Introduction

Propellers

Internal Combustion Engines

Gas Turbine Engines

Chemical Rockets

Non-Chemical Space Propulsion Systems

AER 710 Aerospace Propulsion

C-130

Nieuport N.28C-1

Introduction to the Propeller

• The rotating blade of a propeller shares similar characteristics to a wing passing through the air

• A propeller blade generates thrust F through an aerodynamic lift force component, demands an engine torque Q to overcome aerodynamic drag, and will stall if the local resultant angle of attack of the blade exceeds max

• Additional factors: trailing vortex generation, tip losses, compressibility

Martin MB-2

DH-98 Mosquito

Forces acting on wing airfoil section (above) and propeller blade section (below)

• For evaluation of propeller performance, one can apply a simple analytical approach using the principle of linear momentum conservation, and treating the propeller as an actuator disk where there is a step increase in pressure

Actuator Disk Theory

)VV(VA)VV(mF 033303 Thrust generated by disk:

)pp(AF 121 Alternatively:

211

200 2

1

2

1VpVp

Bernoulli’s eq. applied from upstream to front of disk:

233

222 2

1

2

1VpVp

Similarly, downstream of disk:

)VV)(VV()VV(pp 03032

02

312 2

1

2

1

Noting po = p3 , and V2 = V1, via subtraction one gets:

A3V3 = A1V1

Conservation of mass, incompressible flow:

)VV(VA)pp(AF 0333121

Substituting from earlier:

)VV)(VV()VV(VA

App 0303033

1

312 2

1

which gives the simple result:

and

203

1

VVV

wVV 01

Define propeller-induced velocity w such that:

wVV 203

w)wV(A)VwV)(wV(A)VV(VAF 0100010311 22

and so for thrust,

201

20

2001

20

23 22

2

1

2

1

2

1)wV(wA]V)wV)[(wV(AVmVmP

Ideal power required:

)wV(FP 0

or

Since power from a piston or turboprop engine is relativelyconstant at a given altitude, one can expect the thrust todrop as the airplane picks up airspeed, according to thiscorrelation.

022 012

1 Fw)VA(w)A(

If one wishes to find w as a function of F, from earlier:

1

20

0 2

2

1

2 A

FV

Vw

giving

1

23

2 A

FwFPP

/o

ooo,indo

Ideal static power (Vo = 0):

0

0

0

1

1

V

w)wV(F

FVi,pr

Ideal propeller propulsive efficiency:

1

11

2

qA

Fi,pr

or via substitution (q is dynamic pressure):

i,prS

pr P

FV

Actual propeller propulsive efficiency, in terms of useful(thrust) power and engine shaft power PS :

SP)()wV(FP factor correction0

Correction factor, less than 1, for ideal power estimate:

Variable-pitch propeller better able to approach theideal power requirement, as compared to a fixed-pitchpropeller, in accommodating different flight speedsand altitudes.

Exercise

• To propel a light aircraft at an absolute velocity of 240 km/h against a head wind of 48 km/h a thrust of 10.3 kN is required. Assuming a theoretical efficiency of 90% and a constant air density of 1.2 kg/m3 determine the diameter of ideal propeller required and the power needed to drive it. Sketch the velocity and the pressure profile along the slipstream boundary.