Physics In an Automotive Engine

In my entire life, I have only ever seen very superficial presentations regarding the functioning of an automotive engine, usually just enough to tell various alternatives apart! Therefore, I have felt it appropriate to present a Physics perspective on the subject!

I am going to assume that you have at least a vague understanding of what goes on in an automotive engine, and that the words piston, crankshaft, connecting rod, and cylinder are understood.

In this drawing, we are looking at the end of the crankshaft, and the crankshaft is going to rotate counter-clockwise. Therefore, at this moment, the crankshaft is pushing the piston upward in the cylinder, and it is currently half way up. This is during the stage called Compression, where the gas-air mixture above the piston is getting compressed by the upward movement of the piston.

I'm going to simplify some things to clarify some points, such as treating valves as being able to operate instantly, which they definitely do not do in real life. However, if the intake valve had closed when the piston was at is lowest point (90° of crankshaft rotation before this drawing, the total amount of gas-air mixture in the cylinder (then at approximately atmospheric pressure of 15 PSI) is just the volume of the cylinder above the piston.

We should clarify that pressures can be described in two different ways, Absolute and Gauge. In this case, we know that the air is at the natural pressure of 15 PSI, which is an Absolute pressure, so it is sometimes written PSIA. If you measured that pressure with an air pressure gauge, it would read 0 PSI, because there is no difference in pressure from natural. This is called gauge pressure, and would be written 0 PSIG. They mean the same thing, and absolute pressure is always 15 higher than gauge pressure.

This discussion is going to be about the so-called spark-ignition or Otto cycle engine, the process that virtually all cars and trucks operate on. There are a couple common alternatives: The compression-ignition or Diesel cycle and the Brayton or Joule cycle. The majority of this discussion actually applies to all three, but there are some differences. In Physics-talk, an Otto cycle has an isentropic compression, followed by a constant volume combustion explosion, followed by an isentropic expansion. In contrast, a Diesel cycle has an isentropic compression followed by a NON-explosive combustion at (relatively) constant pressure, followed by the isentropic expansion. Enough of that! They're much alike in many ways, and you can consult any College Engineering textbook regarding the differences.

If we discuss a very popular engine, the so-called small-block Chevy engine, we can put some numbers in here. The bore (diameter of the cylinder) is 4", and the stroke (twice the crankshaft throw radius) is 3.5". The volume of that cylindrical volume is then (PI) * R² * H or 3.1416 * 2 * 2 * 3.5 or around 44 cubic inches. (Since that engine has eight cylinders that are each that volume, its total 'displacement' is 44 * 8 or around 350 cubic inches. This engine is generally called the Chevy 350 V-8.)

The area shown at the top of the drawing is an additional volume that remains even when the piston is at the very highest point, a location called TDC for Top Dead Center, which will mean more in our second drawing. The space above the piston at TDC is carefully designed. In this specific case, it has a volume of around 6.3 cubic inches.

When the piston began its upward movement (at BDC, bottom dead center), there was then a volume of gas-air mixture above it of (44 + 6.3) or 50.3 cubic inches. When the piston has gotten to TDC, as in this drawing, all that gas-air mixture has now been compressed into the remaining 6.3 cubic inches. The ratio of these numbers, 50.3 / 6.3 is called the Compression Ratio of the engine. In this case, it is about 8.0.

This drawing shows the moment when that gas-air mixture is most compressed. The 8.0 compression ratio means that the 15 PSIA beginning mixture, is now at 8.0 times that pressure, or around 120 PSIA. The cylinder compression is measured and is essentially this number. Except that that device is a gauge, so the reading would be 105 PSIG.

Most superficial descriptions of automotive engines then say that the gas-air mixture is ignited at that moment and that the even higher pressure of the exploding gas drives the piston down, turning the crankshaft. Reference is usually even made of 'advancing the timing' of the ignition spark, so it occurs maybe 10° or 20° BEFORE TDC, so the explosion has a moment to build up its full power by the time it gets to TDC. If you look at this drawing for a while, you should be able to see that that is impossible! If the explosion (and all its effects) occurred exactly at the moment shown in this drawing, at TDC, the crankshaft would not be given any rotation at all! Virtiually the entire force of the explosion initially acts to try to drive the piston, connecting rod and crankshaft downward, out of the bottom of the engine, without giving it any rotation at all! (When this actually happens, VERY bad things tend to happen to the engine!)

All actual internal combustion engines rely on KEEPING that explosion pressure for as long as possible! In Calculus terms, the total effect regarding rotating the crankshaft is the Integral of the net force actually applied to the crankshaft by that connecting rod for as long as there is explosive pressure inside the cylonder. In an engine that is operating properly, contributions to this Integral begin at the instant of ignition and end when the exhaust valve begins to open. The instantaneous force applied as torque in rotating the crankshaft continuously changes during this "power stroke". It actually begins with a slight negative contribution since ignition is timed to occur before TDC, but not much pressure yet develops since the flame is still spreading inside the cylinder. The contribution becomes exactly zero at TDC, and then quickly rises as the internal burning and pressure continues and the leverage angle at the crankshaft improves. Eventually, the piston goind down reduces the presssure, and engine cooling also does, and good design times the exhaust valve to begin opening about when productive torque is no longer available.

So, from a truly accurate (Physics) perspective, a VERY complicated graph of resultant torque would first need to be determined, and then that graph would be Integrated to determine actual engine torque generated, at that engine speed and under those conditions of spark advance and the rest. Such analysis is rarely actually done, and nearly always, simply experimental measurements of real engines is found by experiment to learn these things.

You might note that the pressure must be maintained within the cylinder throughout the entire power stroke for decent performance. This explains why an engine loses much of its power once the piston rings are worn (and therefore leaking pressure) or the valve seats become worn or distorted (and therefore leaking pressure). If the engine actually just relied on the instananeous effects of the explosion, worn rings or valves would be of minimum importance, but the fact that the basic design relies on HOLDING the pressure before actually using it make those components extremely important.

It turns out to be sort of fortunate that the "speed" of the explosion of the gasoline-air mixture is relatively slow! Under the conditions that generally exist inside a cylinder, the flame front velocity is usually around 90 feet per second, or 60 mph. Mark's Standard Handbook for Mechanical Engineers, Section 9, Internal Combustion Engines, Flame Speed.

By the time that a maximum amount of the gas-air mixture is burning, the crankshaft has rotated a slight distance past TDC. This situation, and its consistency (due to consistency of the quality and burning characteristics of the gasoline), enables a modern engine to avoid seriously trying to spin backwards! The mathematics below shows that, for an engine speed around 1500 rpm (a normal driving situation) this is commonly around 10° AFTER TDC, when the greatest explosion pressure is present in the combustion chamber. Let's look at some preliminary calculations.

It is very well established that the explosion, and therefore the heat created, causes the gases in the combustion chamber to obey standard rules of Chemistry, such as the Ideal Gas Law. Because of the sudden heat, the gases try to expand immediately, but they cannot, so the pressure in those hot gases greatly and rapidly increases. Very consistently, the explosion pressure in an internal combustion engine rises to between 3.5 and 5 times the compression pressure. Since our example engine had a compression pressure of 120 PSIA, this results in a momentary explosion pressure that peaks at around 500 PSIA.

Since the piston is 4" in diameter, the top surface of it is just PI * (4/2)² or around 12.6 square inches. Each of those square inches experiences the 500 PSI pressure, so the total force then instantaneously applied to the top of the piston is 12.6 * 500 or around 6300 pounds.

Because of the geometry of the situation when the crankshaft has progressed 10° after TDC, the force diagram indicates that this downward force must be multiplied by (approximately) the sine of 10°, in order to determine the tangential force applied to the crankshaft. Approximately, because the connecting rod is no longer parallel with the axis of the cylinder bore, the actual angle being slightly higher, and an exact angle is easy to calculate with a thorough analysis. For now, 10° will give an approximate result for our purposes.

Therefore, the tangential (rotative) force actually transferred to the crankshaft is around 6300 * sin(10) or 6300 * 0.174 or around 1100 pounds. Since this force is applied to the throw of the crankshaft, at 1.75" radius from the centerline of the crankshaft, the torque transferred to the crankshaft is therefore 1100 * 1.75" or 1100 * 0.146 foot or 160 foot-pounds of torque. This calculation is in ball-park agreement with the published maximum torque curves for such engines, at 1500 rpm.

Notice that the radial force applied to the crankshaft (bearings) is around 6300 * cos(10) or around 6200 pounds! At that moment, the vast majority of the power of the explosion is trying to drive the crankshaft down out of the engine, without rotating it! And in seriously trying to abuse the bearings! Without engine oil, under pressure, in the bearings, they do not last long with 6200 pounds force against them!

In traditional automotive thinking, this sort of makes sense! As long as the piston rings do not leak too much and the valves do not leak too much, then those expanded gases inside the combustion chamber cannot escape. That means that, until the exhaust valve starts to open, all the pressure will act to push the piston downward. In order to get the most total power, it makes sense to keep that pressure acting as long as possible. This means that having the maximum pressure developed as soon as possible after TDC gives the most possible available degrees of productive crankshaft rotation. The benefit of this is seriously affected by the fact that, as the piston moves downward, the volume inside the combustion chamber increases, so the pressure drops. From a beginning pressure of 500 PSI in our example, at the later instant when the crankshaft had rotated 45° the volume has increased such that the pressure drops to around 200 PSI (without any leakage) and by the time the crankshaft has advanced 90° the pressure is down to around 125 PSI. The AVERAGE pressure during this 90° of rotation is referred to as Mean Effective Pressure (mep) and is commonly around 200 for common engines under power. (This description is for best conditions, fairly high power and revs).

There are several important points to be made here.

• At lower engine speeds, such as at idling at say 500 rpm, the very same explosive force is created, but since the crankshaft is rotating only 1/3 as rapidly, the maximum pressure tends to occur much closer to TDC, say around 3° or 4° after TDC. The sine of 3° is around 0.052, so only around 57 foot-pounds of torque are (momentarily) transferred to the crankshaft. The relatively long times involved allow moderate leakage past the rings and through valve leakage. The main effect, though, is that the gases inside the cylinder are cooled by the presence of the water-cooled metal (cylinder walls) engine block and head. This cooling is necessary, to permit lubricants to keep the engine running reliably, but it takes an amazing amount of energy from the cylinders! If an engine is rated at 200 HP, then the cooling system removes an ADDITIONAL 200 HP to 300 HP worth of energy from the cylinder walls and heads! (This is part of why internal combustion engines have such terrible overall efficiency, rarely higher than the low 20% range (discussed below).

  The engine cooling system must be able to remove all that heat when the engine is under full load and power, so cooling systems are really pretty efficient. At 5,000 rpm, there is only about 0.003 seconds available to remove most of the extreme heat from the cylinder walls and head, and the gases inside start out at around 4000°F. As that heat is removed from the cylinder walls and head, the gases inside cool down. At 5,000 rpm, and in 0.003 second, the amount of cooling is limited. But now look at the engine while idling at 500 rpm. That (cold) 200°F water flowing through the block and heads now has ten times as long to cool everything as the piston lowers. In ten times as long, the gases inside the cylinder can get really cooled off. That is bad because lower temperature means lower pressure (Ideal Gas Law) and so less pressure pushes down on the piston.

  Between the natural pressure reduction due to the expansion as the piston goes down, and the forced cooling system cooling the gases and therefore also reducing the pressure, the momentary 500 PSI that existed near TDC quickly dissipates, and there is a rather short and somewhat weakened force/pressure pushing the cylinder down to create productive work. The mep drops way off and the full 90° of productive effect does not occur.

  At even slower engine speeds, the engine is not able to reliably create the necessary amount of torque necessary to overcome friction and to drive the water pump, alternator and other systems, and to provide enough momentum to a flywheel to do the work of exhausting, intaking and compressing the gas-air mixture for the next explosion. This is why an automotive engine cannot run reliably at under an idling speed, often around 500 rpm, which is necessarily higher when the added load of an air conditioner is running (generally then at least 700 rpm) because it requires additional torque/power.

• At higher engine speeds, the crankshaft is rotating more rapidly so that it is farther past TDC at the moment of maximum dynamic pressure in the cylinder (even though the ignition advance has been increased even more). This again creates essentially the same explosive pressure in the cylinder. But now everything occurs in a shorter time, so less leakage can occur and less gas cooling occurs to the cooled walls of the engine block and head. This allows the advanced crankshaft angles to be more able to transfer torque to the crankshaft. Our initial 6300 pounds of force on the top of the piston is reduced (by the increase in volume, since the piston has moved downward more than half an inch) to around 2500 at the point that it is 45° past TDC. This indicates that the torque transferred to the crankshaft at that instant would be 2500 * sin(45°) * 0.146 or 250 foot-pounds of torque.

  

• At extremely high engine speeds, this is all still true, except that the slowness of the burning always causes some of the gas-air mixture to not even burn until well after TDC. This results in a delay and a time-spreading of the maximum dynamic pressure, to occur even later after TDC. This causes the first few degrees of crankshaft rotation to not yet have the full pressure developed inside the combustion chamber. (This cannot be avoided and is due to the slow speed of the spread of the flame inside the cylinder.) Therefore the mean effective compression pressure starts to drop off at extremely high engine speeds. (There are less degrees of crankshaft rotation available before the exhaust valve starts to open) Therefore the torque transferred to the crankshaft drops off at very high engine speeds, which is one of the main reasons for a "top end" of engine performance. (There are other reasons: At such high engine speeds, the intake and exhaust valves are not open very long, and so the removal of waste gases and the intake of new fuel-air mixture to replace it becomes less efficient. Air flow speeds through intake manifolds and exhaust systems becomes very high so extra frictional resistance exists. And of course, there is the matter of making sure the engine doesn't fly apart!

  In our example engine, at the situation shown here, our effective compression pressure is only 30 PSI (the piston now being halfway down or a 2:1 compression ratio). Therefore the combustion pressure is only around 125 PSI and the total force on the piston is around 1600 pounds. So even though the geometry is the best possible, with a sine(90°) = 1.0, the total torque transferred to the crankshaft is around 1600 * 1.0 * 0.146 or around 230 foot-pounds of torque. In real engines, it is usually actually less than this because the exhaust valve has already begun to open, releasing the pressure of the combustion chamber.

• These two effects just described, the extensive cooling and leakage at low rpm and the reduced (delayed) effective compression pressure at high rpm, are the primary reasons that an engine has a "torque curve". The actual torque developed would be relatively constant at various engine speeds except for these two effects.

• Nearly everyone's impression about "octane ratings" of gasoline are exactly opposite of what is the truth! Low octane gasoline burns VERY rapidly, so rapidly (and somewhat unpredictably) that the crankshaft angle might not always get to TDC before maximum pressure is developed. This both wastes some of the explosion power (fighting itself as regarding rotating the crankshaft) and represents the possibility of extreme wear on engine pistons and bearings, as compared to slower-burning higher octane gasolines. Because high-octane gasoline burns more slowly, it is less subject to "engine knock" (too much combustion before TDC) and generally is able to produce more total engine torque because of the more reliable geometrical advantage of the later crankshaft angle.

• It was discovered long ago that there was an advantage of triggering the ignition spark several degrees of crankshaft BEFORE TDC. Otherwise, the maximum pressure only develops so long after TDC that the piston has dropped and less pressure and force are created, as described above. This spark advance situation causes the interesting effect that an engine begins building up combustion pressure BEFORE TDC, which actually would have the effect of making the engine rotate backwards! Some early engines had a serious susceptibility to this, and many people who used early crank starters (before electric starters) were seriously injured when the engine kicked backwards.

  Under the conditions of our engine running at 1500 rpm, the "flame-front speed" (essentially the rapidity of the explosion) is around 90 feet/second inside the combustion chamber. A little geometry and algebra easily shows that the flame front has progressed across half of the combustion chamber (2") while the crankshaft has rotated around 18°. If the ignition spark was timed for around 15°BTDC, this would suggest that the maximum pressure in the combustion chamber would then occur around 18° later or 3° after TDC, as is commonly intended.

  The actual reality is quite a bit more complicated than this, and we have simplified some things in the interest of clarity. As the flame-front progresses across a combustion chamber, the exploding gases act to additionally compress the gas-air mixture that has not yet ignited. The result is that the pressure created is not a symmetric smooth curve, but rather a curve that has generally greater pressures in the later portion of the actual combustion. Where we have considered the maximum combustion pressure to occur when the flame-front has progressed halfway (2") across the chamber, it generally occurs a little later than that due to these very complicated effects.

  Actually, a reference in Mark's Standard Handbook for Mechanical Engineers, Section 9 states that the optimum spark advance is approximately 5/9 of the combustion time. This means that more time of combustion happens BEFORE TDC than after! This makes the point of the more powerful portion coming late in the combustion process, to not only overcome that 5/9 of combustion that acted to make the engine turn backwards, but also emphasizes the very small crankshaft angles involved that are the main point of this description! If the combustion had proceeded linearly (as we have implied in this simplified presentation) the engine would not even run (with standard spark advance), since over half of the combustion time occurs before TDC!

  As with most everything else here, the situation is actually a little more complicated than that! The force applied to the top of the piston is proportional to the pressure of the gases applied to it, and THAT is proportional to the temperature of the gases inside the combustion chamber (all other things being equal!) The early part of the combustion process IS burning fuel and building up pressure, but the TOTAL pressure is cumulative. In ritzy math terms, it would be called the Calculus Integral of the pressure over time. So even though 5/9 of the TIME of burning may occur before TDC, the pressure is still not fully developed by then, and the cumulative pressure AFTER TDC is much higher. Which is why the maximum torque is developed when the spark is advanced around 5/9 of the total combustion time. But note that all of the combustion is DONE before the piston is able to move very far down the cylinder, again meaning that the maximum force (pressure) is developed fairly close to when the crankshaft throw is nearly straight up, the worst possible mechanical (dis)advantage.

  Between the additional benefit of this later development of maximum combustion pressure, and the negative value of the very early stages of combustion that occur before TDC, we have for simplicity treated the two as effectively canceling out each other, and that the entire combustion process occurred as if it happened instantaneously at a single 3° to 10° ATDC crankshaft angle. In reality, they seem to be relatively comparable effects, but there is no actual reason for insisting that they exactly cancel out. Spark advance, fuel-air ratio, octane rating of the fuel, temperature and many other effects affect each of them differently.

  You can probably imagine why engine designers measure the performance of a new engine at every possible crankshaft angle (actually spark advance angle) and RPM speed, to determine the very best ignition advance for all situations. They actually have the freedom to create an "advance curve" for most power or for best fuel economy. Usually, any vehicle you buy has an advance curve that is somewhere in between. But this issue explains why there are "performance chips" available for most computer controlled engines. Such chips simply replace the tame ignition advance curve with one that is better for maximum performance. Not much else is changed by such chips. They tend to cause poorer fuel economy and poorer environmental performance.

  I am somewhat surprised that no manufacturer has yet offered a "switchable chip" capability! If three chips were installed, then normally the Middle (like previous chips) would be in effect. When a cruise control was engaged, a maximum economy chip would take over. When the driver hit a special GO button, for 30 seconds, a maximum performance chip would take over. The best of three worlds, I would think!

  If an engine were intended to run at a constant speed with a constant load, it would be possible to fine-tune the exact best spark advance angle. However, vehicle engines must be able to go from idle to maximum performance rather quickly. There are many other engine conditions that also affect the amount of ideal spark advance, such as the relative richness of gas in the mixture and whether the air intake path is restricted or open. All these things are important for the following reason. When the ignition spark occurs substantially before TDC, a significant combustion pressure starts to build up even before TDC. If the engine was not already spinning, this could act to make it rotate backwards! Only the momentum of the crankshaft and flywheel makes it overcome this backward torque to get past TDC when good things start to happen.

  Under some circumstances, too much of the mixture burns before TDC. Prior to no-lead gasolines, carbon deposits tended to develop inside the combustion chamber, and these deposits would sometimes become very hot. When fresh gas-air mixture would be introduced through the open intake valve, the hot carbon could spontaneously ignite it before the spark plug fired. This condition, while the intake valve was still open, would send a flame-front backwards up through the intake manifold and carburetor, causing what is called a backfire, flames actually coming up out of the carburetor. If the intake valve was nearly closed, then the explosion would try to rotate the engine backwards, which causes incredible stresses in almost everything and some internal part might break. Since unleaded gasolines have been used, carbon deposits are less common, and combined with computer controlled spark advance, backfiring is now very unusual.

  However, if too low an octane gasoline is used in an engine, the flame-front can sometimes travel too rapidly across the combustion chamber. It might seem odd, but LOW octane gasoline has faster flame-front speeds than HIGH octane gasoline does! This causes too high a combustion pressure to develop during the 5/9 of the combustion period that occurs before TDC. That cylinder then does not contribute to the intended productive power but rather causes an effect that partially tries to make the engine run backwards. This causes tremendous stresses to occur in an engine, and the power of the explosion has no obvious method of release. The rotational momentum of the engine and flywheel permit the engine to continue past this event, but the instantaneous effect is a slight flexing of the top of the piston head, which makes a very unique metallic sound. This situation is called "engine knock" or "ping". It is quite undesirable. Regular engine knocking can cause a "blown piston" where a hole is blown through the weakest surface of the combustion chamber, the piston head.

• The numbers calculated above are Instantaneous values of the torque produced. In a V-8 engine, the eight cylinders fire during two revolutions of the engine, so a single cylinder provides the power for 90° of crankshaft rotation. Essentially, in a real engine, this is from just after TDC to a point when the piston is slightly more than halfway down the cylinder, when the exhaust valve opens. The torque created right near TDC is minimal, it increases to a maximum value and then drops off. When the torque of an engine is measured, it is the AVERAGE that actually gets measured. Where we had calculated instantaneous torques as high as 300 ft-lb, the average will always be less than that, in this case, around 200 ft-lb. If the torque is calculated for every degree of crankshaft rotation, and an average taken of those 90 values, the result should be very close to the rated engine torque.

In many engines, the radiator hose is around 1 1/2" in inside diameter, which gives around 2 square inches of cross sectional area, a situation that is true for most parts of a well designed cooling system. The water pump pushes that water at around 15 ft/sec (10 mph) through the passageways, when the automatic thermostat is fully opened. This means that about (15 * 12 * 2) 360 cubic inches of water per second is circulated, which is about 12 pounds of water per second. It is common for the water to be heated by around 15°F in taking that wasted heat away from the cylinder walls and heads. It takes 1 Btu to raise one pound of water by 1°F, so we're talking about (12 * 15) 180 Btu/second of heat being removed. That might not sound like much, but it is! In an hour (3600 seconds), this is about 650,000 Btu! (More than ten times as much heat as most entire houses need in the dead of winter!) Down below, we will mention that 2544 Btu/hr is equal to one horsepower, so this wasted heat represents around 250 horsepower of wasted energy from the gasoline, and heat that then contributes to global warming and all that other bad stuff.

(We can therefore see that the cooling system necessarily removes an enormous fraction of all the energy/power that an internal combustion engine creates, which causes the "overall thermal efficiency" of any conventional automotive engine to have low thermal efficiency, even separate from all the mechanical losses related to the engine's operation. The calculations are extremely complex, and include variations depending on water flow rates and cooling system design, but they generally indicate that a conventional internal combustion engine cannot have an overall efficiency of greater than around the low 30% range. As noted below, there have been some experimental engines designed that have been measured at around 28%, but the most efficient production engines are around 25% and most vehicles on the highways now have engines which have around 21% overall efficiency.

There is a linked presentation in this Domain which analyzes the performance of vehicles regarding the usage of the power supplied by any power source, which discusses the aerodynamic drag (front of the vehicle having to push air out of the way and rear of the vehicle causing turbulence drag) and tire friction drag. It is possible to calculate the vehicle performance with an "ideal engine" in it. For a medium sized car, the best that vehicle could theoretically do is around 65 mpg of gasoline (using the energy in that gallon with the minimal theoretical losses). A compact car has a theoretical maximum of around 80 mpg, and motorcycles can have theoretical maximum efficiencies of over 150 mpg. These figures are for driving at a constant highway speed. If someone wanted to be intentionally deceptive, it would be possible to change the gearing of a vehicle to move at, say, 3 mph, walking speed, where both aerodynamic and tire friction is far less, to get an experimental mileage number that was far higher! Some companies have done this in the past, and then never bothered to mention that the 150 mpg mileage figure they bragged about in advertising was only for a walking speed! These inserted comments are to relate to the seemingly endless line of products that are sold that claim to cause a standard car engine to achieve 125 mpg or 150 mpg or 180 mpg, where readers tend to believe them! The Laws of Physics limit the accomplishments of internal combustion engines as discussed here, and such claims are made only to sell more products, and NO ONE can actually accomplish such things in a conventional car at highway speeds!)

Up above, we mentioned that the cooling system, at 5,000 rpm engine speed, only has around 0.003 second to remove the heat from the one cylinder that happens to be firing at that moment. (The reality is that heat is still removed from the heated metal for a longer time, but then the cooling system is primarily busy removing heat from a DIFFERENT cylinder which has just fired. For simplicity, we are considering individual cylinders. OK. We know that a total of about 180 Btu/second is being removed from the engine, so in 0.003 second, a little over 0.5 Btu gets removed.

That heat started in only one place, the 4000°F heated gases inside that cylinder. The cylinder started with about 50 cubic inches of air-fuel mixture, which weighed about 0.0022 pounds. A characteristic called the Heat Capacity of the fuel-air mixture is about 0.25 Btu/lb. As a result of all this, the 4000°F fuel-air exploded mixture inside the cylinder has about (4000 - 70) * .0022 * 0.25 of heat in it, or about 2.16 Btu.

At 5,000 rpm, this is good! Only around 0.5 Btu gets removed while the piston is still trying to do productive work, and so the overall performance is good. (Normal automobile cooling systems are actually intended to start to overheat at high revs like this, for the lower speed efficiency concepts being considered here!) However, now consider the situation at 1500 rpm, about the engine speed during most highway driving. Same amount of energy in the hot gases, 2.16 Btu. But now, instead of 0.003 second, the cooling system has more than three times as long, 0.010 second, to be removing heat from the cylinder and head. What used to be a loss of 0.5 Btu is now 1.7 Btu. By the time the piston is halfway down, still trying to do productive work, the gases behind it have cooled tremendously. The combination of the efficient cooling system and the cooling due to the increasing volume behind the piston, that pressure is fairly likely to be around 300°F to 400°F. At such temperatures, there is almost no useful pressure acting on the piston, and the power cycle is done!

I know that you are way ahead of me now! At a 500 rpm idling speed, the cooling system has already removed virtually all the heat from those hot gases before the crankshaft has even rotated by 45°. It can never even get to having a beneficial mechanical leverage on the crankshaft before it has already gone fizzle!

See the situation? The cooling system MUST have adequate performance to be able to remove enough heat when the engine is wound out, but that results in it having too good a performance at all lower engine speeds. Such really good cooling performance makes engines last longer, so they have THAT going for them! But the basic performance of all internal combustion engines is tremendously reduced by how well the cooling system has to work!

The cooling system also always includes a "modulating thermostat" which partially blocks off the water flow when the water temperature is less than the maximum it was designed for. This eliminates the chance of the engine cooling system ever removing too much heat and keeps the engine at a relatively constant operating temperature. The effects of the thermostat (both its design temperature and its actual operation) have significant effects on calculations regarding the efficiency of an engine, and can cause some calculations to be off.

You might see why the cooling water pump is driven by the engine. At high speed, it runs very fast, to accomplish the full cooling described above. At slower engine speeds, the water is pushed more slowly so that it is able to capture less heat from the cylinder walls and heads. But these things do not eliminate the problem. The slower water speeds reduce some of the numbers described above, but it is still true that every running vehicle constantly discards more of the gasoline's energy as wasted heat than it uses to move the vehicle.

Older vehicles also had their very large radiators very exposed openly to the air at the front of the vehicle, because at that time COOLING was considered the central factor (related to engine survival!) As gasoline got more expensive and actual engine efficiencies have improved, modern vehicles tend to have very small radiator openings in the front of a vehicle, along the theme of causing the engine to operate at a higher temperature. With that smaller opening, less air can pass through the radiator and also less air passes alongside the engine itself, causing the now desirable higher engine temperatures! Now you know! By the way, long ago, it was easy to work on nearly any engine, because it was in such an open area of the vehicle. Modern vehicles have many accessories right against the engine, so it is often hard to actually even see the engine when the hood is opened! That great difference is actually an intended difference!

In case you are curious, about 60% of the cooling is usually done through the cylinder walls and the remaining 40% through cooling the heads. This will probably NEVER come up in Trivial Pursuit!

Another related subject: Remember that I mentioned above that the standard cooling system design intentionally allows the engine to start to overheat when really revved up? (The expectation of the designers is that no standard driving would ever involve extended driving at such high revs.) If a vehicle is to be used for towing a heavy trailer, generally there is an extra-cost option of a "heavy duty" cooling system. When towing such a trailer, the engine can spend longer times at higher engine speeds and loading, where it would normally overheat. The extra cost "heavy-duty" cooling system rarely involves stronger water pumps or bigger hoses. Almost always, it only involves REDUCING the size of the water pump pulley (so it spins faster) and a thicker radiator (so there is more heat exchange surface to cool the water). From the above discussion, you probably realize that such a "heavy-duty" cooling system causes the engine to have WORSE efficiency and performance at low engine speeds, due to excessive cooling of the engine cylinders then! Less heat remains in the hot compressed gases in the cylinder pushing the piston downward, because the excessive cooling lowered that pressure due to the Ideal Gas Law! (The modulating thermostat mostly resolves this complication).

Prior to around 1980, cars and trucks had large radiators and very free airflow through them, and engines ran fairly cool. Even the standard thermostats were 180°F, again permitting cool engine operation, with the intention of enabling long engine life. When fuel efficiency and air pollution came to be politically important, the advantages described above, of intentionally reducing the effectiveness of the cooling system to reduce the cylinder heat losses to increase efficiency, started appearing. Now, nearly all vehicles have rather small radiators and they have small grilles allowing air in to them! Modern radiators are actually too small to avoid overheating and so cooling fans are necessary to keep engines from boiling over. Similarly, modern thermostats are generally 195°F, which raises all the engine temperatures by 15°F. Look in any engine compartment today and you see a clutter of things surrounding the engine. That was not the case long ago, when free air flow around an engine was desired for engine durability. Now, the highest possible engine operating temperature is used, (reduced cooling performace described above) to improve engine efficiency and performance, which also reduces the amount of air pollution created in the process. Engine durability is less than it used to be, but people rarely seem to keep vehicles as long as they used to, so it is apparently not considered a problem.

Finally on this tangent: Consider dragsters (rails) in a 1/4 mile drag race. They have no radiators or water pumps, but they are filled with (cold) water just before a race. That seems certainly necessary to keep the engine from blowing up. But an ideal situation would be that the water was ferociously boiling at the Finish Line when the engine was shut down, because that would indicate the highest possible engine (cylinder) temperatures during the race. I don't know if any research has ever been done on this, but I suspect that if two identical dragsters raced, the one that had had its engine running 30 seconds longer before the race should always win! The hotter engine cylinders should allow several percent additional power to remain to drive the pistons downward, particularly at the important start of the race. Engine durability would probably be severely reduced, but people who drag-race only think of winning! (Notice how Physics shows up in unexpected places and in unexpected ways?) (And, of course, that seriously overheated engine is more likely to blow itself apart, too!)

Hemi Head Engine

A hemi head is actually a hemispherical head. Virtually all the other styles of overhead valve engine heads have relatively flat pistons and heads that have a relatively shallow recess in their heads, for the combustion to occur. Remember the roughly 6 cubic inches that must remain at TDC? With a 4" diameter cylinder, that equals roughly 1/2" in cylinder height, near the sides near zero and near the spark plug maybe 3/4 inch. Now, a cylinder has to have both an intake valve and an exhaust valve, both in the head (in overhead valve engines, the most efficient designs). The flat shape of the combustion chamber limits the diameter of those valves, to well under half of the entire distance across.

The hemi head uses a VERY deep combustion chamber, so that the distance across is about half the circumference of a circle (1.56 * diameter) rather than being only slightly more than the diameter. This allows a lot more available space for the two valves. The single actual advantage of a hemi head engine is that it has much larger valves! This allows the fuel-air mixture to get in easier and the exhaust to get out easier. Bigger valves is a very good thing, and the hemi head design is the simplest way to provide the space for really large valves.

Since the hemispherical chamber is so tall, a flat-top piston would allow too much remaining volume for a good compression ratio, so all hemi head engines have to have dome-top pistons. So if you ever see a flat-top piston, it is from a non-hemi, and a significantly domed piston is always from a hemi. (An engine can have flat-top pistons replaced with slightly domed pistons to increase compression ratio, but that is a very different effect.) Also, if you happen to see an unusually large valve, it is likely to have come from a hemi engine.

So, a hemi is not "magical" or anything, but merely is a design that permits bigger valves for better engine breathing. There is no other sinificant advantage of it. And, actually, the domed piston somewhat interferes with airflows and makes it less likely to get really uniform distribution of the gas-air mixture, and really good removal of all exhaust products, so some of the benefits of being a hemi are given up in exchange.

You may be aware that there are some newer engines that have four (smaller) valves per cylinder. This provides the improved breathing of the hemi while not having the disadvantages of domed pistons. But the engine is much more complex, and expensive.

This geometrical mechanical advantage was a standard feature of the old steam engine locomotives, where the entire available steam force was always applied at the best possible mechanical advantage. In comparison, internal combustion engines are rather pitiful regarding mechanical efficiency! However, this hypothetical arrangement is not possible in a normal automotive engine. It is easy to see from geometrical analysis that the piston necessarily has dropped exactly halfway down the cylinder, with the loss of almost all compression advantages and there is no flexibility on this point.

"Ground transportation vehicles are powered, by and large, exclusively by internal-combustion engines. In passenger vehicles in particular, the thermal efficiency of the [engine] cycle is of the order of 10 to 15 percent." from Mark's Standard Handbook for Mechanical Engineers, Tenth Edition (1995), page 9-29.

(That particular reference had been composed for an earlier Edition of Marks of the late 1970s, and the number had gotten somewhat outdated by the 1995 Edition.)

YOU can actually confirm this for yourself with your own car! I will use the example of one my Corvettes. At a constant 60 mph on a straight and level Interstate Highway, I get around 25 mph, which sounds GOOD for a Corvette! OK. According to GM information, the frontal area of the car is around 19 square feet, the aerodynamic coefficient of drag (due to the shape of the car, and fairly constant for different speeds) is 0.330 and the tire resistance drag is around 0.015 (depending on tire type, inflation pressure, temperature and speed). From this we can calculate that the Aerodynamic Drag at 60 mph (88 ft/sec) is 19 * 0.330 * (88)²/(13*32) pounds of force (the last factor being the air density in slugs per cubic foot), which gives 116.7 pounds of aerodynamic drag, at 60 mph. (at 70 mph, it is easy to calculate that it rises to 158.9 pounds.) Tire resistance drag is 0.015 * 3200 pounds (the vehicle weight) or 48 pounds at 60 mph (and around 60 pounds at 70 mph). This makes the Total Drag as 116.7 + 48 or 164.7 pounds at 60 mph (and 218.9 pounds at 70 mph) (and 51.9 + 32 or 83.9 pounds at 40 mph).

At 60 mph, the total required horsepower to overcome this and maintain a constant speed is 164.7 * 88 / 550 or 26.4 horsepower. (at 70 mph it is 40.9 HP, a considerably higher drag load!) A horsepower is equivalent to 2544 Btu/hr (from above) so this is 67,200 Btu/hr (26.4 * 2544) of needed (or usable) output. In one hour of driving at that constant speed, we would therefore use up an amount of energy equal to 67,200 Btu. (at 70 mph, 104,000 Btu.)

A gallon of nearly any type of gasoline contains around 126,000 Btu of chemical energy. In the hour of driving, I would cover 60 miles and get the 25 mpg, which means that I would use 60/25 or 2.4 gallons of gasoline. That much gasoline has 126,000 * 2.4 or 302,000 Btus in it. Since the car used 67,200 Btu to maintain that 60 mph constant speed, the overall thermal efficiency is 67,200/302,000 or 22.2%.

At 70 mph, I tend to get around 21 mpg, and therefore would use up 3.3 gallons in traveling those 70 miles, or a gasoline energy content of 420,000 Btu. So we would have 104,000/420,000 or around 24.8% overall thermal efficiency. Interestingly, the thermal efficiency is actually higher at the higher speed, but it is more than overcome by the far greater total drag, which is why gasoline mileage goes down at high speeds.

A primary reason for this disappointing efficiency is this unfortunate mechanical arrangement where the majority of the force applied to the top of the pistons is NOT able to get transferred into torque in the crankshaft but instead attempts to drive the whole crankshaft down out of the engine. (Since pressure remains in the cylinder, it eventually gets to a point of having a better mechanical advantage, but by then the pressure in the cylinder has dropped quite a bit due to the piston lowering and the cooling system effectiveness.) A large amount of wasteful frictional and cooling system heating is the result of this inherent characteristic of automotive engines, and the engine bearings take a serious beating. The engine then needs a variety of systems (lubrication system, cooling system, etc) to then discard all this heat energy that is wasted.

We mentioned above that enormous amounts of heat must be removed (and discarded) from the cylinder walls and heads, an amount generally equal to 100% to 150% of the rated output of the engine. This should seem a shocking statement, that a 200 HP engine necessarily wastes 200 HP to 300 HP of energy through its cooling system! A lot of this has to be wasted because, when the explosion first created the maximum dynamic pressure in the cylinder, the piston had nowhere to go, being virtually at TDC. (This is essentially the definition of the Otto cycle engine, that of a constant volume combustion.) So those 4000°F gases are trapped above the piston, surrounded by a really efficient cooling system! Before the crankshaft has advanced enough degrees to start being able to transfer useful torque to the crankshaft, the cooling system has necessarily already greatly cooled off the hot gases! Does this seem like a poor design, or what? Enormous waste of energy is built into the design! ALL internal combustion engines face this situation!

There is another way to indicate this poor overall efficiency of automotive engines. Consider a small-sized, reasonably aerodynamic automobile, with an engine that is considered efficient, traveling at a constant 60 mph on a highway, with no significant wind. Because of the alleged efficiency, this vehicle gets 30 miles per gallon at that constant speed.

The total vehicle drag (F) can be shown to be around 140 pounds, 110 of which are due to aerodynamic drag and 30 of which are due to tire resistance frictional losses. The total actual power needed to overcome this drag is given by F * V (velocity). Our numbers are then 140 pounds * 88 feet/second or around 12,300 ft-lbs/sec. Dividing this by 550 converts it to horsepower, or around 22 actual horsepower. (Very streamlined cars will have even lower aerodynamic drag and so this required power could be even less).

Since this vehicle has a 30 mpg gasoline consumption, it would use up exactly two gallons of gasoline to travel the 60 miles covered in one hour. Each gallon of gasoline contains about 126,000 Btu of available chemical energy. Therefore, two gallons contains 252,000 Btu, so the vehicle is using 252,000 Btu/hr. It is a fact that 2544 Btu/hr is equal to one horsepower, so this amount of energy in the gasoline represents around 100 horsepower.

The vehicle / engine efficiency would then be 22 hp / 100 hp, or around 22%, which confirms the earlier statement about the overall efficiency of this equipment.

Long ago, it occurred to me that NO ONE actually NEEDS or USES the 451 horsepower of a recently advertised car! That such great power is only ever used for less than 30 seconds at a time. That otherwise, most cars only need around 40 horsepower or less to cruise at constant speed on an expressway. Detroit never seemed to realize that, and they designed many vehicles with huge engines that were tremendous gas-guzzlers.

Around twenty years ago, in the late 1980s, I had a Oldsmobile Cutlass Ciera, which was a front-wheel drive car. I also had the carcass of an extremely old Volkswagen van from the 1960s. Something then occurred to me that has amazingly seemed to have never occurred to anyone in Detroit! If you have followed all this stuff up to here, this should make incredibly good sense to you! The rear axle of the Ciera didn't actually do much other than support the rear end of the car. So I dragged the Volkswagen "pancake" engine and transaxle across my yard and saw that it probably would have fit under the rear of the Ciera (if I removed the gas tank and put it somewhere else, as it was the ONLY apparent interference!).

So I was considering adding the second engine to the Ciera! A TINY engine! As near as I could tell, the pancake engine was flat enough that no actual changes should have been necessary to the Ciera, to allow it to remain at the same height. In other words, from an appearance point-of-view, the Ciera would have remained absolutely normal looking!

Have you caught on of why I thought this might be a good idea? At the time (late 1980s) I was one of very few people who seemed to really care about fuel efficiency. But I thought I had come up with a really good and really obvious solution. It seems to me that it still is just as valid today!

I was aware that my Ciera generally got around 17 or 18 MPG on the highway, but it was fun to drive because the 3.8 liter engine had a decent amount of power.

So, I intended to rig up the gas pedal where if it were pressed HALFWAY DOWN OR FARTHER, the (front) Ciera engine would start up, but otherwise it would NEVER actually be running! So during normal driving, the 1.2 liter Volkswagen engine would have powered the car. I was confident that it would have gotten at least 30 MPG, and reasonably likely around 35 MPG on the highway. The little engine had enough power to easily maintain the Ciera at 60 mph highway speed. So the vehicle would have gotten about the best gas mileage of any vehicle of that era!

Now say that I wanted to do a hole-shot from a stoplight, or wanted to pass a car on a two-lane road. The Ciera engine would start up, and actually I would have had TWO engines both accelerating the Ciera! It likely would have had better acceleration than any other Ciera, due to the two engines!

So I would have wound up with a car that LOOKED absolutely normal, had acceleration at least as good as original and maybe better, and yet possibly TWICE the gas mileage! Cool?

It turned out that my life got extremely busy and I never got around to doing that interesting experiment! And since shortly after that I started driving my two Corvettes, and they are rear-wheel drive, I never considered any personal motivation to remain! Also, I am not sure that I would have wanted to maltreat a Corvette quite that badly!

I realize that adding an entire extra engine would add to the cost of manufacturing vehicles, when the manufacturers hire people exclusively to find ways to eliminate a tenth of a penny from the cost of the cigarette lighter! So maybe that is why they have never even thought of this concept. Seems pretty obvious to me though!

I must admit that I had earlier personally tried a truly stupid idea that was vaguely similar, and maybe those bad memories caused me to think of it during the 1980s. When I was in College, I drove two 1956 Ford convertibles. That year happened to have a very tall trunk. The motors in those cars were considered decently powerful, being V-8 292 cid engines. But as a young kid who liked to fool around with cars, well ...

I happened to have rebuilt a Mercury 383 engine, and I had toyed around with the idea of replacing the 292 with the 383 for, as Tim Allen would say "more power!". But I thought I came up with a better idea yet! I measured and measured and found a way to fit the large 383 engine inside the rear trunk of the '56 Ford! I decided to install it backwards, with the idea of having a normal (but much shorter) driveshaft. I got two spur gears, and put one on the snout of the 292's driveshaft and the other was rigidly mounted to the actual second driveshaft. The fact that the rear engine rotated backwards was then a good thing, where either or both could then drive the car.

Well, it actually worked, for a few days! If I ONLY used the 292, and left the other transmission out of gear, only the second driveshaft rotated, and everything worked pretty normally. And I drove it a little with ONLY the 383 powering it. It was a little flaky but generally worked fine, although I never really pushed it hard. The car's handling was VERY strange, as the big old engine's 500 extra pounds so far in the rear made it somewhat spooky to drive.

I was still young, and my knowledge of Physics and Engineering was still limited. That's my story and I am sticking to it! But I had not realized that the big-bore 383 had a torque curve that was at much lower engine speeds than the smaller 292. On the single day when I fired up both engines and thought I was going to have really impressive acceleration from over 500 hp, that little detail very quickly sheared off all the teeth of the gears! As I was sitting just a foot away, I was hit by several of them as they exited the scene! I guess there was such a great torque difference between the engines that it happened at very low speed, which might have kept me from being killed, if it had happened when they were spinning very fast.

I always wondered after that what might have happened if I had been more conservative and put a second 292 in the trunk! But I suspect my knowledge of gears at the time was not sufficient even for that. So that car pretty much just sat after that until I eventually took the rear engine back out.

But maybe that experience caused me to even think that a second engine might make sense, many years later. By then, I had also seen in hot rod magazines where a few people had done what I had tried to do, but far more successfully!

Another way of describing that flame speed characteristic is to say that the pressure increases within the combustion chamber at a certain rate, such as of about 20 PSI/degree of crankshaft rotation (for the average operating circumstances we have been considering). During the approximate 18° of crankshaft rotation we have been considering (starting with advanced spark ignition), the pressure rises around 360 PSI, from the original 120 PSIA compression pressure up to around the 500 PSI we have been discussing. All the other calculations are the same as above. Again, because of many complexities in the details of how the flame-front progresses and affects the remaining gas-air mixture, a constant value of such a number is not precisely accurate. Even the flame-front speed is not constant during the combustion process because, as the local pressure increases due to the shock wave of the mixture that already burned, the flame-front speed rises. Therefore, the very late stages of the combustion process occur more rapidly that we have suggested here. However, it permits basic calculations and analysis. It also presents a way of seeing how and why the pressure and force are greater during the later stages of the combustion process.

The actual thorough presentation of the mathematics follows the logic and the examples above. There are some additional complications. (1) The actual angle between the connecting rod and the tangent to the crankshaft throw is always slightly larger (better) than in the simplified geometry presented above. See Section 3 in Mark's Standard Handbook for Mechanical Engineers for a good example of the geometrical considerations and the force diagrams. (2) A lot of characteristics are constantly changing. A reasonably accurate analysis should probably include calculations like those above for every degree of crankshaft rotation, considering the instantaneous volume of the combustion chamber and the instantaneous pressure due to the explosion, as well as the angle of the connecting rod and that of the crankshaft throw. The instantaneous torque transferred to the crankshaft would then be known for every degree of rotation. A numerical Integration could then determine the average (practical) torque that is developed. (3) Exhaust valves begin opening even while the power cycle is still proceeding, such that they will be adequately open when the exhaust (upward) stroke begins. A tradeoff in engine design is that the old waste gases must be removed, and then the entire combustion chamber filled with new fresh gas-air mixture from the intake valves, all in very small fractions of a second. It is an imperfect arrangement. Some exhaust gases always remain in the cylinder, keeping some fresh gas-air mixture from ever being able to enter. In both cases, the valves are always slightly open during the early stages of compression (intake valves) and the late stages of power (exhaust valves). All of these considerations act to reduce the actual amount of power that can be developed in a real engine.

This practical (average) torque is also lower than the maximum numbers presented here. In a V-8 4-cycle engine, each piston is responsible for developing torque over a 90° range of crankshaft rotation, before the next piston can take over. We have generally been discussing maximum instantaneous torque for specific crankshaft positions. It should be clear that the measured torque of any engine will be less, because it represents the average of torque developed during that entire 90° of crankshaft rotation, because no other cylinder is yet firing.

The crankshaft angle torque curves vary greatly in shape for different engine speeds, being very narrow at low engine speeds and rather broad and fairly constant at high engine speeds. The very narrow angle range of productive power for an engine at idle combines with the earlier mentioned geometrical disadvantage to fully explain why automotive engines can stall at low idle speeds.

Hydrogen as a Potential Fuel in Internal Combustion Engines

Hydrogen has all sorts of DISADVANTAGES regarding being a motor fuel. Primarily, it DOES NOT EXIST NATURALLY and must be produced, by any of several processes that are all extremely expensive and high-tech to actually do on any decent scale. But it happens to have another disadvantage which relates to the subject of this presentation.

Consider the inside of an engine cylinder in a normal car engine traveling down the highway. The engine may be rotating at 2,000 rpm, or 33 revolutions per second. The piston must therefore move upward and downward 33 times every second, and piston head speed in the middle of its stroke is around 45 feet/second. If a fuel burning in the cylinder is to actually push down on the piston, in order to do actual work in propelling the vehicle, the fuel-air mixture needs to burn at a flame-front speed FASTER than the piston is moving! Otherwise, the slow-burning mixture would actually act to SLOW DOWN the piston! But hydrogen only has a flame-front speed of around 8 feet/second! Mark's Standard Handbook for Mechanical Engineers, Section 7, Gaseous Fuels, graph It would not only not do productive work, but it would require work FROM the piston.

The fact that a Hydrogen-air mixture has a flame-front speed of around 1/10 that of a gasoline-air mixture seems to indicate that only a very slowly moving mechanism could be used. That might be possible, but it suggests that yet another hurdle might lie in front of Hydrogen ever becoming a common motor fuel. For reference, most of the hoped for Hydrogen applications in vehicles have to do with what are called fuel-cells, devices that are not yet decently developed, but which are expected to convert the energy in the Hydrogen into ELECTRICITY, which might then be used by electric motors to actually drive a vehicle. It may be another ten or twenty years before fuel-cell technology has developed to the point of that becoming realistic.

An Interesting Situation!