Air vehicle performance

Name: Air vehicle performance
Uploaded: 2017-10-20T18:00:20+00:00
Duration: PTM43S24
Channel: Douglas O’Connor’
Description: Air vehicle performance

Air vehicle performance
Design of UAV Systems Review - Air vehicle performance c LM Corporation Lesson objective - to discuss Air vehicle performance including Mission segment performance Breguet range and endurance and typical design applications Expectations - You will understand when and how to calculate mission performance 21-1

Discussion subjects Design of UAV Systems Mission segments Start Taxi
Air vehicle performance c LM Corporation Discussion subjects Mission segments Start Taxi Takeoff Climb Cruise Loiter Acceleration Turn performance Descend and land 21-2

Performance will be calculated by mission segment
Design of UAV Systems Air vehicle performance c LM Corporation Overall approach We will develop air vehicle performance equations for a typical mission from engine start through landing - Some of the equations will be exact, most will be approximate to simplify analysis Performance will be calculated by mission segment - Using simplified performance methods For each segment we will first discuss methodology and then address application - Using our example UAVs from the previous lesson The methods will be applied to the turboprop (TBProp) UAV example - We will take it through full mission analysis 21-3

Mission definition Design of UAV Systems Notation Terminology
Air vehicle performance c LM Corporation Mission definition 0 Engine start 1 Start taxi 2 Start takeoff 3 Initial climb 4 Initial cruise 5 Start pre-strike refuel 6 End pre-strike refuel Start cruise 7 Start loiter 8 End loiter, start cruise 9 Start ingress 10 Combat 11 Weapon release 12 Turn 13 Start egress 14 End egress, start cruise 15 Start post-strike refuel 16 End post-strike refuel 17 End cruise 18 Start hold 19 End hold Notation Border - Standoff Loiter/Penetrate Penetrate/Loiter 2 3 4 5 6 7 8 10 11 12 13 15 16 17 18 19 Standoff - Distance from loiter or combat to border (+/-) Standback - Distance from refuel to border Ingress - To target at penetration speed Egress - From target at penetration speed Range (Rge) = 2*Radius(R) Terminology 1 14 9 21-4

Start-taxi-takeoff fuel
Design of UAV Systems Air vehicle performance c LM Corporation Start-taxi-takeoff fuel At a detail level, fuel requirements for engine start taxi and takeoff (Wfstto) are defined by power settings and times - typical examples - Engine start and taxi = 20 minutes at idle power - Idle fuel flow = X% WdotF0 - Takeoff = 1 minute at maximum power Therefore Wfstto/W0 = [(20*X+1)/60]*(T0/W0)*TSFC (21.1) - Or for a typical transport where T0/W0 = .3, TSFC0 = .4, X = .1, we calculate Wfstto = 0.006*W0 - While for a typical non A/B fighter T0/W0 = .5, TSFC0 = 1.0, X = .1, we calculate Wfstto = 0.025*W0 These values compare to RayAD Equation 6.8 suggested values where Wfstto = ( )*W0 where and 21-5

- Engine start and taxi = 30 minutes at idle power
Design of UAV Systems Air vehicle performance c LM Corporation Typical application The resized/converged example TBProp UAV has a takeoff gross weight (W0) of 2184 lb (chart 20-30), fuel fraction of 0.175, wing reference area (Sref) of 72.8 sqft, a takeoff power-to-weight (Bhp0/W0) of 0.092, and SLS specific fuel consumption (SFC0) of 0.73, where: - Engine start and taxi = 30 minutes at idle power Idle fuel flow = (X%/100)*WdotF0 where x = 10% - Takeoff = 1 minute at maximum power From Eq 21.1 Wfstto/W0 = [(30*X+1)/60]*(BHp0/W0)*SFC0 = .0045 and Wfstto = *W0 = 10 lbm Weight at liftoff (W3) = = 2174 lbm or W3/Sref = 2174/72.8 = psf 21-6

Example UAV - takeoff performance
Design of UAV Systems Air vehicle performance c LM Corporation Example UAV - takeoff performance Takeoff distance is estimated from RayAD Fig. 5.4 - In Lesson 18, we calculated takeoff at 110% stall speed where Clto-max = 1.8 (plain flap) and: (W/Sref)/Clto = qto = *Vto^ (21.2) where Vto = takeoff speed in knots - For our TBProp example, Clto = 1.8/(1.1^2) = 1.49, qto = /1.49 = 20.1 psf and Vto = 77 kts - Takeoff parameter (TOP) was previously estimated at 220 which is consistent with a 1500 ft ground roll and an approximate balanced field length (BFL) of 3000 ft See RayAD page 98 for additional information 21-7

Hdot/V + Vdot/g = (Ta-D)/W* (21.3)
Design of UAV Systems Air vehicle performance c LM Corporation Climb performance Generalized performance for any non-equilibrium flight condition (including climb) is defined by Hdot/V + Vdot/g = (Ta-D)/W* (21.3) where (See RayAD Eq. 5.4 and Chapter 17.6) Hdot = Rate of climb (fps) V = Speed (fps) Vdot/g = Axial acceleration (g’s) Ta = Thrust available (lbf) D = Drag W = Weight (lbm) For a typical climb Vdot/g << Hdot/V and L  W so that Hdot = V*(Ta-D)/W = V*(Ta/W - 1/(L/D)) (21.4) * Hdot/V is defined as climb gradient, (Ta-D)/W as flight path acceleration (FPA) and FPA*V as specific excess power (Ps) 21-8

Therefore, we need a better climb methodology
Design of UAV Systems Air vehicle performance c LM Corporation Climb methodology Raymer suggests use of a weight fraction (RayAD Table 3.2) or a Mach number parametric (RayAD Eq’s 6.9 and 6.10) to estimate fuel required for climb These equations, however, do not take into account key design features such as T/W, AR or speed Therefore, we need a better climb methodology Our options are to develop a parametric that includes key performance features or to simply calculate it Performance calculation is actually straight forward We can make a first order climb speed approximation by assuming climb at (L/D)max (LoDmax) where … = (W/S)/sqrt(*AR*e*Cd0) … and Lesson 17 aerodynamic and Lesson 18 engine models are used to estimate drag, thrust and fuel flow 21-9

Climb speed and distance
Design of UAV Systems Air vehicle performance c LM Corporation Climb speed and distance Even though climb performance can be integrated numerically, it is a little awkward for spreadsheet computations and we will use a simplified approach We will assume climb at constant EAS at LoDmax and calculate performance at 2 conditions Right after takeoff (assumed to be at sea level) and again at cruise altitude (hcr) - Performance will be averaged between the two - We will assume that the average climb air speed and ground speed are about the same Climb distance can be calculated from time to climb (TTC) and climb speed (V-clmb) We impose a climb stall margin = 1.25 and assume Clmax = 1.2 or Clmax useable = 1.2/(1.25^2) = 0.768 21-10

There are few parametrics available for estimating climb performance
Design of UAV Systems Air vehicle performance c LM Corporation Climb parametric There are few parametrics available for estimating climb performance There are many variables that affect performance Data scatter is relatively large but the can still be used to check calculations Some examples: Global Hawk 21-11

Example UAV application - climb
Design of UAV Systems Air vehicle performance c LM Corporation Example UAV application - climb Our TBProp at W3/Sref = 29.86, Bhp0/W0 = climbs to 27.4 Kft, Swet/Sref = 4.77 and b^2/Swet = 4.21,  For Cfe = , e = 0.8, from equations - LoDmax = 0.5*sqrt[(*0.8/0.0035)*(4.21)] = 27.4 - Cd0 ≈ Cfe*(Swet/Sref) = .0035*5.16 = .017and - LoDmax = .95 which exceeds Clmax = so q3 = 29.86/.768 = 38.8 psf , V3 = 107 kts and Cdi = Cl^2/*A*e = and Cd = Cd0+Cdi = 0.030 From our Lesson 18 TBProp model (spreadsheet) at sea level and V3 = 107 kts (M = 0.16, q = 38.8 psf) Bhp3 = 232, Ta3 = 564 lbf and WdotF3 = 149 pph By definition D3 = Cd*q3*Sref = 0.030*38.8*78.4 = 80 lbf and Hdot3 =V3*(Ta3-D3)/W3 = 40.2 fps or 2414 fpm 21-12

UAV application - climb
Design of UAV Systems Air vehicle performance c LM Corporation UAV application - climb If the TBProp climbed at a constant Hdot = 2414 fpm and WdotF = 149 pph, time to climb (TTC) to 27.4 Kft would be 11.3 min and fuel required would be 28 lbm - We add this to Wfssto and make a first approximation estimate of initial cruise weight (W4est)  2147 lbm At 27.4 Kft we recalculate performance at KEAS = 107 kts (q = 38.8 psf) or KTAS = 167 kts and M = 0.28 - From our TBP spreadsheet model, Bhp = 100, Ta = 156, WdotF = 49 pph - At W4est = 2147 lbm, Cl = 0.78, Cd = 0.030, D = 80 lbf - Hdot = V*(Ta-D)/W = 167*1.689*(156-80)/2147 = 10 fps or 600 fpm The averages of the sea level and 27.4 Kft climb performance parameters are: Hdotavg = 1507 fpm, WdotFavg = 99 pph, KTASavg = 137kts 21-13

Overall climb performance
Design of UAV Systems Air vehicle performance c LM Corporation Overall climb performance Using the averages - Time to climb (TTC) = 27.4 Kft/1507 fpm = 18.2 min - Fuel to climb = (18.2/60)*99 = 30 lbm - Distance to climb (Dcl) = (18.2/60)*137 = 42 nm - Initial cruise weight (W4) = 2145 vs. est. = 2147 lbm Fuel to takeoff and climb = 9.8% Or Kttoc = 0.098 21-14

Parametric comparison Design of UAV Systems
Air vehicle performance c LM Corporation We can compare our performance estimates to the previous climb parametric - Our calculated sea level rate of climb is 2414 fpm - Distance to climb to 27.4 Kft is 42 nm or 1.5 nm/Kft - The T0/W0 parametric is based on uninstalled sea level static where Ta = 1129 lbf or T0/W0 = 0.48 The parametric plots suggest our climb performance may be a little optimistic but it fits 21-15

Wing loading drives cruise altitude (see chart 20-9)
Design of UAV Systems Air vehicle performance c LM Corporation Cruise Cruise speed and altitude are selected to maximize range factor (V*[L/D]/SFC) or nm/lb of fuel Assuming sufficient thrust (Ta) is available, cruise speed (Vcr) and altitude (hcr) are driven by lift coefficient (Cl) and wing loading (W/S) - see RayAD Eq’s Cruise lift coefficient is determined by airfoil design (see RayAD Chapter 4.2, airfoil selection) and requirements to operate at or near LoDmax Wing loading drives cruise altitude (see chart 20-9) Cruise speed is typically a requirement or a limit Propeller aircraft engines are typically sized by speed Jet aircraft typically cruise just below some limit such as transonic drag rise (0.6<Mdd<0.95) or flutter 21-16

Basic form of the equation (see RayAD Eq. 3.5)
Design of UAV Systems Air vehicle performance c LM Corporation Breguet range - review Basic form of the equation (see RayAD Eq. 3.5) R = [V/TSFC][L/D] Ln[Wi-1/WI] (21.5) where R = Cruise range (nm) V = Cruise speed (KTAS) TSFC = Thrust specific fuel consumption (lbm/hr-lbf) L/D (LoD) = Cruise lift-to-drag ratio Wi-1 = Weight at beginning of cruise segment Wi = Weight at end of cruise segment Cruise = any unaccelerated flight segment The basic form can also be expressed in terms of horsepower (Bhp) using the definition HP = T(lbf)V(KTAS)/[325.64*p] (21.6) p = propeller efficiency 21-17

Breguet range (horsepower)
Design of UAV Systems Air vehicle performance c LM Corporation Breguet range (horsepower) In Bhp form, specific fuel consumption is expressed in terms of HP where SFC = lbm/hr-hp (21.7) where by definition TSFC/SFC = [lbm/hr-lbf]/[lbm/hr-hp] = hp/lbf (21.8) or from Eq (21.5) TSFC = SFCV(KTAS)/[325.64*p] (21.9) By substituting this into the Breguet equation for jet aircraft (21.5) we develop the Breguet range equation for propeller driven aircraft R = [p/SFC][L/D]Ln[Wi-1/WI] (21.10) 21-18

- Fuel flow (WdotF), therefore, is minimized
Design of UAV Systems Air vehicle performance c LM Corporation Loiter The objective of a loiter segment is to maximize endurance ([L/D]/SFC) - see next chart - Fuel flow (WdotF), therefore, is minimized Loiter speed typically occurs at or near L/Dmax - Even though Raymer and Roskam focus on different L/D strategies for prop and jet aircraft, we will assume both loiter (or cruise) at or near L/Dmax - See RayAD Eq for issues - We won’t get hung up on the issues and simply try to maximize overall performance Loiter (and cruise) are easy mission segments to analyze since, by definition: Ta ≈ D and L ≈ W For either segment, a Breguet type equation is used to estimate performance 21-19

Breguet endurance - review
Design of UAV Systems Air vehicle performance c LM Corporation Breguet endurance - review A similar form expression is used to calculate endurance (See RayAD Eq. 3.7) E = [1/TSFC][L/D]Ln[Wi-1/WI] (21.11) where E = Endurance (hrs) TSFC = Thrust specific fuel consumption (lbm/hr-lbf) L/D = Loiter lift-to-drag ratio Wi-1 = Weight at beginning of loiter segment Wi = Weight at end of loiter segment Loiter = unaccelerated minimum fuel flow flight condition (from L=W, TSFC*D = fuel flow) or expressed in terms of horsepower E = [(325.64*p)/(VSFC)][L/D]Ln[Wi-1/WI] (21.12) V = Loiter speed (kts) 21-20

- The effects are different for the jet and prop equations
Design of UAV Systems Air vehicle performance c LM Corporation Installation effects Installation affects the TSFC and SFC terms when calculating Breguet range and endurance - The effects are different for the jet and prop equations First the jet range form R = [V/TSFC][L/D] Ln[Wi-1/WI] - The basis of the derivation is that L=W and T=D so that [V/TSFC][L/D]  VW/WdotF - For T to equal D, TSFC must be based on installed thrust so TSFC  WdotF/T-installed In the prop form R = [325.6p/SFC][L/D]Ln[Wi-1/WI] - Here also L=W and T=D but having p in the numerator requires that SFC be based on uninstalled power or SFC  WdotF/HP-uninstalled The same logic follows for the endurance equations 21-21

- By definition RF = 400kts40Klbm/2Kpph = 6000 nm
Example Design of UAV Systems Air vehicle performance c LM Corporation Notional TBF : V = 300 kts, W = 40Klbm, L/D = 10, WdotF = 2Kpph, installation loss = 20% - By definition RF = 400kts40Klbm/2Kpph = 6000 nm - For T = D, T(inst) = 4Klbf and T(uninst) = 5Klbf or TSFC (installed) = 0.5 and TSFC (uninstalled) = 0.4 - By inspection [V/TSFC][L/D] must be based on TSFC (installed) = 0.5 Notional TBP : V = 300 kts, W = 40Klbm, L/D = 10, WdotF = 2Kpph, p = 0.8 (includes all losses) - By definition RF = 400kts40Klbm/2Klbmph = 6000 nm - For T=D, T(req’d) = 4Klbf and HP(req’d) = 4Klbf*300kts/[325.6*0.8] = 4607 hp (uninstalled) and SFC (uninstalled) = 0.434 - By inspection [325.6p/SFC][L/D] must be based on SFC (uninstalled) 21-22

The same applies to internal combustion engines
Simple solution Design of UAV Systems Air vehicle performance c LM Corporation We can eliminate the thrust vs. horsepower differences by expressing engine performance in terms of one or the other conventions Example: TBProp performance can be expressed in terms of thrust (Raymer Table E.3) or horsepower The same applies to internal combustion engines In the early days of the jet era, some tried to describe jet engine performance in terms of horsepower But it was a problem under static conditions, since as V 0, thrust   Therefore, thrust became the standard measure of jet engine performance Our spreadsheets use this approach, all engine performance is calculated in terms of Ta and TSFC Including internal combustion (IC) engines TBProp and IC input values, however, are in HP 21-23

Acceleration is estimated using Eq. 21.3 with Hdot = 0 or
Design of UAV Systems Air vehicle performance c LM Corporation Acceleration Acceleration is estimated using Eq with Hdot = 0 or Vdot/g = (Ta-D)/W ≈ (V/t)*g (21.13) Acceleration fuel required (Wfacc) is calculated using numerical integration or approximate methods similar to climb UAVs typically do not have acceleration requirements - UCAVs could Time and distance to accelerate from climb speed to cruise speed should be included in mission performance analysis 21-24

Ta = 156 lbf, D = 90 lbf and WdotF = 49 ppm
Design of UAV Systems Air vehicle performance c LM Corporation Another example How long would it take the TBProp UAV to accelerate from final climb speed to a cruise speed of 180 kts? - We use our climb performance spreadsheet to estimate thrust (Ta),drag (D), weight (W4 = 2145 lbm) and WdotF at 27.4Kft and 167 kts at maximum power or Ta = 156 lbf, D = 90 lbf and WdotF = 49 ppm - From equation 21.13, Vdot = g*(Ta-D)/W = V/T or Vdot = *( )/ 2145 = 1.14 ft/sec^2 - At 180 kts and maximum throttle setting, Ta = 149 lbf, D = 83 lbf and W ≈ 2145 lbm and Vdot = *( )/ 2145 = 0.99 ft/sec^2 - We calculate acceleration time using the average value of Vdot = 1.07 ft/sec^2 or Tacc = ( )*1.689/ 1.14 = 19.2 sec or 0.32 minutes 21-25

- Sustained turns are at constant speed (and altitude)
Design of UAV Systems Air vehicle performance c LM Corporation Turn performance Typically two types of turn performance are of most interest - turn rate and time to turn (both instantaneous and sustained) - Sustained turns are at constant speed (and altitude) - Maximum sustained turn rate is at “corner speed”, the speed for LoDmax (See RayAD Fig 17.6) - By definition Ta = D - In instantaneous turns, speed (or altitude) can be lost - Maximum turn rate is at Clmax or max g’s (Nz) In a level turn (RayAD Fig 17.5) L*cos() = W or  = arccos(1/Nz) (21.14) and d/dt = (g/V)*sqrt(Nz^2-1) (21.15) where  = bank angle and d/dt = turn rate Time to turn = time to bank + turn angle () ÷ (d/dt) 21-26

UAV application Design of UAV Systems
Air vehicle performance c LM Corporation Although UCAVs eventually may have maneuver and dash requirements to allow them to operate with manned aircraft, UAVs currently do not - In the future,however, we should anticipate UAV requirements on turn performance - The requirements will probably be driven by platform reaction time, for example, to turn X degrees in Y seconds in order to position a sensor on a target Consider a loitering UAV with a forward looking sensor, flying a race track pattern. border assigned sector platform sensor field of regard maximum rate turn incident 21-27

From 21.14,  = arccos(1/Nz) =  = arccos(1/3) = 70.5
Design of UAV Systems Air vehicle performance c LM Corporation Example We assume that an incident occurs when the UAV is looking directly away from it - How long does it take for a 3 g, 180 kt UAV to put its sensor on target assuming a  30 degree field of regard, that is the UAV has to turn 150 degrees, assuming a roll rate of 30 degrees/second From 21.14,  = arccos(1/Nz) =  = arccos(1/3) = 70.5 - Time to bank = 70.5/30 = 2.4 seconds - d/dt = (g/V)*sqrt(Nz^2-1) = (g/(180*1.689))*(9-1)^.5 = 0.3 rad/sec = deg/sec Therefore, time to turn = /17.15 = 11.1 sec border assigned sector platform sensor field of regard maximum rate turn incident 30 deg 21-28

We will use this ground rule for pre-concept studies
Design of UAV Systems Air vehicle performance c LM Corporation Descent and landing For pre-concept design, mission rules typically give no range credit (and no fuel penalty) for descent We will use this ground rule for pre-concept studies For conceptual and preliminary design, glide (idle thrust) performance can be calculated at L/Dmax Mission rules typically specify landing fuel reserves in terms of endurance plus a percentage of total fuel For small UAVs we will use a 10% reserve (0.1*Wf) For UAVs operating from manned airfields we will use one hour endurance (Ello = 1 hr) + 5% fuel (0.05*Wf) Landing distance typically is about equal to takeoff Specifying balanced field length for takeoff assures that landing requirements will not be critical See RayAD 17.9 for landing analysis methodology 21-29

1. The weight at the beginning of cruise
Design of UAV Systems Air vehicle performance c LM Corporation Example – cruise range In order to calculate cruise range for the example TBProp UAV we need to know two (2) weights 1. The weight at the beginning of cruise - Which we assume is the weight at the end of climb i.e. we ignore fuel required to accelerate from climb speed (167 kts) to cruise speed (180 kts) 2. The weight at the end of cruise Which we assume is equal to the weight at the beginning of the landing loiter To calculate landing loiter weight, we work backwards from the landing weight (W19) which, by definition is empty weight + Wmisc + landing fuel reserves or W19 = W0 – 0.95Wf = 1960 lbm Which we assume is also the weight at the end of loiter 21-30

Landing loiter and final cruise
Design of UAV Systems Air vehicle performance c LM Corporation Landing loiter and final cruise Best loiter speed at LoDmax = 25.8 and 1821 lbm (W18/Sref = 25) is 98 kts - From Cllo(max) = .768 and q18 = 25/.768 = 32.5 psf or Mlo = and Vlo = 98 kts From the TBProp engine model, sea level TSFC at 98kts is or LoD/SFC = 104.9 The endurance requirement is 1 hour - Fuel required (equation 21.11) is calculated at 17 lbm - Weight at the start of loiter (W18) is 1838 lbm Loiter range factor (RFl0) is calculated at nm By our mission rules W17 = W18 Working backward and forward we now have final and initial cruise weights 21-31

By definition cruise speed is 180 kts at 27.4 Kft
Design of UAV Systems Air vehicle performance c LM Corporation Cruise range By definition cruise speed is 180 kts at 27.4 Kft - W/Sref at the start of cruise = 2145/72.8 = 29.5 psf and L/D = 25.9 - At the end of cruise W/Sref = 1838/72.8 = 25.2 psf and L/D = 23.0 - TSFC at both conditions is and average cruise range factor (RFcr) is nm - Calculated cruise distance = 2109 nm - Climb distance plus cruise distance = 2151 nm Total cruise mission time (less landing loiter) = 11.7 For our operating distance of 200 nm, about 10 hrs of operational loiter will be available vs. 12 hrs specified - Fuel fraction, therefore, needs to increase, the air vehicle needs to be resized and all performance needs to be recalculated This is why from this point on we will use spreadsheets to calculate weights, geometry and performance 21-32

You should now understand Parametric performance, range and endurance
Design of UAV Systems Air vehicle performance c LM Corporation Expectations You should now understand Parametric performance, range and endurance Where they come from How they are used The limits of their applicability 21-33

Start taxi and takeoff fuel Climb performance, fuel, time and distance
Design of UAV Systems Air vehicle performance c LM Corporation Homework Work your way through the example problems in this lesson and check/document the calculations (team grade) Start taxi and takeoff fuel Climb performance, fuel, time and distance Acceleration performance Turn performance Landing loiter fuel Cruise range 2. Calculate initial start/taxi/takeoff fuel required; climb performance, fuel, time and distance; landing loiter and maximum cruise range for your design projects (individual grade) 21-34

Design of UAV Systems Intermission Air vehicle performance
c LM Corporation Intermission 21-34

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