1. 18-1 Design of UAV Systems Propulsionc 2002 LM Corporation Lesson objective - to discuss Propulsion and propulsion parametrics including … Rationale Applications Models Expectations - You will understand when and how to use parametric propulsion relationships

2. Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation 18-2 Definitions From Webster’s New Collegiate Dictionary Parameter – any set of physical properties whose value determine the characteristics or behavior of a set of equations Our definition Propulsion parametric – fundamental design parameter whose value determines the design or performance characteristics of an engine Usually (but not always) a multi-variable relationship -e.g., SFC (WdotF/Bhp), Bypass ratio (BPR), etc. Parametric model – Parametric based design approach to define, size, estimate performance and do trade offs on propulsion systems -Different from the traditional approach

3. Parametrics models Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation Simple models that correlate thrust or power, weight, fuel flow, speed and altitude - Most based on historical and technology trend data - Others based on simple definitions - Some based on non-dimensional analysis (See RosAP6.2.5) Internal combustion (IC) engines are easiest to model - Simple (and generally independent) variables - One complexity is fixed pitch propeller performance Jet engines are more difficult to model parametrically - Many interrelated design and operating variables Turboprop (TBProp) parametric models are in between Propulsion parametrics can be used for pre-concept design but engine company models should be used as soon as they are available 18-2a

4. 18-3 Design of UAV Systems Propulsionc 2002 LM Corporation Engine Power-to-weight ratio (HP0/Weng) - HP0 = Maximum power (hp, uninstalled, sea level static) - Weng = Engine weight (lbm, uninstalled) Engine thrust-to-weight ratio (T0/Weng) - T0 = Maximum thrust (lbf, uninstalled, sea level static) - Weng = Engine weight (lbm, uninstalled) Specific Fuel Consumption (SFC) SFC = Fuel flow/Power (WdotF/HP) SFC0 = WdotF0/ HP0 (lbm/hp-hr) Thrust Specific Fuel Consumption (TSFC) TSFC = Fuel flow/Thrust available(WdotF/Ta) TSFC0 = WdotF0/T0 (lbm/hp-hr) Specific Thrust (Fsp) - Fsp = Thrust/Airflow (T/WdotA) - Fsp0 =T0/WdotA0 (lbf-sec/lbm) Key parametrics or Note - “0” postscript indicates sea level static (V=0) conditions or

5. Engine size Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation Any number of performance requirements can drive engine size (See RayAD 5.2) - Takeoff - Ground roll and distance over an obstacle - And/or balanced field length (BFL) - Time and/or distance to climb - Cruise altitude and/or speed - Acceleration and/or turn performance - Engine out performance (for multi-engine aircraft) Historical thrust-to-weight or power-to-weight data can be used for first pass sizing - See RayAD Tables 5.1 and 5.2 UAV historical data is limited and we will use takeoff requirements for initial sizing - See RayAD Figure 5.4 18-4

6. 18-5 Design of UAV Systems Propulsionc 2002 LM Corporation Sizing - manned vs. unmanned UAV data from various sources including Janes, Unmanned Air Vehicles Raymer (power-to-weight) GA Single0.07 GA Twin0.17 Twin turboprop0.20 Raymer (thrust-to-weight) Trainer0.4 Bomber0.25 Transport0.25

7. IC engines Engine power available (BHP) Output per unit size varies by type - Small piston engines run at high RPM, have higher output per unit size. Same for rotary engines For given engine at given altitude and RPM - Almost no variation with speed At given RPM, manifold pressure varies with altitude Max power varies with air density ratio (see RayAD Eqn13.10) - Bhp = Bhp0*(8.55*  -1)/7.55 (18.1) Engine SFC Runs high for small and rotary engines For given engine varies slightly with power available - Typically 5-10% lower at cruise condition Engine power-to-weight varies with engine type Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation 18-6

8. 18-7 Design of UAV Systems Propulsionc 2002 LM Corporation IC engine parametrics Compilation of data from various sources including: Roskam, Aerodynamics & Performance (RosAP); Janes, Aero Engines; Janes, Unmanned Air Vehicles; www.tcmlink.com/producthighlights/www.lycoming.textron.com/main

9. 18-8 Design of UAV Systems Propulsionc 2002 LM Corporation IC engine size Compilation of data from various sources including: - Roskam, Aerodynamics & Performance (RosAP) - Janes, Aero Engines - Janes, Unmanned Air Vehicles - www.tcmlink.com/producthighlights/ -www.lycoming.textron.com/main (a) (b) (c) Charts 18-7/8 show only contemporary IC engines Earlier engines were much larger  = 20 pcf  = 40  = 30

10. Propellers Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation Two basic types of propellers ( See RayAD10.4 & 13.6 ) - Fixed pitch and Variable pitch Efficiency (  p) varies with design and installation - Blockage and flow “scrubbing” generate losses Fixed pitch efficiency varies with advance ratio (J) - See RayADFig13.13 - Props generally designed for climb or cruise Variable pitch efficiency typically constant over range of design speeds - Use a nominal  p = 0.8 for an initial guess Thrust horsepower (THP) defined by - Thp = Bhp*  p =Ta*V(fps)/550=Ta*V(KTAS)/325.6 Where ……….Ta = Thrust available Therefore…….. - Thrust available decreases with speed Ta = 325.6*BHP*  p /KTAS (18.2) 18-9

11. Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation 18-10 Propeller size Key sizing constraint is tip speed (Mach number) - Linear function of engine RPM (V=R*  ) Lightest-most reliable design is direct drive - No gear reduction Some UAVs use high RPM engines with belt systems for speed reduction - Manned aircraft prop sizing can be used for UAVs - There will always be exceptions for special application aircraft (e.g.Altus) Compilation of data from unpublished sources plus: - Janes, Unmanned Air Vehicles

12. 18-11 Design of UAV Systems Propulsionc 2002 LM Corporation Propeller parametrics Nb = Number of blades Rp = Prop radius (in) Weight/Total blade length(in) ≈ 0.8 lb/in Raw data from Janes All the Worlds Aircraft

13. Turboprop engines Design of UAV Systems Lesson 5a - Air vehicle parametricsc 2002 LM Corporation Have typical prop characteristics (and constraints) plus jet exhaust for thrust augmentation Thrust component is added for equivalent shaft HP, the difference between Shp and EShp (see RayAD 13.7) Power available decreases with altitude Decreases with pressure  (see RayAD Table E.3) SFC variation with altitude less severe than jet Typical Lth/Dia = 2 - 3 Typical density = 22 pcf Typical diameter = [4*Vol/(  *L/D)]^1/3 - From Vol(cyl) = [  /4]  [D^2]  L  [D/D] 18-12

14. 18-13 Design of UAV Systems Propulsionc 2002 LM Corporation Turboprop engines Data compiled from RosAP and Janes Aero Engines Typical TBProp parametrics

15. 18-14 Design of UAV Systems Propulsionc 2002 LM Corporation Jet engines Includes turbojet (TBJet) and turbofan (TBFan) engines Thrust, weight, airflow and TSFC depend on design and technology content and operating conditions Difficult to capture in general purpose parametrics Thrust available decreases with altitude - all engines TSFC decreases with altitude - all engines Effect of speed on thrust varies with bypass ratio (BPR) Low BPR - thrust generally increases with speed High BPR - thrust decreases with speed See RayAD Appendix E for specific examples Thrust-to-weight varies with engine size, BPR and advanced technology content Physical geometry primarily a function of design BPR Physical installation reduces thrust by 5-20%

16. 18-15 Design of UAV Systems Propulsionc 2002 LM Corporation Generic jet engine Gas Generator (GG) GG thrust Fan Fan thrust Fan Airflow GG Airflow V Bypass ratio (BPR) = Fan airflow/total airflow WdotAgg  WdotA*1/(BPR+1) WdotAfn  WdotA*BPR/(BPR+1) Turbojet (TBJ) BPR = 0, Turbofan (TBFan) BPR > 10

17. 18-16 Design of UAV Systems Propulsionc 2002 LM Corporation Typical TBJet parametrics SFC0 - Small turbojets 0.5 1 1.5 0100020003000 T0 (lbf) All engines (more later) Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines

18. 18-17 Design of UAV Systems Propulsionc 2002 LM Corporation Typical TBFan parametrics Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines (lbm/hr-lbf)

19. 18-18 Design of UAV Systems Propulsionc 2002 LM Corporation TBJet and TBFan size Despite its apparent simplicity, Raymer’s engine size parametric correlates well with our database - One difference is that Raymer bases his correlation on engine inlet diameter - Our data shows that it correlates with overall engine diameter Parametrics are for uninstalled engine weight - Nominal TBFan T0/Weng = 5.5 - An installation factor of 1.3 is applied to estimate installed engine weight

20. 18-19 Design of UAV Systems Propulsionc 2002 LM Corporation Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines TBFan parametrics – cont’d

21. 18-20 Design of UAV Systems Propulsionc 2002 LM Corporation Afterburning Way to augment jet engine performance to meet peak thrust requirements such as….. Takeoff….combat maneuvers….supersonic flight Works by injecting fuel into engine exhaust to react residual oxygen and increase temperature/jet velocity Inefficient turbojet engines and turbofans can achieve high augmentation ratios - lots of air to “burn” Efficient turbojets achieve low augmentation ratios - Most of the air already “burned” Essentiallya ramjet on the rear of the engine Only works for low-to-moderate BPR turbofans - High BPR fans have insufficient overall pressure ratio Relatively light weight but very fuel inefficient High noise levels limit civil applications

22. 18-21 Design of UAV Systems Propulsionc 2002 LM Corporation A/B parametric data Data from Roskam, Aerodynamics & Performance (RosAP) and Janes, Aero Engines

23. 18-22 Design of UAV Systems Propulsionc 2002 LM Corporation TBProp baseline ground roll = 220 or: 220 = [W0/Sref]/[Clto*T0/W0] For Clto = Clmax/(Vto/Vs^2) = 1.49 and W0 = 1918 lbm BHp0/W0 = 0.092 BHp0 = 176.5 BHp BHp0/W0 correlates well with our parametric data We will use parametric data to make a first pass engine size estimate for our example UAV (see chart 15-40) We assume a nominal TBProp UAV wing loading (W0/Sref) = 30 psf, a typical plan flap Clmax =1.8 (See RayAD Fig 5.3) and a standard Vto/Vs = 1.1 From RayAD Figure 5.4, required takeoff parameter (TOP) for a 1500 ft takeoff

24. 18-23 Design of UAV Systems Propulsionc 2002 LM Corporation Chart 18-13 shows turboprops of this small size class should be available at 2.25 Shp/lb - Nominal weight would be 78.4 lbm -At a density of 22 lb/cuft, volume would be 3.6 cuft -At nominal Lth/Diam = 2.5, engine diameter (Deng) = [4*Vol/(  *Lth/Deng)]^1/3 ≈ 1.22ft and length (Leng) = 3ft -SFC0 would about 0.65 lbm/hr-Bhp In reality, however, there are no TBProps this small Application – TBProp

25. 18-24 Design of UAV Systems Propulsionc 2002 LM Corporation TBFan alternative ground roll = 100 or: 100 = [W0/Sref]/[Clto*T0/W0] For Clto = Clmax/(Vto/Vs^2) = 1.49 and W0 = 2939 lbm T0/W0 = 0.269 T0 = 790 Lbf T0/W0 correlates well with our parametric data We will also use parametric data to make a first pass engine sizing for the TBFan alternative We assume a nominal TBFan UAV wing loading (W0/Sref) = 40 psf, a typical plan flap Clmax =1.8 (See Raymer AD Fig 5.3) and a standard Vto/Vs = 1.1 From RayAD Figure 5.4, required takeoff parameter (TOP) for a 1500 ft takeoff

26. 18-25 Design of UAV Systems Propulsionc 2002 LM Corporation TBFan From charts 18-16/17 we estimate T0/Weng ≈ 5.5 - Our TBFan would weigh 144 lbm - At BPR = 5, WdotAmax = 790/30 = 26.3 pps - From charts 18-16/17 Deng ≈ 12 in, Leng ≈ 24 in From charts 18-17/19 TSFC0 ≈ 0.4 and TSFCcr ≈ 0.65 -But unfortunately, there are no BPR = 5 turbofans of size class (see ASE261.Engine database.xls) -However, there might be some under development

27. 18-26 Design of UAV Systems Propulsionc 2002 LM Corporation Overall results The TBProp parametrics show the SFC0 value assumed in the Lesson 15 example is low (0.4 vs 0.65) -Small engines are less efficient than larger ones -The performance impact will significant but it will make make the results fit better with our sizing parametrics -And there are no engines available at the size required The TBFan parametrics show that Raymer’s values of cruise TSFC are optimistic (which we already knew) and that there are also no small BPR = 5 TBFan engines - Size effects are likely to reduce TSFC also However, we will continue our study as if engines were available since we really don’t know yet what size air vehicle we will end up with - We will, however, note these issues as development risk items and consider the implications when we select our final configurations

28. 18-27 Design of UAV Systems Propulsionc 2002 LM Corporation Next subject From Webster’s New Collegiate Dictionary Parameter – any set of physical properties whose value determine the characteristics or behavior of a set of equations Our definition Propulsion parametric – fundamental design parameter whose value determines the design or performance characteristics of an engine Usually (but not always) a multi-variable relationship -e.g., wing loading (W0/Sref), Swet/Sref, etc. Parametric model – Parametric based design approach to define, size, estimate performance and do trade offs on propulsion systems -Different from the traditional approach

29. 18-28 Design of UAV Systems Propulsionc 2002 LM Corporation Parametric models In the absence of real data, engine parametric models can be used to provide reasonable trends for use in pre-concept and conceptual design -For example, Equation 5.4 (RayAD Eq. 13.10) captures IC engine altitude effects and is useful for initial design -No similar effects are captured in traditional jet engine parametric models such as RayAD Eq. 10.5-10.15 -Mach and altitude effects are absent -More general purpose thrust and fuel flow models are needed and none exist Therefore, we will have to develop our own jet engine models (both TBJet and TBFan) -We will use the engine performance charts in RayAD, Appendix E as the basis for these models

30. 18-29 Design of UAV Systems Propulsionc 2002 LM Corporation IC parametric model Use Equation 18.1 (RayAD Eq. 13.10) to calculate maximum power as a function of altitude BHP = BHP0*(8.55*  -1)/7.55 (18.1) where BHP0 = maximum power, SLS (sea level static)  = air density ratio Calculate cruise performance at 75% takeoff power Assume nominal 80% propulsion efficiency (  p) Estimate thrust available from Ta = 325.6*BHP*  p/KTAS(18.2) Estimate fuel flow from WdotF = SFC*BHP where SFC assumed constant (use SFC0 from chart 18-7) Estimate engine weight from chart 18-7 For supercharged engine, assume pressure ratio/stage = 2 See Raymer Figure 13.10 (page 394) Adjust engine weight as appropriate

31. 18-30 Design of UAV Systems Propulsionc 2002 LM Corporation Jet parametric model Assumptions GG Fsp = constant = Fsp-gg Fan Fsp = (V0/V)*Fsp-fn(SLS) BPR = Constant Gas Generator (GG) GG thrust Fan Fan thrust Fan Airflow GG Airflow V Bypass ratio (BPR) WdotAgg  WdotA*1/(BPR+1) WdotAfn  WdotA*BPR/(BPR+1) Turbojet BPR = 0, Turbofan BPR > 10

32. 18-31 Design of UAV Systems Propulsionc 2002 LM Corporation Jet parametric model Assume jet engine thrust (subsonic) can be modeled as the sum two (2) simplified components - “Gas generator”(gg) - the core engine of a turbofan or turboprop - “Fan” (fn) - the fan or propeller Assume core engine thrust varies with core airflow (constant core engine Fsp - a very simple approximation) Assume fan Fsp varies inversely with speed ratio (V0/V) - Like a propeller - Select non-zero V0 to fit data as appropriate Assume fan bypass ratio remains constant Assume all other engine parameters follow “corrected” performance relationships (See P&W handbook, page 129) - Ta = Ta0*  (18.3) - WdotF = WdotF0*  *sqrt(  ^k) (18.4) - SFC = SFC0*sqrt(  ^k) (18.5) - WdotA = WdotA0*  /sqrt(  )(18.6) - f/a = (f/a0)*sqrt(  )*sqrt(  ^k) ≈ (f/a0)*  ^.75 (18.7) k = f(cycle) but ≈ 0.5

33. 18-32 Design of UAV Systems Propulsionc 2002 LM Corporation Jet parametric model (cont’d) Using these simplifying assumptions, thrust available can be estimated from: Ta = WdotA*Fsp = WdotA*[Fsp-gg/(1+BPR) + Fsp-fn*(V0/V)*(BPR/(1+BPR)] (18.8) where WdotA = Total airflow (note :WdotA-gg = gg airflow) Fsp-gg = Core engine Fsp Fsp-fn = Fan Fsp (varies with number of fan stages) V0 = Non-zero reference speed (select to fit data) BPR - Fan bypass ratio (given by design) Estimate installation losses at 5-20% (more to follow) Estimate airflow from WdotA = WdotA0*delta/sqrt(  ) (18.9) where  = (  @h)*(1+.2M^2)^3.5 (18.10)  = (  @h)*(1+.2M^2) (18.11) Estimate fuel flow from WdotA-gg*corrected fuel/air ratio = WdotA/(1+BPR)*(f/a0)*  ^.75

34. 18-33 Design of UAV Systems Propulsionc 2002 LM Corporation RayAD model matching RayAD Appendix E engines (Table E.1 - Low BPR, Table E.2 - High BPR and Table E.3 - TBP) were modeled parametrically using the following values: Core Fsp (sec) Fan Fsp (sec) V0 (KTAS) BPR Fuel/air ratio LBPRHBPRTBP 909090 66255 10010050 0.48133 0.02920.0292 0.0292 Even though our parametric model is unique to this course, engine companies often provide generic “cycle decks” which produce similar (but more accurate) results

35. 18-34 Design of UAV Systems Propulsionc 2002 LM Corporation Model input rationale Core engine Fsp Fan Fsp V0 BPR Fuel/air ratio - Value (90 sec) selected from chart 18-17 for BPR = 0 - LBPR value selected to match data, HBPR Fsp scaled based on fan pressure ratio differences (1.6 vs. 4.3), TBP Fsp estimated at 20% HBPR Fsp. - Values selected to match data - Given values used except for TBP which was selected to match data - Value selected to match data

36. 18-35 Design of UAV Systems Propulsionc 2002 LM Corporation Model correlation - LBPR (lbm/hr-lbf)

37. 18-36 Design of UAV Systems Propulsionc 2002 LM Corporation Model correlation - HBPR (lbm/hr-lbf)

38. 18-37 Design of UAV Systems Propulsionc 2002 LM Corporation Model correlation - TBP (lbm/hr-lbf)

39. 18-38 Design of UAV Systems Propulsionc 2002 LM Corporation Database comparison - TBF Even though model Fan Fsp values generally match Raymer’s models at BPR = 0.8 and 8.0 by definition - We have no idea what Fan Fsp might look like at intermediate BPR values - And we have no idea how they correlate with real ones We can get answers by assuming values of Fsp-gg and use Eq 18.18 to calculate Fan Fsp for typical engines Fsp-fn parametric (Assumed Fsp-gg = 80) 0 20 40 60 80 100 0246810 BPR Calculated values Model values Fsp-fn parametric (Assumed Fsp-gg = 90) 0 20 40 60 80 0246810 BPR Calculated values Model values Est. upper bound The Fsp-gg = 80 data looks like it provides a better fit

40. 18-39 Design of UAV Systems Propulsionc 2002 LM Corporation Other data comparisons Actual engine performance data can also be used to check and/or calibrate parametric model estimates -For example, parametric model performance estimates for typical TBProp and TBFan engines can be compared to actual engines under the same flight conditions -But because of design differences, even real engines will show performance variations -Nonetheless, the comparisons can be used to generate multipliers to ensure the model estimates match actual engine performance ranges Comparisons with database TBProp and TBFan engine performance are shown in the following chart -TBProp model thrust available and SFC are seen to fit within the data spread, albeit somewhat optimistically -TBFan thrust fits the data but TSFC is about 15% high -A 0.87 TBFan TSFC multiplier will compensate for it

41. 18-40 Design of UAV Systems Propulsionc 2002 LM Corporation Performance correlations - Propulsion model estimate TBProp power ratio at 250 kts 0.3 0.5 0.7 0.9 1.1 1020304050 Altitude (Kft) TPE331-14 PT6A-41 (Flat rated) Other TBProp SFC at 250 kts) 0.40 0.45 0.50 0.55 0.60 1020304050 Altitude (Kft) TPE331-14 PT6A-41 (Flat rated) Other Data from Roskam, Aerodynamics & Performance (RosA)P and Janes, Aero Engines

42. 18-41 Design of UAV Systems Propulsionc 2002 LM Corporation A note about Turboprops Raymer’s Appendix E.3 TPB model is somewhat unique in that performance is expressed in terms of thrust and TSFC, not Shp or Eshp and SFC = WdotF/Hp - This makes us work the problem backwards - In a traditional propeller aircraft analysis, we first calculate Bhp available and then multiply by  p to determine thrust horsepower (Thp) available - The Breguet range equation includes  p in the numerator and SFC is based on uninstalled Bhp - In our model we calculate thrust and fuel flow directly - We, therefore, have to calculate Thp from the definition Thp = T*V(fps)/550 = T*V(kts)/325.6 and then divide by  p to get Shp - Then we calculate SFC from fuel flow and Shp

43. 18-42 Design of UAV Systems Propulsionc 2002 LM Corporation Installation losses We will capture these effects using simple installed performance knock down factors - We will use 0.8 - 0.95 for TBJ and TBF installations -  p will capture all losses for ICs and TBPs During conceptual design, actual performance losses should be calculated for the specific designs studied An important issue for any engine model or data is installation losses - All installations degrade power or thrust available compared to engine company test stand-type data - The differences are large enough to effect even pre- concept design estimates Jet engine losses derive from multiple factors - Inlet and nozzle losses - Power extraction Turboprops also have to deal with prop efficiency IC engine installations have similar losses (air induction system, mufflers, generators and props) - Bleed air - Etc.

44. 18-43 Design of UAV Systems Propulsionc 2002 LM Corporation Example - TBProp 1. Our TBProp UAV weighs 1918 lbm, has a balanced field length requirement of 3000 ft (ground roll = 1500 ft) and Clto = 1.49 and wing loading of W0/Sref = 30 psf (qto = 20.2 psf, takeoff speed = 77.2 kts). We assumed a nominal cruise of 180 kts at 27.4Kft, an initial cruise weight (w4) = 1726 and a cruise lift-to- drag ratio (LoDcr) of 23. What size engine is required for takeoff and will it meet cruise requirements? 2. From RayAD Figure 5.4, the required prop aircraft ground roll takeoff parameter for is 220 where TOP =[W0/Sref]/[  CLt/o*(Bhp0/W0)] = = qt/o/(Bhp0/W0) Bhp0/W0 = qto/220 = 0.092 - Engine size, therefore, is BHP0 = 1918Klb*0.092 = 176.5 Bhp or

45. 18-44 Design of UAV Systems Propulsionc 2002 LM Corporation TBProp takeoff estimate 3. Because propeller models have singularities at V=0, the TBProp is sized at V = V0 = 50 kts (M = 0.076) - At an assumed  p = 0.8*, takeoff thrust (T0) can be calculated directly by definition of BHP or T0  Bhp0*550*  p/KTAS*1.689 = 919.6 lbf - Equation 18.8 is solved for total airflow using chart 18.33 TBP model values or Wdota = 919.6/[90/134 +5*(50/50)*(133/134)] = 163.2 pps - Knowing WdotA0, the TBP model can now predict thrust, airflow and fuel flow at cruise conditions - For simplicity, this will be done only once at Vcr = 180 kts and an altitude of 27.4 Kft (M=0.3) - Then it will be programmed in a spreadsheet *  p is assumed to account for all installation losses

46. 18-45 Design of UAV Systems Propulsionc 2002 LM Corporation TBProp cruise estimate 4.Equations 18.9-11 provide estimates of total airflow (WdotA) at cruise (M=0.302), where  = (  a@27.4Kft)*(1+.2M^2)^3.5 = 0.3556  = (  a@27.4Kft)*(1+.2M^2) = 0.8264 WdotA = WdotA0*  /sqrt(  ) = 64 pps - Core airflow by definition of BPR is Wdota/(BPR+1) or for BPR = 133, Wdota-gg = 0.48 pps - Fuel flow is calculated using the model fuel-to-air ratio value f/a = 0.0292 corrected for , or …. WdotF = WdotA-gg*(f/a)*  ^.75 = 0.012 pps or 43.4 pph - Equation 5.8 is used to calculate Ta where Ta = WdotA*(Fsp-gg/(1+BPR)+Fsp-fn*(V0/V) *(BPR/(1+BPR)) = 64*(90/134+5*(50/180)*(133/134) = 130.9 lbf

47. 18-46 Design of UAV Systems Propulsionc 2002 LM Corporation TBProp cruise - cont’d - Thp is calculated using Eq 18.2 or Thp =130.9*180/325.6 = 72.4 Hp while Shp = 72.4/0.8 = 90.4 Bhp - Finally SFCcr  WdotF/Shp is calculated and found to be SFCcr = 43.4pph/90.4Bhp = 0.48 pph/Bhp - Next we need to compare thrust “available” against thrust “required”  drag - We get this by dividing weight by LoDcr or D ≈ 1726lbm/23 = 75 lbf which is 57% of Ta and shows that the TBProp meets cruise thrust requirements at 180 kts

48. 18-47 Design of UAV Systems Propulsionc 2002 LM Corporation TBProp summary 1. Select takeoff speed (Vto), calculate qto  [W/S]/Clto 2. Estimate takeoff Bhp0 required (RadAD Fig 5.4) 3. Select takeoff “sizing” speed = V0 (i.e. 50 kts) 4. Calculate Tavail at sizing speed (Ta0 = 325.6  p  Bhp0/V0) 5. Calculate WdotA0 from Fsp and Ta0 at V0 (Eq 18-8, BPR = 133) TBP sizing 1. Select speed (KTAS) & and altitude (h) 2. Calculate ,  and M at h (atmosphere spreadsheet) 3. “Correct”  and  for M (Eqs 18-10 and 18-11) 4. Calculate total (prop+engine) WdotA (Eq 18-9) 5. Calculate engine airflow (WdotA-gg = WdotA/[BPR+1]) 6. Calculate corrected fuel-to-air ratio (Eq 18.7) 7. Calculate fuel flow (WdotF= WdotA-gg  corrected fuel-to-air ratio) 8. Calculate thrust available (Eq 18-8) 9. Calculate uninstalled Bhp (= Ta  KTAS/[325.6  p) 10. Calculate uninstalled SFC [SFC = WdotF/Bhp(uninst)] 11. Check that Ta > D = W/LoD TBP performance

49. 18-48 Design of UAV Systems Propulsionc 2002 LM Corporation Typical example - TBFan 1.Our TBFan alternative weighs 2914 lbm, has a balanced field length requirement of 3000 ft (ground roll = 1500 ft) and Clto = 1.49 and wing loading of W0/Sref = 40 psf (qto = 26.9 psf, takeoff speed = 89.1 kts). We assumed nominal cruise at 300 kts at 27.4Kft, an initial cruise weight (w4) = 2645lbm and a cruise lift-to-drag ratio (LoDcr) of 22.5. 2. From RayAD Figure 5.4, the required jet aircraft ground roll takeoff parameter for is 100 where TOP =[W0/Sref]/[  CLt/o*(T0/W0)] = = qt/o/(Bhp0/W0) T0/W0 = qto/100 = 0.269 - Engine size, therefore, is T0 = 2914*0.269 = 784 lbf

50. 18-49 Design of UAV Systems Propulsionc 2002 LM Corporation TBFan performance where 3. The TBF model also has a singularity at V=0 and is sized at V = V0 by solving for WdotA0 Fsp0 = Fsp-gg/(1+BPR)+ Fsp-fn*(BPR/(1+BPR) T0 = WdotA0*Fsp0 4. Therefore for BPR = 5.0, Fsp-gg = 90, Fsp-fn = 30 (vs. 25 at BPR = 8) and T0 = 784 lbf WdotA0 = 784/(90/6+30*5/6) = 19.6 pps 5. Performance at other conditions is determined using Equations 18.9-11 and V0 = 100 kts. For example, at h = 27.4 Kft, V = 300 Kts (M = 0.503) :  = (  @27.4Kft)*(1+.2M^2)^3.5 = 0.37969  = (  @27.4ft)*(1+.2M^2) = 0.8527 WdotA = WdotA0*delta/sqrt(  ) = 8.4pps where and

51. 18-50 Design of UAV Systems Propulsionc 2002 LM Corporation - By definition core airflow (Wdota-gg) = Wdota/(BPR+1) or for BPR = 5, Wdota-gg = 1.4 pps - Fuel flow is calculated using the model fuel-to-air ratio value f/a = 0.0292 corrected for , or WdotF = WdotAgg*(f/a0)*  ^.75 = 0.037 pps or 131 pph - Equation 18.8 once again is used to calculate thrust T = WdotA*[Fsp-gg/(1+BPR)+Fsp-fn*(V0/V) *(BPR/(1+BPR)] = 8.4*(90/6+30*(100/300)*(5/6)) = 197 lbf and TSFC = 131pph/197lbf = 0.67pph/lbf - At a LODcr of 22.5 and initial cruise weight =2623 lbm, D = 116.6 lbf compared to TBFan T (uninstalled) = 198 lbf. If we assume a 5% installation loss, Ta = 188 lbf, which is enough to meet the cruise thrust requirements TBFan performance - cont’d

52. 18-51 Design of UAV Systems Propulsionc 2002 LM Corporation TBFan summary 1. Select speed (KTAS) & and altitude (h) 2. Calculate ,  and M at h (atmosphere spreadsheet) 3. “Correct”  and  at M (Eqs 5-13 and 5-14) 4. Calculate WdotA (Eq 5-12) 5. Calculate core airflow (WdotA-gg = WdotA/[BPR+1]) 6. Calculate corrected fuel-to-air ratio (Eq 5.10) 7. Calculate fuel flow (WdotF = WdotA-gg  corrected fuel-to-air ratio) 8. Calculate uninstalled thrust (Eq 5-11) 9. Calculate installed thrust (Tinst = Tuninst  installation factor) 10. Calculate installed TSFC (TSFC = WdotF /Tinst 11. Check that Tinst > D = W/LoD TBF performance 1. Select BPR 2. Select Fsp-fn = f(BPR) Chart 5b-13 3. Select takeoff speed (Vto), calculate qto  [W/S]/Clto 4. Estimate takeoff T0 required (RadAD Fig 5.4) 5. Select takeoff “sizing” speed = V0 (i.e. 100 kts) 6. Calculate WdotA0 from Fsp and T0 at V0 (Eq 18-8) TBF sizing

53. 18-52 Design of UAV Systems Propulsionc 2002 LM Corporation Concluding remarks Our parametric models predict reasonable performance for a range of types, altitudes and subsonic speeds Although approximate, they capture effects not included in traditional parametrics, e.g. RayAD equations 10.4-15. - They can be used for pre-concept design studies until better data is available The models are approximate and are valid only at subsonic speeds The models do not capture temperature or RPM limits obvious in RayAD Appendix E plots The models do the best job of predicting airflow The model do the worst job of predicting HBPR and TBP performance at low-altitude and high-speeds. -Typically, these engines are not operated under such conditions and the errors have little practical effect During conceptual design engine company models should be used

54. 18-53 Design of UAV Systems Propulsionc 2002 LM Corporation Expectations You should now understand Propulsion parametrics and parametric models Where they come from How they are used The limits of their applicability

55. 18-54 Design of UAV Systems Propulsionc 2002 LM Corporation Homework 1.Write spreadsheet programs to calculate uninstalled IC, TBProp and TBFan engine performance with airspeed (or M) and altitude (or delta & theta) as inputs - (team grade) 2. Run your TBProp and TBFan models for the example problems (charts 18-43 through 18-50) and compare results (team grade) -Identify any errors in my example problems 3. Using a balanced field length criteria for takeoff, size engines for your proposed air vehicle (individual grades) 4. Use the team spreadsheets to calculate uninstalled engine performance at takeoff and dash (target ID) speeds for your proposed air vehicle (individual) 5. Compare TBProp and/or TBFan results to ASE261.Engine.Models.xls and identify differences (individual grades) Week 2

56. 18-55 Design of UAV Systems Propulsionc 2002 LM Corporation Intermission