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Referred Parameter Turboshaft Engine Model 139
for i =2to I. Another format is a set of I +1break points, with the values at the i-th point (θbi, Kbi).
Then the coefficients between i and i +1are
K0i = Kbiθ b(i+1) − K b(i+1)θbi
θ b(i+1) − θbi
K1i = −Kbi + K b(i+1)
θ b(i+1) − θbi
for i =1to I. The interpolation is performed using K = K0i + K1iθ for θ in the range θbi to θ b(i+1).
Outside the defined regions, the linear expression is continued; hence θbi is used only for i =2to I.
18–7 Performance at Power Required
The engine performance (mass flow, fuel flow, and gross jet thrust) is calculated for a specified power
required Pq (which might equal the power available), flight condition, and engine rating. Installation
losses Ploss are added to Preq (Pq = Preq + Ploss). The referred quantities (relative to SLS static MCP
quantities) are approximated by cubic functions of q = Pq(Nspec)/(P0Cδ √ θ):
˙wreq = ˙w0C
˙mreq = ˙m0C
δ √ θ
δ/ √ θ
Kffq0 + Kffq1q + Kffq2q 2 + Kffq3q 3 [θM ] −Xffq
Kmfq0 + Kmfq1q + Kmfq2q 2 + Kmfq3q 3 [θM ] Xmfq
Fg = Fg0C (δ) Kfgq0 + Kfgq1q + Kfgq2q 2 + Kfgq3q 3 [θM ] Xfgq
at Nspec, with ˙w0C = sfc0CP0C. The mass flow and fuel flow are primarily functions of the gas power PG,
and are assumed to be independent of ηt, hence independent of turbine speed. However, these equations
are functions of Pq(Nspec), obtained from Pq(N) using
Pq(Nspec) =Pq(N) 1 −|(Nspec/Nopt) − 1| XNη
1 −|(N/Nopt) − 1| XNη
Then the installed net jet thrust FN and momentum drag Daux are calculated.
18–8 Scaling
The parameters of the engine model can be defined for a specific engine, but it is also necessary to
scale the parameters as part of the aircraft sizing task, in order to define an engine for a specified power.
In addition, advanced technology must be represented in the model. Scaling and advanced technology
are handled in terms of specific power and specific fuel consumption (at SLS static conditions, MCP,
and Nspec).
The engine model includes reference values of the engine performance parameters: P0R, SP0R,
PmechR, sfc0C, SF0C, Nspec, Nopt0C. Mass flow and fuel flow are obtained from ˙m0R = P0R/SP0R and
˙w0C = sfc0CP0C. The reference power at each engine rating R defines a ratio to MCP: rp0R = P0R/P0C.
Similarly for specific power and mechanical limits: rs0R = SP0R/SP0C, rm0R = PmechR/P0C. These
ratios are kept fixed when the engine is scaled.
The engine size is specified as takeoff power Pto = Peng, which is the power at rating R for SLS
static conditions and specification turbine speed Nspec. Hence the MCP is P0C = Pto/rp0R, and the
power at all other ratings follows.