Aircraft Performance I

7/28/2019 Aircraft Performance I

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Problems in Aircraft Performance Aircraft Performance

as a subject is

concerned with Maximum range Maximum speed Maximum endurance Best rate of climb Minimum takeoff distance Minimum turn radius

etc.

To estimateperformance, we need toknow how aerodynamicforces and propulsiveforces vary with aircraft

velocity.


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Aircraft in Steady, Level FlightFor an aircraft to be in steady ( V = constant ), level

flight, the forces must balance (no accelerations).

Recall that (neglecting compressibility effects)


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Information we may want from this

graph: What is the maximum speed of this aircraft at 35,000

ft?

What is the minimum speed of this aircraft at 35,000ft?

At what speed should the DC-10 fly for maximumrange?

At what speed should the DC-10 fly for maximumendurance?

To answer these, we must know how the DC-10 engineperforms at 35,000 ft.


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DC-10 Powerplant

General Electric CF6-6

High-Bypass RatioTurbofan

Static Thrust at Sea Level: 40,000 lbs

Max Continuous Static Thrust at Sea Level:32,000 lbs

Max Continuous Thrust at 35,000 ft: 9,600 lbs*We will simplify engine performance by assuming thrust doesnot vary with Mach number. In general, thrust decreases asMach number increases, especially at low altitude.


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What is the aircrafts maximum speed at 35,000 ft? Find where T avail = D Hard to tell from the figure. By extrapolation, we estimate

approximately 650 kts.

What is the aircrafts minimum speed at 35,000 ft? About 250 kts according to the figure.

Must consider stalling speed:

Using an estimated C Lmax = 1.5, V stall = 436 ft/s or 258

kts.


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Effect of Compressibility Drag


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We see that the actual maximum cruisingspeed at 35,000 ft is approximately 506 kts ( = 855ft/s = Mach 0.88).

Now we concern ourselves with

how long can the aircraft stay in the air (endurance)?

how far can the aircraft fly (range)?


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Turbofan Aircraft Endurance Let W I be the weight at the start of cruise and W 0 be

the weight at the end of cruise then W I - W 0 is thefuel weight, W f .

In steady, level flight, T = D , but the drag, and hencethe thrust, changes as the weight decreases (as fuelis burned).

If the fuel flow ( cT ) remained constant, we could justdivide to get the total time in hours: ( W I - W 0 )/ cT

However, since the fuel flow does not remainconstant, we have to integrate to get the expressionfor endurance.


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Turbofan Aircraft Endurance, cont.

Using standard units, the expression for endurance isin hours:

Note the following: Arriving at this expression required that C L / C D remains

constant throughout the flight The speed for maximum endurance occurs at minimum

drag. Thus the speed for maximum endurance will changethroughout the flight.

The speed for minimum drag is the same as the speed for maximum C L / C D .


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Example Problem

Estimate the maximum endurance of the DC-10aircraft.

C = 0.6 lb fuel / lb thrust / hr W I = 500,000 lb W 0 = 370,000 lb

You may assume that the L / D remains constantthroughout the flight.


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Turbofan Aircraft Range

The range is the distance traveled on a tank of fuel. To find the range, need to know the specific range:

Note that a unit conversion must be done to get SR in

consistent units. A typical unit for SR is Nmi / lb fuel:

If SR remained constant, we could multiply SR by W f to get total range in Nmi


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Turbofan Aircraft Range, cont. SR does not remain constant because the thrust required

changes as the weight changes (as fuel is burned). Therefore, we must integrate to account for the change in

weight:

This is called the Breguet Range Equation for jets. It assumesthat V and L/D are constant throughout the flight. (Altitude mustchange.)

Note that the formula in the book assumes that the altitude isconstant throughout the flight.

Note that the speed for best range occurs where V L/D ismaximized.


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Example Problem

A DC-10 is begins its cruise at 35,000 feet. It weighs500,000 lbs at the beginning of cruise and 370,000

lbs at the end of cruise. Find the speed for best range for these starting conditions. Find the maximum range of the aircraft. How much time does it take to fly the maximum range?


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Speed for minimum D

Speed for minimum D/V

V

D1tan

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Aircraft Performance I