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where rc = V3</V2 (Figure 3.7) is called the cutoff ratio and is the expansion ratio during the combustion period.

80 r

Gasoline Alcohol

4 8 12 16 Compression ratio

Figure 3.8 The efficiency of an Otto and a diesel engine as a function of their compression ratios.


In practice, diesels engines operate with higher efficiency than those based on the Otto cycle, because the latter must operate at lower compression ratios to avoid knocking. (Section 3.6).

Efficiency can be improved by

1. raising 7, and

2. raising the compression ratio.

As 7 is larger for air than for fuel vapors, the leaner the mixture, the higher the efficiency. This is in part counterbalanced by the tendency of lean mixtures to burn slowly causing a departure from the ideal Otto cycle. In addition, if mixtures become too lean, ignition becomes erratic—the engine runs "rough" and tends to backfire.

The stoichiometric air/fuel ratio for gasoline, is 14.7:1. However, maximum power is achieved with a very rich mixture (12:1 to 13:1), while maximum efficiency requires lean mixtures (16:1 to 18:1). The stratified combustion engine achieves an interesting compromise by injecting fuel and air tangentially into the cylinder so that, owing to the resulting centrifugal force, the mixture is richer near the cylinder wall and becomes progressively leaner toward the axis. Combustion is initiated in the rich region and propagates inward. While the mean mixture is sufficiently lean to ensure high efficiency, ignition is still reliable. Incidentally, diesel engines can operate with leaner mixtures than spark-ignition engines.

As we are going to see, the nature of the fuel used in Otto cycle engines limits their maximum usable compression ratio in. Too high a ratio causes the engine to "ping," "knock," or "detonate," particularly during acceleration. Compression ratios that allow a car to accelerate without detonation are too small for efficiency at cruising speeds. This can be ameliorated by changing the ignition timing. The spark is retarded during acceleration and advanced for cruising. An ingenious variable compression ratio engine was developed by Daimler-Benz. The cylinder has two pistons, one connected to the crankshaft as usual and an additional one that sits freely above the first. A variable volume of oil can be inserted between these two pistons regulating their spacing thereby adjusting the compression ratio.

Consider a gasoline engine with a 9:1 compression ratio using a fuel-air mixture with a 7 of 1.3. Its ideal efficiency is about 50%.

The efficiency is reduced by departures from the ideal cycle, such as

1. failure to burn fast enough. The combustion does not occur at constant volume. On the other hand, high speed diesels tend to burn not at constant pressure, but at a somewhat rising pressure.

2. heat loss through the cylinder wall and through the piston and connecting rod. Thus, the heat generated by the burning mixture does not all go into expanding the gas. Design efforts have focused on producing a more nearly adiabatic cylinder.


Typically, these departures reduce the efficiency to some 80% of ideal. The engine in the example would then have a 40% efficiency.

It can be seen that for high efficiency one needs:

1. high compression ratio,

2. fast combustion,

3. lean mixture, and

4. low heat conduction from cylinder to the exterior.

There are numerous losses from friction between solid moving parts (rubbing friction) and from the flow of gases (pumping friction). Rubbing friction can be reduced by clever design, use of appropriate materials, and good lubricants. Pumping friction can be managed by adequate design of input and exhaust systems. Losses can be reduced by increasing the number of valves (hence the popularity of cars with 4 valves per cylinder). Also, part of the power control of an engine can be achieved by adjusting the duration of the intake valve opening, thereby avoiding the resistance to the flow of air caused by the throttle. Cars may soon be equipped with electronic sound cancellation systems, a technique that dispenses with the muffler and therefore permits a better flow of the exhaust gases.

An engine must use ancillary devices whose efficiency influences the overall performance. These include the alternator, the water pump, and the radiator cooling fan. In modern cars, the latter typically operates only when needed instead of continuously as in older vehicles. About half of the engine output is consumed by these devices. In the example we are considering only some 20% of the combustion energy is available to the accessories (e.g., air conditioner and power steering) and to the transmission. The latter is about 90% efficient, so the residual power available to the propulsion of the car could be as little as 18% of the fuel energy.






n = 0.5

from ideal



To improve n:


n = 0.2

Raise r

n = 0.4

Rubbing losses

(limited by knocking)

Better oil

Time the ignition

Pumping losses

Variable r?

Large valve area


Raise y

Slow burn

Avoid throttle


(stratified combustion)

Heat losses

Eliminate muffler

Water pump


Air drag Tire drag Brake losses

Air cond. Power steer. (Accessories)

Figure 3.9 Drive train and end use in a spark-ignition vehicle. With a compression ratio of 9:1 and with an air/fuel mixture having a gamma of 1.3, the ideal engine has 50% efficiency. Assorted losses and ancillary equipment reduce the final efficiency to less than 18%.


Engine, transmission and ancillary parts constitute the drive train. The load on the power train (e.g., tire drag, aerodynamic losses, brake losses, and accessories) constitute the end use load. We saw that, roughly, the end use load is 18% or less of the fuel energy.

3.5 Gasoline

Without a doubt the most popular automotive fuel currently is gasoline. Gasoline is not a chemically unique substance—it's composition has been continuously improved since its introduction and is also adjusted seasonally. It is a mixture of more than 500 components dominated by hydrocarbons with 3 to 12 carbon atoms. Most are branched (see discussion of the difference between octane and isooctane in the next section). For this book, the two main characteristics of gasoline are the following.

3.5.1 Heat of Combustion

Since the composition of gasoline is variable, its heat of combustion is not a fixed quantity. One may as well use the values for heptane or octane (« 45 MJ/kg) as a representative higher heat of combustion.

3.5.2 Antiknock Characteristics

As far as energy content is concerned, gasoline has a decisive advantage over alcohol. However, there is no point in using a high energy fuel if this leads to a low engine efficiency. As discussed previously, the efficiency is determined in part by the compression ratio which, if too high, causes knocking (see next section). Alcohols tolerate substantially higher compressions than most gasolines and therefore lead to greater engine efficiencies. This somewhat compensates for the lower specific energy of these fuels. Gasolines with better anti-knock characteristic (higher octane rating) do not necessarily have higher energy content, in fact, they tend to have lower energy. It makes sense to use the gasoline with the lowest possible octane rating (i.e., the cheapest) compatible with the engine being fueled. On the other hand, cheaper gasolines, independently of their octane rating, may cause gum formation and other deposits in the engine and may result in more exhaust pollution.

3.6 Knocking

The efficiency of an engine increases when the compression ratio increases. In spark ignition engines, the compression must be limited to that tolerated by the fuel used. Compressions that are too high cause detonation or knocking, a condition that, in addition to being destructive to the pistons, leads to a reduction in the power of the motor.


The difference between explosion and detonation is the rapidity of combustion. Gunpowder, for instance, will explode when confined but will only burn with a hiss when ignited in free air. On the other hand, substances such as nitrogen triiodide will decompose so fast that, even unconfined, will make a loud noise—they detonate.

An explosion within a cylinder exerts a steady force on the piston analogous to the force a cyclist puts on the pedal of his bike. A detonation is as if the cyclist attempted to drive his vehicle with a succession of hammer blows.

The ability of a fuel to work with a high compression ratio without detonating is measured by its octane rating. A fuel is said to have an octane rating, Of if it behaves (as far as detonation is concerned) like an isooctane/n-heptane mixture containing Of % octane. The fuel need contain neither octane nor heptane.

A fuel may have an octane rating larger than 100%—a result of extrapolation.

Experimentally, the octane rating of fuels with Of > 100 is determined by comparing with isooctane to which a fraction, L (by volume), of tetraethyl lead, (C2H5)4Pb, has been added. The octane rating is given by

An addition of 0.7% (i.e., of a fraction of 0.007) of tetraethyl lead to isooctane leads to a 120 octane ratio, a value common in aviation gasoline.

Notice that the compound used is isooctane. The reason is that n-octane—normal or unbranched octane—has extremely poor knocking behavior whereas isooctane resists knocking well.

The critical compression ratio of hydrocarbonst decreases rapidly with the number of carbons in the molecule. Thus, methane may have a CCR of 13 while that of n-heptane is down to 2.2 and that of n-octane is even lower.

However, if the structure of the molecule is changed (i.e., if a different isomer is used), the knock resistance may increase substantially: Isooctane has a CCR of 6, Benzene, the basic aromatic hydrocarbon, has a CCR of 15, For this reason, unleaded gasoline may contain considerable amounts of aromatics to insure a high octane rating.

Compare the structure of two isomers of octane (CsH1s)

t The critical compression ratio, CCR, is the compression ratio that just causes knocking to begin under given experimental condition, such as 600 rpm and 450 K coolant temperature.





Iso octane:


The formula above shows that isooctane is technically pentane in which three hydrogens have been replaced each by a methyl (CH3) radical. Two of the substitutions occur in position 2 and one in position 4 of the molecule. Hence isooctane is 2,2,4-trimethylpentane.

The effective octane rating of a fuel depends on the conditions under which it operates. For this reason, more than one octane rating can be associated with any given fuel. The rating displayed on the gas station pump is usually an average of two differently measured values. A more complete discussion of this topic can be found in a book by J. B. Heywood.

Additives increase the octane rating of gasoline. Iodine can be used, but is expensive. Up to a few years ago, tetraethyl lead was the standard additive in leaded gasolines. Environmental concerns have eliminated this type of fuel. High octane rating is now achieved by increasing the percentage of cyclic (benzene series) hydrocarbons. Thus, one avoids poisoning by increasing the risk of cancer and, incidentally, paying more for fuel.

The presence of ethanol in gasoline increases its resistance to detonation as indicated in Figure 3.10. It can be seen that the addition of 30% ethanol to low grade gasoline raises its octane rating from 72 to 84. The octane rating, Om, of gasohol (gas/alcohol mixture) can be calculated from the octane rating, Og of the original gasoline and from the blending octane value, B, of the alcohol:

where x is the ratio of the additive volume to that of the gasoline. Depending on the initial quality of the fuel, the blending octane value of ethanol can be as high as 160. Methanol has a B of 130, although, when used alone, its rating is only 106. Gasohol can achieve high octane ratings without the use of lead and with only moderate addition of cyclic hydrocarbons. Thus, gasohol brings substantial public health advantages1

1 This may not be quite true when the additive is methanol because of the formaldehyde in the exhaust. With ethanol, the exhaust contains, instead, some acetaldehyde, a relatively innocuous substance.


Figure 3.10 Addition of ethanol to gasoline results in a mixture with higher octane rating.

Since 1516, Brazil has been the worlds leading sugar cane producer. The widely fluctuating international price of sugar prompted Brazil to develop gasohol as a means of disposing of excess production. In years when the price was low, the alcohol percentage in Brazilian gasoline was high (typically, 24%). When sugar prices were high, much less ethanol found its way into automotive fuel (say, 5%). Starting in the 1970s Brazil decided to sell pure (hydrated) alcohol as fuel for its fleet of specially designed cars thus achieving a certain independence from the importation of oil.

Alcohol is more than an additive—it is, itself, a fuel. However, its energy content is lower than that of gasoline (Table 3.6). Per unit volume, ethanol contains only 71% of the energy of heptane, the main constituent of gasoline. Nevertheless, Brazilian alcohol-driven cars (using gasoline-free ethanol) have a per liter kilometrage that approaches that of gasoline engines. This is due to the higher efficiency of the high compression ethanol motors. However, at present ethanol is, per liter, more expensive than gasoline and the Brazilian program requires a substantial government subsidy to make the use of pure alcohol acceptable to the public.

Because water can be mixed with alcohol—inviting the "stretching" of the fuel sold at refueling stations—Brazilian pumps are equipped with den-sitometers permitting the consumer to check on the quality of the product.

Table 3.6

Properties of Two Important Alcohols Compared with Heptane and Octane.

Higher heats of combustion for fuels at 25 C













(rel. to

(rel. to






















1.00 6








3.7 Hybrid Engines for Automobiles

Automobile emission standards are established individually by each state, but the leader is the California Air Resources Board (CARB) which has proposed the most stringent emission specifications in the country. These included a requirement that, by a given date, 2% of the vehicles sold in California be "zero emission vehicles (ZEV)." This requirement was later postponed. Automobile manufacturers have spent considerable effort in the exegesis of the expression, ZEV.

Clearly, a purely electric vehicle (EV) emits no noxious gases. Nevertheless, it consumes electricity that is generated in part by burning fossil fuels which produces pollutants. An EV does pollute, albeit very little compared with a conventional internal combustion vehicle (ICV). Some argue that if an automobile equipped with an internal combustion engine emits the equivalent amount of pollution (or less) than the total emission from an EV, then such an ICV should also be considered a "zero emission" car. The general interest in this type of vehicle is attested by the great popularity of the Toyota Prius.

A hybrid vehicle is an electric car equipped with an additional fuel-driven power source. There are several reasons why hybrids lead to a substantial lowering of emission:

a. Whereas a normal automotive engine has to operate over a wide range of powers, from idling to full acceleration, the battery-charging engine of a hybrid is optimized for operation at constant power and can be fine tuned for maximum efficiency and minimum pollution.

b. There is no waste during the frequent idling periods that occur in normal city driving.

c. Regenerative braking that returns power to the battery during deceleration can be implemented in a relatively simple manner.

There are two general categories of hybrid vehicles: series and parallel. In series hybrid vehicles, the power applied to the wheels comes entirely from the electric motor(s). The fuel driven component simply recharges the battery.

In parallel hybrids, wheel power is derived from both electric and IC motors. Clutches are used to couple these different power plants to the wheels according to the requirements of the moment.

Series hybrids are relatively simple but require large electric motors capable of delivering full acceleration power. They must, in addition have auxiliary systems to maintain battery charge. Thus series hybrids have large drive motors, a charging motor and a generator. The sum of the powers of these three components substantially exceeds the power necessary to drive the vehicle. This can be expensive.


In parallel hybrids the electric motors can be much smaller, and the additional surge power comes from the IC power plant. However, the extra power plant in a hybrid does not have to be a heat engine. Fuel cells may prove ideal for such an application.

3.8 The Stirling Engine

Had the early automobile developers opted for a Stirling engines rather than an Otto, it is possible that present day combustion vehicles would be more efficient and less polluting. But a quirk of history tipped the scales away from the Stirling.

Stirlings have the following advantages:

a. They are more efficient than Otto and diesel engines.

b. They can operate with a wide variety of fuels.

c. Being an external combustion engine they tend to generate less pollutants. They still produce large amounts of carbon dioxide, but, owing to their greater efficiency, they produce less than current automotive engines of equivalent power. They can operate well with fuels having a low carbon-to-hydrogen ratio, thus producing more energy per unit amount of carbon emitted.

d. They are low-noise devices because no explosions are involved.

In addition to its application to engines, the Stirling cycle can be adapted for refrigeration without needing CFCs.

With the rapidly approaching era of fuel cells, the future of any new mechanical heat engine is, at best, questionable. Nevertheless, a more detailed examination of the Stirling cycle is an excellent tool for gaining a certain insight into the analysis of combustion engines in general.

The Stirling cycle consists of an isothermal compression, an isometric heat addition, an isothermal expansion, and an isometric heat rejection (c.f., Table 3.4). Its great efficiency results from the possibility of heat regeneration described in more detail later in this chapter. A number of Stirling engine configurations have been tried. Table 3.7 lists the most common.

Table 3.7

Several Stirling Engine Configurations

{( Alpha (two cylinders, two pistons) Kinematic < Beta (one cylinder w/ piston & displacer)

[ Gamma (one cylinder w/ piston, another w/ displacer)

Free piston Ringbom


In all configurations, two pistons are employed. In some cases one is the power piston and the other is the displacer. The distinction will become clear when we examine examples of the engine.t In kinematic engines, both pistons are driven by the crankshaft, in general by means of connecting rods. In the free piston configuration, the pistons are not mechanically connected to any part of the engine.

The Ringbom configuration uses one kinematic and one free piston.

Since the alpha-configuration is the easiest to understand, we will examine it in more detail.

Consider two cylinders interconnected by a pipe as shown in Figure 3.11. One cylinder (labeled "HOT") is continuously heated by an external source, which can be a flame, a radioisotope capsule, concentrated solar energy, and so on. The temperature of the gas in this cylinder is TH. The other cylinder (labeled "COLD") is continuously cooled by circulating cold water or blowing cool air or, in small engines, perhaps simply by convection. The temperature of the gas in this cylinder is TC. At any rate, there is, as in any other heat engine, a heat source and a heat sink.

The space above the pistons is filled with a working gas (in practical engines, this may be hydrogen or helium). In order to follow the cycle, we will use a specific example. A gas with a 7 = 1.40 is used. The volume of each cylinder can, by moving the piston, be changed from 10-3 m3 to 0 m3 —that is, from 1 liter to 0 liters.

Initially (State 0), the "cold" piston is all the way down. The volume in this cylinder is VC0 = 10-3 m3, the temperature is TCo = TC = 300 K, and the pressure (in both cylinders), is pCo = pHo = 105 Pa or 1 atmosphere.

From the perfect gas law, pV = ^RT, we can calculate that the amount of gas in the "cold" cylinder is 40.1 x 10-6 kilomoles.

The amount of gas in the connecting pipe and in the "hot" cylinder (VHo) is assumed to be negligible.

Hot Cold

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Solar Stirling Engine Basics Explained

Solar Stirling Engine Basics Explained

The solar Stirling engine is progressively becoming a viable alternative to solar panels for its higher efficiency. Stirling engines might be the best way to harvest the power provided by the sun. This is an easy-to-understand explanation of how Stirling engines work, the different types, and why they are more efficient than steam engines.

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