PRELIMINARY SIZING OF LARGE PROPELLER DRIVEN AEROPLANES

Transcription

1 PRIMINARY SIZING OF ARG PROPR DRIVN AROPANS Dieter Scholz Haburg University of Applied Sciences Berliner Tor 9 D Haburg info@profscholzde Mihaela Niţă Haburg University of Applied Sciences Berliner Tor 9 D Haburg ihaelanita@haw-haburgde Abstract Different types of aeroplanes (sall / large, propeller / jet) require their own type of preliinary sizing ethod One of theses ethods differs only in a few but iportant aspects fro the other For the sake of efficient teaching of students and easy application in practice, the authors ask for the definition of a set of clearly defined step by step preliinary sizing ethods Based on the rather well known sizing ethod for large jet aeroplanes, the paper derives a preliinary sizing ethod for large propeller driven aeroplanes In this way the paper tries to contribute to the definition of the set of ethods The sizing ethods are all based on a atching chart that helps to graphically solve a two-diensional optiization proble The atching chart draws the optiization variable thrust-to-weight ratio (for jets) respectively power to ass ratio (propeller driven planes) versus wing loading for all basic requireents, which the aeroplane has to fulfill The sizing ethod for propeller driven large aeroplanes is explained in detail and applied to a redesign study of the ATR 7 All equations are given in a for readily available for use This requires in soe cases the evaluation of proportionality factors based on aircraft statistics Given are factors taking into account statistics for landing distance, take-off distance and axiu glide ratio for large propeller driven passenger aircraft Furtherore, generic equations for the variation of power with altitude and speed of turboprop engines is given as well as a chart to deterine the propeller efficiency Keywords aircraft, design, preliinary sizing, atching chart, propeller, ATR 7, redesign 1 Introduction 11 Preliinary Sizing In literature and in practice, aircraft developent has been repeatedly broken down into different phases Various approaches have been followed Figure 1 shows one approach of dividing aircraft developent into phases and shows key ilestones The developent of large civil aircraft has inspired this exaple Typical aircraft design activities take part priarily in the feasibility, concept and definition phase Preliinary sizing is the first step in aircraft design and as such part of the feasibility phase, which is followed by conceptual design in the concept phase 1

2 Figure 1: Phases of aircraft developent Preliinary sizing of an aircraft is possible without knowledge of the aircraft s geoetry In preliinary sizing the aircraft is ore or less reduced to a point ass However concrete ideas about the aircraft need to exist: What type of configuration will be selected? What aspect ratio can be expected? What cruise Mach nuber and type of propulsion syste will be selected? With these first considerations, realistic requireents can be forulated These requireents (soe of the depending on the certification rules see below) will enter the preliinary sizing phase: Payload P, Range R, Mach nuber in cruise M R or speed V R, Take-off field length s F, anding field length s F, approach speed V APP or stall speed V S, lib gradient γ during second segent, lib gradient γ during issed approach Preliinary sizing yields basic aircraft paraeters like Take-off ass M, Fuel ass F, Operating epty ass O, Wing area S W, Take-off thrust T or take-off power P 1 Aeroplane ategories, Propulsion Syste and ertification Rules When attepting to do the preliinary sizing of a passenger aircraft, it has to be differentiated a) the type of propulsion syste (propeller or jet), b) the certification rules for the aircraft

3 The certification rules depend as uch on the category and size of the aircraft as on the propulsion syste et s differentiate these categories of aeroplanes: 1 large jet aeroplanes are certified to S-5 [S-5] respectively FAR Part 5 [FAR Part 5], very light jets are certified to S-3 [S-3] respectively FAR Part 3 [FAR Part 3], 3 large propeller driven aeroplanes are also certified to S-5 respectively FAR Part 5 4 saller propeller driven aeroplanes (noral, utility, aerobatic and couter aeroplanes) are certified to S-3 respectively FAR Part 3, 5 very light propeller driven aeroplanes (up to a axiu take-off ass of 750 kg) can be certified to S-VA [S-VA], 6 different certification rules exist for ultra light aircraft 13 Preliinary Sizing Methods Different preliinary sizing ethods are needed for the various categories of aeroplanes given in (1) through (6) above, because equally (a) and (b) have an ipact on the underlying flight echanics of the sizing proble Aircraft design text books or lecture notes do not always see to present a clear step by step ethod for preliinary sizing One early text book with a clear step by step ethod for preliinary sizing was orning [orning 1964] oftin [oftin 1980] proposes a preliinary sizing ethod for large jet aeroplanes (1) Roska [Roska 1989], Scholz [Scholz 008] and others base their preliinary jet sizing ethod on oftin oftin [oftin 1980] proposes also another ethod for saller propeller driven aeroplanes (4) What sees to be issing in the literature is a set of clearly defined step by step preliinary sizing ethods for each category of aeroplane This set of ethods has to be built in such a way that the user easily understands the siilarities and differences of the various ethods Ai of this paper is to present a sizing ethod for large propeller driven aeroplanes (3) that follows as closely as possible the better known ethod for large jet aeroplanes (1) and work in this way towards the goal of a unified and coplete set of sizing ethods for the ost iportant categories of civil aeroplanes 14 General Approach A atching chart should be at the heart of each sizing ethod The atching chart helps to graphically solve a two-diensional optiization proble Keeping in ind that flight echanic calculations for propellers are based on power P, whereas calculations for jets are based on thrust T, the two optiization variables as proposed here are: a) thrust-to-weight ratio T / ( g) respectively power to ass ratio P / and b) wing loading / S M W Figure shows a generic atching chart for large jet aeroplanes Fro the various requireents, either the wing loading or the thrust-to-weight ratio (or a function of one versus the other) can be calculated For all calculations it is ensured that wing loading and thrust-to-weight ratio always refer to take-off conditions, which akes it possible to copare the values of different flight phases The results are plotted on the atching chart The atching chart for large propeller driven airplanes only differs by putting P / on the ordinate and will be explained in the ain part of this paper 3

4 Figure : Hypothetical atching chart for a large jet aeroplane The ai of optiization is to achieve the following: Priority 1: to achieve the sallest possible thrust-to-weight ratio (respectively power to ass ratio) Priority : to achieve the highest possible wing loading (if not other design requireents indicate to decide otherwise) Overview An overview of the proposed preliinary sizing ethod for large propeller driven aeroplanes is given in Figure 3 The blocks in the first colun convert the requireents into the optiization paraeters, which are power to ass ratio P / and wing loading M / SW (shown in Figure 3 in the second colun) In detail, we have: Block 1 "ANDING FID NGTH" provides a axiu value for the wing loading / S (reference value: M / SW ) The input values of the calculation are the axiu lift coefficient with flaps in the landing position ax,, as well as the landing field length s F according to S/FAR The axiu lift coefficient ax,, depends on the type of high lift syste and is selected fro data in the literature (see textbooks and lecture notes) 4

5 Block "TAK-OFF FID NGTH" provides a iniu value for the power-to-ass ratio as a function of the wing loading: P / = f ( / S ) with reference value: P / M The functional connection P / = f ( / S ) is dependent on the axiu lift coefficient with flaps in the take-off position ax,,, propeller efficiency η P and the take-off field length s F The axiu lift coefficient ax,, is selected with the aid of data in the literature In a first attept it is often assued that ax,, is 80% of ax,, Blocks 3 exaines the "SOND SGMNT IMB GRADINT" and Block 4 the "MISSD APPROAH IMB GRADINT" The blocks provide iniu values for the power-to-ass ratio P / The input value for the calculations: the lift-to-drag ratio / D and the propeller efficiency η / D is estiated on the basis of a siple approxiation calculation P Block 5 "RUIS MATHING ANAYSIS" represents the cruise analysis that provides a iniu value for the power-to-ass ratio as a function of the wing loading: P / = f ( / S ) The power-toass ratio thus deterined is sufficient to facilitate a stationary straight flight with the assued cruise Mach nuber M R or cruise speed VR for the respective wing loading The calculation is carried out for the design lift coefficient DSIGN, The cruise altitude is also obtained fro the cruise analysis Input values are the lift-to-drag ratio = / D during cruise, the assued cruise Mach nuber M = M R or speed V = VR, engine and propeller characteristics and the characteristics of the atosphere The output values of the blocks in the first colun of Figure 3 provide a set of relationships between the power-to-ass ratio and the wing loading Taken together, these relationships give, in a "SIMUTANOUS SOUTION" (Blocks 6) a single pair of values: power-to-ass ratio and wing loading ( P / ; / S ) (Block 7) that eets all requireents and constraints in an econoical anner Blocks 8 and 9 stand for "WIGHT ANAYSIS" The relative operating epty ass O / M or the relative useful load u are estiated M is the axiu take-off ass The relative useful load is defined as u = F + M P = 1 O M Various ethods exist in the literature for estiating O / M or u For propeller driven aeroplanes, the power-to-ass ratio (fro Block 7) could be used as an input value for a ass estiate according to statistics In Block 11 "RANG QUATION" yields the relative fuel ass F / M (Block 10) which is calculated, using the "Breguet Range quation" for propeller aircraft, based on the RANG RQUIRMNT (Block 1) Other input values are the assued cruise Mach nuber M = M R or cruise speed V =, the lift-to-drag ratio during cruising = / D, the specific fuel consuption VR c = SF R and the propeller efficiency η P during cruise 5

6 In Block 14 axiu take-off ass M is calculated fro relative useful load u, relative fuel ass F / M and the payload requireent P (Block 13) With the axiu take-off ass M the necessary take-off power P = P and the wing area S = S W can then be calculated in Block 15 fro power-to-ass ratio P / and wing loading / S Figure 3: Overview of the preliinary sizing ethod for large propeller driven aeroplanes 6

7 3 Optiization Paraeters fro Requireents Optiization paraeters are power to ass ratio requireents are specified for the various phases of flight P / and wing loading / S The M W 31 Approach Speed The landing requireents can be stated in ters of approach speed VAPP or landing field length s F Assuing siilar braking characteristics of the aircraft of one category, stateents of either approach speed or landing field length are equivalent ones Based on statistics one stateent can be transfored in the other: s F V APP = k APP The proportionality factor was evaluated (see Figure 4) fro data selected for this category of large passenger turboprop aircraft: k APP = 164 s It also would have been possible to calculate k APP fro k (see Subsection 3 for k ) g 13 k = k = 50 k to yield APP ρ0 a better value for large passenger turboprop aircraft: k APP = 193 s The two approaches do not result in exactly the sae value because the evaluation was based on different aircraft data xperience shows that reported values for approach speed are often not given accurately and do not always refer to the V APP = 13 V S reference speed For this reason, better results can be obtained when using landing distance data In coparison, large passenger jets [7], [9]: k APP = 170 s Based on the latter two values for k APP, turboprop aircraft achieve a shorter landing field length at the sae approach speed (by a factor of 19) This is due to the their better reverse thrust capabilities, which in turn also resulted in a lower safety factor in the deterination of landing field length fro landing distance for turboprop aircraft: 1/07 = 149 for turboprop aircraft versus 1/06 = 1667 for jets [1] The turboprop advantage coes out as 1667/149 = 1167 which is about the ratio that resulted fro aircraft data 7

8 Figure 4: Statistical factor k APP for approach speed calculation fro landing field length for turboprop aircraft 3 anding Field ength anding field length yields the optiization paraeter wing loading M / S W k σ, ax, sf / M M The proportionality factor was evaluated (see Figure 5) fro data selected for this category of kg large passenger turboprop aircraft: k = In coparison, kg large passenger jets [7], [9]: k = have a lower value than the 0137 kg/ 3 fro above, which eans that turboprop aircraft on average achieve a shorter landing field length with the sae wing loading 8

9 Figure 5: Statistical factor k for calculating wing loading fro landing field length and axiu lift coefficient upon landing for turboprop aircraft ρ 8815K σ = = ρ K+ T is the density ratio σ differs fro unity, if landing requireents have to be et at a high (or lower) teperature than following fro International Standard Atosphere (ISA) at Mean Sea evel (MS) M / M has to be selected It ay not be too low, otherwise fuel reserves or reaining fuel upon landing due to favorable flight conditions could result in a landing ass greater than axiu landing ass > M that is clearly not perissible Typical values for large propeller driven aeroplanes are in the range between 095 and 100 On average a value of 097 ay be selected These aircraft are short range aircraft For this reason the value is always very close to Take-Off Field ength Take-off field length yields a fixed ratio between the optiization paraeters power to ass and wing loading In the atching chart this fors a straight line through the origin P / M k V g / S s σ η M W F, ax, P, 9

10 The proportionality factor was evaluated (see Figure 6) fro data selected for this category of large passenger turboprop aircraft: In coparison, large passenger jets [7], [9]: 3 k = 5 kg 3 k = 34 kg have practically the sae value Figure 6: Statistical factor k for calculating the take-off optiization paraeter fro take-off field length and axiu lift coefficient upon take-off for turboprop aircraft The speed V is the average speed during take-off Averaging is done with respect to dynaic pressure which yields V = V / V is the take-off safety speed that has to be reached at the end of the take-off distance It is usually taken as V 1V S, = New aendents of S-5 [1] also indicate the possibility to set V as low as V = 113V S, Take-off stall speed depends on flap setting and hence selected lift coefficient Making a connection to high lift capabilities during landing, we get 10

11 V,ax = V S, S,,ax Older aircraft were designed to V APP = 13V S, New aendents of S-5 [1] also indicate the possibility to set V APP as low as V APP = 13V S, VAPP VAPP So V S, = or V S, = VAPP = kapp SF ρ 8815K σ = = ρ K+ T The propeller efficiency η P, for take-off is obtained fro Figure 7 for the average speed V (see above) and a disc loading P = σρ S 0 D calculated fro take-off power, density and disc area During the first run of the sizing progra the take-off power is not known Instead a propeller efficiency is erely estiated fro Figure 7 In a second iteration applying the sizing ethod, the take-off power fro Block 15 can be used for a better estiate of the propeller efficiency with the help of Figure 7 At this point we should also be ore specific about was is eant here with engine power: The power indicated is always the shaft power P = P S and P = P S, 11

12 Figure 7: Propeller efficiency for variable pitch propellers as a function of aircraft speed and disc loading (the reference surface area is the propeller disc area) Adapted fro [10] 34 lib Rate during nd Segent nd segent clib rate yields the optiization paraeter power to ass P n 1 V g + sinγ M n 1 η P, n stands for the nuber of engines = /D is the glide ratio during take-off estiated fro aspect ratio A, Oswald factor e : = = D, DP, DP, + π A e = (for 1 1), e = 07,,ax, = 1 The clib rate (sin γ) is given in [1]: The steady gradient of clib ay not be less than 4% for twoengined aeroplanes, 7% for three-engined aeroplanes and 30% for four-engined aeroplanes V and η P, fro Section 33 η P, is calculated with a speed V Note correct propeller efficiency calculation requires iteration 1

13 35 lib Rate during Missed Approach Missed approach clib rate puts once again a boundary condition on the optiization paraeter power to ass P n 1 VAPP g M + sinγ M n 1 η P, M This tie the estiate for = /D is done with = = D e = 07,, D, P D, gear DP, + = 13 π A e,ax, = (for 1 1), Dgear, = 0 for[1] and Dgear, = for [] The clib rate (sin γ) is given in [1]: The steady gradient of clib ay not be less than 1% for twoengined aeroplanes, 4% for three-engined aeroplanes and 7% for four-engined aeroplanes V APP is taken fro Section 33 M / M is taken fro Section 3 η P, fro Section 33, calculated with a speed V APP Note correct propeller efficiency calculation requires iteration 36 ruise ruise atching is based on the assuption of steady state straight flight Fro the requireent of a certain cruise speed V R or cruise Mach nuber M R, the power to ass ratio and the wing loading are deterined In order to achieve this, two equations can be used: ift = Weight and Drag = Thrust Thrust will be replaced by power in the last equation Both equations include atospheric and/or engine paraeters that are a function of cruise altitude Since cruise altitude is not known when starting the sizing ethod, the power to ass ratio and the wing loading are calculated for a range of possible cruise altitudes Data fro this table is later drawn into the atching chart and stays for the cruise requireent 361 ift = Weight M MR γ = p( H) or S g W V H = S g M ρ0 R σ( ) W It is / = 1/( V / V ), so the lift coefficient in cruise follows fro with,, d d d π Ae = ax d, = ( V / Vd ) 13

14 V / V d is an input paraeter to the sizing ethod to help atch the cruise perforance Maxi glide ratio ax fro Section 363 σ(h) is the relative density fro the ISA, ρ 0 = 15 kg/ 3 is the density of the air at MS fro ISA γ = 14 is the ratio of specific heats 36 Drag = Thrust P MR a( H) g = P / P η M R P, R or P VR g = P / P η M R P, R = 1 + d, d, ax with / = 1/( V / V ), d d V / V d is an input paraeter to the sizing ethod to help atch the cruise perforance η P,R fro Section 33, fro Section 363, P R /P fro Section 364 a(h) is the speed of sound fro the ISA 363 Maxiu Glide Ratio stiation Maxiu glide ratio ax = (/D) ax is estiated fro aspect ratio A and wetted area S wet The ratio S wet / S wet for large turboprop aeroplanes is between 5 and 7 with an average at about 6 ax = k S wet A / S W The proportionality factor was evaluated (see Figure 8) based on data fro [11] for this category of large passenger turboprop aircraft: k = 11 In coparison [9], large passenger jets, long range: k = 175, large passenger jets, ediu range: k = 1619, large passenger jets, short range: k = 1515 It can be deterined that statistically, the axiu lift coefficient (at the sae aspect ratio and wetted area ratio) is saller for aircraft with saller range Since the turboprop aircraft offer usually a saller range than jets their axiu glide ratio is saller (does not need to be that high) 14

15 Figure 8: Statistical factor k for calculating the axiu glide ratio ax, for turboprop aircraft based on data fro [11] 364 ngine Power stiation In Section 36 the ratio P R /P is used This is the relative aount of engine shaft power left at altitude and at a certain aircraft speed Since the sizing ethod should be a generic one, a data sheet that applies only for one specific engine ay not be so helpful For this reason, different sources with specific and generic engine perforance data where studied in [13] Furtherore, published equations to calculate P R /P were investigated and fitted to the available data As a result of the investigation an equation was recoended for use: P/ P 0 n = AM σ with paraeters A, and n fro Table 1 Table 1: Paraeters A, and n to calculate the relative aount of engine shaft power P R /P as a function of altitude (expressed by σ) and Mach nuber M Author RefNr Page ngine A n Schaufele [14] 187 generic Brüning [15] 58 T 64-G Russel [16] 16 Rolls-Royce oftin [7] 375 generic Mcorick & Barnes [17] 351 PW Average

16 4 obining Results Values of optiization paraeters are drawn in the atching chart An exaple is given in Section 5 The design point is found as explained in Section The rest of the sizing process is straight forward and does not differ uch fro that process for large jet aeroplanes (see [9]) The required fuel ass is calculated using fuel fractions Fuel reserves have to be included Doestic and international flights are distinguished For turboprop aeroplanes usually doestic reserves apply The additional distance for the flight to an alternate, which is norally assued to be 00 NM for larger jets, ay also be selected as a shorter distance for turboprops that are not so big Reserve loiter tie is 45 inutes As in all other sizing processes, it is iportant to ake a clear stateent about the payload range requireents Payload and range ust fro a pair of values in the payload range diagra (not any payload cobined with any range) The fuel reserves and the cruise speed ust be clearly stated together with the payload range requireents The fuel fractions for cruise flight, flight to the alternate and for loiter has in this sizing process to be based on the range equations for propeller aircraft The Breguet factor for propeller aircraft B s ηp = SF g is used to calculate the segent fuel fraction for the cruise flight phase OI R s R Bs = e s R is the distance flown in cruise If the distance to the alternate and the distance covered during loiter is added, no other equation is needed Other segent fuel fractions (eg for take-off and landing) ay be taken fro tables [8] All segent fuel fractions cobined yield relative fuel ass F / M Maxiu take-off ass is finally calculated fro M = F 1 M P O M 5 xaple alculation: ATR 7 The sizing ethod was put to a test with the redesign of an ATR 7 The requireents for the sizing task were taken fro the anufacturers web page anding: Take off: S = 1067 F S = 190 F nd Segent: n = sin γ = 004 Missed Approach: n = sin γ = 001 ruise: M =

17 Range: Payload: R = 715 NM P = 6460 kg Table : Results fro the redesign sizing prozess of an ATR 7: Aerodynaic paraeters and propeller efficiency Flight Phase,ax ax η P anding 5 Take-off nd Segent Missed Approach ruise Power to ass ratio [W/kg] Segent Missed Approach Take off anding Wing loading [kg/ ] Figure 9: Matching chart for the sizing process of the ATR 7 17

18 Table 3: Results fro the redesign sizing prozess of an ATR 7: Mass, wing area, power Paraeter Original ATR 7 Redesigned ATR 7 Difference M [kg] % [kg] % O [kg] % S W [ ] % b [] % P (one engine) [kw] % M /S W [kg/ ] % P / M [W/kg] % ruise altitude, deterined fro the design point: H = 3888 R 6 onclusion A preliinary sizing ethod for turboprop aeroplanes was presented The ethod includes where necessary equations based on aircraft statistics The preliinary sizing ethod was tested with a redesign task of an ATR 7 The redesign with the proposed ethod was possible with only inor difference between the respective ATR value fro the redesign case and the original ATR 7 value References [1] uropean Aviation Safety Agency: ertification Specifications for arge Aeroplanes, S5, Aendent 4, 7 Deceber 007, [] US Departent for Transportation, Federal Aviation Adinistration: Federal Aviation Regulations, Part 5, Transport ategory Airplanes, 007, [3] uropean Aviation Safety Agency: ertification Specifications for Noral, Utility, Aerobatic, and outer ategory Aeroplanes, S3, Decision 003/14/RM, 14 Noveber 003, [4] US Departent for Transportation, Federal Aviation Adinistration: Federal Aviation Regulations, Part 3, Noral, Utility, Aerobatic and outer ategory Airplanes, 007, [5] uropean Aviation Safety Agency: ertification Specifications for Very ight Aeroplanes, S-VA, Decision No 003/18/RM, 14 Noveber 003, [6] orning, G: Supersonic and Subsonic Airplane Design Published by orning, G, 1964 [7] oftin, K: Subsonic Aircraft : volution and the Matching of Size to Perforance NASA Reference Publication 1060, 1980 [8] Roska, J: Airplane Design Vol 1: Preliinary Sizing of Airplanes Ottawa, Kansas, 1989, - Sale: Analysis and Research orporation, 10 ast Ninth Street, Suite, awrence, Kansas, 66044, USA [9] Scholz, D: Short ourse, Aircraft Design Haburg University of Applied Sciences, May 008, 18

19 [10] Markwardt, K: Unterlagen zur Vorlesung Flugechanik I, Fachhochschule Haburg, Fachbereich Fahrzeugtechnik, 1998 [11] Babikian, R: The Historical Fuel fficiency haracteristics of Regional Aircraft Fro Technological, Operational, and ost Perspectives SM Thesis, MIT, June 001 Quoted fro: [1] [1] Waitz, A: Unified ecture #, Breguet Range quation, Unified ngineering ectures, MIT, USA, 003, [13] Niţă, M: Aircraft Design Studies Based on ATR 7, Project, Haburg University of Applied Sciences, Depatent of Autootive and Aeronautical ngineering, 008, [14] Schaufele, R D: The eleents of Aircraft Preliinary Design, Santa Ana, alif : Aries, 000 [15] Brüning, G; Hafer, X: Flugleistungen : Grundlagen, Flugzustände, Flugabschnitte Berlin : Springer, 1978 [16] Russel, JB: Perforance and Stability of Aircraft ondon : Arnold, 1996 [17] Mcorick, Barnes W: Aerodynaics, Aeronautics, and Flight Mechanics New York : John Wiley&Sons,