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

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 300-600B	Airbus A 310-300	Airbus A 340-300	Antonov AN 124	Boeing B 737-600	Boeing B 777	McDonnell Douglas MD11	Tupolev TU 204
Takeoff thrust Takeoff weight [ - ]	0.308 - 0.324	0.290 - 0.356	0.220 - 0.240	0.231	0.307	0.292 - 0.304	0.299 - 0.309	0.341 - 0.413
Wing loading [kg/m²]	634.6	684.9	707.8	644.9	520.7	567.2	806.4	518.6

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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 m_MPL (passengers+cargo) is a given requirement, the fuel mass m_F 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 m_OE 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 SFC_T 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

n_PAX ×	m_PAX	+ m_CARGO
×	93 kg	+ [ kg ]
×	97.5 kg	+ [ kg ]

= m_MPL
= kg

max. takeoff thrust to weight: = [ - ]	range of aircraft: s_CR = [ 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: SFC_T = [ 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 ] 165000 73500 257000 405000 65090 229520 4717 10659 273289 94600

Takeoff thrust [ kN ] 498 - 524 222.4 - 235.8 555.2 - 604.8 916 195.8 658 - 684 16.9 40.92 801 - 828 316.6 - 383.4

Wing area [ m² ] 260 122.4 363.1 628 125 427.8 22.30 24.57 338.91 182.4

Max. operating
empty mass [ kg ] 90067 41908 126873 175000 36441 135580 2856 6559 130165 58300

Max. fuel mass [ kg ] 49786 19159 N/A N/A N/A 94210 1460 3588 N/A 24000

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 ]	165000	73500	257000	405000	65090	229520	4717	10659	273289	94600
Takeoff thrust [ kN ]	498 - 524	222.4 - 235.8	555.2 - 604.8	916	195.8	658 - 684	16.9	40.92	801 - 828	316.6 - 383.4
Wing area [ m² ]	260	122.4	363.1	628	125	427.8	22.30	24.57	338.91	182.4
Max. operating empty mass [ kg ]	90067	41908	126873	175000	36441	135580	2856	6559	130165	58300
Max. fuel mass [ kg ]	49786	19159	N/A	N/A	N/A	94210	1460	3588	N/A	24000

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Thomas Perthel, thomas.perthel@gmx.de