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Result: Matching Chart


The following results were saved:

Requirement 1:
Landing field length
Requirement 2:
Takeoff field length
Requirement 3:
Second segment climb
Requirement 4:
Missed approach climb
chart for calculated results
Figure 1: chart for calculated results

In the diagram above, the optimal parameters respectively the match point can be determined as follows:
1.- the thrust to weight ratio should be as low as possible,
2.- the wing loading should be as high as possible without any increase of the thrust to weight ratio.

Some more details:
- the point has to be above (and on the left) of all coloured curves in the matching chart,
- hatching indicates inadmissible side of curves.
The determination of the cruise requirement (black curve) was not shown in this course.
With the intension to get the optimal parameters, a typical cruise condition for a short-range aircraft is shown with the other curves.











 Results compared

Takeoff thrust to takeoff weight ratio and wing loading of selected aircraft JANE'S 1995-98
Aircraft Airbus A 300-600BAirbus A 310-300Airbus A 340-300Antonov AN 124Boeing B 737-600Boeing B 777McDonnell Douglas MD11Tupolev TU 204
Takeoff thrust
Takeoff weight   [ - ]
0.308 - 0.3240.290 - 0.3560.220 - 0.2400.2310.3070.292 - 0.3040.299 - 0.3090.341 - 0.413
Wing loading [kg/m²] 634.6684.9707.8644.9520.7567.2806.4518.6

 
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 Further Aircraft Parameters

Maximum Takeoff Mass

The maximum takeoff mass of the aircraft can be determined according to:

where the maximum payload mMPL (passengers+cargo) is a given requirement, the fuel mass mF is determined with all mission segment mass fractions:

The fractions are:
  m2 /m1 = Engine start + Warm-up, not necessary for the takeoff mass estimation
  m3 /m2 = Taxiing, not necessary for the takeoff mass estimation
  m4 /m3 = Takeoff, determined in a statistic in ROSKAM 1989
  m5 /m4 = Climb, determined in a statistic in ROSKAM 1989
  m6 /m5 = Cruise, calculated with the Breguet factor
  m7 /m6 = Loiter, calculated with the Breguet factor
  m8 /m7 = Descent, determined in a statistic in ROSKAM 1989
  m9 /m8 = Landing, determined in a statistic in ROSKAM 1989.

The operating empty mass mOE is calculated according to a statistic from LOFTIN 1980 as follows:
.

Operating Empty Mass, Fuel Mass, Takeoff Thrust, Wing Area

With the mass above all other parameters can be calculated with the following equations:
operating empty mass:fuel mass:takeoff thrust:wing area:

 
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 Calculation

Finally, with the parameters determined in the diagram the calculation can be done with several assumptions:
- the passenger + baggage mass is 93 kg for short & middle range, 97.5 kg for long range (ROSKAM 1989),
- Specific fuel consumption SFCT is taken from statistics, e.g. JANE'S 1995-98,
- (L / D)max is given. An estimation procedure for (L / D)max has not been programmed for this module.
- The loiter time t is 45 minutes for range less than 3000 N.M.(5600 km), then 30 minutes plus 10% of the flight time,
- 200 NM (370.4 km) will be added to the range to reach an alternate airport (FAR Sec. 125.377).

Typical start values for a short-range aircraft are already entered in the tables.
calculation:
maximum payload
nPAX × mPAX + mCARGO
× 93 kg +  [ kg ]
97.5 kg
= mMPL
= kg
 
max. takeoff thrust to weight:
=  [ - ]
range of aircraft:
sCR =   [ km ]
(370.4 km will be added)
mission segment fuel mass fractions:
takeoff m4 /m3  [ - ]
climb m5 /m4  [ - ]
descent m8 /m7  [ - ]
landing m9 /m8  [ - ]
wing loading:
=  [ kg/m² ]
specific fuel consumption:
SFCT =  [ mg/N/s ]
Mach number  [ - ] in cruise height  [ km ] lift to drag: (L / D)max =  [ - ]
maximum takeoff mass :  [ kg ] takeoff thrust :  [ kN ] wing area :  [ m² ]
operating empty mass :  [ kg ] mission segment mass fractions:
fuel mass :  [ kg ] loiter m7 /m6: cruise m6 /m5:

 Results compared

Comparison parameters of selected aircraft JANE'S 1995-98
Aircraft Airbus
A 300-600B
Airbus
A 320-200
Airbus
A 340-300
Antonov
AN 124
Boeing
B 737-600
Boeing
B 777
Cessna 525
CitationJet
Learjet
60
McDonnell
Douglas MD11
Tupolev
TU 204
Max. Takeoff mass [ kg ] 165000735002570004050006509022952047171065927328994600
Takeoff thrust [ kN ] 498 - 524222.4 - 235.8555.2 - 604.8916195.8658 - 684 16.9 40.92 801 - 828316.6 - 383.4
Wing area [ m² ] 260122.4363.1628125427.822.3024.57338.91182.4
Max. operating
empty mass [ kg ]
9006741908126873175000364411355802856655913016558300
Max. fuel mass [ kg ] 4978619159N/AN/AN/A9421014603588N/A24000

 
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© 1999 mail Thomas Perthel, thomas.perthel@gmx.de