Aircraft Propulsion

Propellers

Piston Engines

Thrust Equation

Turbojet Engines

MAE 155A

Curtis Wright R-2600

2MAE 155A

Propellers

The propeller is made up of a series of rotating wings or “blades”.

Propeller theory is more complex than simple wings.

The blades may have complicated shapes that vary with span.

The aerodynamic flow around each blade may interact.

r

V∞r

V∞

Airflow direction over propeller blade

Velocity from propeller rotation

Propeller blade pitch angle

Freestream velocity

r=blade radial position= propeller angular velocity=r=blade pitch angle

3MAE 155A

Propeller Forces

Engine power is used to overcome drag forces on the propeller blades.

Lift from each propeller blade creates a thrust force to propel the airplane forward.

r

V∞

dTdL

dD

dT=dL cos−dD sin

=−

dL=lift incrementdD=drag incrementdT=thrust force

dQ=torque increment

dT=dL cos−−dD sin −

Recall that lift and drag are defined relative to the local velocity vector

dQ=r [dLsin −dDcos − ]

4MAE 155A

Propeller Efficiency

The propeller efficiency is the ratio of power available from the propeller (to move the airplane) to the power delivered by the engine.

=T AV ∞

P

= propeller efficiencyT A=thrust available move airplane

V∞=airspeedP=engine shaft brake power

Define power and thrust coefficients as follows:

cP=P

n3D5cT=

T A

n2D4

cT=thrust coefficient

cP= power coefficient

=atmospheric densityD= propeller diameter

=2n= propeller angular velocityJ=advance ratio

=T AV ∞

P=n2D4cT V ∞

n3D5cP= cTcP V∞

n D = cTcP J J= V ∞n D

5MAE 155A

Example Propeller Charts

Advance Ratio (1/rev)

Advance Ratio (1/rev)

Effi

cien

cy

Thr

ust C

oeffi

cien

t

McCormick, B.W., Aerodynamics,Aeronautics, and Flight Mechanics, Wiley, 1979.

6MAE 155A

Piston Engines

A reciprocating engine produces power by moving a piston inside a cylinder.

A typical engine has intake, compression, power (ignition), and exhaust strokes.

A normally aspirated engine (no turbo or supercharger) loses power as altitude increases.

A turbo- or super-charged engine maintains constant power up to a critcal altitude of about 20,000 ft.

Below critical altitude:

Above critical altitude:

P=PSL[ SL

− 17.75 1−

SL ]≃PSL SL

P≃PSL

P≃PSL crit

P=engine power at altitudeP SL=engine power at sea level

=density at altitudeSL=density at sea level

=density at altitudeSL=density at critical altitude

7MAE 155A

Thrust Equation

A jet engine produces thrust by taking a small amount of air and giving it a lrage increase in velocity (thereby changing its momentum).

The thrust equation is obtained by considering changes in momentum of the airflow entering and exiting the engine.

V a V e

Ae

pape

T=mairm fuel V e−mairV a pe Ae− pa Aa

T=net thrustmair=airmass flow

m fuel= fuel mass flow

Ve=exit velocity

pe=exit static pressure

Ae=exit area

V a= freestream velocity

pa=ambient static pressure

Diff

use

r

Com

pre

sso

r

Bu

rne

r

Tur

bin

e

Noz

zle

Aa

8MAE 155A

Jet Engine Types

A turbojet has all inlet air passing through the combustion area of the engine.

The thrust of a turbofan engine is a combination of thrust produced by fan blades and jet thrust produced from the exhaust nozzle.

The ratio of the weight of air bypassing the combustion area to total weight of air entering the engine is called the bypass ratio.

A turboprop uses a gas turbine to drive a propeller.

Both the turbofan and turboprop impart momentum to greater volumes of air that a turbojet, but the velocity added to the air is less.

9MAE 155A

Turbojet Example

The mass flow of fuel is usually small compared to the mass flow of air.

JetCat P80-SE Turbojet

Idle Rotational Speed 35,000 rev/minMax Rotational Speed 125,000 rev/minIdle Static Thrust 3 NMax Static Thrust 97 NIdle Fuel Consumption 0.075 kg/minMax Fuel Consumption 0.233 kg/minAir Mass Flow Rate 0.25 kg/sExhaust Gas Temperature 510 – 700 CExhaust Gas Velocity 1397 km/hrPressure Ratio 2.4

T≃mairV e=0.25 kgs 1397 kmhr hr3600 s 1000mkm s2Nkg m =97 N=22 lbstatic thrust:

T=mair V e−V a pe Ae− pa Aa

10MAE 155A

Pratt & Whitney JT4A-3 Turbojet

McC

orm

ick,

B.W

., A

ero

dyn

am

ics,

Ae

ron

aut

ics,

and

Flig

ht

Mec

ha

nics

, Wile

y, 1

979

.

Sea Level 45,000 ft