WO1986004111A1

WO1986004111A1 - Internal combustion engine

Info

Publication number: WO1986004111A1
Application number: PCT/GB1986/000002
Authority: WO
Inventors: John Heath Greenhough
Original assignee: John Heath Greenhough
Priority date: 1985-01-05
Filing date: 1986-01-03
Publication date: 1986-07-17
Also published as: GB2169960B; AU5304786A; GB8519987D0; GB2169960A; GB8500270D0; EP0207970A1; GB8600101D0

Abstract

An internal combustion engine which includes means for injecting fuel (petrol or diesel) into a working chamber (cylinder) during a compression stroke. In a lower portion of the power range of the engine from tickover (A) to a transition point (B) a single main fuel charge is injected which may vary from 15% stoichiometric at tickover up to 40% stoichiometric at the transition point (B). In an upper portion of the power range, from B to C, an additional secondary charge of fuel is introduced prior to the main injection and with air in the cylinder forms a mixture which ignites and burns with the main charge. The quantity of the second charge increases from the transition point up to full power C. The secondary fuel can be introduced by a second injection into the cylinder or can be introduced into air aspirated in an induction stroke.

Description

INTERNAL COMBUSTION ENGINE

This invention relates to a four-stroke internal combustion engine. Over the last sixty years there have been many attempts to develop an engine that would bridge the gap between the pre-mixed spark ignited and the compression ignition cycles. This has not heretofore been achieved because the processes that control the burning of hydrocarbon fuels in the cylinder of the engine are complex and have not been fully understood. Combustion occurs between limited fuel-air ratios that will be affected by cylinder temperature, volatility and boiling point of the fuel, and method of introduction. After ignition takes place there is a minimum temperature that must be maintained for flame propogation to continue. Most fuels of the higher hydro-carbons have two temperature/pressure/ignition stages. There is a high temperature/ pressure region and a low temperature/pressure region. When fuel and air are compressed, before ignition, in the pre-mixed "petrol" engine cycle, organic peroxides are generated by the chemical changes that take place. These peroxide gases cause a first stage ignition (cool flame). This first combustion generates gases that on reaching a minimum concentration affect the spontaneous ignition temperature. When fuel is injected into the cylinder in the compression ignition cycle, the temperature necessary for the generation of organic peroxides has already been exceeded, so that ignition is initiated in the high temperature/ pressure region. Fuels have been selected and anti-oxidants added (tetra-ethyl lead etc.,) to retard the first ignition (cool flame). These fuels are used in the premixed engine. Fuels with low resistance to second stage spontaneous ignition are selected for. compression ignition engines. It is the purpose of this invention to use the best features of both compression ignition and pre-mixed engine cycles to achieve an engine with greater overall efficiency, The introduction of fuel into an engine in two stages is well known in the internal combustion engine. The usual reasons for this are the burning of alcohol-base fuels or the introduction of two fuels of different qualities which are then ignited by spark or compression ignition. There are also two stage injections for ease of starting. When the engine reaches a pre-determined speed, the fuel injection reverts to single stage.

The next type of two stage injections is the pilot charge method. A small charge of fuel is injected ahead of the main charge in the compression ignition cycle. This commences to burn. The main charge is then injected. This is ignited on entry by the pilot charge. This reduces the delay so that combustion can progress smoothly. There is also a two-stage method with a main and secondary injection in the compression ignition cycle. The secondary injection is generally less than the main injection. According to this method there is a phased difference between the two injections ranging from 320°-360° of crank shaft rotation. The essential conditions necessary to attain improved results, according to this known proposal, is to inject a first fraction of the fuel charge into the hot residual gases remaining in the cylinder towards the end of the exhaust stroke. By injecting fuel into the low-oxygen high-temperature residual exhaust gas it is subjected to partial combustion and chemical reaction. This reaction continues until the fresh air entering the cylinder reduces the temperature of the gases thereby quenching the reaction. By subjecting the fuel to low oxygen combustion, the fuel is converted to carbon monoxide gas which is burned with the main charge at the end of the compression stroke. Carbon monoxide inhibits pre-flame reaction. This method of operation takes no account of the different chemical mechanisms in the two-stage ignition ranges. The behaviour of any fuel in the engine is influenced by the chemical reaction that takes place. Both the first and second stage ignition is controlled by temperature and pressure and the intensity is governed by the air-fuel ratio.

In the standard compression ignition cycle because temperature and pressure are the main factors governing ignition, injection is delayed as late as possible in the compression stroke so that the fuel will spontaneously ignite more readily. This limits the time available for injection. Although there is a degreee of pre-mixing before the quantity of fuel injected is sufficient to form an ignitable mixture and maintain it long enough for ignition to take place, most of the fuel burns in a diffuse flame as it leaves the injector. As the fuel is injected in droplet form, it is impossible to attain the same heat release as a completely-vaporised mixture of the same fuel-air ratio. Because of this the compression ignition engine has a poor power output when compared with the pre-mixed engine. The limits set by inadequate mixing control the quantity of fuel that can be burned without the generation of a smoky exhaust. Although the pre-mixed spark ignited engine has a big power advantage over the compression ignition engine it is not as economical because at light load it has difficulty in igniting or maintaining combustion when the mixture content in the cylinder is less than 80% stoichiometric chemically correct, hereinafter referred to as by the abbreviation 'STO'. Although the lean limits of flammability can be extended (ie reduced) by raising the compression temperature, the compression ratio is governed by the fuel's resistance to pre-flame reaction and detonation. Any fuel for pre-mixing in the compression ignition cycle must enter the cylinder with a boiling point and rate of evaporation that will allow complete mixing. The amout of fuel injected must be governed by its resistance to pre-flame reaction (cool flame). This hydrocarbon oxidation is a chemical process that will vary from a modest reaction at low pressure to a greatly intensified reaction as the pressure increases. With high velocity compression an appreciable amount of reaction occurs in the cool flame. When pre-mixed fuel is subjected to compression, thermo-chemical ignition (cool flame) will occur regardless of the fuel's concentration but the leaner the mixture the lower the intensity of the reaction. Although pre-flame reaction will speed up spontaneous combustion, the pre-mixing of fuel can only begin when the compression ignited defused flame combustion has raised the overall combustion chamber content to the temperature necessary for flame propogation to continue. When the compression ignition engine is in operation the fuel is heated up in the injector nozzle. Under load the fuel will be over 200 °C at the start of injection. Although the speed of vaporization increases with the temperature, the bulk of diesel oils has a boiling temperature and evaporation lifetime that is too high for pre-mixing. When diesel is injected into the cylinder early in the induction stroke the rate of evaporation will be retarded when the liquid fuel strikes the cool cylinder wall. Because of this the mixing will be incomplete and the engine efficiency will be impaired.

When injection is delayed until the start of compression the fuel will enter the cylinder under pressure. This will cause the boiling point to rise. With increased pressure the evaporation lifetime of the fuel will be extended so that the degree of mixing will be retarded. Because of poor mixing, pockets of fuel will ignite long before the piston reaches top dead centre. This will cause knocking and power loss and engine overheating. To overcome the problem of vaporizing high boiling point fuel it would be possible to use the heat from the exhaust manifold to vaporize the fuel before it enters the inlet manifold. Any gain in power would be nullified by a decrease in volumetic efficiency because of the higher inlet mixture temperature.

When fuel is burned in the internal combustion engine because of the very wide operating conditions the boiling point and the rate of vaporization are important factors to be taken into consideration. In the pre-mixed engine cycle the fuel must contain a reasonable proportion of low boiling point highly volatile fuel for cold starting. There must also be a fair proportion of less volatile, higher boiling point fuel for ease of starting when the engine is hot. There must also be fuel in the middle boiling range to meet the normal working requirements.

Although the proportions can vary from winter to summer a good pre-mixed engine fuel will have a boiling range from 25°C-210°C. When fuel is injected into hot compressed air in the compression ignition engine there is no need for low boiling point highly volatile fuel for cold starting because the cylinder will always have sufficient heat for a percentage of the fuel to vaporize. The only requirement is that the boiling range must be at a level to maintain the vaporizing fuel in sufficient concentration for spontaneous combustion to take place. At speed and load when the cylinder temperature is high a significant portion of the fuel must remain in sufficient concentration long enough for spontaneous combustion to take place before evaporation dilutes the fuel below the limits of combustion. A good diesel fuel to meet these requirements will have a boiling range from 150°C -350°C.

Because of the high boiling fuel requirements of the compression ignition engine it is impossible to achieve the degree of mixing that is required to achieve maximum combustion efficiency. To overcome this big disadvantage the higher boiling fraction of the fuel must be reduced, and to compensate for this increased spontaneous ignition delay that this reduction would cause a pre-mixed fraction of fuel is subjected to heat and compression to generate a pre-flame reaction that will accelerate the onset of combustion. By this method of operation the power of the compression ignition engine can be extended. The ideal fuel for this mode of operation would have a boiling range from 100°C-280°C.

Because the pre-mixed fuel is pre-heated in the injector nozzle a wide boiling range fuel can be used.

The same wide boiling range fuel must be vaporized on the back of the hot inlet valve so that no pre-heating in the manifold is required.

Kerosene Diesel Oil Vaporizing Oil

Initial Boiling Point 160°C 180°C 145°C

50% over at 210°C 260°C 196°C Final boiling point 285°C 360°C 266°C

Gasolene - Boiling Bange 25°C - 210°C Total Vaporization Summer Winter

Volume up to 70°C 15% - 40% 20% - 45% Volume up to 100°C 42% - 65% 45% - 70% " " " 180°C 90% 90%

Final Boiling Point 215°C 215°C

It is an object of the present invention to provide an improved combustion engine and a method of operating an internal combustion engine.

The invention provides a method of operating a four-stroke compression ignition internal combustion engine including a cylinder whose volume varies cyclically, and which is provided with means for injecting a hydrocarbon fuel into the cylinder during a compression stroke of the engine, wherein over a lower part of a power range thereof, from tickover up to a transition point, engine power is varied by varying the quantity of a main injection of fuel late in the compression stroke from a minimum at tick-over up to higher value at the transition point, and wherein over a higher part of the power range from the transition point up to full power, the main injection of fuel is supplemented by a secondary introduction of the same fuel, which is initiated earlier in the compression stroke and which mixes with air in the cylinder to form a combustible mixutre which is burnt simultaneously with the main injection of fuel, the secondary injection of fuel taking place under conditions of temperature and pressure which ensure evaporation thereof, and sufficiently early to allow a pre-flame reaction to occur in the mixture of secondary fuel and air before the main injection of fuel.

In the engine of the invention low octane non-leaded fuel in the Kerosene and Gasoline boiling range can be burned at high compression ratios without knock with fuel-air ratios that are continuously variable from 15% to 100% stochiometric (chemically correct).

The invention will be described further, by way of example, with reference to the accompanying drawings, wherein:-

Fig. 1 is a set of diagrams illustrating operation of a conventional compression ignition engine;

Fig. 2 is a similar set for a first preferred engine of the invention; Fig. 3 is a similar set for a second preferred engine of the invention; and

Fig. 4 is a similar set for a third preferred engine of the invention;

Fig. 5 is a similar set for a fourth, but with a lower BP fuel;

Fig. 6 is a similar set for a fifth, but with higher resistance to pre-flame reaction. In each of the sets of diagrams 'TDC' indicates top dead centre in a cylinder of a reciprocatingpiston engine, other angles being given in relation to TDC. A main injection of fuel is indicated by vertical hatching, and a secondary introduction of fuel by horizontal hatching. STO is used as an abbreviation for stoichiometric. In each set of the diagrams the far left-hand diagram (A) illustrates lowest power (tickover) and the far right diagram (C or D) indicates full power. In each case diagram (B) indicates a transition point.

In the conventional compression-ignition engine using " diesel"fuel, illustrated in Fig. 1, there is a single main injection of fuel which usually commences at or about 25° before TDC. At this point the cylinder is hot enough to initiate ignition of the injected fuel and the combustion starts immediately after injection commences, and finishes shortly after injection ceases. At full power injection may continue up to or beyond TDC, although 70% STO tends to be a maximum, value, higher values causing a smoky exhaust. The diagrams are drawn to illustrate progressively longer periods of injection from low to high power, consistent with an injector construction and size wherein the rate of injection is constant the quantity of fuel injected being varied by varying the period of operation of the injector. This is in accord with conventional practice, but it will be appreciated that with appropriate re-design of the injection system fuel quantity could be regulated by variation of the rate of supply instead of or as well as the period of injection. A first preferred embodiment of engine operating in accordance with a first preferred method of the invention is identical to the Fig. 1 engine over a lower part of its power range from A to B. The transition point B is chosen in relation to the characteristics of the fuel to occur at that position wherein after combustion of the main fuel portion the temperature within the cylinder is everywhere greater than 1200°C. This is usually at a position wherein the quantity of fuel injected in the main injection is about 35%-45% of and usually 40% STO. Above the transition point B up to maximum power (diagram C) , the quantity of the main fuel injection is progressively increased up to 60% STO at full power, but the increase is less than would occur in the conventional engine of Fig. 1. From the point B upwardly in the power range an additional injection of fuel takes place before the main injection and with air in the cylinder forms a mixture which is ignited upon ignition of the main injection of fuel. The engine of Fig. 2 uses an additional fuel injection from the same injector as supplies the main fuel charge, and this can very simply be achieved in a conventional injector arrangement by a relatively minor modification to the reciprocating pump member of the injector arrangement. The quantity of fuel in the secondary charge varies from 0%STO at B up to 25%STO at maximum power. Because the additional fuel is pre-mixed, it is possible by this means to increase the maximum power of the engine. The maximum power is that which is generated by an 85%STO mixture rather than 70%STO in a conventional diesel without a smoky exhaust.

It is important that the secondary fuel charge mixes well. The bulk of diesel oil has a boiling point too high for pre-mixing.

It is therefore necessary to reduce the boiling point of the fuel. It is desirable that a liquid fuel such as kerosene or petrol in the boiling range 100°C-280°C must be used. Such a fuel mixes well at the temperatures apertaining to the conventional compression ignition engine. Any increase in volatility in the conventional compression ignition engine will retard the onset of spontaneous combustion. This will be detrimental at speed and load. It is an object of the present invention to overcome this delay by using the thermo-chemical changes that take place when pre-mixed fuel is subjected to compression. By the use of pre-flame reaction as a trigger mechanism to speed up the onset of spontaneous combustion a wide range of fuels can be used in the compression ignition engine cycle.

Most fuels of the higher hydro-carbons will have pre-flame reaction when pre-mixedandsubjected to compression This reaction will vary in intensity from high to low depend ing on the types of hydro-carbon used.

Assuming the engine to be asperating unheated ambient air it is desirable to commence injection of secondary fuel when the piston has reached bottom dead centre. At this stage the air will have gained sufficient heat for rapid evaporation. Also at this point fuel will be at its lowest boiling point and highest rate of evaporation due to the partial vacuum created by incomplete filling of the cylinder, With the sudden reversal of air motion caused by the change in piston direction accelerated mixing and distribution takes place. Although this is the optimum for good pre-mixing, these limits are by no means rigid providing the fuel is all evaporated before its boiling point is raised by excessive pressure rise. The optimum timing will be between bottom dead centre and 140°C before top dead centre to coincide with the closing of the inlet valve. However, this can be varied by changes in inlet valve timing fuel volatility and the onset of pressure rise so that injection can take place up to 100° before T.D.C. without detriment. Injection can start up to about 25° before B.D.C.

Fig. 3 illustrates a variation on the method illustrated in Fig. 2 in which a low boiling point fuel in the kerosene petrol range with a higher resistance to pre-flame reaction. The principles are the same as those described in relation to Fig. 2 except that the main charge increases after the transition point B from 40% STO up to a maximum of say 50% STO at about three quarters power (C) and thereafter remains constant up to full power. The quantity of the second charge rises slowly from 0%C STO at B to 10%STO at C and more rapidly from 10% STO at C to 40% at D (full power)

Fig. 4 illustrates a variation on the method illustrated in Fig. 2 in which high boiling point fuel

(diesel) is injected via a second injector on to the back of the hot inlet valve during the induction stroke of the engine to provide a pre-mixed charge prior to the main charge. Because of its high boiling point diesel fuel will not evaporate when injected into the asperated air in the inlet manifold during the induction stroke of the engine because it requires a temperature of 300 °C at atmospheric pressure to vaporize.

Under load the inlet valve or valves of the compression ignition engine vary in temperature from 350°-450 °C and in an engine operating in accordance with the preferred method of this invention will reach a temperature over 300°C at the transition point B.

At this point the secondary fuel is impinged on the inlet valve so that instant vaporization takes place at the time of maximum air speed through the inlet port. This causes instantaneous and complete mixing.

With this method of operation it has been found that the main injection can rise to 65% STO at full power and the quantity of the second charge can rise to 25% STO. This gives a maximum power equivalent to 90%STO without a smoky exhaust. This is close to the maximum theoretical power and still gives a clean burn with minimum emission of noxious exhaust components.

Fig. 5 illustrates a method identical to the method illustrated in Fig. 4 but the fuel used is in the kerosene, petrol boiling range and has a low resistance to pre-flame reaction.

Fig. 6 illustrates a variation on the method illustrated in Fig. 4 and Fig. 5 in which a low boiling point fuel in the kerosene, petrol boiling range, with a higher resistance to pre-flame reaction is used. This cycle would be suitable for use in a supercharged engine wherein temperaturesare higher.

The principals are the same as those described in relation to Fig. 4 and Fig. 5 except that the main charge increases after the transition point B, from 40%STO up to a maximum of say 50%STO at about three quarters power and thereafter remains constant up to full power. The quantity of the second charge rises slowly from 0%STO at B to 10%STO at C and more rapidly from 10%STO to 40%STO at D (full power).

Actual engines embodying the invention are not described in detail as they differ from conventional engines only in their fuel introduction means and methods. As has been mentioned, a conventional diesel injector system can be very easily modified to cause it to operate in accordance with the invention. Electronically controlled fuel injection systems for petrol engines can be easily modified for operation in accordance with the invention. Although described in relation to reciprocating piston engines, it will be appreciated that the invention is equally applicable to all four stroke internal combus

tion engines in which there is cyclic variation of the size of a working chamber (conveniently referred to as a "cylinder"). Thus the invention can be applied to rotary engines such as the Wankel engine. The methods of the invention allow "diesel" engines to have much higher power than present diesels and a much livier response without excessively high compression ratios and without excessively smoky exhausts. In the "petrol" engine low octane, unleaded fuel can be used without problems of pre-ignition and with the economies that the use of low octane and the elimination of pre-ignition suppression agents can bring. Further, the petrol engine has a low quantity of unwanted products of combustion in its exhaust and its economics are good. Although described as primarily for use in a four-stroke engine, the invention is equally applicable to a direct-injected diesel two-stroke engine. The secondary fuel will normally be injected prior to the main injection after closure of the scavenge ports, but it is possible to use an injection into the air as pivoted via the crank-case, provided lubricant is added or the problems of crank-case lubrication is otherwise considered.

The average temperature of the inlet valve is between 350°C to 450°C in the diesel engine at full load. The fuel is impinged on the inlet valve during the induction stroke so that instantaneous vaporization takes place at the time of maximum air speed through the inlet port. This causes instantaneous and complete mixing.

The amount of fuel injected must be governed by but the leaner the mixture the lower the intensity of the reaction. Although pre-flame reaction will speed up spontaneous combustion, the pre-mixing of fuel can only begin when the compression ignited defused flame combustion has raised the overall combustion chamber content to the temperature necessary for flame propogation to continue.

When the compression ignition engine is in operation the fuel is heated up in the injector nozzle. Under load the fuel will be over 200°C at the start of injection. Although the speed of vaporization increases with the temperature, the bulk of diesel oils has a boiling temperature and evaporation lifetime that is too high for premixing. When diesel is injected into the cylinder early in the induction stroke the rate of evaporation will be retarded when the liquid fuel strikes the cool cylinder wall. Because of this the mixing will be incomplete and the engine efficiency will be impaired.

When injection is delayed until the start of compression the fuel will enter the cylinder under pressure. This will cause the boiling point to rise. With increased pressure the evaporation lifetime of the fuel will be extended so that the degree of mixing will be retarded. Because of poor mixing, pockets of fuel will ignite long before the piston reaches top dead centre. This will cause knocking and power loss and engine overheating.

To overcome the problem of vaporizing high boiling point fuel it wouid be possible to use the heat from the exhaust manifold to vaporize the fuel before it entered the inlet manifold. Any gain in power would be nullified by a decrease in volumetic efficiency because of the higher inlet mixture temperature.

It is an object of the present invention to provide an improved combustion engine and a method of operating an internal combustion engine in which low octane non-leaded fuel in the kerosene and gasoline boiling range can be burned at high compression ratios without knock with fuel-air ratios that are infinately variable from 15% to stochiometric chemically correct.

Claims

1. A method of operating a four-stroke compression ignition internal combustion engine including a cylinder whose volume varies cyclically, and which is provided with means for injecting a hydrocarbon fuel into the cylinder during a compression stroke of the engine, wherein over a lower part of a power range thereof, from tickover up to a transition point, engine power is varied by varying the quantity of a main injection of fuel late in the compression stroke from a minimum at tick-over up to higher value at the transition point, and wherein over a higher part of the power range from the transition point up to full power, the main injection of fuel is supplemented by a secondary introduction of the same fuel, which is initiated earlier in the compression stroke and which mixes with air in the cylinder to form a combustible mixture which is burnt simultaneously with the main injection of fuel, the secondary injection of fuel taking place under conditions of temperature and pressure which ensure evaporation thereof, and sufficiently early to allow a pre-flame reaction to occur in the mixture of secondary fuel and air before the main injection of fuel.

2. A method as claimed in claim 1 , wherein said transition point is chosen to be at or slightly above these conditions of temperature and pressure, which, related to the nature of the fuel involved, are such as to cause the secondary introduction of fuel, when mixed with air in the cylinder, to form a mixture which will propagate flame.

3. A method as claimed in claim 1 or 2 , wherein the transition point occurs at a point at which the amount of fuel injected during main injection is sufficient, after burning to raise the temperature everywhere within the cylinder to a value at least equal to 1200°C.

4. A method as claimed in claim 1, 2 or 3, wherein the transition point is chosen to coincide with a point at which the ratio of the main injection of fuel to the quantity of air in the cylinder is from 35% to 45% stoichiometric.

5. A method as claimed in claim 4, wherein the transition point is chosen to coincide with a main fuel injection quantity which is 40% stoichiometric.

6. A method as claimed in any preceding claim wherein over the higher part of the power range the quantity of fuel introduced during the main injection remains constant, the quantity of the secondary fuel being progressively increased.

7. A method as claimed in any of claims 1 to 5 , wherein over the upper part of the power range the quantity of fuel introduced in the main injection increases progessively.

8. A method as claimed in any preceding claim wherein the secondary fuel is introduced by a secondary injection into the cylinder chronologically before the main injection.

9. A method as claimed in any of claims 1 to 7 , wherein the secondary fuel is introduced into the air supply to the cylinder.

10. A method as claimed in claim 9, wherein the secondary fuel is introduced by means of a secondary injection into the air supply, such as into the inlet manifold.

11. A method as claimed in claim 9 , wherein the secondary fuel is introduced by means of a carburettor.

12. A method as claimed in any preceding claim wherein the fuel is diesel fuel and ignition is initiated by the main fuel injection.

13. A method as claimed in any preceding claim wherein the fuel is petrol and ignition is initiated by a spark after the main injection.

14. A method of operating an internal combustion engine substantially as hereinbefore described with reference to and as illustrated in Figs . 2 , 3 or 4 of the accompanying drawings.

15. A method as claimed in any preceding claim wherein the fuel has a boiling point in the kerosene-gasoline range from 100°C to 300°C and the secondary injection is affected directly into the cylinder at a stage in the compression stroke when the temperature within the cylinder is at or above the boiling point of the fuel and before the pressure rise within the cylinder has risen sufficiently to elevate the boiling point.

16. A method as claimed in any of claims 1 to 14, wherein the fuel has a mean or median boiling paint in the range 250°C to 350 °C ie diesel fuel, and the secondary injection step includes directing a stream of fuel to impinge on a surface which is at a temperature at or above the fuel boiling point.

17. A method as claimed in claim 16, wherein the said surface is a surface of a valve.

18. A method as claimed in claim 15, wherein the fuel is 28 seconds heating oil.

19. An internal combustion engine including a cylinder whose volume varies cyclically and which has means for injecting a hydrocarbon fuel into the cylinder during a compression stroke, control means being provided and connected between a power control of the engine, said means for injecting and a secondary fuel injection means if provided, said control means being operative to control the engine in accordance with the method of any preceding claim.

20. An engine as claimed in claim 15 and being a reciprocating piston engine.

21. An engine as claimed in claim 15 and being a rotary engine.

22. An internal combustion engine substantially as hereinbefore described with reference to and as illustrated in Figs. 2 , 3 or 4 of the accompanying drawings.