• Section 7.2 reviews the most common types of power plants available for or used in modern aircraft. Design information regarding piston engines, turboprops, turbojets, turbofans, and electric motors is presented. In addition, methods to estimate power and thrust as a function of atmospheric conditions and airspeed are provided.

• Section 7.3 discusses topics that affect the installation of engines. Topics ranging from fireproofing to inlet sizing are presented.

• Section 7.4 presents specialized topics related to engines, ranging from how to account for gearboxes, to the extraction of power information from typical engine performance charts, and the use of the ‘petty equation’ for the prediction of the same.

(1) Piston engines (piston propellers)

(2) Gas turbines (turboprops)

(3) Jet engines (turbojets and turbofans)

(4) Pulsejets (very rare)

(5) Rockets (very rare, sometimes supplements other engines for T-O)

(6) Electric motors (propellers).

Piston Engines

Piston engines typically operate in accordance with a thermodynamic theory known as the four-stroke Otto cycle. In this cycle, the first step entails a compression of a mixture of air and fuel inside the combustion chamber. This process is shown in Figure 7-1 as a reduction in volume (horizontal axis) and an associated increase in pressure (side 1-2). This is accomplished by moving the piston inside the cylinder so the volume is decreased. The next step is the combustion, in which chemical energy obtained by the rapid burn of the fuel-air mixture increases the pressure without additional change in volume. This is depicted as the vertical increase in pressure (side 2-3). This pressure forces the piston in the opposite direction, increasing the volume as shown by side 3-4. Finally, once the piston reaches the position of maximum volume, a valve is opened, allowing the gases to escape (exhaust). This will drop the pressure inside the cylinder without additional change in volume (side 4-1). This operation is then repeated in the engine.

Gas Turbines

A similar thermodynamic cycle for gas turbines is called the Brayton cycle (see Figure 7-1). In this cycle, air enters the intake to the engine at a specific pressure. It is then compressed using a multi-bladed compressor and forced through ducting that reduces the volume of the air (side 1-2). The air is then directed into a combustion chamber, at which point it mixes with fuel, and the mixture is ignited. The geometry of the chamber forces volumetric expansion without change in pressure (side 2-3). The fuel-air mixture rushes through an opening in the combustion chamber, and impinges on a turbine wheel(s) with the associated conversion to mechanical energy. As this happens, the pressure of the mixture drops and its volume increases (side 3-4). Side 4-1 represents the completion of this cycle as fresh air again enters the inlet to the engine.

Propeller and Gas Turbines

The magnitude of is generally so small that it can be ignored. Therefore, we rewrite Equation (7-3) as follows:

(7-4)

The only issue here is the determination of the inlet and exit airspeed and pressures. It is possible to extend Equation (7-4) to include propellers by assuming that ; and that the distance between A_e and A_i approaches zero, so A_e = A_i. This is the result of what is called the actuator-disc or Rankine-Froude momentum theory, presented in Chapter 14, The anatomy of the propeller.

Rockets

For rockets, the values of and V_i are zero, since no air is introduced (it is effectively replaced by the oxidizing chemical), so takes on a governing role and is more appropriately referred to as where . Additionally, A_e and A_i both refer to the area at the nozzle exit plane and p_i is the ambient pressure. Therefore, we rewrite Equation (7-3) as follows:

(7-5)

Thrust-to-weight Ratio

The thrust-to-weight ratio, denoted by T/W, is a very important figure of merit for aircraft. It ranges from a value of 0 for un-powered aircraft, to values in the ballpark of 1.1 for many fighter aircraft (see Table 7-2). Of course, thrust changes with airspeed, and weight with time aloft, so the true value of T/W changes in flight. Therefore, the stated T/W usually refers to a specific weight, such as maximum gross weight or some other specific weight, while the thrust refers to the maximum static thrust.

The importance of high enough T/W cannot be over-emphasized. As an example, the de Havilland DH-106 Comet 1 suffered two hull losses, one with fatalities, both directly attributed to its low T/W of 0.18. The first incident occurred on October 26, 1952, and the second on March 3, 1953 [2]. In general, due to the low T/W, the airplane had to be rotated with utmost care to avoid a sharp rise in drag and a subsequent reduction of acceleration. In comparison, the modern jetliner has a T/W of the order of 0.3–0.35.

Brake Horsepower (BHP)

BHP usually refers to the amount of power delivered at the engine output shaft of a piston engine. It is measured using an instrument called a dynamometer, which is a mechanical or electric braking device. In the UK system, the horsepower corresponds to the work required to raise a weight of 33,000 lb_f, 1 ft in 1 minute. This also corresponds to the work required to raise a weight of 550 lb_f, 1 ft in 1 second. This is written as follows: 1 hp = 33,000 ft·lb_f/min = 550 ft·lb_f/s. Horsepower can be converted to watts (J/s) in the SI system by multiplying by a factor of 746. In other words:

Shaft Horsepower (SHP)

SHP refers to the amount of power delivered at the propeller shaft of a gas turbine engine. If the engine features a gear reduction drive (to reduce the RPM to keep the propeller tip airspeed below the speed of sound), sometimes called a propeller speed reduction unit (PSRU), this value may be somewhat less than the horsepower generated by the engine due to losses in the mechanism.

Equivalent Horsepower (EHP)

EHP is a term used only for turboprops and refers to the combination of the SHP and the residual thrust available from its jet exhaust. The EHP is usually about 5% higher than the SHP.

Thrust Horsepower (THP)

THP refers to the amount of power used to propel an aircraft through the air in terms of horsepower. The thrust of turbojets, turbofans, pulsejets, and rockets is generated by accelerating the fluid directly. For that reason, such engines are always rated in terms of the thrust they generate. This contrasts with piston engines and turboprops, whose mechanical work is used to rotate a propeller, which then creates the thrust. This way, it is not the engine per se that generates the thrust, but the propeller, and this is why it is more appropriate to rate such engines in terms of their power. This is easier to see by noting that the thrust generated by such engines depends on the propeller – for instance, one can mount two different types of propeller on the same engine and generate two different levels of thrust at the same power level. This is not the case for a turbofan or a turbojet. One of the nuisances with this difference is that sometimes it is helpful to convert the thrust into horsepower, for instance, to compare the effective power of a piston or a turboprop to a turbofan. This must be done by multiplying the thrust T of the turbofan (or turbojet or pulsejet, etc.) with the airspeed V at which it is flying. If working in the UK system, the thrust is given in lb_f and the airspeed in ft/s. The unit for the power is thus in terms of ft·lb_f/s, which can be converted to horsepower (i.e. THP) by dividing the product by 550, using the expression below:

Engine Torque and Turboprop Engines

The power output of turboprop aircraft is often represented using torque and RPM, rather than horsepower. Consequently, when considering performance data for turboprop aircraft, it is often helpful to convert the torque and RPM into horsepower.

Torque is equivalent to work (force × distance) and not power (force × speed). Thus, torque is power × time, or power is torque divided by time. Consider a rotating arm of length d rotating at rate RPM due to the force F. Then the work done each minute by the force F is the product of it and the distance over which it is applied. For rotary motion, this can be written as F·2πd·RPM. If we use the UK system of units, this will be in terms of ft·lb_f/min. It can, thus, easily be converted to horsepower by dividing by 33,000 ft·lb_f/min, yielding the following relationship:

Thus, a turboprop operating at a torque of 1500 ft·lb_f and 2000 RPM is delivering 571 SHP of power.

Engine Power and Thrust Ratings

The following concepts are frequently used when specifying engine power and thrust ratings:

Density of Aviation Gasoline (Avgas)

The density of avgas is 0.71 kg/liter. In the UK system, its weight is 5.9–6.0 lb_f/gallon. For analysis work in this text, a weight of 6.0 lb_f/gallon is always assumed.

Energy Content of Fuel for Piston Engines

Piston engine power is directly related to the amount of air mass flow into the intake manifold.

The theoretically ideal (stochiometric) ratio for piston engines is 1 kg of fuel to 14.7 kg of air. When achieved, this ratio results in the highest temperature during combustion and is, therefore, of concern when it comes to engine durability. If the air-to-fuel mixture is less than 14.7:1 (e.g. 14:1), it is called rich. If greater (e.g. 15:1), it is called lean. These two concepts are of great importance to pilots.

The energy content of a 1 lb_f of avgas is 14,800,000 ft·lb_f (20.07 MJ). Burning 1 lb_f of avgas in 1 minute with 100% efficiency would generate:

A typical, modern medium-sized piston engine, such as the Continental IO-360, delivers 200 BHP at maximum power, while consuming 16 gallons of avgas per hour; 16 gal/h amounts to 16 gal/h × 6 lb_f/gal = 96 lb_f of fuel per hour, which amounts to 96 lb_f/60 = 1.6 lb_f/min. The equivalent energy content of this fuel is:

However, only some 200 BHP is delivered as mechanical energy. The resulting efficiency is thus 200/716.8 or 27.9%. In a long-range cruise mode, the same engine delivers 55% of its rated power (110 BHP), while consuming some 8.4 gal/h. Applying the same calculation method we find the efficiency amounts to 29.2%.

Fuel Octane Rating and Fuel Grades for Piston Engines

Fuel octane rating is a measure of the capability of a fuel to resist compression before it spontaneously self-ignites. Thus, fuel with a higher octane number can withstand greater pressure inside the cylinder before igniting in this fashion. For this reason high-octane-number fuel must be used in high-compression (high-performance) engines or they will suffer from engine knocking. That aside, the concept is one that is often misunderstood as there are a number of different octane ratings (e.g. Research Octane Number, RON; Motor Octane Number, MON, etc.). These definitions are outside the scope of this book.

Fuel used to power piston engines aircraft is commonly known as avgas, or aviation gasoline. This contrasts with mogas, or motor gasoline, which is used in cars and some experimental and a few GA aircraft. The difference between the two is that avgas contains a toxic chemical called tetraethyl lead (TEL), which is used to improve the combustion properties of the fuel. The fuel octane rating is used to differentiate between a few grades of fuel, which are offered in different colors to prevent incorrect selection (see Table 7-3).

Fuel Grades for Jet Fuel

There is also a wide range of fuel grades intended for jet engines. Table 7-4 lists those most common for civilian aircraft. A range of jet fuel with specifications for different countries is available to, but not presented here. More details are available from Ref. [4]. For analysis work in this text, a density of 6.7 lb_f/gallon is always assumed.

Specific Fuel Consumption (SFC)

Specific fuel consumption (SFC) is one of the most important metrics employed in aviation. It is important not only in aircraft design but also in the operation of the aircraft. First and foremost, SFC indicates how efficiently a power plant converts chemical into mechanical energy. While there is usually not a great variation in SFC between engines within a specific class of power plants, there is a huge variation between the classes. Thus, piston engines are generally more efficient than turbo machinery, which is far more efficient than, say, rockets. This is important when ensuring the selection of power plant matches the mission of the airplane, although most of the time this is not a problem. The primary importance is when estimating range and endurance of the aircraft.

As discussed in Section 7.1.5, General theory of thrust generation, the operation of any mechanical engine requires chemical energy to be converted into mechanical energy, typically by an intermediary conversion to thermal energy. In conventional piston and jet engines, the chemical energy stored in the fuel is consumed in an exothermic chemical reaction (via combustion) that adds considerable thermal energy to the air, rapidly increasing pressure or volume. The change in these states is then used to move the mechanical elements of the machine.

Consider two engines, call them A and B. If engine A requires less fuel to generate a given power (or thrust for jet engines) than engine B, then we say it is the more efficient of the two. This would place engine B at a competitive disadvantage. So, efficiency clearly plays an imperative role in the marketability of an engine (just like weight).

It is crucial for the engineer to be able to compare the efficiency of different power plants for design purposes and this is accomplished by the definition of fuel consumption as the quantity of fuel burned in a unit time (lbs/hr, kg/min, etc.). This is sometimes referred to as fuel flow (FF). We then define specific fuel consumption (SFC) as the quantity of fuel burned in unit time required to produce a given engine output. SFC is a technical figure of merit that indicates how efficiently the engine converts fuel into power.

We will now consider SFC for jet engines and piston engines separately.

SFC for Jets

The fuel consumption of jet engines is always measured in terms of mass or weight of fuel flow, per unit time, per unit thrust force. For instance, a small jet engine may burn some 1600 lb_f (725 kg) of fuel in a matter of an hour at a T-O thrust setting. If the thrust of the engine is known, the SFC can be computed as shown below:

The pure turbojet, of the kind used in the early days of the jet propulsion, has very poor efficiency. The high-bypass turbofan, in comparison, has superb efficiency, something that explains their wide use in modern passenger transport aircraft.

SFC for Pistons

The fuel consumption of piston engines is always measured in terms of mass or weight of fuel flow per unit time, per unit of power. For instance, a small piston engine may burn some 100 lb_f (45 kg) of fuel in a matter of an hour at a T-O power setting. If the power of the engine is known in BHP or kW, the SFC can be computed as shown below:

Two-stroke versus Four-stroke Engines

Two-stroke engines are valve-less so they are simpler, lighter, and less expensive to manufacture. They are less durable than four-stroke engines because they lack a dedicated lubrication system. Instead, they require oil to be mixed in with the fuel (about 4 oz per gallon of fuel). For this reason they burn a considerable amount of oil when compared to the four-stroke engine.

A two-stroke engine will exhaust combustion gases and draw in a fresh fuel/air mixture on the down-stroke. It will then compress and ignite the mixture on the up-stroke. A four-stroke engine will ignite with a subsequent down-stroke. On the following up-stroke the combustion gases are forced out of the cylinder. As the piston’s next down-stroke begins, the fuel/air mixture will be drawn into the cylinder and be compressed and ignited on the subsequent up-stroke. Thus, ignition occurs once every revolution in a two-stroke engine, but once every other revolution in a four-stroke. This gives the two-stroke engine a significant power boost and allows it, potentially, to double the power for the same-displacement engine. A two-stroke engine manufactured by Hirth Engines is shown in Figure 7-4.

The operation of a two-stroke engine is less efficient than that of a four-stroke engine. This results from the use of cleaner gasoline in a four-stroke engine, which is not mixed with oil as is the fuel for two-stroke engines. As a consequence the combustion burns the fuel more completely and at a higher temperature than possible in a two-stroke engine and both lead to higher efficiency. Additionally, the two-stroke approach leaves remnants of combusted gases inside the cylinder during compression and ignition and forces unburned gas into the exhaust, resulting in greater emission of environmentally harmful chemicals.

Operation of the Four-stroke Engine

Figure 7-3 shows a schematic of a four-cylinder internal combustion engine. The piston and cylinders have been labeled 1 through 4 and are shown during the four stages of the Otto cycle (refer to Figure 7-1).

There are a number of concepts concerning piston engines that one must be aware of.

Air-to-fuel Ratio

As stated in Section 7.1.7, Fuel basics, the ideal stochiometric (air-to-fuel) ratio is 14.7:1 and it yields the least amount of carbon monoxide emissions. However, the engine’s maximum power is generally achieved at about 12:1 to 13:1 (rich mixture). On the other hand, minimum fuel consumption is achieved at approximately 16:1 (lean mixture).

Compression and Pressure Ratios

The compression ratio is defined as the ratio between the volume of the cylinder with the piston in the bottom position, V_bottom (largest volume), and in the top position, V_top (smallest volume). The higher this ratio, the greater will be the power output from a given engine. It is generally in the 6–10 range.

Similarly, the pressure ratio is defined as the ratio of the pressures inside the cylinder with the piston in the top and bottom positions, denoted by p_top and p_bottom, respectively. Assuming adiabatic compression inside the cylinder (no heat energy is added when compressing the gas), the relation between the pressure and volume can be shown to comply with the following expression:

(7-13)

Displacement

Displacement is the total volume of the combustion chamber in the piston engine. The diameter of each cylinder is called a bore. The total distance a piston moves is called a stroke. The displacement of an engine with N cylinders is defined as follows:

(7-14)

The displacement represents the maximum volume of the combustion chambers of all the cylinders assuming the piston is simultaneously at the bottom of the stroke for all (an impossible scenario).

Typical Specific Fuel Consumption for Piston Engines

The fuel consumption of piston engines varies by type, as shown in Table 7-7.

A typical breakdown of how energy is wasted in piston engines can be seen in Table 7-8.

Effect of Airspeed on Engine Power

Generally, the power generated by a piston engine is assumed constant with airspeed, making it an airspeed-independent power plant. Effectively, this means that if a piston engine produces 100 BHP at a specific power setting, say, at stalling speed, it will also generate 100 BHP at the same power setting at its maximum airspeed. In real applications, however, the power output from the engine depends on the pressure recovery at the manifold. If the pressure recovery is airspeed-dependent, for instance as a consequence of the changes in the attitude of the aircraft, then the engine power will become airspeed-dependent, albeit only slightly so. However, for all intents and purposes, during design work, piston engine power output can be considered independent of airspeed.

Effect of Altitude on Engine Power

The power output of normally aspirated engines depends on how efficiently the mixture of air and fuel burns inside the cylinder during combustion, a process that sharply increases the pressure inside the cylinder and pushes the piston in the opposite direction. This, in turn, depends on the total quantity of oxygen molecules (O₂) initially inside the cylinder as the piston begins the compression stroke. The quantity of molecules inside the enclosed volume of the cylinder, of course, is the density and it is directly related to the initial pressure in the cylinder, as realized through the equation of state. For this reason, pressure and density are fundamental variables in the operation of piston engines. This, of course, implies that such engines are highly dependent on the density of air, which is a function of altitude.

Initial pressure in the cylinders can be increased by two means: by recovering as much ram air pressure as possible in the engine manifold (pertains to normally aspirated engines); and by artificially increasing the pressure in the manifold. The former is achieved by ensuring the intake is not blocked and is located in an area where air is allowed to stagnate with minimum losses. The latter can be done through the process of turbo-charging or turbo-normalizing.

To estimate the impact of altitude on the power output of an engine some specialized models are applied. The simplest one, presented below, assumes that the engine power is directly dependent on the density ratio:

where P, ρ and σ are power, density, and density ratio at altitude, respectively; and P_SL and ρ_SL correspond to S-L values. Another more accurate altitude model for piston engines is the Gagg and Ferrar model [8], here presented in its three most frequently encountered forms:

where

The two expressions above are used with normally aspirated engines only. Figure 7-5 shows a comparison between the simplified and Gagg and Ferrar models. The horizontal axis shows the percentage power and the vertical altitude in ft. One way of reading the graph is to ask how much power a piston engine delivers at a given altitude. For instance, how much power does an engine rated as 200 BHP at S-L deliver at full throttle at 15,000 ft? By tracing the horizontal line extending from 15,000 ft to the point where it intersects the thick curve of the Gagg and Ferrar model, it can be seen it delivers approximately 57.5% power, or 0.575 × 200 = 115 BHP. By the same token, consider the same engine, at S-L, at some arbitrary throttle setting that generates 100 BHP. At the same altitude it will deliver a mere 57.5 BHP at the same throttle setting. The Gagg and Ferrar model matches manufacturers’ data far better than the former and is recommended for design work.

Straight lines representing 55%, 65%, and 75% power have been plotted in Figure 7-5, but these represent typical power settings reported by manufacturers or widely known publications such as Jane’s All the World’s Aircraft. It can be seen that once the engine is at 8283 ft, even at full throttle the maximum engine power will not exceed 75% of its rated S-L value as long as it is normally aspirated. Corresponding altitudes for 65% and 55% are shown as 12,106 ft and 16,324 ft, respectively. In order to prevent this sort of power loss with altitude, the air flowing into the manifold must be introduced at a higher pressure. It must be pre-pressurized.

Ideal manifold pressure for a normally aspirated engine is around 29.92 in Hg, depending on the ambient pressure, so ideally such pre-pressurization should maintain this pressure to as high an altitude as possible, and even boost it a tad. There are three common ways of doing this: by supercharging, turbo-charging, or turbo-normalizing. Discussing these devices in detail is beyond the scope of this book, so only a few introductory facts will be included here.

Supercharging is the oldest method known to pre-compress air prior to entering the cylinder of a piston engine. A supercharger is a compressor, often of a centrifugal design, that is directly or indirectly connected to the engine. Such devices may operate at rotation rates as high as 120,000 RPM. And while requiring additional energy from the engine to drive it, the increase in power far overweighs the cost of its production. A supercharger will often generate manifold pressure in the 50–60 in Hg range. For instance, Ref. [9] specifies 52 inHg MAP for the C-46 Commando, a twin-engine heavy transport aircraft from the Second World War era.

A turbocharger is a centrifugal compressor that features a turbine that is driven by the hot exhaust gases from the engine. For this reason, when operating at optimal conditions it puts no additional load on the engine. Rather it utilizes the thermal energy that otherwise would go unharnessed into the environment. This causes it to inflict reduced load on the engine, making it more efficient than a supercharger. However, its presence causes back-pressure to mount in the exhaust manifold, reducing the efficiency of the engine. The magnitude of the back-pressure is largely dependent on a complex interaction between important parameters such as RPM, throttle setting, ambient pressure, and geometry of the inlet [10]. Back-pressure is the obstruction to free flow of the exhaust gases through the tailpipe. Additionally, an exhaust-driven compressor is less efficient than a mechanically driven one.

The third type is turbo-normalization, which really is a turbocharger designed to limit (or normalize) the manifold pressure to that at S-L up to its critical altitude, hence its name. The critical altitude is one at which the ambient pressure has dropped so much that the compressor can no longer deliver air at S-L pressure into the manifold. The turbo-normalizing differs from turbocharging in that it limits the maximum manifold pressure to that of the S-L pressure up to the critical altitude. The turbocharger, on the other hand, increases the manifold pressure above what is possible at S-L. Thus, super- and turbochargers may maintain the manifold pressure to between 32 and 38 in Hg, in contrast to 29.92 inHg average pressure at S-L. The increased pressure implies a greater number of air molecules that must combine with fuel to ensure proper combustion and, therefore, the process increases power, but fuel consumption and engine wear. Turbo-normalizing, in theory, maintains rated S-L power and fuel consumption with altitude. Thus, its operation at altitude is not unlike what it is at S-L.

The impact of altitude on turbocharged and turbo-normalized engines is shown in Figure 7-5. The turbocharged engine is shown to yield power higher than that possible at S-L. The turbo-normalized engine, on the other hand, provides S-L power up to its critical altitude. The critical altitude differs from installation to installation. Some typical installations have a critical altitude of 18,000 ft, while some GA aircraft are capable of even higher altitudes. For instance, the Cirrus SR22 is offered with a turbo-normalized engine capable of S-L power up to 25,000 ft. Such a feature has great customer value because it effectively means its maximum available power is independent of altitude.

Engines that are pressurized in this fashion can be analyzed by assuming power to decrease after the critical altitude has been achieved in accordance with the Gagg and Ferrar model. Mathematically, if the S-L power is given by P_SL and critical altitude by h_crit, then power can be estimated using the following expression:

It is inevitable that the compression of air greatly increases its temperature. Therefore, some such mechanical systems use intercoolers to cool the air exiting the centrifugal compressor. The temperature rise can be approximated by assuming a thermodynamic process called an isentropic process (an isotropic process is one which is both adiabatic and reversible). Using this process, the change in temperature can be estimated from:

(7-19)

Effect of Temperature on Engine Power

Since power is affected by density and pressure, it follows suit that it is also influenced by temperature. The following expression is used to correct power at non-standard temperature conditions:

(7-20)

where

Note that Equation (7-20) is recommended by several piston engine manufacturers without specifically presenting derivations for it. As will be demonstrated in the following example, it over-estimates the engine power when compared to the Gagg and Ferrar model with density ratio based on the ideal gas law. The author recommends the latter method as it yields more conservative performance estimations.

Effect of Manifold Pressure and RPM on Engine Power

The relationship between the manifold pressure and RPM is complex and is usually presented by the piston engine manufacturer in the form of a special graph called an engine performance chart. An example of such a chart is shown in Section 7.4.2, Step-by-step: Extracting piston power from engine performance charts. The primary drawback of this plot is that it lends itself very poorly to modern utilization in spreadsheets. The solution to this remedy is found in a specialized formula, called the Petty equation. This powerful tool is presented in Section 7.4.3, Extracting piston power using the Petty equation.

Typical Fuel Consumption

One of the primary drawbacks of turbo machinery is high fuel consumption. This makes gas turbines primarily useful for high-altitude operation, where low-density-reduced fuel consumption (as a consequence of maintaining a constant fuel-to-air ratio) and high true airspeed make their use practical. Table 7-9 shows the typical specific fuel consumption of selected turboprop engines.

Turboprop Inertial Separators

The proximity of the tip of a rotating propeller tends to throw up a cloud of dust and particles that can get sucked into the inlet of gas turbine engines. For this reason many are equipped with an inertial separator that the pilot can activate while maneuvering at low speeds on the ground. The inertial separator refers to the geometry of the inlet, which forces air to make a sharp turn before entering the engine inlet. The sharp turn cannot be made by heavy particles, which get separated from the stream of air and are thrown out of the engine inlet. Inertial separators save a lot of engines from great harm.

Throttle Ratio (TR)

Ambient air is the propellant in gas turbine engines. For this reason, it should not be surprising that atmospheric properties significantly influence their performance. The pressure of air affects engine thrust through its effect on mass flow rate and, since both pressure and density are lower at higher altitudes, engine thrust will also reduce with altitude. However, the total temperature, T_t0, of which static temperature, T₀, is a part per the expression T_t0 = T₀[1 + (γ − 1)M²/2], affects engine behavior in more profound ways than both pressure and density.

As the flight Mach number and altitude change, so does the total temperature. Engine materials and cooling methodologies place limitations on compressor exit temperature (CET) and turbine entry temperature (TET). The former is the temperature of air as it leaves the last compressor stage and the latter is the temperature after combustion immediately before it enters the first turbine stage. In order to keep compressor efficiencies at a practical level, the engine may operate at its maximum TET and maximum compressor pressure ratio only at one specific value of T_t0, say, T_t0des (call it design total temperature). The ratio of this total temperature to standard S-L temperature (518.67 °R) is known as theta-break. If the actual T_t0 is less than T_t0des (which could be caused by lower flight Mach number or higher altitude) then TET must be decreased to maintain efficiency. If the actual T_t0 is greater than T_t0des (due to operation at higher Mach or lower altitude) then the power generated by the turbine is reduced, causing the compressor pressure ratio to decline.

High compressor pressure ratio results in good thrust specific fuel consumption (TSFC) and high TET yields high specific thrust , where F is the thrust generated and is the mass flow rate through the engine. These imply that it is best to operate the engine always at its theta-break; however, this is never possible since an engine is required to satisfactorily operate at various Mach numbers and altitudes. As a compromise, an engine may be designed so that it has a theta-break value roundabout the most desired combination of altitude and Mach number. The engine is then said to have throttle ratio (TR) equal to the theta-break value. For instance, if the desired combination is, say, M = 0.6, sea level, then the theta-break will be (T_t0/T_std) = 1.072, and the engine has TR = 1.072. On the other hand, if M = 0 and h = 0 (takeoff condition) is chosen as the desired combination, then the theta-break (and TR) will be 1.

To the extent of the author’s knowledge, the concept of throttle ratio was first introduced by Mattingly, Heiser, and Pratt [13], in their aircraft engine design textbook. The book presents a very convenient method to estimate the thrust of gas turbine engines (turboprops, turbojets, and turbofans) as a function of flight conditions. The fundamentals of the method were developed by Mattingly [14] and utilizes simple empirical algebraic equations dependent on Mach number and altitude to determine the change in thrust from some baseline thrust value. The method is ideal for use in spreadsheets or software routines during the conceptual and preliminary design stage of aircraft featuring such engines (for instance see the Microsoft Excel Visual Basic routine presented in the Section 7.2.6, Computer code: Thrust as a function of altitude and Mach number).

The TR is selected by the engine manufacturer and is required for an accurate prediction of engine thrust and, thus, for aircraft performance analysis. An important consequence of the selection of TR can be seen from the following: as stated above, an engine with TR = 1 will be at its theta-break point at M = 0, h = 0, and, consequently, its TET will be at its maximum (assuming standard day conditions – ISA). Therefore, no further increase in the turbine entry temperature is possible. This means that when the aircraft is operating at an elevated temperature, say for instance 20 °C above ISA, the turbine power will be reduced. This, in turn, will detrimentally affect the T-O distance and rate of climb. It is possible to restore some of this loss using technology such as water injection.

By the same token, an engine selected so its TR > 1, say TR = 1.072, will operate at less than its maximum TET at M = 0, h = 0. In response to elevated ambient temperature the TET may be raised to compensate, and this allows constant thrust to be maintained up to some specific altitude. In this case, the thrust may be maintained up to ambient temperature of 518.67 × 1.072 = 556 °R (87 °F or 35 °C). From the standpoint of aircraft design, this is very favorable as it permits a far more impressive performance on hot days.

The name “theta-break” can be inferred from gas turbine performance graphs (e.g. see Figure 6.E8 of Ref. 13), which show a decisive break in each curve. For instance, in the cited figure, the break occurs at M = 0.6 at S-L, but at M = 1.45 at 36,000 ft. The particular engine has a unique TR (1.07 in this case), but the break shifts to higher Mach numbers with increasing altitude due to decline in T₀. Beyond 36,000 ft, however, the break remains at the same Mach number (stratosphere).

Step-by-step: Effect of Altitude and Airspeed on Turboprop Engine Thrust

The effect of altitude and airspeed on the thrust of turboprop engines can be modeled using the Mattingly method of Ref. [13].

Step 1: Determine the baseline thrust to use at S-L, F_SL, for instance the maximum static thrust at ISA.

Step 2: Calculate temperature ratio:

(7-21)

Step 3: Calculate pressure ratio

(7-22)

Step 4: If M ≤ 0.1 then

(7-23)

If M > 0.1 and θ₀ ≤ TR then

(7-24)

If M > 0.1 and θ₀ > TR then

(7-25)

where

The thrust of a generic turboprop engine is plotted for several altitudes as a thrust ratio (i.e. as F/F_SL) in Figure 7-7 using the above formulation and a TR = 1.072. The sharp drop around M = 0.1 occurs when the TET reaches a maximum because of the increase in total air temperature. Until that point, it is possible to maintain constant thrust – something that offers great performance improvements in the operation of turboprop aircraft. Of course, this comes at the cost of a reduction in compression ratio at elevated temperatures in order to keep the TET below its maximum permissible value. In other words, the engine is flat-rated to a given thrust output at standard atmospheric conditions (ISA), even though, theoretically, it could generate thrust greater than what its flat-rating indicates. Plotting the thrust ratio, as is done in Figure 7-7, rather than for a specific rated S-L thrust, allows the curves to be applied to nonspecific turboprop engines. It can be shown using the formulation that at an altitude of approximately 7800 ft the maximum thrust has fallen to 75% of the rated S-L value.

Austyn-Mair and Birdsall [15] present the effect of altitude and airspeed on turboprop power rather than thrust using the following expression:

(7-26)

where

The engine-dependent constants A and n must be selected based on engine data provided by the engine manufacturer. The designer should request power output at specific altitudes and Mach numbers and use this to determine both constants. The constant n is a fraction between 0 and 1, and is often close to 0.5. It reflects the fact that the available shaft power increases with ram pressure in the engine intake.

Typical Fuel Consumption

Table 7-10 shows the typical specific fuel consumption of selected turbojet engines. Note that the reported values are all at a maximum T-O thrust.

Step-by-step: Effect of Altitude and Airspeed on Turbojet Engine Thrust

Reference [14] also presents a method to estimate the effect of altitude and airspeed on the thrust of turbojet engines, similar to the method of Section 7.2.2, Turboprops. Turbojets are typically used in military applications and, thus, feature formulation for maximum and military thrust (with afterburner used).

Step 1: Calculate temperature ratio:

(7-21)

Step 2: Calculate pressure ratio

(7-22)

Step 3a: Maximum thrust (means afterburner is on)

Step 3b: Military thrust (means afterburner is off)

where

The thrust of a generic turbojet engine is plotted for several altitudes as a thrust ratio (i.e. as T/T_SL) in Figure 7-8 using the above formulation and a TR = 1.072.

Typical Fuel Consumption

Table 7-11 shows the typical specific fuel consumption of selected turbofan engines.

Step-by-step: Effect of Altitude and Airspeed on Turbofan Engine Thrust

Reference [13] also presents a method to estimate the effect of altitude and airspeed on the thrust of turbofan engines, similar to those presented above. There are generally two classes of turbofans: those with low and those with high bypass ratios. A low-bypass-ratio turbofan is one whose bypass ratio is less than 1. Low-bypass-ratio turbofans are usually intended for military applications whereas high-bypass-ratio are typically used in civilian applications. For this reason, two types of formulation are presented, one for each type.

Step 1: Calculate temperature ratio

(7-21)

Step 2: Calculate pressure ratio

(7-22)

Step 3a: Maximum thrust of low-bypass-ratio turbofans

Step 3b: Military thrust of low-bypass-ratio turbofans

Step 3c: High-bypass-ratio turbofans

(7-36)

where

The thrust of a generic-low-bypass ratio turbofan engine is plotted for several altitudes as a thrust ratio (i.e. as T/T_SL) in Figure 7-10 using the above formulation and a TR = 1.072. The thrust of a generic high-bypass-ratio turbofan engine is also plotted for several altitudes in Figure 7-11 as a thrust ratio in using the above formulation and a TR = 1.072.

Energy Density

Energy density is the amount of energy stored in a unit weight of a battery. It is denoted by E_BATT and is typically given in terms of watt·hours/kg or Wh/kg for short. The energy density of even the best batteries (LiPo) is substantially lower than that of fossil fuels, about 60 times less [17], leaving electric aviation at a significant disadvantage. The energy density for typical aircraft battery packs is given in terms of kWh (kilowatt-hours). A 5.6 kWh battery can deliver 5600 W over a period of an hour. This corresponds to the energy required to keep a 100-watt light-bulb lit for 56 hours (2.3 days) or a 1500 W microwave running for 3.7 hours.

Batteries

A battery is a device that converts chemical energy into electrical energy (or the other way around). It can also be thought of as a device that allows electrical energy to be carried around. The invention, according to some, is ancient and dates back to the beginning of the Common Era, some 2000 years ago, with the so-called Parthian batteries. While this is debated, it is known that the battery in the modern form dates back to the 1800s with the invention by Alessandro Volta (1745–1827). The battery has come a long way since then and currently, spurred by growing interest in environmental protection, there is considerable research going on. Some of what is said here will possibly be obsolete in a few years time and the reader is encouraged to do their own research to ensure up-to-date information.

There are several issues that concern batteries and must be kept in mind:

The ideal battery for use in airplanes should be light, rechargeable, have a long durability, and with the highest energy density possible. The current state of technology has been largely driven by demand for laptop computers and cell phones, where bright screens and long endurance is of the essence. Batteries of the kind people are mostly familiar with, such as those used for flashlights (D, C, AA, and AAA style) or conventional car batteries, are not suitable at all, due to low energy density and high weight. The modern lithium-ion battery is a huge improvement over the batteries of the past, although it is in fact marginal. Currently, two types of batteries are suitable for use in aircraft: LiFePO₄ and LiCoO₂. Both have their pros and cons.

The current battery technology consists of the types of batteries listed in Table 7-12.

Fuel Cells

A fuel cell is a device that produces electricity by combining hydrogen and oxygen, forming water and heat as byproducts (see Figure 7-14). The fuel cell is superior to batteries in many ways. It has the potential of being a zero-emission device (if the electrical energy is generated using renewable energy) and it overcomes a serious drawback of chemical batteries in which voltage reduces as a function of the battery charge. For batteries, this effectively means that as its charge drains it is no longer possible to get maximum power obtained as when it was fully charged. For airplanes, this means reduced and “variable” top performance, one which depends on charge remaining. In order for electric aircraft to be truly compatible with a conventional fuel-powered aircraft, it is necessary that maximum power can be drawn regardless of the state of charge. This is not an issue with fuel cells and renders them particularly attractive for use in electric aircraft.

While there are several types of fuel cells, this text only considers those that consist of a thin membrane, called a proton exchange membrane (PEM). One side of it is exposed to pure hydrogen gas (H₂) and the other to oxygen (O₂). The PEM catalytically strips the electrons off the hydrogen, converting it into hydrogen ions (H⁺). Furthermore, it ensures the ions can only pass through it in one direction: to the side that is bathed in oxygen. The electrons that were stripped off take a different path and flow through the anode to the cathode, generating electric current in the process. At the same time, the hydrogen ions that pass through the PEM encounter oxygen and the electrons flowing through the cathode react to form H₂O, completing the process.

Hybrid Electric Aircraft

The low energy density of electric motor installations has led to the introduction of engine configurations that bridge the gap between gasoline engines and electric motors through hybrid functionality. A hybrid electric aircraft is one that features a combination of electric motor and some other type of power plant. Strictly speaking, such a power plant can be any of the other types discussed in this section. However, in this text the use of the term will be limited to aircraft driven by a propeller powered by a combination of an electric motor and a piston engine or a gas turbine. In this context we further classify hybrid electric aircraft into the following types:

In 2011, Embry-Riddle Aeronautical University flew a modified Stemme S-10 (parallel) hybrid-powered sailplane using a Rotax 912 and an electric motor coupled to the same driveshaft – arguably the first hybrid light plane in the history of aviation. In this configuration, the airplane uses conventional piston power for T-O and climb, but once reaching cruise altitude the gasoline engine is turned off and the electric power is switched on for cruise.

The Pure Electric Aircraft

Electric propulsion has a number of advantages over propulsion that depends on fossil fuel. Among those is the very quiet operation of such engines. This is compounded using large-diameter, low-RPM propellers that also generate relatively low noise. This contrasts with noisy piston or gas turbine engines and propellers associated with conventional installations. The operation of electric motors is practically without vibration as long as the propeller is well-balanced. The other usual nuisances of gasoline engines are absent as well. There are no residues, odors, or stains associated with the operation of such motors – they are extremely clean. Additional advantages include a very simple and reliable start and operation of the motor. The motor itself is a very reliable device that requires minimal maintenance when compared to a piston engine. Tune-ups and expensive overhauls are not required. Another important consideration is pilot and passenger safety; since no fossil fuels are consumed there is no chance of carbon monoxide poisoning. Another advantage is that batteries can be recharged by simply plugging them into a household outlet and, at this time, recharging batteries is inexpensive. Electric airplanes are also environmentally friendly and don’t emit greenhouse gases, although this is offset by the fact that in many places the production of electricity releases harmful greenhouse chemicals into the environment. This holds for electricity produced by oil or coal plants. Renewable energy is of course the answer, giving the electric airplane a unique potential as an environmentally friendly transportation vehicle.

Unfortunately, the production of electricity is not the only drawback. One of the most important downsides is the storage of the energy on board an aircraft. There are primarily two ways electrical energy is provided to run the motor: via batteries or via fuel cells. At this time, both options are very heavy and a high toll must be paid in terms of reduction in useful load. In fact, as will be discussed later, an airplane really must be specifically designed to effectively use electric propulsion; it is very impractical to convert existing gasoline-powered aircraft into electric ones. One of the issues with batteries is their relatively low energy content. For longer flights this calls for a large amount of matter (i.e. mass) to be carried around, which reduces the useful load of the airplane. Fuel cells, on the other hand, require large quantities of hydrogen to be carried in highly pressurized bottles, sometimes as high as 5000–10,000 psi. In comparison, the pressure inside the combustion chamber of the Space Shuttle main engine is in the 3000 psi range. This means that if the hydrogen bottles burst, they pose a serious threat to the airplane and its occupants.

Formulation

The following expressions are helpful when solving various problems that involve electrical power.

where

I = current (amps)

P = power (watts)

R = resistance (ohms)

V = voltage (volts)

Fireproofing

On the 2nd of June 1983, a DC-9 commercial jetliner en route from Dallas/Fort Worth to Toronto, Canada, suffered a cabin fire thought to have originated behind in the aft lavatory, perhaps by a careless smoker who threw a cigarette, not yet extinguished, into a paper towel container.² The fire spread between the outside wall of the aircraft and the inside decorative walls. The cabin filled with toxic smoke, causing it to be diverted to an alternative airport, the Greater Cincinnati International Airport, Covington, Kentucky. Once on the ground, some 60 to 90 seconds after the cabin doors were opened, fresh oxygen fueled the fire now extensively burning, although hiding under the decorative wall, causing it to quickly engulf the cabin. The fire killed 23 of the 46 occupants on board [18]. Consequently, the installation of smoke detectors and fire extinguishers as well as proper training of crew members found their way into current Federal Aviation Regulations. This tragedy serves as a reminder that in many ways the aviation regulations are written in the blood of victims; they make flying safer for the rest of us.

Fire is a real threat in all aircraft. Unlike a car, the inability to stop the vehicle on a moment’s notice makes fire in airplanes a very serious issue. Fireproofing is the addition of fire-resisting or retarding material and the installation of fire-suppression chemical dispensers to aircraft intended to make it more fire-resistant and, thus, safer in the case of such an emergency. There are three areas in an aircraft that are more susceptible to fire than others: the engine compartment, the cabin area, and anywhere electrical wiring is placed. Designing the fireproofing does not require much mathematics, but rather should demonstrate compliance with the applicable federal regulations. GA aircraft must comply with the regulation of 14 CFR Part 23:

The Firewall

Piston and turboprop engines are typically mounted on a truss structure made from welded chrome-molybdenum steel (SAE 4130), which is then mounted to the airframe and separated from it via the firewall. Its purpose is to prevent fire from spreading beyond the engine compartment. The firewall is usually made from stainless steel or other heat-resistant material. Per 14 CFR 23.1191, some materials are exempt from fire retardation testing and these are listed below:

Additionally, steel or copper base alloy firewall fittings are exempt as well. Other materials must be demonstrated to provide fire resistance – for instance, they must be subjected to a flame that is 2000 ± 150 °F for at least 15 minutes without penetration. Furthermore, the material must be protected against corrosion.

External jet engine installations also feature firewalls on the pylon, as will be discussed later.

Danger Zones Around Propeller Aircraft

Awareness of danger zones around the aircraft that stem from an engine selection is important. The following applies to both piston and turboprop engines. These introduce two kinds of danger zones: those while operating on the ground and those while while airborne. These are due to propwash, turbine exhaust (applies to turboprops only), prop strike (a person walking into the prop), and blade separation. These are depicted in Figure 7-15.

Prop wash can be dangerous if it picks up and blows heavy objects that may harm a person standing behind it. The exhaust zone contains dangerous fumes from the engine that can be harmful if inhaled and can burn a person standing close to the exhaust. Sadly, people walk into rotating propellers several times each year. Not much needs to be said about the outcome of that battle. Blades separating from propeller hubs are, fortunately, very rare, but can happen both in flight and also for reasons that may be easily overlooked. For instance, propeller blades often break off during emergency landings, when landing gear has failed to extend or lock. One of the precautions enforced in such situations in commuter aircraft is to move the passengers inside the danger zone to a different part of the airplane.

(1) Be structurally sound enough to react all loads generated by the engine.

(2) Allow for easy access for maintenance.

(3) Allow engine controls to be easily routed to and from the engine. This includes the electrical system, fuel plumbing, and engine controls (throttle, mixture, pitch control).

(4) The installation must be resistant to fire.

(5) The propeller must have a type certificate and be free of vibration.

(1) Simultaneous application of max T-O thrust, torque, and 75% of the limit load factor (see Table 1-2 for load factors).

(2) Simultaneous application of max continuous thrust, torque, and 100% of the limit load factor.

(3) For turboprops, to account for a sudden malfunction (e.g. quick feathering), the simultaneous application of max T-O thrust, torque, and 1g load, multiplied by 1.6.

(4) For turbine engine installations, torque due to sudden engine stoppage (such as compressor jamming) or maximum acceleration of the engine.

(5) For all engine types, account for a lateral loading by multiplying engine weight by n₁/3, where n₁ is the limit load factor, with a minimum value of 1.33.

• Turboprops multiply by 1.25.

• For piston engines with five or more cylinders, multiply by 1.33.

• For piston engines with fewer than five cylinders, multiply by (6−N_cylinder).

Systems Integration

Figure 7-17 shows a typical installation of a small piston engine and identifies a number of different systems required for proper operation of the engine. This means that a number of perforations have to be made through the firewall. For typical piston engine installations, provisions have to be made for the following instruments:

These call for electrical connectors and instruments to be mounted on either side of the firewall. Additionally, the following electrical and fuel related equipment must be accounted for:

Types of Engine Mounts

There are three common means of mounting a piston engine to the airplane. Dynafocal mounts arrange the fastener pattern such that the fasteners point toward the CG of the engine. This reduces engine vibration, but requires the engine mount and motor pads to be welded at an angle, making their fabrication harder. Conical mounts align the fasteners parallel to the crankshaft, while bed mounts align the fasteners perpendicular to the crankshaft (see Figure 7-18).

Fuel System

A typical fuel system layout for a low-wing high-performance piston-engine airplane is shown in Figure 7-19. Normally, there are two fuel tanks, one in each wing. The fuel is gravity-fed from each tank into special tanks called collector tanks. Their purpose is to ensure that maneuvering the airplane will not result in a drop in fuel pressure that might interrupt the engine operation. Float-type sensors in each tank detect remaining fuel quantity.

Since the collector tank is below the engine, it must be pumped to the engine’s injector manifold, where it is delivered to individual cylinders. Two fuel pumps are used for this purpose – one is driven directly by the engine and the other is electric and is used when starting the engine and during critical operations, such as T-O and landing. It is also used for vapor suppression during climb and is left on for up to 30 minutes once the plane levels off for cruise. The pumps draw fuel from the collector tank selected by the pilot. Excess fuel not used in the manifold is returned to the selected fuel tank.

The operation of the fuel system depends on proper venting. If venting were not provided, the pressure in the tank would reduce as the fuel is consumed. Eventually this would lead to decreased flow of fuel and an inevitable engine fuel starvation and stoppage. The fuel vents ensure ambient pressure is provided no matter the remaining fuel quantity. This is often done by exposing a vent line to a stagnation pressure port. This will pressurize the tank and help with suitable fuel flow.

Method 1: Inlet-exit-dependent Heat Transfer

This method assumes that the inlet area must be equal to the exit area required to carry the engine heat away. The heat carried away by the air flowing through the engine compartment can be found from:

(7-37)

where

For air, the value of C_p is as follows:

The mass flow rate is given by

(7-38)

where

This can be used to solve for A_E, which then can be used as the inlet area, A_I:

(7-39)

The resulting area will be highly dependent on the selection of the exit airspeed, V_E. Therefore, the engineer should evaluate area requirements during climb (low speed, full power), approach (low speed, low power), and cruise (high speed, moderate power) on hot days and use these to evaluate the area. The fact that it takes the engine some time to overheat is sometimes used to get by with smaller inlets and outlets. Some airplanes have insufficient cooling capability during climb and depend on the airplane reaching higher (and cooler) altitudes quickly so cruise can commence, where cooling is usually sufficient.

Exit Area and Cowl Flaps

Equation (7-39) shows the exit area is a function of the airspeed. When the airspeed is high, such as at cruise, the required exit area is small. When the airspeed is low, a larger area is required. It is to be expected that a small area that generates relatively low cooling drag at cruise may lead to cooling problems at lower airspeeds, such as before landing. This makes it tricky to determine an area that works for both conditions. Sometimes this is impossible to accomplish and potential for over-heating must be solved using a so-called cowl-flap, a mechanical device that is used to adjust the exit area on a need-to basis.

Many high-performance piston-engine aircraft feature such flaps. Normally, the cowl-flap is open for low-speed operations (T-O, climb, landing) and closed during cruise. Cowl-flaps are also useful when operating the engine in very cold climate, when over-cooling the engine is a realistic possibility. In such conditions the cowl flap is kept closed, ensuring the engine runs at ideal cylinder-head temperature.

Method 2: Inlet-radiator-exit Method

McCormick [19] presents the following method, derived from recommendations by Lycoming for estimating cooling drag for piston engines. The method is also helpful when sizing their inlet and exit area as well. Its primary drawback is that it requires data from the engine manufacturer, which, unfortunately are not always available. The piston engine (or a heat exchanger, such as a radiator) can be analyzed based on the idealized configuration shown in Figure 7-24.

The method idealizes the engine by considering it as a system of inlet-radiator-exit. Then, it is assumed that adiabatic compression and expansion of air takes place inside the inlet and exit, shown in Figure 7-25, which themselves are idealized as a diffuser and nozzle, respectively.

The method assumes that air entering the diffuser will slow down gradually to a minimum value at the forward face of the radiator. The effectiveness of the cooling requires a pressure differential to exist across the radiator (i.e. between its forward and aft faces). This pressure differential is referred to as a “pressure drop” and is imperative as it forces air to flow through the radiator and carry away thermal energy. The process can be improved by greater slowing of air in the inlet, i.e. by a greater recovery of the far-field dynamic pressure. A common pressure recovery in airplane piston engine cowling inlets is of the order of 60–80%, based on airspeed. For carefully designed scoops, it can be as large as 80–90% depending on airspeed.

Figure 7-26 shows the model with the flow properties identified at each important station. The flow conditions can be estimated to the front face of the radiator using the flow conditions upstream, assuming an adiabatic compression. Similarly, it is possible to estimate the conditions up to the aft face of the radiator using the downstream conditions, assuming an adiabatic expansion. It remains to tie the two together, something that requires the change across the radiator to be known (information the engine manufacturer should be able to provide). The temperature and pressure in an adiabatic compression or expansion can be estimated using the isentropic flow relations:

(7-40)

where

The factor k indicates how much of the dynamic pressure is preserved as the speed of the airflow is slowed down and is an indicator of the efficiency of the diffuser. If k = 0, there is no recovery and the total pressure remains that of the ambient pressure in the far-field. If k = 1, there is 100% recovery and all the dynamic pressure is converted into total air pressure without any losses. This is generally highly desirable.

With the pressure known, the airspeed at condition can be determined using the compressible Bernoulli equation:

(7-41)

Determining the pressure drop through the radiator is not a simple task. Usually this is done by empirical methods (read as trial and error). However, the pressure drop across baffle depends on:

(7-42)

where

(7-43)

This implies that the drop in pressure is related to the mass flow rate and density as described by the following relationship, which is derived by inserting Equation (7-43) into (7-42):

(7-44)

Installation of Jet Engines

Installation of jet engines must comply with largely the same requirements as piston engines, with some exceptions. Jet engines are installed either internally (inside a fuselage) or externally (on a pylon). However, in either case, identical connectors and lines are required. Figure 7-30 shows a schematic of a typical jet engine installation. Internal and external engine installations are also equipped with fire-suppressant systems, which increase the weight further. Additionally, if the aircraft is to be certified for flight into known icing (FIKI), the leading edge of the inlet (usually called inlet lip) must feature anti-ice capability, compounding the complexity.

Installation of Turboprop Engines

Turboprops typically follow a similar process to the piston engine. They are substantially lighter and, while longer than piston engines of comparable power, their girth (diameter) is more compact. For instance, the 400 BHP Lycoming IO-720 weighs about 600 lb_f, whereas the 600–1100 SHP Pratt & Whitney Canada PT6 weighs about 350–400 lb_f. For this reason, if a piston engine is to be replaced with a turboprop, the installation will require the propeller to be mounted farther forward, giving the airplane a very distinct appearance. Consequently, all forces acting on the propeller result in higher moments, which call for greater control surface authority to react.

Turbo Machinery and Rotor-burst

The compressor and turbine in a typical gas turbine rotate at very high rates when compared to a piston engine. The typical gas turbine rotates at 20–40 thousand RPM. This means the compressor or turbine blades react a substantial centripetal force and, if one breaks off, two things will happen:

It is an extremely dangerous event that must be accounted for in the detail design of the airplane.

(1) Flow no longer slows down isentropically, which leads to lower total pressure inside the inlet.

(2) The separated region along the inside wall narrows the effective cross-sectional area, which leads to higher than desired airspeed (and thus lower total pressure) at the front face of the compressor.

(3) The separated flow is inherently unstable and looses “smoothness” as it enters the compressor, reducing its efficiency and stability of operation.

Inlet Types for Jet Engines

Two types of installation methodologies are used for jet engines; external and internal (see Figure 7-31). The external inlet is also called a pitot inlet. For internal inlets, there are predominantly two main subtypes: the NACA inlet and the bifurcated inlet. These inlets have the following pros and cons.

From an operational standpoint, the external (or pitot) inlet offers great pressure recovery for the entire range of AOA and AOY the aircraft is likely to see in practice. It is easier to access for maintenance and engine removal and replacement. However, it also generates more aerodynamic drag due to the nacelle and pylon.

The internal bifurcated inlet is a good solution for single-engine installations, allowing the engine to be placed behind the cabin and be positioned so thrust effects on stability and control are minimized. This tends to result in less aerodynamic drag since the engine installation adds much less wetted area than the external one. Of course placing the fuselage in front of the inlet will cause boundary layer growth to be ingested, unless steps are taken to avoid it, such as the use of boundary layer diverters. This can be problematic if the airplane yaws and separated air enters the inlet on one side. Other problems are pressure losses due to bending of the internal inlet, as well as problematic ice accretion that may occur on the forward-facing curves of the inlet, which requires anti-ice remedies for aircraft certified for FIKI.

The internal NACA inlet generates even less aerodynamic drag than the bifurcated inlet and can be the right solution for specific single-engine installations. It more often sees use as a generic low-drag inlet for engine or component cooling than as a jet engine inlet, because it suffers from much greater pressure losses than its bifurcated counterpart. Since turbofan engines are more sensitive to inlet pressure losses, it can be argued that the NACA inlet is better suited for turbojet applications and should be avoided for turbofans.

The Diffuser Inlet

The process of slowing air down with minimal losses in pressure recovery is most effectively accomplished using adiabatic expansion. As stated earlier, this is imperative, as any reduction in the total pressure at the front face of the compressor will lead to reduced thrust. The most efficient inlet geometry for this purpose is the diffuser (see Figure 7-32). A diffuser has a capture area slightly smaller than the compressor disc area.

The airspeed of an airplane has a profound effect on the nature of how a jet engine ingests air. Two extremes are shown in Figure 7-33. At rest, the jet engine will effectively ingest air from around and in front of the inlet, a very important fact for technicians to keep in mind while working on the ground near such machines. The inflow can be tremendously powerful and, sadly, every year an unfortunate mishap takes place in which a person is sucked into a large jet engine with fatal consequences. It also shows the engine can easily draw in FOD off the ground and sustain considerable damage.

As the speed of the airplane increases, the streamlines shown in the upper diagram become more and more aligned with the engine axis and begin to form a distinct streamtube. A distinct streamtube means that only air inside this volume will be ingested by the engine. The lower diagram of Figure 7-33 shows this at cruising speed, during which much more air than required by the engine is available.

While the design of the inlet is best implemented with the participation of the engine manufacturer, the airframe designer may want to perform preliminary sizing of the inlet to expedite the layout of the airplane. The following Step-by-step is provided for that purpose. Note that Flack [20]; Seddon and Goldsmith [21]; and Mattingly [14] provide good guidance for the general inlet design and should be referenced as well.

The inlet design involves a number of important geometric parameters to be considered. For analysis reasons, three stations of interest have been superimposed on the engines of Figure 7-33, denoted by , , and . The inlet sizing requires the flow conditions and geometry to be known at each station and these are pressure, density, temperature, airspeed, and cross-sectional area. Station represents the far-field. In this way, at rest, the far-field area is infinite in size and the Mach number is thus assumed zero. However, at cruise, the area in the far-field is substantially smaller and is less than the area at the inlet lip, denoted by . Generally, the following procedure can be used to determine the inlet lip geometry.

Step 1: Required Mass Flow Rate

Obtain the maximum mass flow rate required by the engine and call it . This information is usually provided by the engine manufacturer and is usually dictated by the engine performance at static T-O thrust, making it the critical flight condition for the design. This contrasts with the cruise condition, in which the airspeed is so high that the inlet stream tube necks down in the far-field as shown in Figure 7-33, indicating plenty of air can enter the engine. The remaining steps assume this to be the case.

Step 2: Determine Airspeed Limitations at the Inlet Lip and Compressor

Generally, the airspeed at the inlet lip (station ) should not exceed Mach 0.8. Similarly, the airspeed at the front face of the compressor (station ) is limited to Mach 0.4 to 0.5 and is ultimately specified by the engine manufacturer. This is intended to prevent the airspeed at the tip of the fan becoming too high, resulting in decreased efficiency.

Step 3: Establish Known and Unknown Flow Conditions

The knowns and unknowns can be established in a format similar to the one shown below. Question marks indicate the parameter is initially unknown. Recall that the total pressure is the sum of the ambient and dynamic pressures. Thus, if the engine is moving at some airspeed V, the total pressure is given by . However, as stated above, for this particular condition the engine is assumed to be at rest, so . For this reason, the total pressure in the far-field is simply the ambient pressure.

Step 4: Determine Conditions at Station

Even though the airspeed in the far-field is zero as the engine spools up to T-O thrust, air can easily accelerate to very high airspeeds at the inlet lip. Normally, the inlet lip area is sized so the airspeed does not exceed Mach 0.8. If it is assumed that isentropic flow relations hold between stations and and that the ratio of specific heats of air is γ = 1.4, it is possible to determine the flow variables P_T, T, and ρ, to be determined as follows (using M₁ = 0.8):

Step 5: Determine Conditions at Station

Assuming the airspeed (M₂) at the front face of the compressor to be in the Mach 0.4 to 0.5 range, the remaining parameters are again determined using isentropic flow relations between stations and :

Again, it is important to remember that the above equations reflect the assumption the engine is at rest.

Pressure Recovery

For perfect inlets, the pressure recovery ratio, π₂, is 1. This will yield the maximum thrust for a given flight condition. Short inlets common to podded jet engines of the type shown in Figure 7-33 usually have π₂ close to 1. Integrated inlets (see below) have π₂ values that are often well below 1.

Inlet Lip Radius

It is imperative that the lip radius is carefully designed. A small radius can cause flow separation at high AOA or AOY. A large lip radius tends to reduce pressure distortion at high AOA or AOY and it also results in higher nacelle drag. A pressure distortion is localized deviation of the expected average pressure at the front face of the compressor, usually as less than the average pressure. This is very undesirable as it may cause oscillation in the airloads of the fan blades. Practical lip radii for subsonic aircraft range from about 6% to 10% of the inlet diameter.

Diffuser Length

The length of the diffuser is of great importance as well. A schematic of a pitot inlet is shown in Figure 7-34. The parameters of importance are the included angle, θ, the diffuser length, L, and the inlet lip diameter, D₁. The ratio L/D₁ is called the inlet aspect ratio. For a given aspect ratio, L/D₁, too large an included angle θ indicates the diffuser is expanding too rapidly. This promotes detrimental flow separation on the inside wall. Conversely, for a given θ, too long a diffuser also promotes flow separation. The phenomenon is detailed by Schlichting [22, pp. 222–224], who demonstrates that no matter the included angle, if the diffuser length exceeds a certain distance, separation is inevitable. Additionally, such a diffuser is bound to have a larger nacelle wetted area and, therefore, increases the aerodynamic drag of the installation in addition to being heavier. There is also a range of dimensions for which the formation of the flow separation is transitory; i.e. flow separation may fluctuate. The result may be compressor blade flutter and onset of early fatigue due to oscillatory loading of the blades.

As indicated by Flack [20], the optimum pressure difference between stations and should comply with:

The pressure between the stations must be allowed to rise over a suitable distance and this usually requires more sophisticated analysis methods that can account for the intricacies of the desired geometry. However, in the absence of such schemes, a convenient empirical method for simple diffusers is provided by Flack [20] to evaluate whether the geometry will be prone to separation. Separation is unlikely if the included angle θ is less than the minimum value obtained from the following expression:

Conversely, separation is all but guaranteed if the included angle θ is greater than the maximum value obtained from the expression:

(7-54)

where θ is in degrees. In between the two values is the transitory separation, in which there may or may not be separation. The trends based on this formulation are plotted in Figure 7-35. As an example consider an inlet with an aspect ratio of 3. The graph shows that keeping the included angle less than 15° will prevent flow separation inside the inlet.

Stagger or Rake Angle

Stagger refers to lip geometry in which the upper lip is forward of the lower one (see Figure 7-32). The arrangement improves flow quality at higher AOAs, by reducing the airspeed at the lower lip and, thus, reduces tendency for flow separation [21]. Staggering is usually very modest in subsonic aircraft and ranges from 0° to perhaps 5°.

Derivation of Equation (7-48)

Of the set of equations, only Equation (7-48) needs to be derived. First, the required mass flow rate is given by:

(i)

The airspeed, V₁, is Mach number multiplied by the speed of sound, i.e. V₁ = M₁·a, where a is the speed of sound at the inlet lip. The speed of sound can be calculated from the ideal gas expression:

Inserting this into Equation (i) and expanding and subsequently solving for the inlet area yields:

QED

RPM of gearwheel 2:

(7-55)

Torque of gearwheel 2:

(7-56)

Power of gearwheel 1:

(7-57)

Power of gearwheel 2:

(7-58)

T_std = standard day temperature at altitude

T_OAT = outside air temperature at condition

P_BHP = horsepower at condition (specified MAP, RPM, and altitude)

P_{BHP max} = maximum S-L horsepower as a function of RPM (typically a polynomial)

P_FHP = friction horsepower as a function of RPM (typically a polynomial – PFHP = PBHP at MAP = 0)

h = pressure altitude in feet

MAP = manifold pressure in inches Hg

MAP_max = maximum manifold pressure as a function of RPM (typically a polynomial)

R_m = manifold pressure ratio = MAP/MAP_max

R_f = friction horsepower ratio = |PFHP|/PBHP _max (always a positive value)

σ = density ratio for standard atmosphere =

Determination of the Polynomials Describing P_{BHP max} and P_FHP

Consider the engine performance chart of Figure 7-37, in particular the sea level performance side. The trick to creating these polynomials is to tabulate the endpoints and then fit a curve to these (see Table 7-13). For instance, consider the generation of the polynomial for the values of P_{BHP max}. Column contains the selected RPM values. Column contains the corresponding values of P_{BHP max}, which have been obtained by extending all the curves to a MAP of 29.

The next three columns pertain to the determination of P_FHP. The easiest way to determine the values of P_FHP is to read the value of the MAP for P_BHP = 0, and then use the equation of a line to determine the values of P_FHP when MAP = 0. These values can be seen in column . Column contains the slope of the lines calculated from:

Then, the P_FHP, which is contained in column , can be calculated as follows:

The points from Table 7-13 have been plotted in Figure 7-38. Then, it is an easy task to determine the best fit curve. Here, an equation of a line turned out to provide an acceptable fit, but this is not guaranteed. Commonly one must resort to quadratic and even cubic polynomials.

Derivation of Equation (7-59)

Consider the simplified performance chart in Figure 7-39, on which only a single RPM is shown. The sea level curve, in the sea level performance side, extends from a negative friction power (P_FHP), which is the norm at MAP = 0, to a maximum power, P_{BHP max}, at the maximum manifold pressure, MAP_max. The representative P_BHP versus Altitude curve is shown in the altitude performance side. It depends on σ and extends from the S-L P_BHP value to where MAP can no longer be maintained. The locus of these limit points results in a specific P_BHP versus Altitude curve for each RPM, starting at σ = 1 to σ = 0.117.

The sea level performance curve can be easily represented using the following parametric expression (noting that the MAP axis extends from 0 to MAP_max so the parameter can be defined as ):

(i)

Then, define the ratio . Then, rewrite Equation (i) and insert this definition and simplify.

Note that in order to prevent sign errors from occurring, the ratio R_f will from hereon be considered positive. However, since P_FHP is always negative, the above result is rewritten as follows, as this will preserve the sign:

(ii)

The altitude performance curve is based on the Gagg and Ferrar piston engine power correction of Equation (7-16), here repeated for convenience.

(iii)

where the subscript “a” indicates this is taken from the altitude side. The manifold pressure for each RPM varies linearly with the pressure ratio and, thus using Equation (16-6), can be written as follows:

(iv)

Or, conversely:

(v)

Then, substitute Equation (v) into Equation (iii) to yield:

(vi)

P_{BHP a} is the power corrected for altitude effects only and this remains to be adjusted to standard day and corrected for temperature at the flight altitude, h. The adjustment takes place by locating the uncorrected power, denoted by P_{BHP b}, along the constant manifold pressure line on the altitude side of the performance chart using the equation:

(vii)

where

Inserting this into Equation (vii) yields:

(viii)

Further algebraic manipulations:

(ix)

The uncorrected power must then be corrected for temperature and this is done using Equation (7-20):

(x)

And this is the power that one would used in performance calculations. Combining Equations (ii), (iii), (v), and (ix) with (x) leads to the following expression:

Further simplification yields:

(xi)

This is the Petty equation.

QED