The payload-range diagram
UNICADO has the ability to generate a payload-range diagram based on the performance characteristics of your aircraft design. The payload-range diagram is one of the most essential ways of visualizing the transport capabilities of your configuration. Furthermore, it combines performance characteristics from aerodynamic, engine to payload. With an abundance of information it is a fundamental tool in comparing aircraft designs as well as airline fleet planing.
Input
In order to perform the payload-range diagram generation the following input parameters or input files are needed:
- Payload capabilities
- Mission profile
- Initial cruise Mach number
- Aerodynamic polars
- Engine decks
Calculation method
The calculation of the payload-range diagram is based on the Breguet range equation as stated below.
R = \frac{V \cdot \frac{L}{D}}{g \cdot SFC} \cdot ln\left(\frac{m_{initial}}{m_{final}} \right)
The used parameters are defined as follows:
- V - speed
- L - lift
- D - drag
- g - gravitational constant
- SFC - specific fuel consumption
- m_{initial} - mass at the beginning of the cruise segment
- m_{final} - mass at the end of the cruise segment
The equation is valid for steady, level flight and is based on the assumption, that the change in mass of an aircraft is proportional to the fuel mass flow. For the use in UNICADO the Breguet range equation is adapted as follows:
R = \frac{V \cdot \frac{L}{D}}{g \cdot SFC} \cdot ln\left(\frac{0.9065 \cdot TOM}{OME + m_{payload}} \right) \cdot CF
In contrast to the original Breguet range equation the initial mass of the cruise segment m_{initial} is approximated through 90.65% of the take off mass (TOM). Hence, accounting for the fuel consumed until reaching cruise altitude. Furthermore, a calibration factor (CF) is introduced. The calibration factor is calculated based on the ratio of the design range, as defined in the acXML by the user, and the range calculated from the adapted Breguet range equation (assuming a CF of 1 for this purpose) under design point conditions.
In order to approximate the ambient condition for a multi step cruise flight, the cruise altitude is averaged over the weighted segment lengths. Thereafter, the ambient condition is calculated following the International Standard Atmosphere. Based on the previously mentioned assumptions, and for the cruise Mach number at the initial cruise altitude the lift, drag as well as SFC are calculated.
Output
The output of the payload-range diagram generation can be found in the folder reporting where beside the individual plot in .svg format a html report depicting the plot as well as the data of the corner points and design point. Furthermore the ranges of the corner points of the payload-range diagram can be found under the tab performance/range.