Calculation of the engines’ partial powers by successively activating their chambers of combustion

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March 2009 Adapted from original document February, 11th 2005

Setting of survey

POGDC engine with 1652,65 cm3 from 1 central chamber and 4 auxiliary chambers PRBC engine with 1149,09 cm3 from 4 same chambers The engines (or joined engines) which will be analysed are : - only 1 POGDC engine - only 1 PRBC engine - 1 POGDC engine and from 1 to 4 PRBC engines - 2 POGDC engines Chamber central auxiliary - 2 PRBC engines unit max 313,09 256,62 - 2 POGDC engines and from 1 to 8 PRBC volume (cm3) The 5 main data of the survey are : - the number of POGDC engines : = N O - the number PRBC engines : = N R - the maximum volume of a central chamber - the maximum volume of an auxiliary chamber - the maximum volume of a PRBC’s chamber

unit power (HP)

20,35x2 = 40,70 (2 cycles / 2 rounds of crankshaft)

16,68 (1cycle/ 2 rounds of crksft)

of PRBC 287,27 18,67 (1cycle / 2 rounds of crksft)

One deducts from this 5 values : - the number of the engine’s central chambers : N cc = N O - the number of the engine’s auxiliary chambers : N ca = 4 N O - the number of all the PRBC’s chambers : N cp = 4 N R - the effective used volume, then the real available power, according to the number and type of active chambers. The power of the central chamber must be doubled because it supplies 2 cycles on 2 crankshaft’s rounds, either 2 times more than other types of chambers, recovering by hypothesis 65 HP/1000 cm3. For each engine, one classifies the set of the combinations of active rooms by increasing available powers. One gets from it a picture assigning a number to every combination and a diagram that represents the steps of possible powers in partial use of the motor. The number of combinations is computed with the following reasoning : -

No active chamber : 1 possibility Only central chambers are active : possibilities = N O

-

Only auxiliary chambers are active : possibilities = 4 N O

-

Only PRBC’s chambers are active : possibilities = 4 N R

-

Only central and auxiliary chambers are active : possibilities = Ncc x Nca = 4 N O2

-

Only central and PRBC’s chambers are active : possibilities=Ncc x Ncp = 4 N O N R

-

Only auxiliary and PRBC’s chambers are active : possibilities=Nca x Ncp = 16 N O N R

-

All types of chambers are active possibilities = Ncc x Nca x Ncp = 16 N O2 N R

Either the total number of cases N tot = 1 + 5 N O + 4 N R + 4 N O2 + 20 N O N R + 16 N O2 N R Exclusive intellectual property of SYCOMOREEN, authorized reproduction solely for non-profit scientific research or educational and school applications

2 One notices that the number of possibilities explodes very quickly without giving big values to NO and NR, as the picture indicates it below : (The motors studied in this annex are pasted in yellow) Number of POGDC (NO) 0 0 0 0 1 1 1 1 1 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3

Number of PRBC (NR) 1 2 3 4 0 1 2 3 4 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 9 10 11 12

Number of possibilities 5 9 13 17 10 50 90 130 170 27 135 243 351 459 567 675 783 891 52 260 468 676 884 1092 1300 1508 1716 1924 2132 2340 2548

One will use in the pictures below the following notations : - Nb HP cent actives : number of active central chambers on POGDC engines - Nb HP auxiliaires actives : number of auxiliary active chambers on POGDC engines - Nb HP mot. cyl. actives : number of active chambers on PRBC engines - Max volume capacity utilisée : sum of the max volumes of each active chamber - Puissance dispo : available power in HP on the base of 65 HP/1000 cm3 - %Puiss maxi : 100 x available power / max power. Naturally, the maximal power is given by the activation of all rooms without exception. For the associations of motors where there is a very elevated number of cases (> 100), we will give the diagram of the possible percentages solely because it permits a more synthetic overview. Exclusive intellectual property of SYCOMOREEN, authorized reproduction solely for non-profit scientific research or educational and school applications

3

Analysis of only 1 POGDC engine max volume capacity 1652,7 cm3, maximal power 107,5 HP

Possible percentages in partial use of the engine

cas n°

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4

Analysis of only 1 PRBC engine max volume capacity 1149,1 cm3, maximal power 74,7 HP

Possible percentages in partial use of the engine

cas n°

Analysis of 2 joined PRBC engines max volume capacity 2298,3 cm3, maximal power 149,4 HP

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5

Possible percentages in partial use of the engine

cas n°

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6

Analysis of 1 POGDC engine joined with 1 PRBC engine max volume capacity 2801,7 cm3, maximal power 182,1 HP

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7

Possible percentages in partial use of the engine

cas n°

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8

Analysis of 1 POGDC engine joined with 2 PRBC engines max volume capacity 3950,9 cm3, maximal power 256,8 HP

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9

Possible percentages in partial use of the engine

cas n°

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10

Analysis of 1 POGDC engine joined with 3 PRBC engines max volume capacity 5099,9 cm3, maximal power 331,5 HP 130 possible cases

Possible percentages in partial use of the engine

cas n°

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11

Analysis of 1 POGDC engine joined with 4 PRBC engines max volume capacity 6249 cm3, maximal power 406,2 HP 170 possible cases

Possible percentages in partial use of the engine

cas n°

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12

Analysis of 2 joined POGDC engines max volume capacity 3305,3 cm3, maximal power 214,8 HP

Possible percentages in partial use of the engine

cas n° Exclusive intellectual property of SYCOMOREEN, authorized reproduction solely for non-profit scientific research or educational and school applications

13

Analysis of 2 POGDC engines joined with 1 PRBC engine max volume capacity 4454,4 cm3, maximal power 289,5 HP 135 possible cases

Possible percentages in partial use of the engine

cas n°

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14

Analysis of 2 POGDC engines joined with 2 PRBC engines max volume capacity 5603,5 cm3, maximal power 364,2 HP 243 possible cases

Possible percentages in partial use of the engine

cas n°

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15

Analysis of 2 POGDC engines joined with 3 PRBC engines max volume capacity 6752,6 cm3, maximal power 438,9 HP 351 possible cases

Possible percentages in partial use of the engine

cas n°

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16

Analysis of 2 POGDC engines joined with 4 PRBC engines max volume capacity 7901,7 cm3, maximal power 513,6 HP 459 possible cases

Possible percentages in partial use of the engine

cas n°

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17

Analysis of 2 POGDC engines joined with 5 PRBC engines max volume capacity 9050,8 cm3, maximal power 588,3 HP 567 possible cases

Possible percentages in partial use of the engine

cas n°

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18

Analysis of 2 POGDC engines joined with 6 PRBC engines max volume capacity 10199,9 cm3, maximal power 663 HP 675 possible cases

Possible percentages in partial use of the engine

cas n°

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19

Analysis of 2 POGDC engines joined with 7 PRBC engines max volume capacity 11349 cm3, maximal power 737,7 HP 783 possible cases

Possible percentages in partial use of the engine

cas n°

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20

Analysis of 2 POGDC engines joined with 8 PRBC engines max volume capacity 12498,1 cm3, maximal power 812,4 HP 891 possible cases

Possible percentages in partial use of the engine

cas n°

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Conclusion

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Some facts •

•

Case of only PRBC engines o These engines have only one type of chambers, then it is necessary to strongly increase their number if one wants to bring closer the steps of partial powers. o If N PRBC engines are joined, there is 4N steps and this number doesn’t increase a lot with N (linear increase). Thus there is quite few steps regarding the number of chambers.

Steps of partial use for 1 POGDC engine +1 PRBC engine

Case of POGDC engines or associations of joined case n° POGDC/PRBC engines : o One finds on all diagrams of these motors the following facts :
The biggest steps between 2 consecutive partial powers take place : • Nearly the very weak powers • Nearly the very strong powers
The tiniest steps are in the area of low to strong powers, often with an increased sharpness in the medium powers (50% of max power) o The only POGDC engines bring a quite big number of combinations, thus of possible partial powers. o The association of PRBC and POGDC engines leads to an exponential increase of the steps’ number : not less than 50 steps with only one POGDC engine joined with one PRBC engine !

How to choose and make run the engine ? •

First of all, there is a big interest to join one or several PRBC engines with one or several POGDC engines, rather than only several POGDC, or only several PRBC.

•

The fact that steps are bigger at minimum and maximum powers doesn’t worry because the regulating sharpness is there less useful than for medium powers.

•

It won’t probably be necessary to use all available steps of power. After having estimated the ideal power to provide according to sensors’ information, the CPU of the engine will select the preprogramed steps which will optimize : o the transitions of a power to the other by an activation or a deactivation of a minimum of rooms between 2 consecutive steps o the management of the engine by the search for balances when it is running :
in the transmission of the strengths : not to give all the power to only one crankshaft, in order to balance the charges,
in the wear of the parts : during the life of the engine, to solicit the set of the rooms of combustion in an equal way. o the fluctuations of the instantaneous torque on the crankshaft, etc…

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22

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