AE 1350 Lecture Notes #9

We have looked at..

• Airfoil aerodynamics (Chapter 5)• Sources of Drag (Chapter 5)• Induced Drag on finite wings (Chapter 5)• Wave Drag, Profile Drag, Form drag• Airfoil and Aircraft Drag Polar• High Lift Devices

AERODYNAMIC PERFORMACE• Performance is a study to see if the aircraft meets all the requirements.• Level Flight (Is there enough thrust and/or power?)• 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…)• You will learn to evaluate aircraft performance in AE 3310.• Performance engineers are hired by airlines, buyers, and aircraft

companies.

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?

Your transport aircraft has certain requirements, say..

– Payload:150 passengers weighing 205 lb. each including baggage.

– Range:1600 nautical miles, with 1 hour reserve.– Cruise Speed: M=0.82 at 35,000 feet.– Takeoff/Landing: FAR 25 field length

– 5000 feet at an altitude of 5,000 feet on a 95 degrees F day.– Aircraft should be able to land at 85% of Take-off weight

• Performance calculation is the process where you determine if your design will do the job.

Level Flight Performance• We assume that the gross weight GW is available. You will know this for your

aircraft after Homework Set #4. An estimate of wing area S is assumed to be known (Homework, later in the course).

• Select a cruise altitude. Compute the speed of sound • Select a set of M : 0.4, 0.6, 0.8….• Find Aircraft Speed = M times a

• Find CL = GW / (1/2 * * V2 * S)

• Find CD = CD,0 + CL2/( AR e) (this info is given in our course)

• Find Thrust required T = CD * (1/2) * * V2 * S

• Plot Power Required (T times V) or thrust required vs. Speed • Plot Power Available for your Engine (number of engines times T times V) or thrust

available at this altitude and Speed (Supplied by Engine Manufacturer)• Where these two curves cross determines maximum and minimum cruise speeds.

1.4 where RTa

Level Flight Performance

Aircraft Speed (Knots)

PowerHP

Power Required

Power Availablewith all engines

Best speed for longest endurance flightssince the least amount of fuel is burned

Excess Power

Maximum Rate of Climb

• Find Excess Power from previous figure.

• This power can be used to increase aircraft potential energy or altitude

• Rate of Climb=Excess Power/GW

Aircraft Speed (Knots)

PowerHP

Excess Power

Absolute Ceiling

• Absolute ceiling is the altitude at which Power available equals power required only at a single speed, and no excess power is available at this speed.

• Rate of climb is zero. Aircraft Speed (Knots)

PowerHP

Power available

Powerrequired

Equilibrium Gliding Flight

Glide Angle, W cos = LW sin = D

D

W

L

Flight Path

Gliding Distance

Glide Angle,

Flight Path

Ground

Altitude h

Gliding Distance = h/tanh * L/D

Gliding Flight

• D=W sinwhere is the equilibrium glide angle. • L= W cos• Tan = D/L• Glide distance = h/ tan = h ( L/D).

Cruise Speed for Maximum Range

Aircraft Speed (Knots)

V L/D

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 maximumgives maximum range.

Speed for maximum range

Calculation of RangeWe 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 rateper pound of thrust T. This ratio is called thrust-specificfuel 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=VdW/(Tc) =V [W/T](1/c) dW/W

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

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)

Breguet Range Equation

final

initiale WW

DLV

cRange log 1

Propulsion Group/Designer Responsibilityto choose an enginewith a low specificfuel consumption c

Aerodynamics Group/Designer Responsibilityto maximize this factor.

Structures & WeightsGroup/Designer Responsibilityto keep Wfinal small.