957 5295,04412 -85,5634 -3571,19431 -3656,758
70 0,03080 0,1983637 85000 24,741364 1958,89211 -85,5634 -1321,15695 -1406,72
80 0,03794 0,2342844 85000 24,849118 -1165,672 -85,5634 786,1769024 700,6135
90 0,04498 0,26973 85000 24,101334 -3922,2549 -85,5634 2645,329115 2559,7657
100 0,05170 0,3035502 85000 22,621242 -6205,7559 -85,5634 4185,415596 4099,8522
110 0,05791 0,3347908 85000 20,554327 -7968,1353 -85,5634 5374,036288 5288,4729
120 0,06346 0,3627136 85000 18,051777 -9217,299 -85,5634 6216,52342 6130,96
130 0,06824 0,3867937 85000 15,255236 -10009,447 -85,5634 6750,780261 6665,2169
140 0,07219 0,4066963 85000 12,284582 -10436,007 -85,5634 7038,470194 6952,9068150 0,07528 0,4222389 85000 9,2300767 -10606,93 -85,5634 7153,747638 7068,1842
160 0,07749 0,4333462 85000 6,1496229 -10632,52 -85,5634 7171,006452 7085,4431
170 0,07881 0,440004 85000 3,0712146 -10606,154 -85,5634 7153,224052 7067,6607
180 0,07925 0,4422213 85000 0,00000 -10590,088 -85,5634 7142,388611 7056,8252
190 0,07881 0,440004 85529,8462 -3,0712146 -10606,154 -82,8966 7153,224052 7070,3274
200 0,07749 0,4333462 87321,8969 -6,1496229 -10632,52 -73,877 7171,006452 7097,1295
210 0,07528 0,4222389 90460,5965 -9,2300767 -10606,93 -58,0794 7153,747638 7095,6682
220 0,07219 0,4066963 95194,3548 -12,284582 -10436,007 -34,2538 7038,470194 7004,2164
230 0,06824 0,3867937 101917,019 -15,255236 -10009,447 -0,41765 6750,780261 6750,3626
240 0,06346 0,3627136 111227,427 -18,051777 -9217,299 46,4429 6216,52342 6262,9664
250 0,05791 0,3347908 124029,997 -20,554327 -7968,1353 110,88 5374,036288 5484,9164
260 0,05170 0,3035502 141704,981 -22,621242 -6205,7559 199,841 4185,415596 4385,2564
270 0,04498 0,26973 166400,602 -24,101334 -3922,2549 324,137 2645,329115 2969,4664
280 0,03794 0,2342844 201543,005 -24,849118 -1165,672 501,014 786,1769024 1287,1909
290 0,03080 0,1983637 252737,72 -24,741364 1958,89211 758,684 -1321,15695 -562,4727
300 0,02383 0,1632706 329354,821 -23,692957 5295,04412 1144,31 -3571,19431 -2426,885
310 0,01730 0,1303947 447162,424 -21,67015 8647,26194 1737,25 -5832,0671 -4094,816
320 0,01148 0,1011318 631787,743 -18,699495 11798,1922 2666,5 -7957,18335 -5290,687
330 0,00665 0,0767934 918708,749 -14,871257 14529,1853 4110,61 -9799,07675 -5688,466
340 0,00302 0,0585158 1329617,54 -10,33666 16641,7633 6178,77 -11223,8858 -5045,114
350 0,00076 0,0471779 1782109,42 -5,2990907 17977,582 8456,23 -12124,8165 -3668,589360 0,00000 0,0433352 2000392,23 0,00000 18434,598 9554,88 -12433,0468 -2878,171
370 0,00076 0,0471779 7903375,02 5,2990907 17977,582 39265,4 -12124,8165 27140,604
380 0,00302 0,0585158 7745307,52 10,33666 16641,7633 38469,8 -11223,8858 27245,959
390 0,00665 0,0767934 3799740,59 14,871257 14529,1853 18611,2 -9799,07675 8812,1731
400 0,01148 0,1011318 2671236,8 18,699495 11798,1922 12931,3 -7957,18335 4974,1478
410 0,01730 0,1303947 1929462,11 21,67015 8647,26194 9197,87 -5832,0671 3365,8074
420 0,02383 0,1632706 1446927,65 23,692957 5295,04412 6769,21 -3571,19431 3198,0162
430 0,03080 0,1983637 1127761,35 24,741364 1958,89211 5162,8 -1321,15695 3841,6446
440 0,03794 0,2342844 911375,525 24,849118 -1165,672 4073,7 786,1769024 4859,8781
450 0,04498 0,26973 760990,786 24,101334 -3922,2549 3316,79 2645,329115 5962,1227460 0,05170 0,3035502 654204,8 22,621242 -6205,7559 2779,32 4185,415596 6964,7402
470 0,05791 0,3347908 577110,236 20,554327 -7968,1353 2391,3 5374,036288 7765,3331
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480 0,06346 0,3627136 520867,381 18,051777 -9217,299 2108,22 6216,52342 8324,742
490 0,06824 0,3867937 460539,051 15,255236 -10009,447 1804,58 6750,780261 8555,3579
500 0,07219 0,4066963 418394,459 12,284582 -10436,007 1592,46 7038,470194 8630,9281
510 0,07528 0,4222389 381631,557 9,2300767 -10606,93 1407,43 7153,747638 8561,1727
520 0,07749 0,4333462 348417,056 6,1496229 -10632,52 1240,25 7171,006452 8411,2582
530 0,07881 0,440004 325412,605 3,0712146 -10606,154 1124,47 7153,224052 8277,6912
540 0,07925 0,4422213 244578,503 0,00000 -10590,088 717,618 7142,388611 7860,0063550 0,07881 0,440004 232349,578 -3,0712146 -10606,154 656,068 7153,224052 7809,2919
560 0,07749 0,4333462 220732,099 -6,1496229 -10632,52 597,595 7171,006452 7768,6019
570 0,07528 0,4222389 209695,494 -9,2300767 -10606,93 542,047 7153,747638 7695,7942
580 0,07219 0,4066963 199210,72 -12,284582 -10436,007 489,275 7038,470194 7527,7455
590 0,06824 0,3867937 189250,184 -15,255236 -10009,447 439,142 6750,780261 7189,9227
600 0,06346 0,3627136 179787,674 -18,051777 -9217,299 391,516 6216,52342 6608,0398
610 0,05791 0,3347908 170798,291 -20,554327 -7968,1353 346,271 5374,036288 5720,3078
620 0,05170 0,3035502 162258,376 -22,621242 -6205,7559 303,289 4185,415596 4488,7045
630 0,04498 0,26973 154145,457 -24,101334 -3922,2549 262,455 2645,329115 2907,7846
640 0,03794 0,2342844 146438,184 -24,849118 -1165,672 223,664 786,1769024 1009,8406650 0,03080 0,1983637 139116,275 -24,741364 1958,89211 186,811 -1321,15695 -1134,346
660 0,02383 0,1632706 132160,461 -23,692957 5295,04412 151,802 -3571,19431 -3419,392
670 0,01730 0,1303947 125552,438 -21,67015 8647,26194 118,543 -5832,0671 -5713,524
680 0,01148 0,1011318 119274,816 -18,699495 11798,1922 86,9466 -7957,18335 -7870,237
690 0,00665 0,0767934 113311,076 -14,871257 14529,1853 56,9302 -9799,07675 -9742,147
700 0,00302 0,0585158 107645,522 -10,33666 16641,7633 28,4147 -11223,8858 -11195,47
710 0,00076 0,0471779 102263,246 -5,2990907 17977,582 1,32495 -12124,8165 -12123,49
720 0,00000 0,0433352 97150,0835 0,0000 18434,598 -24,4103 -12433,0468 -12457,46
N S/100 T Z M Rm Angle Rm
[grd] [grd] [N] [N] [N] [N] [Nm] [N] [Rad]
0 0,0000000 0,000000 ########## 0,000000 -12433,047 0 12433,04684 0
10 0,0469492 ######### ########## ######### -12036,398 -85,3564 12223,84954 0,1753523
20 0,0925700 ######### ########## ######### -10666,813 -156,18 11358,07933 0,3506815
30 0,1355498 ######### -9976,14960 ######### -8627,7741 -200,471 9976,149602 0,5259646
40 0,1746123 ######### -8166,93347 ######### -6240,2065 -210,884 8166,933465 0,7011793
50 0,2085474 ######### -6048,68938 ######### -3871,1314 -186,029 6048,689375 0,8763045
60 0,2362525 ######### -3761,23762 ######### -1867,1716 -130,688 3761,237616 1,0513209
70 0,2567836 ######### -1454,40770 ######### -491,30661 -54,7924 1454,407701 1,2262122
80 0,2694115 ######### 726,83202 716,375358 122,845944 28,6738 726,8320161 1,4009655
90 0,2736737 ######### 2658,71099 ######### -12,699306 106,417 2658,710994 -1,56602100 0,2694115 ######### 4253,27776 ######### -758,26127 167,515 4253,27776 -1,391561
110 0,2567836 ######### 5467,75037 ######### -1893,089 205,317 5467,750369 -1,217249
120 0,2362525 ######### 6306,13219 ######### -3175,5581 218,072 6306,132189 -1,043074
130 0,2085474 ######### 6812,83268 ######### -4398,1715 208,255 6812,832677 -0,869025
140 0,1746123 ######### 7060,26547 ######### -5422,2826 180,988 7060,265473 -0,695084
150 0,1355498 ######### 7133,61967 ######### -6186,3169 142,181 7133,619669 -0,521233
160 0,0925700 ######### 7115,91015 ######### -6690,6917 96,9827 7115,910154 -0,34745
170 0,0469492 ######### 7075,45718 ######### -6968,9695 48,9493 7075,457175 -0,173714
180 0,0000000 0,000000 7056,82521 0,000000 -7056,8252 0 7056,825213 0
190 ######## ######### 7078,12691 ######### -6971,5991 -48,9677 7078,126908 0,1737135200 ######## ######### 7127,64684 ######### -6701,727 -97,1426 7127,64684 0,3474502
210 ######## ######### 7161,35806 ######### -6210,3718 -142,733 7161,358061 0,521233
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220 ######## ######### 7112,36736 ######### -5462,2968 -182,324 7112,367362 0,6950841
230 ######## ######### 6899,86416 ######### -4454,3565 -210,915 6899,864158 0,8690248
240 ######## ######### 6441,91018 ######### -3243,9314 -222,767 6441,910178 1,0430742
250 ######## ######### 5670,85322 ######### -1963,4089 -212,944 5670,853217 1,2172488
260 ######## ######### 4549,36238 ######### -811,04633 -179,177 4549,362384 1,3915613
270 ######## ######### 3084,24829 ######### -14,73188 -123,449 3084,24829 1,5660198
280 ######## ######### 1335,36042 ######### 225,696732 -52,6805 1335,36042 -1,400966290 ######## ######### -581,54039 547,355126 -196,44741 21,9086 581,540386 -1,226212
300 ######## ######### -2496,22576 ######### -1239,1884 86,7337 2496,225758 -1,051321
310 ######## ######### -4185,50460 ######### -2678,7023 128,726 4185,504605 -0,876304
320 ######## ######### -5372,37955 ######### -4104,9383 138,724 5372,379546 -0,701179
330 ######## ######### -5741,12880 ######### -4965,1583 115,368 5741,128803 -0,525965
340 ######## ######### -5066,80735 ######### -4758,4354 69,6713 5066,807354 -0,350682
350 ######## ######### -3672,63581 640,710004 -3616,3164 25,6452 3672,635806 -0,175352
360 0,0000000 0,000000 -2878,17102 0,000000 -2878,171 0 2878,171021 0
370 0,0469492 ######### ########## ######### 26753,8869 189,726 27170,54361 0,1753523
380 0,0925700 ######### ########## ######### 25697,7635 376,257 27363,11528 0,3506815
390 0,1355498 ######### 8893,75392 ######### 7691,6749 178,721 8893,753916 0,5259646
400 0,1746123 ######### 5050,95278 ######### 3859,34188 130,424 5050,952782 0,7011793
410 0,2085474 ######### 3440,35056 ######### 2201,80743 105,809 3440,350559 0,8763045
420 0,2362525 ######### 3289,38910 ######### 1632,93434 114,293 3289,389101 1,0513209
430 0,2567836 ######### 3971,87505 ######### 1341,72038 149,634 3971,875051 1,2262122
440 0,2694115 ######### 5041,74547 ######### 852,133597 198,899 5041,745474 1,4009655
450 0,2736737 ######### 6192,58278 ######### -29,578807 247,863 6192,58278 -1,56602
460 0,2694115 ######### 7225,37625 ######### -1288,1179 284,572 7225,376254 -1,391561
470 0,2567836 ######### 8028,57533 ######### -2779,7187 301,478 8028,575327 -1,217249
480 0,2362525 ######### 8562,59434 ######### -4311,8373 296,102 8562,594342 -1,043074
490 0,2085474 ######### 8744,83499 ######### -5645,4173 267,312 8744,834989 -0,869025
500 0,1746123 ######### 8764,19685 ######### -6730,9016 224,668 8764,196852 -0,695084
510 0,1355498 ######### 8640,42983 ######### -7493,0315 172,213 8640,429831 -0,521233
520 0,0925700 ######### 8447,42630 ######### -7942,6417 115,13 8447,426295 -0,34745
530 0,0469492 ######### 8286,82254 ######### -8162,1035 57,3297 8286,822537 -0,173714
540 0,0000000 0,000000 7860,00632 0,000000 -7860,0063 0 7860,006325 0
550 ######## ######### 7817,90649 ######### -7700,2448 -54,0857 7817,906495 0,1737135
560 ######## ######### 7802,00650 ######### -7335,7896 -106,333 7802,006504 0,3474502
570 ######## ######### 7767,03993 ######### -6735,6227 -154,805 7767,039928 0,521233
580 ######## ######### 7643,98012 ######### -5870,5753 -195,952 7643,980119 0,6950841
590 ######## ######### 7349,15931 ######### -4744,4087 -224,649 7349,159312 0,8690248600 ######## ######### 6796,84292 ######### -3422,6637 -235,041 6796,842918 1,0430742
610 ######## ######### 5914,22432 ######### -2047,6709 -222,083 5914,224325 1,2172488
620 ######## ######### 4656,68178 ######### -830,1789 -183,403 4656,681778 1,3915613
630 ######## ######### 3020,18216 ######### -14,425869 -120,885 3020,182164 1,5660198
640 ######## ######### 1047,63102 ######### 177,065978 -41,3294 1047,631025 -1,400966
650 ######## ######### -1172,79944 ######### -396,17785 44,1833 1172,79944 -1,226212
660 ######## ######### -3517,09043 ######### -1745,9709 122,205 3517,090425 -1,051321
670 ######## ######### -5840,06286 ######### -3737,6115 179,613 5840,062857 -0,876304
680 ######## ######### -7991,75978 ######### -6106,3594 206,361 7991,759782 -0,701179
690 ######## ######### -9832,33680 ######### -8503,399 197,581 9832,336796 -0,525965
700 ######## ######### ########## ######### -10559,312 154,606 11243,61112 -0,350682
710 ######## ######### ########## ######### -11950,748 84,749 12136,86534 -0,175352
720 0,0000000 0,000000 ########## 0,000000 -12457,457 0 12457,45715 0
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M1 M2 M3 M4 t=Sum(M1,M4)
0 0 0 0 0 0
10 -85,3564 -48,96775 -54,085672 189,72588 1,31603363
20 -156,18 -97,14262 -106,33346 376,25721 16,6015788
30 -200,471 -142,7334 -154,80525 178,72054 -319,28943
40 -210,884 -182,3241 -195,95188 130,42411 -458,7358450 -186,029 -210,9152 -224,64922 105,80905 -515,78464
60 -130,688 -222,7671 -235,04101 114,29296 -474,20295
70 -54,7924 -212,944 -222,08276 149,63373 -340,18543
80 28,6738 -179,1767 -183,40349 198,89878 -135,00763
90 106,4169 -123,4494 -120,88511 247,86287 109,94531
100 167,5154 -52,68048 -41,329443 284,57157 358,077067
110 205,3174 21,908558 44,1832514 301,47794 572,887145
120 218,0718 86,733743 122,204659 296,1023 723,112494
130 208,2548 128,72649 179,612942 267,31225 783,906464
140 180,9885 138,72389 206,360701 224,66841 750,741472150 142,1805 115,36834 197,581424 172,21283 627,343114
160 96,98266 69,671262 154,605558 115,12987 436,38935
170 48,94928 25,645202 84,74904 57,329717 216,673234
180 0 0 0 0 0
190 -48,9677 189,72588 -85,356431 -54,085672 1,31603363
200 -97,1426 376,25721 -156,17956 -106,33346 16,6015788
210 -142,733 178,72054 -200,47135 -154,80525 -319,28943
220 -182,324 130,42411 -210,88398 -195,95188 -458,73584
230 -210,915 105,80905 -186,02931 -224,64922 -515,78464
240 -222,767 114,29296 -130,68779 -235,04101 -474,20295
250 -212,944 149,63373 -54,79237 -222,08276 -340,18543
260 -179,177 198,89878 28,6738 -183,40349 -135,00763
270 -123,449 247,86287 106,416946 -120,88511 109,94531
280 -52,6805 284,57157 167,515418 -41,329443 358,077067
290 21,90856 301,47794 205,317391 44,183251 572,887145
300 86,73374 296,1023 218,071789 122,20466 723,112494
310 128,7265 267,31225 208,254777 179,61294 783,906464
320 138,7239 224,66841 180,988473 206,3607 750,741472
330 115,3683 172,21283 142,18052 197,58142 627,343114
340 69,67126 115,12987 96,9826563 154,60556 436,38935
350 25,6452 57,329717 48,9492755 84,74904 216,673234360 0 0 0 0 0
370 189,7259 -54,08567 -48,967745 -85,356431 1,31603363
380 376,2572 -106,3335 -97,142615 -156,17956 16,6015788
390 178,7205 -154,8052 -142,73338 -200,47135 -319,28943
400 130,4241 -195,9519 -182,32409 -210,88398 -458,73584
410 105,809 -224,6492 -210,91516 -186,02931 -515,78464
420 114,293 -235,041 -222,76712 -130,68779 -474,20295
430 149,6337 -222,0828 -212,94403 -54,79237 -340,18543
440 198,8988 -183,4035 -179,17672 28,6738 -135,00763
450 247,8629 -120,8851 -123,4494 106,41695 109,94531
460 284,5716 -41,32944 -52,680477 167,51542 358,077067
470 301,4779 44,183251 21,9085585 205,31739 572,887145
480 296,1023 122,20466 86,7337428 218,07179 723,112494
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490 267,3123 179,61294 128,72649 208,25478 783,906464
500 224,6684 206,3607 138,72389 180,98847 750,741472
510 172,2128 197,58142 115,368343 142,18052 627,343114
520 115,1299 154,60556 69,6712621 96,982656 436,38935
530 57,32972 84,74904 25,6452016 48,949275 216,673234
540 0 0 0 0 0
550 -54,0857 -85,35643 189,725883 -48,967745 1,31603363560 -106,333 -156,1796 376,257205 -97,142615 16,6015788
570 -154,805 -200,4714 178,720542 -142,73338 -319,28943
580 -195,952 -210,884 130,42411 -182,32409 -458,73584
590 -224,649 -186,0293 105,809047 -210,91516 -515,78464
600 -235,041 -130,6878 114,292959 -222,76712 -474,20295
610 -222,083 -54,79237 149,633729 -212,94403 -340,18543
620 -183,403 28,6738 198,89878 -179,17672 -135,00763
630 -120,885 106,41695 247,862873 -123,4494 109,94531
640 -41,3294 167,51542 284,571569 -52,680477 358,077067
650 44,18325 205,31739 301,477944 21,908558 572,887145
660 122,2047 218,07179 296,102304 86,733743 723,112494
670 179,6129 208,25478 267,312255 128,72649 783,906464
680 206,3607 180,98847 224,668408 138,72389 750,741472
690 197,5814 142,18052 172,212826 115,36834 627,343114
700 154,6056 96,982656 115,129874 69,671262 436,38935
710 84,74904 48,949275 57,3297173 25,645202 216,673234
720 0 0 0 0 0
T1 Z1 T2 Z2 T' Z' Rp
[grd] [N] [N] [N] [N] [N] [N] [N]
0 0,00 -12433,05 0,00 -7056,83 0,00 -9744,94 9744,94
10 -2132,51 -12036,40 -1223,39 -6971,60 -1677,95 -9504,00 9650,99
20 -3901,93 -10666,81 -2426,97 -6701,73 -3164,45 -8684,27 9242,85
30 -5008,50 -8627,77 -3566,00 -6210,37 -4287,25 -7419,07 8568,73
40 -5268,65 -6240,21 -4555,12 -5462,30 -4911,88 -5851,25 7639,62
50 -4647,69 -3871,13 -5269,42 -4454,36 -4958,56 -4162,74 6474,23
60 -3265,05 -1867,17 -5565,53 -3243,93 -4415,29 -2555,55 5101,53
70 -1368,91 -491,31 -5320,11 -1963,41 -3344,51 -1227,36 3562,61
80 716,38 122,85 -4476,48 -811,05 -1880,05 -344,10 1911,28
90 2658,68 -12,70 -3084,21 -14,73 -212,77 -13,72 213,21
100 4185,14 -758,26 -1316,15 225,70 1434,50 -266,28 1459,00110 5129,57 -1893,09 547,36 -196,45 2838,46 -1044,77 3024,63
120 5448,22 -3175,56 2166,92 -1239,19 3807,57 -2207,37 4401,15
130 5202,96 -4398,17 3216,05 -2678,70 4209,51 -3538,44 5499,13
140 4521,75 -5422,28 3465,83 -4104,94 3993,79 -4763,61 6216,29
150 3552,18 -6186,32 2882,32 -4965,16 3217,25 -5575,74 6437,36
160 2422,98 -6690,69 1740,64 -4758,44 2081,81 -5724,56 6091,35
170 1222,93 -6968,97 640,71 -3616,32 931,82 -5292,64 5374,04
180 0,00 -7056,83 0,00 -2878,17 0,00 -4967,50 4967,50
190 -1223,39 -6971,60 4740,04 26753,89 1758,32 9891,14 10046,21
200 -2426,97 -6701,73 9400,27 25697,76 3486,65 9498,02 10117,76210 -3566,00 -6210,37 4465,09 7691,67 449,54 740,65 866,40
220 -4555,12 -5462,30 3258,47 3859,34 -648,32 -801,48 1030,87
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230 -5269,42 -4454,36 2643,49 2201,81 -1312,97 -1126,27 1729,85
240 -5565,53 -3243,93 2855,45 1632,93 -1355,04 -805,50 1576,37
250 -5320,11 -1963,41 3738,39 1341,72 -790,86 -310,84 849,76
260 -4476,48 -811,05 4969,21 852,13 246,36 20,54 247,22
270 -3084,21 -14,73 6192,51 -29,58 1554,15 -22,16 1554,31
280 -1316,15 225,70 7109,63 -1288,12 2896,74 -531,21 2945,04
290 547,36 -196,45 7532,01 -2779,72 4039,68 -1488,08 4305,05300 2166,92 -1239,19 7397,71 -4311,84 4782,32 -2775,51 5529,38
310 3216,05 -2678,70 6678,43 -5645,42 4947,24 -4162,06 6465,13
320 3465,83 -4104,94 5613,03 -6730,90 4539,43 -5417,92 7068,26
330 2882,32 -4965,16 4302,50 -7493,03 3592,41 -6229,09 7190,76
340 1740,64 -4758,44 2876,36 -7942,64 2308,50 -6350,54 6757,11
350 640,71 -3616,32 1432,30 -8162,10 1036,51 -5889,21 5979,73
360 0,00 -2878,17 0,00 -7860,01 0,00 -5369,09 5369,09
370 4740,04 26753,89 -1351,26 -7700,24 1694,39 9526,82 9676,33
380 9400,27 25697,76 -2656,59 -7335,79 3371,84 9180,99 9780,58
390 4465,09 7691,67 -3867,60 -6735,62 298,75 478,03 563,70
400 3258,47 3859,34 -4895,59 -5870,58 -818,56 -1005,62 1296,65
410 2643,49 2201,81 -5612,55 -4744,41 -1484,53 -1271,30 1954,49
420 2855,45 1632,93 -5872,18 -3422,66 -1508,36 -894,86 1753,84
430 3738,39 1341,72 -5548,43 -2047,67 -905,02 -352,98 971,42
440 4969,21 852,13 -4582,08 -830,18 193,56 10,98 193,88
450 6192,51 -29,58 -3020,15 -14,43 1586,18 -22,00 1586,33
460 7109,63 -1288,12 -1032,56 177,07 3038,53 -555,53 3088,90
470 7532,01 -2779,72 1103,86 -396,18 4317,93 -1587,95 4600,67
480 7397,71 -4311,84 3053,11 -1745,97 5225,41 -3028,90 6039,80
490 6678,43 -5645,42 4487,38 -3737,61 5582,90 -4691,51 7292,40
500 5613,03 -6730,90 5155,64 -6106,36 5384,33 -6418,63 8377,94
510 4302,50 -7493,03 4936,30 -8503,40 4619,40 -7998,22 9236,36
520 2876,36 -7942,64 3862,61 -10559,31 3369,48 -9250,98 9845,51
530 1432,30 -8162,10 2117,34 -11950,75 1774,82 ####### 10211,84
540 0,00 -7860,01 0,00 -12457,46 0,00 ####### 10158,73
550 -1351,26 -7700,24 -2132,51 -12036,40 -1741,88 -9868,32 10020,87
560 -2656,59 -7335,79 -3901,93 -10666,81 -3279,26 -9001,30 9580,03
570 -3867,60 -6735,62 -5008,50 -8627,77 -4438,05 -7681,70 8871,57
580 -4895,59 -5870,58 -5268,65 -6240,21 -5082,12 -6055,39 7905,42
590 -5612,55 -4744,41 -4647,69 -3871,13 -5130,12 -4307,77 6698,88
600 -5872,18 -3422,66 -3265,05 -1867,17 -4568,61 -2644,92 5279,00610 -5548,43 -2047,67 -1368,91 -491,31 -3458,67 -1269,49 3684,29
620 -4582,08 -830,18 716,38 122,85 -1932,85 -353,67 1964,94
630 -3020,15 -14,43 2658,68 -12,70 -180,73 -13,56 181,24
640 -1032,56 177,07 4185,14 -758,26 1576,29 -290,60 1602,85
650 1103,86 -396,18 5129,57 -1893,09 3116,71 -1144,63 3320,26
660 3053,11 -1745,97 5448,22 -3175,56 4250,67 -2460,76 4911,57
670 4487,38 -3737,61 5202,96 -4398,17 4845,17 -4067,89 6326,41
680 5155,64 -6106,36 4521,75 -5422,28 4838,69 -5764,32 7525,98
690 4936,30 -8503,40 3552,18 -6186,32 4244,24 -7344,86 8482,96
700 3862,61 -10559,31 2422,98 -6690,69 3142,79 -8625,00 9179,75
710 2117,34 -11950,75 1222,93 -6968,97 1670,13 -9459,86 9606,16
720 0,00 -12457,46 0,00 -7056,83 0,00 -9757,14 9757,14
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Engine's external characteristic calculus
Effective Power:
66 kW
5750 rpm
Specific fuel consumption
298
Fuel consumption per hour
Torque
a b c d k
1 1 1,2 1 0,8
n
(rot/min)
1000 13,127 312,984 4,108645 94,89623
1100 14,579 309,316 4,509653 95,81225
1200 16,049 305,792 4,907521 96,67808
1300 17,533 302,412 5,302074 97,49372
1400 19,030 299,176 5,693181 98,25916
1500 20,537 296,085 6,080748 98,97441
1600 22,054 293,137 6,464715 99,63947
1700 23,576 290,334 6,845059 100,25431800 25,104 287,675 7,221782 100,819
1900 26,634 285,161 7,594917 101,3335
2000 28,164 282,790 7,964517 101,7978
2100 29,693 280,564 8,330657 102,2119
2200 31,217 278,482 8,69343 102,5758
2300 32,736 276,544 9,052944 102,8895
2400 34,247 274,750 9,409318 103,153
2500 35,748 273,101 9,76268 103,3663
2600 37,236 271,596 10,11316 103,5294
2700 38,710 270,235 10,4609 103,6424
2800 40,168 269,018 10,80603 103,7051
2900 41,608 267,945 11,14869 103,7177
3000 43,027 267,017 11,489 103,68
P = P ann
+ b nn
n
n
=3 10
=
+
= 10
P []
P=
=
=
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3100 44,424 266,233 11,82707 103,5922
3200 45,796 265,593 12,16301 103,4541
3300 47,141 265,097 12,49692 103,2659
3400 48,457 264,746 12,82885 103,0275
3500 49,743 264,538 13,15887 102,7389
3600 50,995 264,475 13,48698 102,4001
3700 52,213 264,556 13,8132 102,01113800 53,393 264,782 14,13748 101,5719
3900 54,534 265,151 14,45976 101,0825
4000 55,634 265,665 14,77995 100,5429
4100 56,690 266,323 15,09788 99,95318
4200 57,701 267,125 15,41338 99,31322
4300 58,664 268,072 15,72623 98,62306
4400 59,578 269,162 16,03613 97,88271
4500 60,440 270,397 16,34276 97,09217
4600 61,248 271,776 16,64574 96,25144
4700 62,000 273,299 16,94461 95,36051
4800 62,694 274,967 17,23889 94,41939
4900 63,329 276,778 17,528 93,42808
5000 63,901 278,734 17,81132 92,38658
5100 64,409 280,834 18,08813 91,29488
5200 64,850 283,079 18,35766 90,15299
5300 65,223 285,467 18,61907 88,9609
5400 65,526 288,000 18,87142 87,71862
5500 65,756 290,677 19,11371 86,42615
5600 65,911 293,498 19,34484 85,08349
5700 65,990 296,463 19,56363 83,69063
5800 65,990 299,573 19,7688 82,24758
5900 65,909 302,827 19,959 80,75434
6000 65,745 306,225 20,13275 79,2109
6100 65,496 309,767 20,2885 77,61727
6200 65,160 313,453 20,42458 75,97345
6300 64,735 317,284 20,53922 74,27943
6400 64,218 321,259 20,63054 72,53523
6500 63,608 325,378 20,69656 70,74082
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Rod - Crank mechanism kinematics
- crank angle of rotation
- tilt angle of the rod axis
- angular speed of the crankshaft
S - stroke
R - crank radius
L - rod length
- ratio between crank rad and rod length
602,14 rad/s
R=S/2= 39,62596 mm
=R/L= 1/3,6= 0,277778
max= 15
L=R/= 142,6535 mm
0,005033 m2
Piston movement: D= 0,080052 m
Cylinder volume at a given moment:
Piston speed:
- maximum speed angle
Piston acceleration:
=
4 =
=
30 =
5750
30 =
= +1
1
= 1
41 2
=
2 2
=
4
= 1
4
+1
2
1
4
= 2
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[grd] [grd] SX[m] Vp[l] vp[m/s] j [m/s2]
0 0,00000 0,00000 0,00000 0,00000 18358,114
10 0,04825 0,00077 0,00387 5,27673 17899,163
20 0,09515 0,00303 0,01527 10,29087 16557,973
30 0,13934 0,00668 0,03365 14,80011 14437,824
40 0,17951 0,01154 0,05811 18,60071 11698,940
50 0,21443 0,01738 0,08750 21,54165 8542,05960 0,24295 0,02394 0,12050 23,53359 5188,163
70 0,26408 0,03093 0,15569 24,55152 1856,676
80 0,27709 0,03808 0,19168 24,63126 -1255,372
90 0,28148 0,04513 0,22714 23,86032 -3990,894
100 0,27709 0,05184 0,26094 22,36440 -6245,056
110 0,26408 0,05804 0,29212 20,29121 -7971,081
120 0,24295 0,06357 0,31994 17,79369 -9179,057
130 0,21443 0,06833 0,34390 15,01448 -9928,082
140 0,17951 0,07226 0,36367 12,07353 -10312,917
150 0,13934 0,07532 0,37909 9,06021 -10446,930160 0,09515 0,07751 0,39010 6,03055 -10443,568
170 0,04825 0,07882 0,39669 3,00987 -10398,735
180 0,00000 0,07925 0,39889 0,00000 -10376,325
190 -0,04825 0,07882 0,39669 -3,00987 -10398,735
200 -0,09515 0,07751 0,39010 -6,03055 -10443,568
210 -0,13934 0,07532 0,37909 -9,06021 -10446,930
220 -0,17951 0,07226 0,36367 -12,07353 -10312,917
230 -0,21443 0,06833 0,34390 -15,01448 -9928,082
240 -0,24295 0,06357 0,31994 -17,79369 -9179,057
250 -0,26408 0,05804 0,29212 -20,29121 -7971,081
260 -0,27709 0,05184 0,26094 -22,36440 -6245,056
270 -0,28148 0,04513 0,22714 -23,86032 -3990,894
280 -0,27709 0,03808 0,19168 -24,63126 -1255,372
290 -0,26408 0,03093 0,15569 -24,55152 1856,676
300 -0,24295 0,02394 0,12050 -23,53359 5188,163
310 -0,21443 0,01738 0,08750 -21,54165 8542,059
320 -0,17951 0,01154 0,05811 -18,60071 11698,940
330 -0,13934 0,00668 0,03365 -14,80011 14437,824
340 -0,09515 0,00303 0,01527 -10,29087 16557,973
350 -0,04825 0,00077 0,00387 -5,27673 17899,163
360 0,00000 0,00000 0,00000 0,00000 18358,114370 0,04825 0,00077 0,00387 5,27673 17899,163
380 0,09515 0,00303 0,01527 10,29087 16557,973
390 0,13934 0,00668 0,03365 14,80011 14437,824
400 0,17951 0,01154 0,05811 18,60071 11698,940
410 0,21443 0,01738 0,08750 21,54165 8542,059
420 0,24295 0,02394 0,12050 23,53359 5188,163
430 0,26408 0,03093 0,15569 24,55152 1856,676
440 0,27709 0,03808 0,19168 24,63126 -1255,372
450 0,28148 0,04513 0,22714 23,86032 -3990,894
460 0,27709 0,05184 0,26094 22,36440 -6245,056470 0,26408 0,05804 0,29212 20,29121 -7971,081
480 0,24295 0,06357 0,31994 17,79369 -9179,057
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490 0,21443 0,06833 0,34390 15,01448 -9928,082
500 0,17951 0,07226 0,36367 12,07353 -10312,917
510 0,13934 0,07532 0,37909 9,06021 -10446,930
520 0,09515 0,07751 0,39010 6,03055 -10443,568
530 0,04825 0,07882 0,39669 3,00987 -10398,735
540 0,00000 0,07925 0,39889 0,00000 -10376,325
550 -0,04825 0,07882 0,39669 -3,00987 -10398,735560 -0,09515 0,07751 0,39010 -6,03055 -10443,568
570 -0,13934 0,07532 0,37909 -9,06021 -10446,930
580 -0,17951 0,07226 0,36367 -12,07353 -10312,917
590 -0,21443 0,06833 0,34390 -15,01448 -9928,082
600 -0,24295 0,06357 0,31994 -17,79369 -9179,057
610 -0,26408 0,05804 0,29212 -20,29121 -7971,081
620 -0,27709 0,05184 0,26094 -22,36440 -6245,056
630 -0,28148 0,04513 0,22714 -23,86032 -3990,894
640 -0,27709 0,03808 0,19168 -24,63126 -1255,372
650 -0,26408 0,03093 0,15569 -24,55152 1856,676
660 -0,24295 0,02394 0,12050 -23,53359 5188,163
670 -0,21443 0,01738 0,08750 -21,54165 8542,059
680 -0,17951 0,01154 0,05811 -18,60071 11698,940
690 -0,13934 0,00668 0,03365 -14,80011 14437,824
700 -0,09515 0,00303 0,01527 -10,29087 16557,973
710 -0,04825 0,00077 0,00387 -5,27673 17899,163
720 0,00000 0,00000 0,00000 0,00000 18358,114