Section 13.5: Performance equations to substantiate Bizjet aircraft capabilities Section 13.6: Performance equations to substantiate AJT aircraft capabilities Section 13.7: Discussion in summary form

13.1.2 Coursework Content

Readers perform the following steps for their design projects:

Step 1: Generate the appropriate engine performance graphs from the nondimensional graphs provided in Chapter 10.

Step 2: Using the engine thrust thus obtained, compute the aircraft performances of the sized Bizjet and AJT as coursework exercises. (The instructor’s assistance may be required to compute integrated climb, descent, and specific-range performances.)

Step 3: If aircraft performance requirements are not met, then iterate the aircraft-configuration, sizing, and engine-matching exercises until they are. The spreadsheet method is helpful for the iterations.

13.2 Introduction

The final outcome of any design is to substantiate the performance it is intended to do. In the conceptual design phase, aircraft performance substantiation must be conducted mainly for those critical areas specified by the FAR and customer requirements; a full aircraft performance estimation is conducted subsequently (it is beyond the scope of this book). All worked-out aircraft performance estimations (i.e., Bizjet and AJT) use the standard day. Non-ISA-day performance computations are calculated in the same way using non-ISA-day data.

The sizing exercises in Chapter 11 demonstrate a rapid-performance method to generate relationships between wing-loading (W/SW) and thrust-loading (TSLS/W) to obtain the sizing point that simultaneously satisfies the requirements of the TOFL and LFL, initial rate of climb capability, and maximum speed at initial cruise. The aircraft-sizing point gives the installed, maximum sea-level takeoff static thrust, TSLS INSTALLED, of the matched engines. Chapter 10 presents the generic, uninstalled-engine performances of rubberized engines in nondimensional form, from which the installed-engine performances are obtained.

This chapter develops available engine performance in terms of installed thrust and fuel-flow rates at various speeds and altitudes at the power settings of takeoff, maximum climb, and maximum cruise ratings at standard day, matched for the sized aircraft under study. Applying the installed-engine data, the chapter continues with more accurate computations of aircraft performance to substantiate requirements of the TOFL and LFL, initial rate of climb, maximum speed at initial cruise, and payload range. At this point, it may be necessary to revise the aircraft configuration if performance capabilities are not met. If the aircraft performance indicates a shortfall (or an excess) in meeting the requirements, the design is iterated for improvement. In coursework, normally one iteration is sufficient.

Finally, at the end of the design stage, the aircraft should be flight-tested over the full flight envelope, including various safety issues, to demonstrate compliance.

13.2.1 Aircraft Speed

Aircraft speed is a vital parameter in computing performance. It is measured using the difference between the total pressure, pt, and the static pressure, ps, expressed as (pt − ps). Static pressure is the ambient pressure in which an aircraft is flying. The value of (pt − ps) gives the dynamic head, which depends on the ambient air density, ρ. Unlike the ground speed of an automobile that is measured directly, an aircraft ground speed must be computed from (pt − ps); a pilot reads the gauge that is converted from (pt − ps). Following are various forms of aircraft air speed that engineers and pilots use. As shown, some computations are required – currently, onboard computers perform all computations:

Vi: The gauge reading as a pilot sees it in the flight deck; this is flight speed, which is not the same as ground speed. The instrument includes standard adiabatic compressible-flow corrections for high-subsonic flights at the sea-level standard day; however, it still requires other corrections.

VI: This is the indicated air speed (IAS). Manufactured instruments have some built-in instrumental errors, Vi (typically minor but important considerations when an aircraft is close to stall speed). Manufacturers supply the error chart for each instrument. The instrument is calibrated to read the correct ground speed at the sea-level standard day with compressibility corrections. When corrected, the instrument reads the IAS as

V1 = IAS = Vi + Vi

VC: This is the calibrated air speed (CAS). Instrument manufacturers calibrate an uninstalled, bare instrument for sea-level conditions. Once it is installed on an aircraft and depending on where it is installed, the aircraft flow field distorts the instrument readings. Therefore, it requires position-error ( Vp) corrections by the aircraft manufacturers:

VC = CAS = VI + Vp = Vi + Vi + Vp

VEAS: This is the equivalent air speed (EAS). Air density ρ changes with altitude – it decreases because atmospheric pressure decreases with a gain in altitude. Therefore, at the same ground speed (also known as true air speed [TAS]), the IAS reads lower values at higher altitudes. The mathematical relationship between the TAS and the EAS, reflecting the density changes with altitude, can be derived as TAS = EAS/√σ , where σ is the density ratio (ρ/ρ0) in terms of the sea-level value, ρ0. The constant EAS has a dynamic head invariant. For high-subsonic flights, it requires adiabatic compressibility corrections ( Vc) for the altitude changes:

VEAS = EAS = VC + Vc. = Vi + Vi + Vp + Vc = TAS√σ

TEAS: TAS is the aircraft ground speed. Compressibility corrections for position errors are available; however, at this stage of design, the details can