Lesson objective to discuss

1

• Lesson objective - to discuss
• Propulsion and propulsion parametrics
• including
• Rationale
• Applications
• Models

Expectations - You will understand when and how
to use parametric propulsion relationships
18-1
2
Definitions

• From Websters 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

18-2
3
Parametrics models
18-2a
4
Key parametrics

• 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)

or
or
Note - 0 postscript indicates sea level static
(V0) conditions
18-3
5
Engine size

• 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
Sizing - manned vs. unmanned
Raymer (power-to-weight) GA Single 0.07 GA
Twin 0.17 Twin turboprop 0.20
Raymer (thrust-to-weight) Trainer 0.4 Bomber 0.2
5 Transport 0.25
UAV data from various sources including Janes,
Unmanned Air Vehicles
18-5
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

18-6
8
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.ly
coming.textron.com/main
18-7
9
IC engine size
? 20 pcf
? 30
? 40
(a)
(b)

• Charts 18-7/8 show only contemporary IC engines
• Earlier engines were much larger

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
(c)
18-8
10
Propellers

• 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)/550Ta?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
Propeller size

• Key sizing constraint is tip speed (Mach number)
• - Linear function of engine RPM (VR?)
• 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
18-10
12
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
18-11
13
Turboprop engines

• 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?D2?L?D/D

18-12
14
Typical TBProp parametrics
Turboprop engines
Data compiled from RosAP and Janes Aero Engines
18-13
15
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

18-14
16
Generic jet engine
18-15
17
Typical TBJet parametrics
Data from Roskam, Aerodynamics Performance
(RosA)P and Janes, Aero Engines
All engines (more later)
18-16
18
Typical TBFan parametrics
(lbm/hr-lbf)
Data from Roskam, Aerodynamics Performance
(RosA)P and Janes, Aero Engines
18-17
19
TBJet and TBFan size

• Despite its apparent simplicity, Raymers 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

18-18
20
TBFan parametrics contd
Data from Roskam, Aerodynamics Performance
(RosA)P and Janes, Aero Engines
18-19
21
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
• Essentially a 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

18-20
22
A/B parametric data
Data from Roskam, Aerodynamics Performance
(RosAP) and Janes, Aero Engines
18-21
23
TBProp baseline

• 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

• ground roll 220 or
• 220
• W0/Sref/Clto?T0/W0
• For Clto Clmax/(Vto/Vs2) 1.49 and W0 1918
  lbm
• BHp0/W0 0.092
• BHp0 176.5 BHp
• BHp0/W0 correlates well with our parametric data

18-22
24
Application TBProp

• 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)
  4Vol/(?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

18-23
25
TBFan alternative

• 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

• ground roll 100 or
• 100
• W0/Sref/CltoT0/W0
• For Clto Clmax/(Vto/Vs2) 1.49 and W0 2939
  lbm
• T0/W0 0.269
• T0 790 Lbf
• T0/W0 correlates well with our parametric data

18-24
26
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

18-25
27
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 Raymers 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 dont 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

18-26
28
Next subject

• From Websters 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

18-27
29
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

18-28
30
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

18-29
31
Jet parametric model
18-30
32
Jet parametric model
18-31
33
Jet parametric model (contd)

• Using these simplifying assumptions, thrust
  available can be estimated from
• Ta WdotA?Fsp WdotA?Fsp-gg/(1BPR)
• Fsp-fn?(V0/V)?(BPR/(1BPR) (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
• ? (? _at_h)?(1.2M2)3.5
  (18.10)
• ? (?_at_h)?(1.2M2) (18.11)
  
• Estimate fuel flow from WdotA-gg?corrected
  fuel/air ratio
• WdotA/(1BPR)?(f/a0)?? .75

18-32
34
RayAD model matching
18-33
35
Model input rationale
18-34
36
Model correlation - LBPR
(lbm/hr-lbf)
(lbm/hr-lbf)
18-35
37
Model correlation - HBPR
(lbm/hr-lbf)
(lbm/hr-lbf)
18-36
38
Model correlation - TBP
(lbm/hr-lbf)
(lbm/hr-lbf)
18-37
39
Database comparison - TBF

• Even though model Fan Fsp values generally match
  Raymers 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

• The Fsp-gg 80 data looks like it provides a
  better fit

18-38
40
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

18-39
41
Performance correlations
Data from Roskam, Aerodynamics Performance
(RosA)P and Janes, Aero Engines
- Propulsion model estimate
18-40
42
A note about Turboprops

• Raymers 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 TV(fps)/550 TV(kts)/325.6
  and then divide by ?p to get Shp
• - Then we calculate SFC from fuel flow and Shp

18-41
43
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
18-42
44
Installation losses
Subsonic commercial transports achieve much
higher installed performance levels - Typically
0.9 - 0.95 for TBJ and TBF installations Simple
inlet and nozzle installations reduce losses
18-42a
45
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 27Kft, 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 1918Klb0.092
176.5 Bhp
or
18-43
46
TBProp takeoff estimate
3. Because propeller models have singularities at
V0, 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 (M0.3) - Then it will be programmed in
a spreadsheet
?p is assumed to account for all installation
losses
18-44
47
TBProp cruise estimate
4.Equations 18.9-11 provide estimates of total
airflow (WdotA) at cruise (M0.302), where ?
(?a_at_27.4Kft)?(1.2M2)3.5 0.3556 ?
(?a_at_27.4Kft)?(1.2M2) 0.8264 WdotA
WdotA0??/sqrt(?) 64 pps - Core airflow by
definition of BPR is Wdota/(BPR1) 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/(1BPR)Fsp-fn?(V0/V)
?(BPR/(1BPR)) 64?(90/1345?(50/180)?(133
/134) 130.9 lbf
18-45
48
TBProp cruise - contd
- 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
18-46
49
TBProp summary
TBP sizing
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 performance
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 (propengine)
WdotA (Eq 18-9) 5. Calculate engine airflow
(WdotA-gg WdotA/BPR1) 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
18-47
50
Typical example - TBFan

• 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 29140.269 784 lbf

18-48
51
TBFan performance
where

• 3. The TBF model also has a singularity at V0
  and is sized at V V0 by solving for WdotA0
• Fsp0 Fsp-gg/(1BPR) Fsp-fn?(BPR/(1BPR)
• 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/(90/630?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)
  
• ? (?_at_27.4Kft)?(1.2M2)3.5 0.37969
• (?_at_27.4ft)?(1.2M2) 0.8527
• WdotA WdotA0?delta/sqrt(?) 8.4pps

where
and
and
18-49
52
TBFan performance - contd
- By definition core airflow (Wdota-gg)
Wdota/(BPR1) 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/(1BPR
)Fsp-fn?(V0/V) ?(BPR/(1BPR)
8.4?(90/630?(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
18-50
53
TBFan summary
TBF sizing
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 performance
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/BPR1) 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
18-51
54
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

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Expectations

• You should now understand
• Propulsion parametrics and parametric models
• Where they come from
• How they are used
• The limits of their applicability

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Homework (individual)

• Select an AE261 spreadsheet program and make a
  copy of the engine worksheet to calculate
  uninstalled engine performance (IC, TBProp or
  TBFan as appropriate) for your air vehicle
  concept
• 2. Using a balanced field length criteria for
  takeoff, size an engine or engine(s) for your air
  vehicle
• Estimate HP or thrust
• Estimate weight and size or volume
• 3. Calculate uninstalled engine performance at
  one assumed air vehicle takeoff, cruise, loiter
  or dash (target ID) speeds
• Use the engine worksheet to check your hand
  calculation. Use the spreadsheet to calculate
  performance at the other assumed flight
  conditions
• 4. Compare the model outputs against data on real
  engines (AE261.Engine.database or Janes) and
  assess the results
• 5. Estimate installation losses for your concept
  and explain your rationale

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Intermission
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