The prediction of engine

Data for Podded Engine Configuration Cruise Bypass Ratio: ~22 to 1 Supplied by: Bill Baumgarten email: baum@lerc.nasa.gov phone: 216-977-7028 fax: 216-977-7008 Gross Fuel Mach Alt (ft) Thrust (lb) Ram Drag (lb) Flow (lb/hr) ---- -------- ----------- ------------- ------------ .00 .0 59334.7 .0 11556.5 .00 1000.0 58164.7 .0 11343.1 .20 .0 62043.4 17912.2 11411.0 .20 1000.0 60799.7 17415.0 11208.9 .30 .0 73533.5 29215.8 12920.8 .30 5000.0 64696.5 24966.7 11461.6 .40 .0 80672.7 40829.4 13061.2 .50 5000.0 78503.4 45889.6 11831.9 .50 10000.0 68136.0 38817.7 10492.2 .50 15000.0 58314.5 32499.4 9086.2 .60 5000.0 86144.1 57699.6 11654.6 .60 10000.0 75650.1 49094.9 10605.0 .60 20000.0 55407.5 34290.4 8094.5 .60 25000.0 46891.5 28349.2 6951.5 .70 20000.0 62948.0 42693.5 8516.2 .70 25000.0 53045.0 35239.8 7304.2 .70 30000.0 44491.0 28881.7 6284.6 .80 25000.0 60633.0 43273.9 7749.4 .80 30000.0 50746.4 35475.2 6646.4 .80 35000.0 41534.9 28546.1 5608.5 .85 25000.0 64990.1 47773.9 8000.8 .85 30000.0 54213.7 39112.2 6836.6 .85 35000.0 44538.0 31564.1 5792.8 .85 40000.0 35235.8 24897.0 4614.1Existing analyses in Subroutine Engine have a quadratic fit for

TSFC

where

An array [MH] is constructed with column entries:

1 M Mwhere M is taken from the first column of data listed above, and h is taken from the second column. [MH] will have 24 rows, one row for each line of data. Vector {a} has 6 rows, one for each coefficient in the Thrust equation, and vector {T} has 24 rows, with each entry formed by subtracting the entry in Column 4 of the data table from the entry in Column 3. The normal equations are formed by introducing [MH]^{2}h h^{2}M*h

[MH]

This system is then solved for the optimal coefficients {a}.

A Matlab m-file has been written to solve this problem (listed here ).

The resulting curves for Thrust and TSFC are shown below. (Note that curves are extrapolated beyond the original data set, to low altitude/high Mach Number and high altitude/low Mach Number regions, and predictions are less reliable in these areas). The maximum error in Thrust is 4.4%, so accuracy should be adequate for preliminary design. (Initially a quartic fit was attempted, in the hope that greater accuracy would be achieved with the higher-order approximation. Matlab could not produce an accurate solution, because the system of equations was near-singular.)

The fragment of Subroutine Engine which uses the new quadratic fits for the BWB engine is listed here:

if (Type.eq.0) then c BaseEngine has SLSTH = 58540 lb, SLSsfc = 0.196 h = alt/10000. Thrustavail = 1.e4 * (5.854 - 6.7511 * Mach + 4.2499*Mach*Mach > - 0.6709 * h + 0.0365 * h*h + 0.0044*h*Mach) TSFC = 1.e4*(1.1459 + 0.3117*Mach + 0.0166*Mach*Mach > - 0.2851*h + 0.0092*h*h + 0.0120*h*Mach)/ThrustAvail ThrustAvail = ThrustAvail * SLSTH/58540. * Neng TSFC = TSFC * SFCratio end ifSubroutine Engine has also been modified to read 1 new database variables: