AER 710 Aerospace Propulsion
Introduction
Propellers
Internal Combustion Engines
 Gas Turbine Engines (TPs, TSs)
Chemical Rockets
Non-Chemical Space Propulsion Systems
Lockheed C-130 Hercules
Sikorsky CH-54A Tarhe (“Skycrane”) powered by 2
4000-hp P & W T73-P-1 turboshaft engines
Introduction to Turboprop & Turboshaft Engines
• Both turboprop [TP] and turboshaft [TS] engines
use a gas turbine core engine to drive an output
power shaft for a propeller or helicopter rotor
• The main difference between the two variants is
that a TP engine might also produce a fraction of
its overall thrust via a hot core exhaust jet, while a
conventional TS engine will have a lower exhaust
velocity but correspondingly somewhat higher
shaft power as the tradeoff
• TPs commonly employ a free power turbine to
drive the speed reduction gear that in turn drives
the propeller at a lower rotation speed. This is
typically also true for TS engines, in driving the
main rotor at a significantly lower rotation speed
PT-6
Schematic cutaway diagram of a free-turbine two-spool (LP/HP
core)/three-shaft turboprop engine. Note the reverse flow arrangement
relative to the propeller at left, as a means of avoiding foreign object
damage to the compressor, combustor or turbine, and a means for more
convenient on-wing hot-section (combustor, turbine) maintenance
Schematic cutaway diagram of a fixed single-shaft turboprop engine. The
example engine drive shaft may run at around 40000 rpm, while the
propeller shaft rotates at around 2000 rpm
Overall thrust given by a TP engine driving a propeller :
F overall  F prop  F jet
net

 pr Ps
V
 m a ([ 1  f ] V e ,  V  )
One can define an equivalent power Peq that nominally
comprises both the shaft and jet power contributions:
Peq  Ps 
F jet V 
 pr
 Ps 
m a V 
 pr
([ 1  f ] V e ,  V  )
In the static case (V = 0), no singularity present in solution:
Peq  Ps ,o 
F jet ,o
F o , prop
Ps ,o  Ps ,o ( 1  m a ( 1  f )V e , / F o , prop )
To avoid the singularity issue at finite airspeeds, assume:
Peq  Ps ( hp ) 
F jet ( lb )
2. 5
, hp
assuming 2.5 lb of thrust per horsepower is a reasonable
estimate.
Note that the core jet power can be as much as 20% of
the equivalent power in the static sea-level case, but will
drop to less than 5% at cruise conditions, for those TPs
that utilize a significant portion of the exhaust jet energy
for thrust.
Cycle Analysis of Free-Turbine Turboprop
• As noted for previous gas turbine variants, some of the
baseline equations for turbojet cycle analysis can be
utilized for the turboprop (and turboshaft) case
• Here, let’s look at the one-spool/two-shaft TP engine for
introducing the cycle analysis that can be applied for this
category of engine. The approach for a turboshaft engine
will be similar, with differences noted as we proceed.
• the power output of the LP free turbine (to the speed
reduction gearbox) can be estimated as follows:
Ps   m m t C p ,t ( T 04 .5  T 05 )
The upstream HP turbine must drive the main compressor,
such that:
m a C p ,c ( T 03  T 02 )   m m t C p ,t ( T 04  T 04 .5 )
so that
T 04 .5  T 04 
p 04 .5  p 04 [ 1 
1
m
1
t
( T 03  T 02 )
(1 
T 04 .5
T 04
t
)]
 t 1
Downstream:
T 05  T 04 .5 
Ps
 T 04 .5 
 m m t C p ,t
Ps / m a
 m C p ,t
Recall power demanded by prop:
Ps  C p  n d
3
5
and resulting propeller thrust:
F prop  C T  n d
2
4

 pr C p
n d
2
4

J
 pr PS
V
Once T05 known, can find p05 :
p 05  p 04 .5 [ 1 
1
t
(1 
T 05
T 04 .5
t
)]
 t 1
For the case of a turboshaft engine desiring the ideal
maximum shaft power output,
p 05  p 
Ma e  0
T 05  T e
where for this ideal case,
T e ,ideal
TS
 T 04 .5 { 1   t [(
p
 t 1
)
t
 1 ]}
p 04 .5
For specific power:
Ps
m a
ideal TS
  m C p ,t ( T 04 .5  T e )
In practice, one will likely need Mae to be at least 0.3 in
order for adequate positive throughput of flow (avoiding
transient backflow). In the general (non-ideal) case for
either a TP or TS, specific power becomes:
Ps
m a
TP, TS
  m C p ,t ( T 04 .5  T 05 )
For power-based fuel economics, one uses brake
specific fuel consumption:
BSFC 
m f
Ps

f
Ps
m a
Let’s continue the cycle analysis:
In the typical case that a TP (or TS) would not be using
an afterburner, one can transfer flow property values
immediately from station 5 to station 6 for the nozzle
entry.
The TP’s core exhaust jet is usually unchoked, such that
for a simple convergent nozzle with station 7 as the exit
plane,
p7  p
T7
(
T 06
7 
V e , 
p
 n 1
)
n
p 06
p
RT 7
2 n C p ,n T 06 [ 1  (
p
p 06
 n 1
)
n
]
A e ,  A e
TP or TS thermal efficiency:
 th 
Ps
m f q R

1
BSFC  q R
TP or TS overall efficiency:
 o   pr  th
Shaft power chart for example turboprop engine (maximum cruise
power throttle setting). Engine performance comparable to Pratt &
Whitney PW120, compression ratio c of 12
Shaft static power chart for example turboprop engine (full takeoff
power throttle setting) for takeoff at different outside air
temperatures and airfield altitudes. Engine performance comparable
to Pratt &Whitney PW120 at takeoff throttle setting
Photos of wing-mounted Kuznetsov NK-12 turboprop engines installed on
Tupolev Tu-95MS Bear. Note the use of contra-rotating (4 + 4 blades)
propellers, and rearward-directed exhaust, to maximize thrust from each
engine.
Rolls-Royce T56 turboprop engine being operated on an outdoor test
rig. The reduction gear unit that ultimately rotates the propeller is
positioned well ahead of the main body of the turboprop engine
Pratt & Whitney Canada PT6T twinned turboshaft engine in position on
the upper fuselage of a Bell CH-146 Griffon helicopter