initialSizing.md



Implemented Aircraft Sizing Methods and Models

Initial Takeoff Mass Estimation (MTOM)
The MTOM is initially iterated from Top Level Aircraft Requirements (TLARs), user assumptions and certification requirements.
Methods
Like its name suggests, the Payload is the mass that pays for a trip. It is calculated from the number of passengers (PAX) and additional cargo requirement.
It is a fixed value for the whole iteration.
For the determination the following parameters from the acXML are necessary:

acXML:


Number of PAX  [-]
Mass per person   [kg]
Luggage per PAX  [kg]
Additional cargo mass  [kg]

The Crew mass is not part of the payload but once determined it is also a fixed value for the iteration of the MTOM.
The crew mass is dependent on the different seating classes (FC, BC, EC) and number of PAX in each class the aircraft shall have.
Furthermore, the certification requirements define the number of pilots.
For the determination the following parameters are necessary:

acXML:


Number of PAX in each class  [-]
Mass per person  [kg] and luggage per crew are the same than for the passengers


initialSizing_conf:


Number of pilots  [-]


in source code:


Ratio for flight attendants per PAX amount in each class  [-]: e.g. 1 Flight Attendant per 14 PAX in FC, 1 per 40 in EC

The fuel which is needed for individual mission segments is not calculated in absolute values but as mass fractions from the total remaining fuel. The fuel fractions of the cruise segment, the reserve needed to the flight to an alternate distance and the reserve for a holding time are calculated with the Breguet equation.
For the determination the following parameters are necessary:

acXML:


Design range  [m]
Crusie flight speed [\frac{m}{s}]: automatically calculated from the design mach number
Contingency  [-]: percentage for the reserve of the trip fuel (the fuel necessary for the design range without reserves)
Cruise flight altitutde  [m]: to calculate the air density


initialSizing_conf:


SFC of the engine with regard to fuel type  [-]
Glide Ratio \frac{L}{D}_{cr} in cruise  [-]: Initial assumption given by user
Glide Ratio \frac{L}{D}_{loi} in Loiter  [-]: Initial assumption given by user

The fuel fractions (i.e. engine warm up, taxi, takeoff, climb....) are set as an static input by the user in the config file.
Together with the fuel fractions from the segments calculated with the Breguet equation, the overall fuel fraction of the aircraft is calculated.
In this way of calculating the necessary fuel, the method and also the same static fuel fractions are applicable for various aircraft sizes.
The MTOM is calculated in an iteration because the absolute amount of fuel and the Operating Mass Empty (OME) or (m_e) changes with the aircraft MTOM (m_0).
The initial value for MTOM to start the MTOM iteration is estimated with a simple formula depending on the payload and a static factor only.
For the OME a mass ratio \frac{m_e}{m_0} is used in order to take into account the total aircraft size. Larger aircraft usually have a smaller \frac{OME}{MTOM} ratio.
In each iteration a new \frac{m_e}{m_0} ratio is calculated. Together with the fuel mass fraction, the payload and the crew mass the MTOM is determined. This iteration goes on until the convergence criteria is reached.

Initial Constraint Analysis - Sizing Chart
A constraint analysis is conducted in order to set the initial Design Point for the aircraft. The Desing Point is defined as a wing loading \frac{m_0}{S} and thrust to weight ratio \frac{F}{m_0 \cdot g}.
The constraint analysis is a method to make sure Top Level Aircraft Requirements and certification requirements will be fulfilled by the designed aircraft.
For this a sizing chart is determined and printed by the module.
Methods
The Takeoff constraint makes sure to respect the takeoff field lengt TLAR.
For the determination the following parameters are necessary:

acXML:


Takeoff field lenght (TOFL)  [m]


initialSizing_conf:


Number of engines  [-]: is used to set an engine proportional factor

CL_{takeoff}  [-]

The Climb constraint makes sure to respect the climb ability in the 2nd segment with one engine inoperative (OEI) by the certification standards.
For the determination the following parameters are necessary:

acXML:


Minimum climb angle  [rad]: according to the certification standards and the total number of engines

\frac{L}{D}_{climb}  [-]: with the highlift system in the state of the 2nd climb segment


in source code:


Mass ratio \frac{m_{climb}}{m_0}  [-]

The Cruise Flight constraint makes sure to respect the design cruise speed and altitude TLAR.
For the determination the following parameters are necessary:

initialSizing_conf:


C_{feq}  [-]: Equivalent friction coefficient to estimate parasetic drag coefficient
Oswald efficency factor e  [-]
Wing Aspect Ratio  [-]


in source code:


Thrust ratio \frac{F_{total}}{F_{cruise}}  [-]

\frac{S_{wet}}{S_{ref}} ratio  [-]: Ratio of wetted surface to wing reference area to estimate parasetic drag coefficient
Mass ratio \frac{m_{cruise}}{m_0}  [-]

The Landing constraint makes sure to respect the maximum approach speed TLAR.
For the determination the following parameters are necessary:

acXML:


v_{appr}  [\frac{m}{s}]: Approach speed TLAR


initialSizing_conf:


CL_{Landing}  [-]
Mass ratio \frac{m_{land}}{m_0}  [-]

These constraints open up the design or sizing window of the aircraft where it can fulfill the TLARs and certification standards.

Initial Constraint Analysis - Design Point
The constraints from the section before open up the design or sizing window, where the aircraft can fulfill the TLARs and certification standards.
Selecting the optimal design point within the window is again dependent on various requirements and the constellation of the design window itself.
This would be quite complex to implement in the module. In order to keep the module and the methods simple, only the borders of the desing window are investigated - since in many cases they deliver an optimal design point.
In general, a design point with a wing loading as high as possible and a thrust to weight ratio as low as possible is a good choice.
Methods

This investigation is done by calculating the intersections of the borders.
It is checked how many intersection points of constraints the borders of the desing window has.
It is checked if the CL_{optimal} is within the design window. CL_{optimal} is a user input in the initialSizing_conf.xml and describes the design lift coefficient at initial cruise speed and altitude.
If CL_{optimal} is in the design window the intersection of CL_{optimal} and the design window border is used as design point.
If CL_{optimal} is not in the design window and there is only one intersection from borders in the window this intersection is used as design point.
If CL_{optimal} is not in the design window and there are two intersection from borders in the window, an interpolated point between these two is used as design point.