Category AIRCRAF DESIGN

Computational fluid dynamics (CFD) is a numerical tool for solving equations of fluid mechanics. CFD is a relatively recent development that has become an indis­pensable tool in the last two decades. It was developed originally for aeronautical uses but now pervades all disciplines involving flow phenomena, such as medical, natural sciences, and engineering applications. The built-in codes of the CFD soft­ware are algorithms of numerical solutions for the fluid-mechanics equations. Flow fields that were previously difficult to solve by analytical means – and, in some situ­ations, impossible – are now accessible by means of CFD.

Today, the aircraft industry uses CFD during the conceptual study phase. There are limitations in obtaining accurate results, but research continues in academic and industrial circles to improve prediction. This chapter aims to familiarize newly initi­ated readers with the scope of CFD in configuring aircraft geometry (those already exposed to the subject may skip this chapter). This is not a book about CFD; there­fore, this chapter does not present a rigorous mathematical approach but rather an overview.

CFD is a subject that requires considerable knowledge in fluid mechanics and mathematics. CFD is introduced late in undergraduate studies, when students have mastered the prerequisites. Commercial CFD tools are menu-driven and it is possi­ble to quickly become proficient, but interpreting the results thus obtained requires considerable experience in the subject.

An accurate 3D model of an aircraft in CAD significantly reduces preprocess­ing time. The CAD software format must be compatible with CFD to transfer the drawing models. Together, CAD and CFD provide a CAE approach to paperless, electronic design methods.

Several good commercial CAD and CFD packages are available in the mar­ketplace. Nowadays, all engineering schools have CAD and CFD application software.

14.1.1 What Is to Be Learned?

This chapter covers the following topics:

Introduction to the concept of CFD Introduction to the current status of CFD An approach to and considerations for CFD analysis Case studies

Hierarchy of CFD simulation methods Summary

14.1.2 Coursework Content

There is no coursework on CFD in the first term. However, it is recommended that CFD studies be undertaken in the second term after readers are formally introduced to the subject. Appropriate supervision is required to initiate the task and analyze the results. Any CFD coursework is separated from the scope of this book. The purpose of this chapter is to give newly initiated readers an introduction to aircraft – design work.

14.2 Introduction

Throughout this book, it is shown that the aerodynamic parameters of lift, drag, and moment associated with aircraft moving through the air are of vital importance. An accurate assessment of these parameters is the goal of aircraft designers.

Mathematically, lift, drag, and moment of an aircraft body can be obtained by integrating the pressure field around the aircraft computed from the governing con­servation equations (i. e., differential or integral forms) of mass, momentum, and energy with the equation of state for air. Until the 1970s, wind-tunnel tests were the only way to obtain the best results of these parameters in the various air­craft attitudes representing what can be encountered within the full flight envelope. Semi-empirical formulae generated from vast amounts of test results, backed up by theory, provided a good starting point for any conceptual study.

Numerical methods for solving differential equations prevailed for some time. The Navier-Stokes equations provided an accurate representation of the flow field around the aircraft body under study. However, solving the equation for 3D shapes in compressible flow was difficult, if not sometimes impossible. Mathematicians devised methods to discretize differential equations into algebraic form that are solvable even for the difficult nonlinear, partial-differential equations. During the early 1970s, CFD results of simple 2D bodies in inviscid flow were demonstrated as comparable to wind-tunnel test results and analytical solutions.

The industry recognized the potential and progressed with in-house research; in some cases, complex flow phenomena hitherto unknown were understood. Subse­quently, CFD proliferated in academies and there was rapid advancement in achiev­ing solution techniques. Over time, the methodologies continued to improve. The latest technique discretizes the flow field into finite volumes in various sizes (i. e., smaller when the fluid properties have steeper variations) matching the wetted sur­face of the object, which also needs to be divided into cells/grids. The cells/grids do not overlap the adjoining volumes but rather mesh seamlessly. The mathematical
formulation of the small volumes now can be treated algebraically to compute the flux of conserved properties between neighboring cells. Discrete steps of algebraic equations are not the calculus of limiting values at a point; therefore, errors creep into the numerical solution. Mathematicians are aware of the problem and struggle with better techniques to minimize errors in the algorithms. This numerical method of solving fluid-dynamic problems became computation-intensive, requiring com­puters to tackle numerous cells; the numbers could run into the millions. The solu­tion technique thus became known as computational fluid dynamics, abbreviated as CFD.

Another problem in the 1970s was the inadequacy of the computing power to deal with the domain consisting of the numerous cells and to handle the error functions. As computer power increased along with superior algorithms, the CFD capability gradually became applicable to the industry. Today, CFD is a proven method that is well supported by advanced computing power. CFD started in the industry and has become an indispensable tool for the industry as well as research organizations.

A difficult area of CFD simulation lies in turbulence modeling. Recently, com­putations of 3D Reynolds-average Navier-Stokes (RANS) equations for complete aircraft configurations have gained credence as a solution technique. Reference [13] summarizes the latest trends in turbulence modeling. Numerous credible soft­ware applications have emerged in the market, some catering to special-purpose applications.

CFD still has limitations: Drag is a viscous-dependent phenomenon; inclusion of viscous terms makes the governing equations very complex, requiring intensive computational time. Capturing all of the elements contributing to the drag of a full aircraft is a daunting task – the full representation is yet to achieve credibility in industrial uses. It is not yet possible to obtain an accurate drag prediction using CFD without manipulating input data based on a designer’s experience. However, once it is set up for the solution, the incremental magnitudes of aerodynamic parameters of a perturbed geometry are well represented in CFD. It is a useful tool for obtain­ing accurate incremental values of a perturbed geometry from a baseline aircraft configuration with known aerodynamic parameters. CFD provides a capability for parametric optimization, to a degree (discussed in the next section).

Military aircraft serve only one customer, the Ministry or Department of Defense of the nation that designed the aircraft. Frontline combat aircraft incorporate the newest technologies at the cutting edge to stay ahead of potential adver­saries. Development costs are high and only a few countries can afford to produce advanced designs. International political scenarios indicate a strong demand for combat aircraft, even for developing nations that must purchase them from abroad. Therefore, military aircraft design philosophy is different than civil aircraft design. Here, designers and scientists have a strong voice, unlike in civil design in which the users dictate the requirements. Selling combat aircraft to restricted foreign countries is one way to recover investment costs.

Once a combat aircraft performance is well understood over years of oper­ation, consequent modifications follow capability improvements. Subsequently, a new design replaces an older design – there is a generation gap between the designs. Military modifications for the derivative design are substantial. Derivative designs primarily result from revised combat capabilities with newer types of armament, along with all around performance gains. There is also a need for modifications – perceived as variants rather than derivatives – to sell to foreign customers. These variants are substantially different than civil aircraft variants.

AJT designs have variants that serve as combat aircraft in CAS. AJTs are less critical in design philosophy compared with frontline combat aircraft, but they bear some similarity. Typically, an AJT has one variant in the CAS role produced simul­taneously. There is less restriction to export these types of aircraft.

The military infrastructure layout influences aircraft design; here, the LCC is the primary economic consideration. For military trainer aircraft designs, it is best to have a training base located near the armament practice arena to save time. A dedicated training base may not have a runway as long as a major civil runway. This is reflected in the user specifications necessary for beginning a conceptual study. The training mission includes aerobatics and flying with onboard instruments for navigation; therefore, the training base should be located far from the civil airline corridors.

The AJT sizing point in Figure 11.5 shows a wing-loading, W/SW = 58 lb/ft2, and a thrust-loading, T/W = 0.55, which is a significant margin, especially for the landing requirements. The AJT can achieve a maximum level speed over Mach 0.88, but this is not demanded as a requirement. Mission weight for the AJT varies substantially; the NTC is at 4,800 kg and, for armament practice, it is loaded to 6,600 kg. The margin in the sizing graph encompasses an increase in loadings (the specification used in this book is for the NTC only). There is a major demand for higher power for the CAS variant. The choice of an uprated engine or an AB depends on the engine and the mission profile.

Competition for military aircraft sales is not as critical compared to the civil – aviation sector. The national demand supports the production of a tailor-made design with manageable economics. However, the trainer-aircraft market has com­petition – unfortunately, it is sometimes influenced by other factors that may fail to result in a national product, even if the nation has the capability. For example, the Brazilian design Tucano was re-engined and underwent massive modifications by Short Brothers of Belfast for the United Kingdom, RAF, and the BAe Hawk (UK) underwent major modifications in the United States for domestic use.

The sizing point in Figure 11.3 shows a wing-loading, W/SW = 64 lb/ft2, and a thrust­loading, T/W = 0.32; there is little margin given for the landing requirement. The maximum landing mass for this design is at 95% of the MTOM. If for any reason the aircraft OEW increases, then it is better if the sizing point for the W/SW is somewhat lower than 64 lb/ft2 – for example, 62 lb/ft2 and/or increase T/W to 0.35. A quick iteration resolves the problem; however, this choice is not exercised to keep the wing area as small as possible. Instead, an aircraft is allowed to approach landing at a slightly higher speed because the LFL is generally shorter than the TOFL. This is easily achievable because the commonality of the undercarriage for all variants starts with the design of the heaviest (i. e., for the growth variant), and then the bulky components are reduced for lighter weights. The middle variant is used as the baseline version; its undercarriage can be made to accept the MTOM growth as a result of the OEW growth instead of making the wing larger.

Civil aircraft are recommended to come in a family of variants in order to cover wider market demands to maximize sales. However, none of the three variants is optimized, although the baseline is carefully sized in the middle to accept one larger and one smaller variant. Even when development costs are front-loaded, the variant aircraft cost is low by sharing the component commonality. The low cost is then translated to a lowering of the aircraft price, which absorbs the operating costs of the slightly nonoptimized designs.

It is interesting to examine the design philosophy of the Boeing 737 and the Air­bus 320 families of aircraft variants in the same market arena. Together, more than 8,000 aircraft have been sold in the world market, which is no small achievement in engineering. The cost of these aircraft is about $50 million each (in 2005). For air­lines with deregulated fare structures, making a profit involves complex dynamics of design and operation. The cost and operational scenario changes from time to time (e. g., increases in fuel cost and terrorist threats).

As early as the 1960s, Boeing recognized the potential for keeping component commonality in offering new designs. The B707 was one of the earliest commercial – transport jet aircraft to carry passengers. It was followed by a shorter version, the B720. Strictly speaking, the B707 fuselage relied on the KC135 tanker design of the 1950s. From the four-engine B707 came the three-engine B727 and then the two – engine B737, both of which retained considerable fuselage commonality. This was one of the earliest attempts to utilize the benefits of maintaining component com­monality. Subsequently, the B737 started to emerge in different sizes of variants, maximizing the component commonality. The original B737-100 was the baseline design; all other variants that came later, up to the B737-900, are larger aircraft. This posed certain constraints, especially on the undercarriage length. Conversely, the A320 (serving as the baseline design) was in the middle of the family; its growth variant is the A321 and its smaller variants are the A319 and A318. Figure 4.7 illus­trates how the OEW is affected by the two examples of family variants. A baseline aircraft starting in the middle of a family is better optimized; therefore, in principle, it provides a better opportunity to lower production costs of the variants.

The simultaneous failure of two engines is extremely rare. If it happens after the decision speed is reached and there is not enough clearway available, then it is a catastrophic situation. If the climb gradient is not in conflict with the terrain of operation, it is better to take off with higher flap settings. If a longer runway is available, then a lower flap setting can be used. Takeoff-speed schedules can slightly exceed FAR requirements, which stipulate the minimum values. There have been cases of all-engine failures occurring at cruise due to volcanic ash in the atmosphere, as well as in the rare event of fuel starvation. Fortunately, the engines were restarted just before the aircraft would have hit the surface. An all-engine failure due to a bird strike occurred in 2009 – miraculously, all survived after the pilot ditched the aircraft in the Hudson River in New York.

An aircraft at HSC is at Mach 0.85 (845.5 ft/s) at a 30,000-ft altitude (p = 0.00088 slug/ft3). The fuel burned to climb is computed (but not shown) as 582 lb. The air­craft weight at the altitude is 10,000 lb.

At Mach 0.85, the aircraft lift coefficient CL = MTOM/gSV = 10,000/ (0.5 x 0.00088 x 845.52 x 183) = 10,000/57,561.4 = 0.174.

The clean aircraft drag coefficient (see Figure 9.16) at CL = 0.174 gives CDclean = 0.025 (high speed). The clean aircraft drag, D = 0.025 x (0.5 x 0.00088 x 858.52 x 183) = 0.025 x 5,7561.4 = 1,440 lb.

The available engine-installed thrust at the maximum cruise rating (i. e., 85% of the maximum rating) is from Figure 13.4 at Mach 0.85, and at a 30,000-ft altitude is T = 0.85 x 2,000 = 1,700 lb. (In the industry, the thrust is computed.)

Therefore, the AJT satisfies the customer requirement of Mach 0.85 at HSC.

13.6.2 Fuel Requirements (AJT)

Other than a ferry flight, military aircraft are not dictated only by the cruise sector, unlike in a civil aircraft mission. A short combat time at the maximum engine rating, mostly at low altitudes, is responsible for a suitable part of the fuel consumed. How­ever, the range to the target area dictates the fuel required. A long-distance ferry flight and combat arena require additional fuel to be carried by drop tanks. Imme­diately before combat, the drop tanks (they are empty) by then can be jettisoned to gain aircraft performance capability. The CAS variant has this type of mission profile.

A training mission has a varied engine demand and it returns to its own base covering no range, as shown in Figure 13.19. Mission fuel is computed sector by sec­tor of fuel burn, as shown as follows for the coursework example. To compute the fuel requirement, climb and specific-range graphs for the AJT at NTC are required (Figures 13.22 and 13.23). To compute the varied engine demand of a training – mission profile, Figure 13.4 is used to establish the fuel-flow rate for the throttle set­tings. The graph is valid for 75% rpm to 100% ratings. Typically, it has the approxi­mate following values:

• at idle (50% rpm) « 8 kg/min

• at 75% rpm « 11 kg/min

• at 95% rpm « 16.5 kg/min

Figure 13.22. AJT climb performance

Fuel and time consumed for the NTC of the AJT is shown in Table 13.20.

13.5 Summary

This chapter is the culmination of progress on the configuring, sizing, and substan­tiating of the coursework examples. It is time to review whether the Bizjet and the AJT designs need any revision. With commonality in design considerations, the tur­boprop aircraft is not addressed herein. The remaining chapters contain information on topics in which designers must be knowledgeable.

The sizing exercise (see Chapter 11) provides a simultaneous solution to satisfy airworthiness and market requirements. Wing-loading (W/SW) and thrust-loading (T/W) are the dictating parameters and they appear in the equations for takeoff, second-segment climb, enroute climb, and maximum speed capability; the first two are FAR requirements, the last two are customer requirements. Detailed informa­tion on engine performance is not required during the sizing exercise. Substantiation

of the payload-range estimation, as a customer requirement, is not possible dur­ing the sizing exercise beacuse it requires detailed engine performance data. Sub­sequently, with detailed engine performance data, relevant aircraft performance analyses are conducted more accurately to guarantee airworthiness and market requirements.

A more detailed aircraft performance is estimated during the Detailed Defini­tion Phase, which is beyond the scope of this book. The full aircraft performance does not affect aircraft configuration and mass unless the design review results in new demands for changes. These are management issues that are reviewed with potential customers to decide whether to give a go-ahead. Once a go-ahead is obtained, a full-blown detailed definition study ensues as Phase 2 activities, with significant financial commitments.

Figure 11.3 (Bizjet) and Figure 11.5 (AJT) show the lines of constraints for the various sizing requirements. The sizing point to satisfy all requirements shows a different level of margins for each capability. Typically, the initial enroute climb rate is the most critical to sizing. Therefore, the takeoff and maximum speed capabilities have a considerable margin, which is desirable because the aircraft can do better than what is required.

From statistics, experience shows that aircraft mass grows with time. This occurs primarily due to modifications resulting from mostly minor design changes and changing requirements – at times, even before the first delivery is made. If new requirements demand several changes, then a civil aircraft design may appear as a new variant. However, military aircraft design holds a little longer before a new variant emerges. It is therefore prudent for designers to maintain some margin, especially reserve thrust capability – that is, keep the thrust-loading (T/W) slightly higher. Re-engining with an updated version is costly.

It can be seen that field performance requires a larger wing planform area (SW) than at cruise. It is advisable to keep the wing area as small as possible (i. e., high wing-loading) by incorporating a superior high-lift capability, which is not only heavy but also expensive. Designers must seek a compromise to minimize operating costs (see Chapter 16). Iterations were not needed for the designs worked out in this book.

Military trainers should climb at a much higher rate of climb than civil aircraft. The requirement of 50 m/s (10,000 ft/min) at normal training configuration (NTC) is for an unaccelerated climb for comparison with accelerated climb. Unaccelerated rate of climb varies depending on the constant speed (i. e., EAS) climb, making a comparison difficult. This section presents calculations for both rates of climb.

This section checks only the enroute climb with a clean configuration. The unac­celerated climb Equation 13.7 is used. The MTOM at the NTC is 4,800 kg (10,582 lb). The wing area SW = 17 m2 (183 ft2).

During an enroute climb, the aircraft has a clean configuration. Under maxi­mum takeoff power, it makes an accelerated climb to 800 ft (p = 0.00232 slug/ft3, a = 0.9756) from the second-segment velocity of V2 to reach a 350-KEAS speed schedule to start the enroute climb. During enroute climb, the engine throttle is retarded to the maximum climb rating. The quasi-steady-state climb schedule main­tains 350 KEAS and the aircraft accelerates with an altitude gain at a rate of dV/dh until it reaches Mach 0.8 at around 25,000 ft. From there, the Mach number is held constant until it reaches the cruise altitude. We assume that 100 kg of fuel is con­sumed to taxi and climb to an 800-ft altitude, where the aircraft mass is 4,700 kg (10,362 lb). At 350 kts (590.8 ft/s, Mach 0.49), the aircraft lift coefficient is:

Cl = MTOM/qSw = 10,362/(0.5 x 0.00232 x 590.82 x 183)

= 10,582/74,905 = 0.138

The clean aircraft drag coefficient from (see Figure 9.19) at Cl = 0.141 gives CDciean = 0.023. The clean aircraft drag, D = 0.023 x (0.5 x 0.002378 x 590.82 x 183) = 0.023 x 74,905 = 1,723 lb. The available engine-installed thrust at a maxi­mum continuous rating (95% of maximum thrust, as given in Figure 13.4) at Mach 0.49 (459.8 ft/s) is T = 0.95 x 5,000 = 4,750 lb. From Equation 13.10, the accelerated rate of climb is as follows:

c V[(T – D)/W]

‘ aacl 1 + (V/g)(dV/dh)

At a quasi-steady-state-climb, Table 13.5 gives:

– = 0.56m2 = 0.56 x 0.492 = 0.1345

g dh

From Equation 13.5, the rate of climb is:

R/Cacci = {[590.8 x (4,750 – 1,723) x 60]/10,362}/]1 + 0.1345] = 10, 355/1.1345 = 9,127 ft/min

Therefore, the unaccelerated rate of climb, R/C = 10,355 ft/min. The aircraft speci­fication is based on an unaccelerated climb of 10,000 ft/min, which is just met. (Here, the cabin area is small and the pressurization limit is high.)

Keeping a reserve fuel of 440 lb (200 kg), the landing weight of an AJT is 8,466 lb (wing-loading = 42.26 lb/ft2) and at full flap extended, CLmax = 2.2. Therefore:

Vappr — 1-2Vstall@land — 160ft/s

VtD = 1.1Vstall@land = 146 ft/s

The average velocity from a 50-ft altitude to touchdown = 153 ft/s. The distance covered before brake application after 6 s from a 50-ft altitude:

SG_TD = 6 X 153 = 918 ft

For an aircraft in full braking with qB = 0.45, all engines shut down, and average Cl = 0.5, Cd/Cl = 0.1.

Equation 13.2 for average acceleration is based on 0.7 VTD = 107.1 ft/s. Then: q = 0.5 x 0.002378 x 107.12 = 13.64

Deceleration, a = 32.2 x [(-0.45) – (CLq/42.26)(0.1 – 0.45)] = 32.2 x [-0.45 + (0.15 x 13.64/42.26)] = 32.2 x [-0.45 + 0.0484] = -12.93 ft/s2.

The distance covered during braking, SGLand = (146 x 73)/12.93 = 824 ft. The landing distance SGLand = 918 + 824 = 1,742 ft. Multiplying by 1.667, the rated LFL = 1.667 x 1,742 = 2,904 ft and is expected to be less than the TOFL at an 8-deg flap setting (but not always). This is within the specification of 3,600 ft.

With a single engine, there is no question about the BFL. The military aircraft TOFL must satisfy the CFL. The CFL also can have a decision speed V1 that is deter­mined by whether a pilot can stop within the distance available; otherwise, the pilot ejects.

To obtain the CFL for a single-engine aircraft, the decision speed is at the crit­ical time just before a pilot initiates rotation at VR. Then, the decision speed V1 is worked out from the VR by allowing 1 s for the recognition time. An engine fail­ure occurring before this Vi leads a pilot to stop the aircraft by applying full brakes and deploying any other retarding facilities available (e. g., brake-parachute). There should be sufficient runway available for a pilot to stop the aircraft from this V1.

Engine failure occurring after the V1 means that a pilot will have no option other than to eject (i. e., if there is not enough clearway available to stop). For a multi­engine aircraft, determining the CFL follows the same procedure as in the civil – aircraft computation but it complies with MILSPECS.

Figure 13.21 shows the takeoff speed schedule of a single-engine military type aircraft.

In this book, the following three requirements for the AJT are worked out:

1. Meet the takeoff distance of 3,600 ft (1,100 m) to clear 15 m.

2. Meet the initial rate of climb (unaccelerated) of 10,000 ft/min (50 m/s).

3. Meet the maximum cruise speed of Mach 0.85 at a 30,000-ft altitude.

MIL-C501A requires a rolling coefficient, д = 0.025, and a minimum braking coefficient, дв = 0.3. Training aircraft have a good yearly utilization operated by relatively inexperienced pilots (with about 200 hours of flying experience) carrying out numerous takeoffs and landings on relatively shorter runways. The AJT brakes are generally more robust in design, resulting in a brake coefficient, дв = 0.45, which is much higher than the minimum MILSPEC requirement.

The Bizjet and the AJT have the same class of aerofoil and types of high-lift devices. Therefore, there is a strong similarity in the wing aerodynamic characteris­tics. Table 13.19 lists the AJT data pertinent to takeoff performance.

Equation 13.2 gives the average acceleration as:

a = g[(T/ W – д) – (SbSq/ W)(Cd/Cl – д)]

Using the values given in Table 13.15:

a = 32.2 x [(0.55 – 0.025) – (0*/58)(0.1 – 0.025)]

= 32.2 x [0.525 – (Ctq/773.33)]

Refer to Figure 13.21, which shows the AJT takeoff profile with an 8-deg flap. Distance Covered from Zero to the Decision Speed V1

The decision speed V1 is established as the speed at 1 s before the rotation speed VR. The acceleration of 16 ft/s2 (which can be computed first and then iterated without estimating) is estimated as follows:

V1 = 190.6 – 16 = 174.6 ft/s. Aircraft velocity at 0.7 V1 = 122.22 ft/s. q = (at 0.7V1) = 0.5 x 0.002378 x 0.49V/ = 0.000583 x V/ = 8.7. Up to V1, the average CL = 0.5 (still at low incidence). Then:

a = 32.2 x (0.525 – Cl q/773.33) = 32.2 x (0.525 – 4.35/773.33)

= 32.2 x 0.519 = 16.72 ft/s2

Using Equation 13.3, the distance covered until the liftoff speed is reached:

Sg – 1 = Vave x (V1 – V))/a ft = 87.3 x (174.6 – 0)/16.72 = 912 ft

However, provision must be made for engine failure at the decision speed, V1, when braking must be applied to stop the aircraft. Designers must ensure that the operating runway length is adequate to stop the aircraft.

If the engine is operating, then an AJT continues with the takeoff procedure when liftoff occurs after rotation is executed at VR.

Distance Covered from Zero to Liftoff Speed VLO

Using the same equation for distance covered up to the decision speed V1 with the change to liftoff speed, VLO = 192.5 ft/s. Aircraft velocity at 0.7VLO = 134.75 ft/s, q = (at 0.7Vi) = 0.5 x 0.002378 x 0.49VLO = 10.586. Up to VLO, the average CL = 0.5 (still at low incidence). Then:

a = 32.2 x (0.525 – Cl q/773.33) = 32.2 x (0.525 – 4.35/773.33)

= 32.2 x 0.519 = 16.72 ft/s2

Using Equation 13.3, the distance covered until the liftoff speed is reached:

Sglo = Vave x (V1 – VO/a ft = 96.25 x (192.5 – 0)/16.42 = 1,128 ft

Distance Covered from VLO to V2

The flaring distance is required to reach V2, clearing a 50-ft obstacle height from VLO. From statistics, the time to flare is 3 s with an 8-deg flap and at V2 = 206 ft/s. In 3 s, the aircraft covers SG_LO_V2 = 3 x 206 = 618 ft.

Total Takeoff Distance

The takeoff length is thus SGLO + SGLOV2 = (1,128 + 618) = 1,746 ft, much less than the required TOFL of 3,500 ft for the full weight of 6,800 kg («15,000 lb) for armament training. In this case, a higher flap setting of 20 deg may be required. At a higher flap setting, an aircraft has a shorter CFL for the same weight.

Stopping Distance and the CFL

• distance covered from zero to the decision speed V2, SG2; it was previously computed as 912 ft

• distance covered from V2 to braking speed VB, SG2B

• braking distance from VB («V/) to zero velocity, SgB0

The next step is to verify what is required to stop the aircraft if an engine fails at V2. The stopping distance has the following three segments. (The CFL is normally longer than the TDFL.)

Distance Covered from Vl to Braking Speed VB

At engine failure, 3 s is assumed for a pilot’s recognition and taking action. There­fore, the distance covered from V2 to VB is SG2B = 3 x 174.6 = 524 ft.

Braking Distance from VB (« Vl) to Zero Velocity (Flap Settings Are of Minor Consequence)

The most critical moment of brake failure is at the decision speed V2, when the aircraft is still on the ground. With the full brake coefficient, д = 0.45, and the average CL = 0.5, V2 = 174.6 ft/s. With aircraft velocity at 0.7, Vi = 122.22 ft/s, q = (at0.7V1) = 0.5 x 0.002378 x 0.49 V2 = 0.000583 x V2 = 8.7.

Equation 13.2 for average acceleration reduces to:

a = 32.2 x [(-0.45) – (0.5 x 8.7)/58)(0.1 – 0.45)]

= 32.2 x [-0.45 + (1.52/58)]

= 32.2 x (-0.45 + 0.026) = -13.65

Using Equation 13.3, the distance covered with the liftoff speed is reached:

Sg_0 = Vave x (V1 – V0)/a ft = 87.3 x (174.6 – 0)/13.65 = 1,119 ft

Therefore, the minimum runway length (CFL) for takeoff should be = SG2 + SG2B + SG0. The TOFL = 912 + 524 +1,119 = 2,555 ft, which is still within the specified requirement of 3,600 ft.

The takeoff length is thus 1,746 ft, much less than the CFL of 2,555 ft com­puted previously. The required TOFL is 3,500 ft (computation not shown) for the full weight of 6,800 kg («15,000 lb) for armament training. In this case, a higher flap setting of 20 deg may be required. At a higher flap setting, an aircraft has a shorter CFL for the same weight.

The length of the runway available dictates the decision speed V1. If the airfield length is much longer, then a pilot may have a chance to land the aircraft if an

engine failure occurs immediately after liftoff; it may be possible to stop within the available airfield length, which must have some clearway past the runway end.

This is compared with the minimum MILSPEC requirement of д = 0.3. Equation 13.2 for average acceleration reduces to:

a = 32.2 x [(-0.3) – (0.5 x 8.7)/58)(0.1 – 0.3)] = 32.2 x [-0.3 + (0.87/58)]

= 32.2 x (-0.3 + 0.015) = -9.18

Using Equation 13.3, the distance covered from VB to zero:

SG-0 = Vave X (V1 – V))/a ft = 87.3 x (174.6 – 0)/9.18 = 1, 660 ft

This value is on the high side. The minimum runway length for takeoff should be =

Sqj + Sqj_b + Sq_0.

The CRL = 912 + 524 +1,660 = 3,096 ft is on the high side but within the spec­ification of 3,600 ft. Therefore, the higher brake coefficient of 0.4 is used. This is not problematic because wheels with good brakes currently have a much higher friction coefficient д.

A reduction of the decision speed to 140 ft/s (83 kts) reduces the Sg_o = 1,068 ft, decreasing the CRL to 2,504 ft.

Verifying the Climb Gradient at an 8-Deg Flap

Using AJT V2 = 206 ft/s (see Table 13.15) and W = 10,580 lb (4,800 kg) gives CL = (2 x 10,580)/(0.5 x 0.002378 x 183 x 2062) = 21,160/22,680 = 0.932.

The clean aircraft drag coefficient from Figure 9.16 gives CDclean = 0.1. Add ACoflap = 0.012 and ACd_u/c = 0.022, giving CD = 0.1 + 0.012 + 0.022 = 0.134. Therefore, drag, D = 0.134 x (0.5 x 0.002378 x 2062 x 183) = 0.134 x 22,680 = 3,040 lb. The available thrust is 5,000 lb (see Figure 13.4).

From Equation 13.5, the quasi-steady-state rate of climb is shown by:

V[(T – D)/W]

1 + (V/g)(dV/dh)

At the quasi-steady-state climb, Table 13.5 shows V (dV) = 0.566 m2 = 0.56 x 0.22 = 0.0224. Hence, R/Cacci = {[206 x (5,000 – 3,040) x 60]/10,580}/ [1 + 0.0224] = (206 x 1,960 x 60)/(10,817) = 2,240 ft/min. This capability satisfies the military requirement of 500 ft/min (2.54 m/s). Readers may verify the 20-deg flap setting.

Military aircraft certification standards are different from civil aircraft standards. There is only one customer (MOD) requirement and the design standards vary among countries based on defense requirements. The safety issues are similar in rea­soning but differ in the required specifications. It is suggested that readers obtain the regulatory MILSPECS from their respective Ministry or Department of Defense – they are generally available in the public domain. In this book, the procedure to sub­stantiate performance capabilities is the same as for civil aircraft, covered in detail in the previous section.

13.6.1 Mission Profile

The fuel load and management depends on the type of mission. Military aircraft mission profiles are varied. Figure 13.19 shows a typical, normal training profile used to gain airmanship and navigational skills in an advanced aircraft.

Allowance

and Overs on

Fue

Practice force landing and

Ihree circuits for lancing practice

Take’* AJT Training Profile

Figure 13.19. Normal training sortie profile (60 minutes)

Combat missions depend on the target range and expected adversary’s defense capability. Two typical missions are shown in Figure 13.20. Air defense requires continuous intelligence information feedback. Armament training practice closely follows a combat mission profile.

The study of combat missions requires complex analyses by specialists. Defense organizations conduct these studies and, understandably, they are confidential in nature. Game theory, twin-dome combat simulations, and so forth are some of the tools for such analyses. Actual combat may prove to be quite different because everything is not known about an adversary’s tactics and capabilities. A detailed study is beyond the scope of this book, as well as of most academies.

A typical transport aircraft mission profile is shown in Figure 13.17. Equa­tions 13.14 through 13.18 give the mission range and fuel consumption expressions as follows:

mission range = climb distance(RcUmb) + cruise distance(Remise)

+ landing distance( Rdescent)

where Rciimb = £Asciimb and Rdescent = £Asdescent are computed from the altitude increments.

mission fuel = climb fuel (Fuelciimb) + cruise fuel(Fuelcruise)

+ descent fuel(Fueldescent)

where Fuelclimb = £Afuelclimb and Fueldescent = £Afueldescent are computed from the altitude increments.

The minimum reserve fuel is computed for an aircraft maintaining a 5,000-ft altitude from Mach 0.35 to Mach 0.4 at about 60% of the maximum rating for
45 minutes or a 100 nm diversion cruising at Mach 0.5 and at a 25,000-ft altitude plus 20 minutes. The amount of reserve fuel must be decided by the operator and be suitable for the region of operation. The worked-out example uses the first option.

Fuel is consumed during taxiing, takeoff, and landing without any range contri­bution; this fuel is added to the mission fuel and the total is known as block fuel. The time taken from the start and stop of the engine at the beginning and the end of the mission is known as block time, in which a small part of time is not contributing to the gain in range. The additional fuel burn and time consumed without contributing

Figure 13.17. Transport-aircraft mission profile

to range are shown in Table 13.17, taken from operational statistics. The descent fuel is estimated at 300 lb and the end cruise weight is computed as Wend_cruise =

12.760 + 2,420 + 650 + 300 = 16,280 lb. This is then iterated to correct the descent fuel in the final form, as shown in Table 13.17.

The cruise altitude of a Bizjet starts at 43,000 ft and ends at 45,000 ft (the design range is long in order to make an incremental cruise). The average value of cruising at 44,000 ft (p = 0.00048 slug/ft3) is used. The methods to compute Rciimb and Rdescent are discussed in Section 13.4.3. Using Figures 13.11 through 13.13, the required val­ues are given as Rclimb = 162 nm, Fuelclimb = 800 lb, and Timeclimb = 25 min, and Rdescent = 150 nm, Fueldescent = 340 lbs, and Timedescent = 30 min (in a partial-throttle, gliding descent). Table 13.18 displays the aircraft weight at each segment of the mis­sion profile. The aircraft is at the LRC schedule operating at Mach 0.7 (OEW =

12.760 lb and payload = 2,420 lb).

For reserve fuel, at a 5,000-ft altitude (p = 0.00204 lb/ft3) and Mach 0.35 (384 ft/s) gives CL = 0.323, resulting in CD = 0.025 (see Figure 9.2). Equating thrust to drag, T/engine = 610 lb with sfc = 0.7 lb/hr/lb. For 45 minutes of holding, fuel consumed = 2 x 0.75 x 0.7 x 610 = 640 lbs. For safety, 800 lbs is used (operators can opt for higher reserves than the minimum requirement).

An aircraft must carry a reserve fuel for 45 minutes of holding and/or diver­sion around a landing airfield, which amounts to 600 lb. The range performance can be improved with a gradual climb from 43,000 to 47,000 ft as the aircraft becomes lighter with fuel consumed. From Table 13.18, the midcruise weight is (19,700 +16,240)/2 = 17,970 lbs.

The LRC is at Mach 0.7 (677.7 ft/s). The engine-power setting is below the maximum cruise rating. The aircraft lift coefficient, CL = 17,970/(0.5 x 0.00046 x 677.72 x 323) = 17,970/34,120 = 0.527. From Figure 9.2, the clean aircraft drag coef­ficient, CD = 0.033. The aircraft drag, D = 0.033 x (0.5 x 0.00046 x 677.72 x 323) =

0. 033 x 34,120 = 1,126 lb.

Therefore, the thrust required per engine is 1,126/2 = 563 lbs. Figure 13.3 shows the available thrust of 620 lb per engine at the maximum cruise rating meant for HSC; that is, it allows throttling back for the LRC speed. The sfc is not much affected by the throttling back to the cruise rating. From Figure 10.6, the sfc at the

Figure 13.18. Bizjet payload-range capabi­lity

speed and altitude is 0.73 lb/hr/ lb. The fuel flow per engine = 0.73 x 563 = 411 lb/hr; for two engines, it is 822 lb/hr.

From the initial and final cruise weight, the fuel burned during cruise is 3,460 lb. This results in a cruise time of 3,460/(2 x 411) = 4.21 hr (252.5 min) of cruise time in which the distance covered is 4.21 x 0.68182 (the conversion factor from feet to miles) x 677.7 = 4.21 x 462 = 1,945 miles = 1,688 nm.

This mission range just satisfies the requirement of 2,000 nm. The block time for the mission is 5.38 hours and the block fuel consumed is 4,923 lb (2,233 kg). On landing, the return taxi-in fuel of 20 lb is taken from the reserve fuel of 600 lb. The total onboard fuel carried is therefore 4,923 + 600 = 5,523 lb.

The payload-range graph is shown in Figure 13.18. A summarized discussion of the Bizjet design is in Section 13.7.

The fuel tank has a larger capacity than what is required for the design payload range. The payload can be traded to increase the range until the tanks fill up. Further reductions of payload make the aircraft lighter, thereby increasing the range.

It is also explained in Section 13.1 that only results of the integrated descent perfor­mance in graphical form are provided, as shown in Figures 13.16 through 13.18. It is convenient to establish first the descent velocity schedule (Figure 13.16) and the point performances of the rate of descent (Figure 13.17) down to sea level (this is valid for all weights; the difference between the weights is ignored). When readers redo the calculations, there may be minor differences in the results.

The related governing equations are explained in Section 13.4.3, which also mentions that the descent rate is restricted by the rate of the cabin-pressurization schedule to ensure passenger comfort. Two difficulties in computing the descent per­formance are the partial-throttle engine performance and the ECS pressurization capabilities, which dictate the rate of descent that, in turn, stipulates the descent velocity schedule (these are not provided in this book). Instructors may assist in establishing these two graphs, which – in the absence of any information – may be used. The following simplifications are useful.

The first simplification is in obtaining the partial-throttle engine performance, as follows:

1. The zero thrust at idle rpm is at about 40% of the maximum rated power/ thrust.

2. The maximum cruise rating is taken at 85% of the maximum rated power/ thrust.

3. The descent is carried out from 40 to 60% of the maximum cruise rating.

The second simplification is provision of the descent velocity schedule for the ECS capability.

In the industry, the exact installed-engine performance at each partial-throttle condition is computed from the engine deck supplied by the manufacturer. Also, the ECS manufacturer supplies the cabin-pressurization capability, from which aircraft designers work out the velocity schedule.

The inside cabin pressurization is restricted to the equivalent rate of 300 ft/min at sea level to ensure passenger comfort. An aircraft’s rate of descent is then lim­ited to the pneumatic capability of the ECS. A Bizjet is restricted to a maximum of 1,800 ft/min at any time (for a higher performance at lower altitudes, it can be increased to 2,500 ft/min). The descent speed schedule continues at Mach 0.6 from the cruise altitude until it reaches the approach height, when it then changes to a constant VEAS = 250 knots until the end (for a higher performance, it can be increased to Mach 0.7 and VEAS = 300 knots). The longest ranges can be achieved at the minimum rate of descent; this requires a throttle-dependent descent to stay within the various limits.

It is convenient to establish first the point performances of the velocity schedule (Figure 13.15a) and the rate of descent (Figure 13.15b is for all weights; the variation is minor). The descent is performed within the limits of the passenger comfort level. However, in an emergency, a rapid descent is necessary to compensate for the loss of pressure and for oxygen recovery.

An integrated descent performance is computed in the same way as the climb performance; that is, it is computed in steps of approximate 5,000-ft altitudes (or as convenient) in which the variables are kept invariant. (Computation work is not shown herein.)

Figure 13.16 plots fuel consumed, time taken, and distance covered during the descent from the ceiling altitude to sea level. When readers redo the integrated descent performances, there may be minor differences in the results.