design_method.md



Calculation method

Determination of cabin geometry
Determination of fuselage geometry
Estimation of masses
Generation of fuselage shape

!!! note
Currently the tool supports only one fuselage with one payload tube.

Determine cabin geometry {#cabin-geometry}

Cabin width
The cabin width is estimated using the given class definition.

Determine width of seat row per aircraft side
The width of one seat row/bench w_{\text{bench}} (in inch) can be determined for the left and right side of the aircraft using the following equation:

w_{\text{bench}} = n_{\text{seats}} \cdot w_{\text{seat}} + 2 \cdot w_{\text{armrest}}

In which


n_{\text{seats}} - number of seats per seat bench

w_{\text{seat}} - seat width (taken from lowest class seat)

w_{\text{armrest}} - armrest width (taken from lowest class seat)


Calculate cabin width
The cabin width w_{\text{cabin}} (in inch) can then be calculated:

w_{\text{cabin}} = w_{\text{aisle}} + w_{\text{bench,left}} + w_{\text{bench,right}} + 2 \cdot w_{\text{seat space}}

In which


w_{\text{aisle}} - passenger aisle width

w_{\text{seat space}} - lowest class seat space

In case of a wide-body aircraft configuration there is an additional row in the middle of the aircraft as well as an additional passenger aisle. The width of the seat bench w_{\text{bench,center}} can be calculated using an equation similar to that in the previous section.

w_{\text{bench,center}} = n_{\text{seats}} \cdot w_{\text{seat}} + 2 \cdot w_{\text{armrest,outer}} + (n_{\text{seats}} - 1) \cdot w_{\text{armrest,inner}}

In which


w_{\text{seat}} - seat width (from lowest class seat parameters of right side)

w_{\text{armrest,outer}} - width of outer armrest (from lowest class seat parameters of right side)

w_{\text{armrest,inner}} - width of inner armrest (from lowest class seat parameters of right side)

The equation for the cabin width estimation must be adapted accordingly:

w_{\text{cabin}} = w_{\text{aisle}} + w_{\text{bench,left}} + w_{\text{bench,right}} + 2 \cdot w_{\text{seat space}} + w_{\text{aisle}} + w_{\text{bench,center}}


Cabin slenderness ratio ^[1]

The cabin slenderness ratio describes the ratio of cabin width to cabin length and can be determined using the following equation:

\frac{w_{\text{cabin}}}{l_{\text{cabin}}} = \frac{n_{\text{PAX per class}}}{ab} \cdot \left[ sp + \frac{a_{\text{service}}}{w_{\text{seat}}} + \frac{a_{\text{bulk}}}{\frac{w_{\text{aisle}}}{ab} + w_{\text{seat}}} + x \cdot w_{\text{exit}} \cdot \left( \frac{ab}{n_{\text{PAX per class}}} + \frac{sp}{d_{\text{exits}}} \right)  \right]

In which


x - factor (1 for single-aisle, 2 for wide-body)

n_{\text{PAX per class}} - number of PAX per class

ab - seat abreast

sp - seat pitch

a_{\text{service}} - service area per PAX

a_{\text{bulk}} - bulk area per PAX

w_{\text{exit}} - exit width

d_{\text{exits}} - maximum distance between two exits


Cabin length
Knowing the cabin width and the cabin slenderness ratio, the cabin length (in inch) can be calculated:

l_{\text{cabin}} = \frac{w_{\text{cabin}}}{\frac{w_{\text{cabin}}}{l_{\text{cabin}}}}


Cabin wall thickness
The cabin wall thickness can be estimated using the following calculation:

t_{\text{wall}} = 0.02 \cdot w_{\text{cabin}} + 2.5"


Cabin floor thickness
With the use of the cabin wall thickness, the cabin floor thickness can be calculated:

t_{\text{floor}} = 1.5 \cdot t_{\text{wall}}


Determine fuselage geometry {#fuselage-geometry}
With the calculated cabin the fuselage dimensions can be estimated.

Fuselage length^[2]

The fuselage length can be determined via regression formulas using the cabin length (in meter).
For single-aisle aircraft:

l_{\text{fuselage}} = \frac{l_{\text{cabin}}}{0.23482756 \cdot \log l_{\text{cabin}} - 0.05106017}

For wide-body aircraft:

l_{\text{fuselage}} = \frac{l_{\text{cabin}}}{0.1735 \cdot \log l_{\text{cabin}} - 0.0966}


Fuselage diameters
The fuselage does not necessarily have a circular cross-section. It is more common to design elliptical cross-sections. Because of that, there are several values that must be determined:

Fuselage diameter in y-direction
Fuselage diameter in negative z-direction
Fuselage diameter in positive z-direction


Fuselage diameter in y-direction
The fuselage diameter in y-direction d_{\text{fuselage,y}} can be calculated in the following way:

d_{\text{fuselage,y}} = w_{\text{cabin}} + 2 \cdot t_{\text{wall}}


Fuselage diameter in negative z-direction
The fuselage diameter in negative z-direction d_{\text{fuselage,z,neg}} is determined by the cargo accommodation. It can be calculated in the following way.
At first, the distance to the cargo bottom is calculated:

d_{\text{to cargo bottom}} = h_{\text{ULD,max}} + t_{\text{floor}} + d_{\text{container to ceil}} + o_{\text{cabin floor}}

In which


h_{\text{ULD,max}} - maximum height of unit load device

t_{\text{floor}} - floor thickness

d_{\text{container to ceil}} - distance from the container to the ceiling

o_{\text{cabin floor}} - offset cabin floor

Afterwards, the distance to the lower compartment edge is estimated:

d_{\text{to lower compartment edge}} = d_{\text{container to wall}} + 0.5 \cdot w_{\text{base,max}}

In which


d_{\text{container to wall}} - distance from container to wall

w_{\text{base,max}} - maximum width at container base

Based on the Pythagorean theorem, the inner fuselage diameter (that equals the hypotenuse) can be calculated:

d_{\text{fuselage,z,neg,inner}} = \sqrt{(d_{\text{to cargo bottom}})^2 + (d_{\text{to lower compartment edge}})^2}

Adding the wall thickness results in the fuselage diameter in negative z-direction:

d_{\text{fuselage,z,neg}} = d_{\text{fuselage,z,neg,inner}} + t_{\text{wall}}


Fuselage diameter in positive z-direction
The fuselage diameter in positive z-direction d_{\text{fuselage,z,pos}} is determined by the passenger accommodation. It can be calculated in the following way.
Firstly, the inner fuselage height (equals outer cabin height) can be determined:

d_{\text{fuselage,z,pos,inner}} = h_{\text{aisle,standing}} - o_{\text{cabin floor}} + h_{\text{system bay}}

In which


h_{\text{aisle,standing}} - passenger aisle standing height

o_{\text{cabin floor}} - cabin floor offset

h_{\text{system bay}} - system bay height above cabin

Adding the wall thickness leads to the fuselage diameter in positive z-direction.

d_{\text{fuselage,z,pos}} = d_{\text{fuselage,z,pos,inner}} + t_{\text{wall}}


Fuselage height
The total height of the fuselage can be determined by summing up the fuselage diameters in positive and negative z-direction:

h_{\text{fuselage}} = d_{\text{fuselage,z,pos}} + d_{\text{fuselage,z,neg}}

!!! note
If the force_circle_cross_section mode is selected, fuselage height and width are set to the maximum of both.

Mass estimation {#mass-estimation}
The following masses are estimated:

Fuselage structure
Operator items
Furnishing

Please refer to Synthesis of Subsonic Airplane Design by E. Torenbeek^[3] and the Certification Specifications^[4] for further information.
!!! note
All masses are estimated in accordance with the CPACS standard.


Generate fuselage shape {#generate-shape}
The fuselage shape is generated using the calculated data and the reference ellipses (see the getting started page for more information). The final geometry is written to the fuselage_design_ellipses.json file.
The aircraft is divided into three sections: A cockpit section, followed by a constant section, and the tail section.
The steps of the shape generation are basically the same for all aircraft sections:

Calculate the section length as a percentage of the fuselage length^*.
Proportionally adjust the given reference geometry to match the actual geometry using scaling factors. Therefore, separate scaling factors are calculated for

the x-direction (lengthwise),
the y-direction (widthwise), and
the z-directions (upper and lower heights).


Calculate new coordinates as well as ellipses for visualization purposes.

^* The length of the constant section is determined by subtracting the length of the cockpit and the tail section from the entire fuselage length.

^[1] Prof. Dr.-Ing. Juergen Thorbeck TU Berlin (2006), Script "Flugzeugentwurf I und II" chapter A.

^[2] M.Sc. Andreas Gobbin (2015), Master Thesis "Numerische Modellierung des Auslegungsprozesses für Passagierkabinen von Verkehrsflugzeugen unter Berücksichtigung der wichtigsten Auslegungsforderungen und Implementierung in MatLab".

^[3] Egbert Torenbeek, Synthesis of Subsonic Airplane Design (1982), Delft University Press.

^[4] European Union Aviation Safety Agency (2024),  CS-25 Large Aeroplanes - Amendment 28.