5 - 1 5 Preliminary Sizing The preliminary sizing of an aircraft is carried out by taking into account requirements and constraints (see Section 1). A process for preliminary sizing proposed by Loftin 1980 is shown in Fig. 5.1 and detailed in this section. The procedure refers to the preliminary sizing of jets that have to be certified to CS-25 or FAR Part 25. The procedure could in general also be applied to other aircraft categories as there are • very light jets certified to CS-23/FAR Part 23 • propeller aircraft certified to CS-25/FAR Part 25 • propeller aircraft certified to CS-23/FAR Part 23 • propeller aircraft certified to CS-VLA • ... if the respective special features and regulations are taken into account. For propeller-type aircraft the engine thrust T must be replaced by engine power P in Fig. 5.1. Many changes in the equations result from this modification. Fig. 5.1 Flow chart of the aircraft preliminary sizing process for jets based on Loftin 1980 5 - 2 Fig. 5.1 needs some explanation: The blocks in the first column represent calculations for various flight phases. Block 1 "LANDING DISTANCE" provides a maximum value for the wing loading m / S (reference value: mSMTO/ W ). The input values of the calculation are the maximum lift coefficient with flaps in the landing position CLmaxL,, as well as the landing field length sLFL according to CS/FAR. The maximum lift coefficient CLmaxL,, depends on the type of high lift system and is selected from data in the literature. Block 2, "TAKE-OFF DISTANCE" provides a minimum value for the thrust-to-weight ratio ⋅=() ⋅ as a function of the wing loading: TmgfmS/( ) / with reference value: TmgTO/( MTO ). The functional connection TmgfmS/(⋅= )() / is dependent on the maximum lift coefficient with flaps in the take-off position CLmaxTO,, and the take-off field length sTOFL . The maximum lift coefficient CLmaxTO,, is selected with the aid of data in the literature. Blocks 3 and 4 examine the "CLIMB RATE IN THE SECOND SEGMENT" and the "CLIMB RATE DURING THE MISSED APPROACH". The blocks provide minimum values for the thrust-to-weight ratio Tmg/(⋅ ). The input value for the calculations: the lift-to-drag ratio, 'L over D') L / D is estimated on the basis of a simple approximation calculation. Block 5 "CRUISE" represents the cruise analysis that provides a minimum value for the thrust-to-weight ratio as a function of the wing loading: TmgfmS/(⋅= )() / . The thrust-to- weight ratio thus determined is sufficient to facilitate a stationary straight flight with the assumed Mach number for the respective wing loading. The calculation is carried out for the design lift coefficient CLDESIGN, . The cruise altitude is also obtained from the cruise analysis. Input values are the lift-to-drag ratio E = L / D during cruise, the assumed cruise Mach = number MMCR , engine parameters and the characteristics of the atmosphere. The output values of the blocks in the first column of Fig. 5.1 provide a set of relationships between the thrust-to-weight ratio and the wing loading. Taken together, these relationships give, in a "MATCHING CHART" (Blocks 6 and 7), a single pair of values: thrust-to-weight ratio and wing loading that meets all requirements and constraints in an economical manner. The thrust-to-weight ratio (also referred to as the maximum take-off mass or range by other authors) are the input values for a mass estimate according to statistics. In Blocks 8 and 9, first the OPERATING EMPTY MASS mmOE/ MTO or the RELATIVE USEFUL LOAD u is estimated, defined as 5 - 3 mm+ m u = FPL=−1 OE . (5.1) mMTO mMTO + The useful load is mmFPL, maximum take-off mass mMTO and operating empty mass mOE . In Blocks 10 and 11 the RELATIVE FUEL MASS mmFMTO/ is calculated, using the "Breguet range equation", from the range requirement (Block 12). Other input values are the = = assumed cruise Mach number MMCR , the lift-to-drag ratio during cruising E L / D and = the specific fuel consumption during cruising c SFCCR . "MAXIMUM TAKE-OFF MASS mMTO ", "TAKE-OFF THRUST AND WING AREA": in Block 14 the maximum take-off mass mMTO is calculated from relative useful load u, relative fuel mass mmFMTO/ and the payload requirement mMPL (Block 13). With the maximum take- = = off mass mMTO the necessary take-off thrust TTTO and the wing area SSW can then be ⋅ = calculated in Block 15 from thrust-to-weight ratio Tmg/ and wing loading SSW . 5 - 4 5.1 Landing Distance The basis for analyzing the landing distance are the aviation regulations. The key passages are reproduced here from CS. Further details can be found in the regulations. CS 25.125 Landing (a) The horizontal distance necessary to land and to come to a complete stop from a point 50 ft above the landing surface must be determined (1) The aeroplane must be in the landing configuration. (2) A stabilised approach, with a calibrated airspeed of not less than 1·3 VS, must be maintained down to the 50 ft height. CS - OPS 1.515 Landing - Dry Runways (a) An operator shall ensure that the landing mass of the aeroplane ... allows a full stop landing from 50 ft above the threshold: (1) Within 60% of the landing distance available at the destination aerodrome and at any alternate aerodrome for turbojet powered aeroplanes; or (2) Within 70% of the landing distance available at the destination aerodrome and at any alternate aerodrome for turbopropeller powered aeroplane ... Fig. 5.2 Definition of the landing field length according to CS and FAR An aircraft may land at an airfield if the landing field length sLFL is shorter than the landing distance available, LDA sLDA . The landing field length is calculated according to CS/FAR from the landing distance sL and a safety factor. This safety factor is 1/0.6 = 1.667 for jets and 1/0.7 = 1.429 for turboprops. Fig. 5.2 shows the landing procedure. Loftin 1980 contains a statistic that gives the relationship between the landing field length and the approach speed for aircraft with jet engines. This is summarized as follows (Loftin 1980, Fig. 3.4) =⋅ VkAPP APP s LFL (5.2) with k APP = 1.70 m/s². The wing loading at maximum landing mass is 5 - 5 ρ⋅V 2 mS/ = SL, ⋅ C . (5.3) ML W 2 ⋅ g LmaxL,, ρ is the atmospheric density. To simplify subsequent calculations, we want to relate the ρ ρ atmospheric density to the atmospheric density at sea level 0 =1.225 kg/m³ under standard atmospheric conditions first of all. ρ =⋅σ ρ 0 . (5.4) If we now insert equation (5.2) and equation (5.4) into equation (5.3), we get =⋅⋅σ ⋅ mSkML/ W L C L,, max L s LFL (5.5) with kL = 0.107 kg/m³ . Empirical values for maximum lift coefficients CLmax, are contained in Table 5.1, Fig. 5.3 and Fig. 5.4. Table 5.3 and Table 5.2 contain the ratio of maximum landing mass mML to maximum take-off mass mMTO , which gives mS/ = ML W mSMTO/ W . (5.6) mmML/ MTO This wing loading must not be exceeded if the aircraft is to meet requirements. Table 5.1 Maximum lift coefficients for take-off (TO), landing (L) and cruise configuration (based on Roskam I) type of aircraft CL,max CL,max,TO CL,max,L business jet 1.4 – 1.8 1.6 – 2.2 1.6 – 2.6 jet transport 1.2 – 1.8 1.6 – 2.2 1.8 – 2.8 single engine propeller driven 1.3 – 1.9 1.3 – 1.9 1.6 – 2.3 twin engine propeller driven 1.2 – 1.8 1.4 – 2.0 1.6 – 2.5 fighter 1.2 – 1.8 1.4 – 2.0 1.6 – 2.6 supersonic cruise 1.2 – 2.8 1.6 – 2.0 1.8 – 2.2 5 - 6 Fig. 5.3 Maximum lift coefficient of profiles with different high-lift devices (based on data from Dubs 1987) 5 - 7 Fig. 5.4 Maximum lift coefficient of aircraft with different high-lift devices as a function of wing sweep. For take-off configuration the given values have to be reduced by 20 percent (based on data from Raymer 1989) Table 5.2 Statistical values of maximum landing mass over maximum take-off mass mML / mMTO for different types of aircraft (based on Roskam I) type of aircraft mML mML mML m , inmMTO m ,avMTO m , axmMTO business jet 0.69 0.88 0.96 short range jet transport 0.9 0.93 0.97 medium range jet transport 0.76 0.88 0.95 long range jet transport 0.65 0.78 0.95 ultra long range jet transport 0.65 0.71 0.73 fighter 0.57 - 1 supersonic cruise 0.63 0.75 0.88 Table 5.3 Statistical values of maximum landing mass over maximum take-off mass mML / mMTO for jets of different design range (based on Loftin 1980) design range classification design range (NM) design range (km) mmML/ MTO short range up to 1000 up to 2000 0.93 medium range 1000 – 3000 2000 – 5500 0.89 long range 3000 – 8000 5500 – 15000 0.78 ultra long range more than 8000 more than 15000 0.71 5 - 8 5.2 Take-off Distance The basis for analyzing the take-off distance are the aviation regulations. The key passages are reproduced here according to CS-25. Further details can be found in the regulations.