AE 2350 Lecture Notes #9

1. AE 2350 Lecture Notes #9 May 10, 1999

2. We have looked at.. • Airfoil aerodynamics (Chapter 8) • Sources of Drag (Chapter 8, 11 and 12) • Look at the figures on Chapter 11 and 12 • Induced Drag on finite wings (Chapter 9) • Wave Drag, Profile Drag, Form drag, Interference Drag • Airfoil and Aircraft Drag Polar • High Lift Devices (Read Chapter 14)

3. AERODYNAMIC PERFORMACE • Performance is a study to see if the aircraft meets the all requirements. • Level Flight (Is there enough thrust?) • Climb Performance (Will it meet the requirement that the aircraft can gain altitude at a required rate given in feet/sec?) • Range (How far can it fly without refueling?) • Takeoff and Landing Requirements • Others… (e.g. Turn radius, Maneuverability…) • Read Chapter 15

4. Your Fighter Has Certain Requirements • Level Flight at a Maximum Speed of Mach 2 at 30,000 feet altitude. • Range (1500 Nautical Mile Radius with 45 Minutes of Fuel Reserve) • Takeoff (6000 foot Runway with a 50 foot obstacle at the end) • Landing (6000 foot Runway) • Will your fighter do the job?

5. Level Flight Performance • You are doing this in Homework #5 • Steps: • Select a cruise altitude. Compute the speed of sound a • Select a set of M : 0.4, 0.6, 0.8….2.0 • Find Aircraft Speed = M  times a • Assume maximum gross weight GW is given or known. • Find CL = GW / (1/2 * r * V2 * S) • Find CD = CD,0 + CL2/(p AR e) Use a CD,0 of 0.01 below M =0.8, CD,0 of 0.02 at M =1.2, 0.03 at M =1.6. Interpolate CD,0 linearly at other M. . • The quantity ‘e’ is Oswald efficiency factor. Use 0.9. • Find Thrust required = CD * (1/2) * r * V2 * S • Plot Thrust Required vs. Speed • Plot Thrust Available for your Engine at this altitude and Speed (Supplied by Engine Manufacturer) • Where these two curves cross determines maximum and minimum cruise speeds

6. Level Flight Performance Thrust Required Thrust Available with all engines Drag (lbs) Excess Thrust Aircraft Speed (Knots) Best speed for longest endurance flights since the least amount of fuel is burned

7. Maximum Rate of Climb Drag (lbs) • Find Excess Thrust from previous figure. • Excess Power = Excess Thrust times Velocity • This power can be used to increase aircraft potential energy or altitude • Rate of Climb=Excess Power/GW Excess Thrust Aircraft Speed (Knots)

8. Cruise Speed for Maximum Range V L/D Speed for maximum range Aircraft Speed (Knots) From your level flight performance data plot V L/D vs. V As will be seen later, the speed at which V L/D is maximum gives maximum range.

9. Factors that Affect Range We assume that a cruise Mach number and altitude has been selected. For your fighter design, you may choose the cruise Mach number to be whatever you want it to be, between 0.8 and 1.6, since it was not given. Transport aircraft designers usually select the Mach number that maximizes range as the cruise Mach number. Older fighters F-15, F-14 etc. cruise at or below Mach 0.8, to keep the wave drag small, and keep the V L/D high. F-22 and the Eurofighter can cruise at Mach 1.6 without using afterburners. This is called “Supercruise.” While such a high cruise speed is attractive, other aspects of performance suffer. You may end up with a small AR wing to keep wave drag small. A small aspect ratio wing will have excessive induced drag, have a low CLmax, and long takeoff and landing distances.

10. Calculation of Range We have selected a cruise V. Over a small period of time dt, the vehicle will travel a distance equal to V dt The aircraft weight will decrease by dW as fuel is burned. If we know the engine we use, we know the fuel burn rate per pound of thrust T. This ratio is called thrust-specific fuel consumption (Symbol used: sfc or just c). dt = Change in the aircraft weight dW/(fuel burn rate) = dW / (Thrust times c) = dW/(Tc) Distance Traveled during dt=VdW/(Tc) =V [W/T](1/c) dW/W

11. Calculation of Range (Contd…) • From previous slide: • Distance Traveled during dt=V[W/T](1/c) dW/W • Since T=D and W=L, W/T = L/D • The aircraft is usually flown at a fixed L/D. • The L/D is kept as high as possible during cruise. • Distance Traveled during dt= V[L/D](1/c) dW/W

12. Calculation of Range (Contd…) • From previous slide: • Distance Traveled during dt= V[L/D](1/c) dW/W • Integrate between start of cruise phase, and end of cruise phase. The aircraft weight changes from Wi to Wf. • Integral of dx/x = log (x) where natural log is used. • Range = V[L/D](1/c) log(Wi/Wf)

13. Breguet Range Equation Structures & Weights Group/ Designer Responsibility to keep Wf small. Propulsion Group/ Designer Responsibility to choose an engine with a low c Aerodynamics Group/ Designer Responsibility to maximize this factor.

14. Estimating Fuel Weight in Cruise • Given the range, engine fuel consumption c (in lb mass of fuel per hour per lb force of thrust), and V L/D we can find Wi/Wf • Use V L/D at the cruise speed you selected. Use L = GW, D is found from the level flight performance chart you prepared, at this speed. • Assume Wi = 99% of GW since some fuel is used during takeoff. • After you have found Wf, compute Wi-Wf. • This is the amount of fuel used in cruise.

15. Estimating Fuel Reserve • Use Breguet range equation again.Use Range/V = 0.75 hours • Use for Wi, the value Wf at the end of cruise. • Find Wf. Wi - Wf is the reserve fuel.

16. Total Fuel Weight • Total fuel weight is the sum of fuel burned during take-off( ~ 1% of GW), cruise and reserve. • In the previous slides we found fuel burned during cruise, and fuel needed as reserve. • Add these three up to get the total fuel weight.

17. Improved GW Estimate • Until now we only had a guess for GW from historical data. • We can improve this guess, as follows. • Assume a empty weight = Ks * A * (GW)B • Use A= 1.605, B=0.916 if T/GW > 0.9 • Use A = 0.911, B=0.947 if T/GW < 0.9 • T : Maximum Engine Thrust, with afterburners. • This curve fit is from existing data. http://www.aoe.vt.edu • Ks = Technology factor. Use 0.75. A lower value means improved light weight technology (e.g. all composite construction). • Improved GW estimate = Empty Weight + Fuel Weight + Crew Weight + Payload • Use this GW to revise steady flight performance, fuel weight etc. • Iterate: Correct the fuel and empty weight that depend on GW.