eBook
Unlocking innovation in Aerospace and Defense
Shorten aircraft design cycles with ESTECO’s digital engineering solutions for collaboration, simulation data management and multidisciplinary design optimization.
Webinar
Empowering SPDM with unified CAE workflow automation and Business Process Management
Take a 30-minute deep dive into VOLTA BPM technology and learn how to automate human interactions and integrate simulation execution in a business process workflow.
Search results
Showing 1 - 10 of 10 results
Success story
Optimizing commercial aircraft designs to use future aviation fuels
Learn how ESTECO modeFRONTIER helped Delft University of Technology to perform multi-objective aircraft design optimization to compare future aviation fuels. Pieter-Jan Proesmans, PhD Candidate in the Flight Performance & Propulsion group at Delft University of Technology, used modeFRONTIER to perform multi-objective aircraft design optimization to compare future aviation fuels. ## Challenge
This research has been undertaken in the framework of the GLOWOPT project sponsored by the EU’s Clean Sky 2 program, and under the supervision of Dr.Ir. Roelof Vos, associate professor at Delft University of Technology. The objective is the development and validation of Climate Functions for Aircraft Design (CFAD) with respect to minimizing global warming and their application to the Multidisciplinary Design Optimization (MDO) of next-generation aircraft for relevant market segments.
To reach this goal, novel fuels, such as liquid hydrogen (LH2) and sustainable aviation fuel (SAF) can provide more sustainable solutions. However, the climate objective conflicts with the typical design objective of minimal operating costs. While these two fuels can offer a significant reduction in climate impact, they are also more expensive and have consequences for the aircraft design (in the case of cryogenic LH2 tanks). ## Solution
The modeFRONTIER Multidisciplinary Design Optimization (MDO) framework was selected to investigate the climate impact reduction and operating costs for hydrogen and SAF fuel in regional, medium-range and long-range aircraft categories. The cost-optimal, kerosene-powered aircraft served as the reference case for all multidisciplinary aircraft design optimizations. The MDO process was set-up in a modeFRONTIER workflow. Its Python interface made it possible to orchestrate in-house tools for aerodynamics, propulsion, mission analysis, mass estimation and climate impact. Next, the optimization strategy was executed.
The pilOPT algorithm evaluated thousands of configurations by changing airframe, turbofan engine and mission design variables to obtain the cost versus climate trade-off for all fuel types in the three aircraft categories. ## Benefits
“The easy-to-use parallel coordinates and scatter matrix charts were very helpful in gaining conceptual insights. One of the key finding was that the SAF-powered aircraft are preferred over the cost-optimal hydrogen aircraft for the regional and medium-range categories. With modeFRONTIER, we could perform the multi-objective optimization and post-processing in a much faster and user-friendly way compared to when we had to rely on programming libraries. In the future, we will investigate how to combine the aircraft optimization with a network allocation routine to update not only aircraft design variables, but also top-level aircraft requirements” said Pieter-Jan Proesmans, PhD Candidate in the Flight Performance & Propulsion group at Delft University of Technology.
Success story
Pipistrel: flying straight from simulation to production
The ESTECO optimization technology as a way to skip any prototype phase for a hybrid-electric aircraft propeller
Pipistrel, an aviation & aerospace company based in Slovenia, relied on ESTECO Technologies to design the propeller for a highly efficient, hybrid-electric aircraft. The work was part of the EU-funded project MAHEPA (Modular Approach to Hybrid Electric Propulsion Architecture), that had the aim of advancing two variants of a low emission, serial hybrid-electric propulsion architecture to TRL (Technology Readiness Level) 6. The modeFRONTIER process automation and optimization software allowed automation in the simulation process and identification of innovative and optimized designs in a limited time. ## Challenge
Engineers at Pipistrel had the challenge to design a propeller, driven by hybrid-electric propulsion system taking into account the different conditions the aircraft meets during the four flight phases: takeoff, climb, cruise and descent. Considering speed, power and thrust requirements changing during the flight, the objective was to maximize takeoff thrust and recuperation power during descent and minimize power during climb and cruise phase. The optimization involved three stages: the preliminary propeller optimization, the airfoil optimization, and the final propeller optimization. ## Solution
For this multi-phase optimization project, Rok Lapuh and David Eržen, aero-dynamics engineers at Pipistrel, used modeFRONTIER coupled with CHARM (Comprehensive Hierarchical Aeromechanics Rotorcraft Model) and XFOIL, an interactive program for the design and analysis of subsonic isolated airfoils. Benefiting from the ESTECO process automation technology, Pipistrel could automate the simulation workflows, simultaneously evaluate thousands of designs and identify innovative optimized results.
This process was conducted in a fully autonomous way leaving Pipistrel’s engineers the task to select the most appropriate design. With the first propeller optimization, Pipistrel optimized the chord and twist distribution to get the maximum thrust and minimum power for a given set of airfoils. The results were then used as requirements for the airfoil optimization. The design team used modeFRONTIER to design the airfoil under specific geometry constraints (thickness, cur- vature or leading-edge radius), while increasing the lift and reducing the drag. They started a Design of Experiments phase and then used the HYBRID genetic algorithm to successfully run the airfoil optimization and get the Pareto front with the optimal designs. At last, they used the optimum airfoil for the final propeller optimization. With the ESTECO optimization algorithms, engineers at Pipistrel could evaluate almost five thousand designs in a limited time and increase the thrust by 30% during takeoff. ## Benefits
Before using modeFRONTIER, Pipistrel went through a manual process to simulate multiple designs and choose the preferred one. With the introduction of ESTECO Technology, Pipistrel engineers not only were able to automate this process, but could evaluate options not considered otherwise. “modeFRONTIER optimization technology gave me the opportunity to think outside of the box - said Rok Lapuh, Aerodynamics Engineer at Pipistrel - We could find a design that is completely different from what we’re used to, but that may work even better”. They also dramatically reduced the go-to-market time as they moved from simulation directly to the production. “We trust the results we get with modeFRONTIER so much that we don’t expect we’ll require a prototype - said David Eržen, Aerodynamics Engineer at Pipistrel - We go straight into production”.
Success story
Environmentally friendly aircraft stretches its wings with modeFRONTIER
Aerodynamic performance enhanced by 2.5% and wing weight reduced by 4%
In an ambitious collaborative venture, Leonardo is heading the Green Regional Aircraft (GRA) design team of the The Clean Sky Joint Technology Initiative, committed to developing environmentally-friendly aircraft. The future of domestic air travel lies in: weight reduction, aerodynamic efficiency, high level operational performance, compliance with emission standards and respect of noise limits. ## Challenge
Targeting multiple objectives such as lowering aircraft drag, wing weight and environmental impact of lower speed conditions (i.e. take-off and landing), enhances overall environmental performance, measured by fuel consumption and noise generation. Seeking the most promising solution for this new generation aircraft, two wing shapes were studied using modeFRONTIER optimization. A “thin” configuration was selected to analyze aerodynamic performance, without any structural restrictions to airfoil thickness; a “thick” configuration was chosen reduce the weight of the wing. ## Solution
modeFRONTIER integrated complex objectives, achieving remarkable enhancement for both wing configurations, while still complying with Top Level Aircraft Requirements (TLAR). The design automation process piloted by the modeFRONTIER workflow generated 20,000 design profiles of the 2D wing shape, while incorporating aerodynamic and structural analysis using Leonardo in-house codes. Once the optimal 2D profile was selected, CFD computations were validated by employing a suitable parametric Catia 3D wing-body. Good aerodynamic results were maintained in the 3D analysis. ## Benefits
“modeFRONTIER has proven to be an effective tool for the design team, identifying feasible solutions and achieving a 2.5% enhancement of aerodynamic performance and a 4% wing weight reduction”, says Enrica Marentino, CFD Specialist at Leonardo. modeFRONTIER successfully streamlined the two-step optimization process for wing shape configuration and its multi-objective genetic algorithm (MOGA-II) was profitably used to solve the optimization problem. Correlations among the aerodynamic parameters were explored thanks to modeFRONTIER statistical tools, providing deep insights which helped set up the optimization strategy effectively. The MCDM tool provided a useful framework towards attaining a ranking for the Pareto front solutions, supporting the design team in determining the best outcome. “The optimized configurations, while still matching TLAR requirements, determined substantial advantages compared to the initial wing profiles”, says Enrica Marentino.
Success story
Hyperloop Makers UPV, Universitat Politecnica de Valencia. SpaceX Top Design Concept winners
modeFRONTIER helped the team select the optimum design in terms of travel experience, maximizing energy efficiency while accelerating design iterations and development time.
The Hyperloop Makers UPV team from the Universitat Politécnica de Valencia was awarded the Top Design Concept and the Propulsion/Compression Subsystem Technical Excellence Awards at the 2016 SpaceX international challenge. The goal of the competition, launched by SpaceX CEO Elon Musk, is to perfect its revolutionary land transport system, driven by compressed air and able to connect Los Angeles and San Francisco in 30 minutes. Whereas the majority of the competing teams opted for passive magnetic levitation or designing the passenger pod suspended on air bearings, Hyperloop UPV developed a system that enables levitation through the magnetic attraction of the pod to the top of the tube. This rail-free solution saves up to 30% on Hyperloop tube construction costs. ## Challenge
The engineering challenge consisted in providing the base design for a 30-passenger cabin travelling as fast as possible through a vacuumed tube.
Solution
The technological solutions, in terms of comfort for the travelers subject to such high acceleration and cruise speed, were investigated by the team, assisted by advanced multiobjective optimization techniques. The computations related to the acceleration and cruise phase were set up in Excel and integrated into the modeFRONTIER workflow. The design variables mainly related to the compressor and the turbine (pressure ratio and discharge velocity) were automatically adjusted by the software to optimize the output results: acceleration time, specific energy required, pod mass and travel speed. ## Benefits
“The effects of modifying even a single variable were, at best, difficult to explain as the physical models regarding the behavior of the system were highly interconnected and interdependent. With a traditional approach, this fact would have lead to a slow and difficult system optimum. modeFRONTIER on the other hand, enabled the team to obtain a family of optimum solutions for a range of inputs in a mere fraction of the time” said Germán Torres, Technical Director at Hyperloop Makers UPV Team. In terms of specific energy per passenger/km, the results show the pod consumes ten time less energy and travels ten times faster than traditional road transport. “We are developing a small levitation demonstrator for the next phase of the SpaceX International Challenge”, continued Torres, “in fact we plan use modeFRONTIER again to optimize the new Hyperloop design proposal”.
Success story
M-Fly. The University of Michigan Team at SAE Aero Design Competition
Long, freezing winters in Michigan leave the M-Fly team with only a month and a half to design and test their plane for the SAE Competition. Thanks to modeFRONTIER, the team can save precious time and improve their design.
The SAE Aero Design Competition was created to connect engineering students with real-life engineering experiences and prepare them for their professional paths. As of this year, the M-Fly team participates both in the regular and the advanced class of the Competition. The 2016/2017 regular class objective is to maximize the amount of “passengers” on the plane without leaving empty seats - a realistic challenge faced by commercial airliners. The advanced class includes the design of the internal combustion power, static and dynamic payloads that must be dropped on a target during the flight, as well as the use of sensors and other electronic systems. M-Fly has partnered with ESTECO Academy and will benefit from free training and access to modeFRONTIER optimization platform to improve their aircraft design and validate analysis results faster. At M-Fly, our goal is to teach aerospace engineering, specifically aircraft design through competing at the SAE Aero Design competition. We balance winning and teaching, so we try to involve as many interested University of Michigan students in our project, while still designing the best aircraft for the competition. However, our design cycle is brutal as we have two major factors against us: our school year and the weather. If we want to finish the testing phase before we head to competition, we need to get to the final design by Thanksgiving and finish the construction in January: a very tight schedule. In Michigan, from December through March the temperature highs are hovering at freezing temperatures and opportunities for prime weather conditions to flight test are minimal. If we get lucky, we can perform a flight test or two before we head off to competition which is in the much nicer Southern United States (the competition rotates between Florida, Georgia, and Texas). The more time we have with a full aircraft built, the bigger are the chances of us getting more test flights in. That is where modeFRONTIER comes into play - it allows us to explore a much larger design space in significantly less time than we could do by ourselves. Just the Design of Experiments (DOE) runs give us more data that we have ever gotten in our past design cycles in terms of different configurations.
We are currently using modeFRONTIER to do two things: iterate through many different configurations to optimize and do multi-disciplinary analysis since it interfaces so well with other analysis and CAD software we have here at Michigan such as ANSYS, StarCCM+, and SolidWorks. Instead of a standard design, analyze, build, test, go back to first step and repeat - design cycle, we can multiply the iterations for each step: design x 10000 -> analyze x 10000 -> downselect design -> build -> test and repeat the last 3 steps, with the first 3 steps taking only a couple of hours if needed. modeFRONTIER also has a superb post processing capability that allows us to analyze our results in many different ways to make sure we are choosing the right design, as well as provide insights into our design problem.
Success story
The Naviator. One of the best optimization projects at Rutgers, the State University of New Jersey
The Naviator, optimized using modeFRONTIER, was the first project to demonstrate an unmanned aerial and submersible vehicle that could operate both in air and underwater.
At Rutgers, researchers in the Department of Mechanical and Aerospace Engineering’s Laboratory for Experimental Fluids and Thermal Engineering, under the direction of prof. Diez, invented a remotely controlled drone similar to those used by hobbyists and professionals globally, but with one key difference – it is able to both fly and move underwater. The drone called Naviator, and funded in part by the Office of Naval Research, could speed search-and-rescue operations, monitor the spread of oil spills and even help the Navy rapidly defuse threats from underwater mines. Marco Maia, PhD candidate in Mechanical and Aerospace Engineering (MAE) working under Prof. F. J. Diez in the Rutgers Applied Fluids Lab and student in the Optimal Design course with Prof. Knight, worked at this outstanding project using modeFRONTIER. Most of our research thrusts involve fluids such as in electrokinetics, microfluidics & nanofluidics, wind energy, turbulence, laser diagnostics with PIV, biological flows. We pride ourselves on the applied nature of some of our research topics, such as in the development of electrokinetic thrusters, AUVs & seagliders and unmanned aerial systems. This vehicle gained a great deal of attention and Prof. Diez was able to secure a grant from the Office of Naval Research (ONR) in the amount of ~$600k. Since then, this research project has grown and has been showcased in several news outlets. Recently, National Geographic visited Rutgers University to film our latest multi-medium vehicle in action for use in one of their pieces, which we were told would be unveiled later in the summer. The optimization project in the MAE Optimal Design course with Prof. Doyle Knight was a great opportunity to make the planned improvements to our new multi-medium vehicle platform. We cannot provide too many details on the vehicle itself until its unveiling, but when we designed the new platform we purposely made it into a skeleton that could benefit from aerodynamic volumetric additions. Thanks to ESTECO for kindly making available its technology for the students of this course. With modeFRONTIER I was able to easily integrate several software together, such as MATLAB, Solidworks or ANSYS Fluent and run the necessary simulations to determine the optimal geometry for these volumetric additions using several optimization algorithms. The result was an optimal set of solutions that minimized the drag and weight while maintaining near neutral buoyancy. The autonomy and visual aids of the software were truly remarkable-it definitely streamlines the optimization process. Thank you again for allowing us to use this very useful tool”.
Success story
HI-SEAS. NASA-funded Mars simulation habitat on Mauna Loa volcano, Hawaii
modeFRONTIER helps the astronaut-like researchers develop system models for sustainable living on Mars, in particular in terms of waste reduction and sustainable lifestyle.
Hawaii Space Exploration Analog and Simulation (HISEAS) is a NASA-funded research project aimed to help determine the individual and team requirements for long term space exploration missions, including travel to Mars. HI-SEAS V is an 8-month Mars analog isolation mission that begun on January 19th, 2017. Two 8-month missions are scheduled starting in January 2017 and 2018. During the HI-SEAS Mission V, six researchers are studying human behavior on Mars by entering in a geodesic dome in the isolated environment of Mauna Loa volcano on the Hawaii Big Island, including 20-minutes delayed communication and partial self-sufficiency. The purpose of Campaign 3 is to directly address the IRP Team Risk: “Risk of Performance Decrements Due to Inadequate Cooperation, Coordination, Communication, and Psychosocial Adaptation within a Team”.
Ansley Barnard is the Engineering Officer for Mission V. She is in charge of monitoring their life support systems and fixing things that break down. “On a space mission, the astronaut crew is very limited on what they can bring with them. Launch mass (fully fueled) is highly valuable, so every item you send on a rocket needs to be weight and size efficient, including food, water, research materials, and personal effects. When you are traveling far away, like a manned mission to Mars, you need more supplies and you have to burn more fuel to get everything there - this makes resource optimization even more challenging”. “Parametric modeling and optimization software tools like modeFRONTIER provide us with faster and more robust ways to optimize. It is possible to find trends that your human eyes might have missed, which can yield better solutions in less time. modeFRONTIER is an easy to learn tool with a lot of built-in capability and modular flexibility. It is possible to tailor the software to specific needs, and the modeFRONTIER support people have always been helpful when I feel stuck”.
Moreover, our resources are limited and we have to use them wisely. If we run out of something before we are resupplied, we have to find a way to make do. Sustainable living is important to me on a personal level and is a big motivator for me to use an optimization approach in my engineering work. While in the habitat, I am hoping to learn more skills about efficient living, like using less water and power by making active choices in how I cook, shower or do laundry. These are real skills I can bring home with me. Just like in space, each of us can balance what we use with what resources are available if we have a curious and observant eye.
Tools like modeFRONTIER can help us model systems, but changes are carried out through our actions. By building parametric models of our life support system, I hope to balance our resource needs and find ways for the crew to have energy and water available for all our research and personal uses. My goal is to make a tangible difference in how my crewmates live day-to-day in our mission and provide future HI-SEAS crews with updated engineering information on the habitat life support systems.
Success story
ECS System Simulation - Architecture and Performance Optimization from the Early Phases of the System Design
ECS system simulation - Architecture and performance optimization from the early phases of the system design
The trend today in aircraft thermal design leans towards electronic system integration requiring higher heat densities and a more frequent use of composite primary structures. All these factors require thermal management and architecture design to achieve a suitable robustness, even in the early design stages. The thermal architecture should be able to prevent the risks of damage to temperature-sensitive equipment and limit the expensive overdesign of aircraft systems. ## Challenge
The optimization of the thermal architecture is considered one of the key factors of future aircraft development. It requires a composite pyramid of simulation tasks to be set and managed: from equipment to aircraft section simulation to the global aircraft thermal analysis. Adopting this approach gives rise to a number of difficulties due to the variety of physical models to be integrated and the partners, techniques and tools interacting at each level of the pyramid. This case study from Leonardo’s Environmental Control System (ECS) department shows how the different design disciplines involved are handled effectively through process integration and automation, enabling the optimization of the overall performance from the early stages of system design. One of the systems considered in the ECS design at Leonardo is the air conditioning pack and distribution system. The air, supplied from the engine compressor, is processed in the conditioning pack before being distributed to the fuselage compartments. Enhancing the efficiency of the thermal architecture implies several constraints and requirements relating to standards-compliance and safety regulations. Designers must adhere to given A/C configurations and maintain suitable thermoacoustic insulation and temperature levels for both the cabin and cockpit. ## Solution
First, engineers at Leonardo used the TPM approach to compare the performance of two alternative architectures, preferring a parallel layout composed of an underfloor and a low pressure air line fed from the mixing chamber and distributing the airflow in parallel through a set of risers. Next, after building the model for the selected architecture and its subsystems in LMS.Amesim, the workflow for the air nozzle shape optimization was built in modeFRONTIER. “The optimization platform helped us reduce pressure loss and noise level to the minimum” says Gaetano Mirra (CTO, General Systems - ECS and Ice protection specialist at Leonardo). ## Benefits
“modeFRONTIER automation and integration capabilities enabled us to simultaneously consider the fluid dynamic and acoustic analysis and easily handle the data flow including Catia, StarCCM+ ans PostPRO simulations in a unique environment” continued Mirra. “We found the best configurations possible for the nozzle shape and refined the thermal architecture design, further enhancing passenger comfort in terms of cabin thermal environment”.
Success story
Hybrid rocket lifts off with modeFRONTIER
modeFRONTIER helped the team meet multiple structural constraint and significantly reduce the rocket weight.
Since the early 2000s, the Hybrid Propulsion Team at the University of Brasilia has been a pioneer in the development and test of hybrid rocket engines and small sounding rockets. By following a system design approach based on the multidisciplinary optimization technique, the Team has developed a conceptual hybrid rocket motor, attaining a valuable technological option for the reentry maneuvering system of SARA, the reusable satellite designed by the Brazilian Institute of Aeronautics and Space. ## Challenge
Solid and liquid rocket propulsion systems are traditionally considered the most convenient technological solution for deboost motor systems. Owing to the improvements in solid fuel regression rates, hybrid propellant rocket engines represent a valid alternative. The team analyzed three different propulsion settings, combining the paraffin as solid fuel with cold gas fuel, thereby responding to the SARA reentry procedure requirements. The final design should meet both the geometric constraints, linked to total mass limitation and the performance indicators for the mission: deboost impulse should produce a deceleration ranging from 235 to 250 m/s and the motor burning. ## Solution
The Team took in account the key parameters impacting the performance of the hybrid engine: grain configuration, combustion efficiency, oxidizer tank pressure and nozzle configuration together with geometrical configuration. The two-step sensitivity analysis performed with modeFRONTIER - dedicated tools led to the selection of the variables showing significant dependencies with design constraints and objectives. These key elements were brought together to build a workflow capable of both preserving the simplicity of hybrid propulsion systems. This automatic framework drove the search for the geometric configuration, yielding to the higher mass reduction for each of the three configurations. “The routine piloted by the modeFRONTIER® workflow helped generate, evaluate and select design alternatives along the optimization process, resulting in lighter engines than the liquid and solid motors previously studied.” said Manuel Nascimento Dias Barcelos, head of the Hybrid Propulsion Team. ## Benefits
modeFRONTIER streamlined the design effort conducted for the hybrid propellant engines based on liquefying fuel (solid paraffin) and two different gas fuels: H2O2 and self-pressurizing N2O. The estimated mass of the reentry system for the cases addressed in the study varied from 22 to 29 kg, lower than either liquid bipropellant or solid engines formerly proposed. “The optimization process discussed in this work can be considered an essential tool for the preliminary phase design of hybrid rocket propulsive systems”, concluded Manuel Nascimento Dias Barcelos.
Success story
Optimal Design of an Unmanned High-Altitude Solar-Powered Airplane
Optimal Design of an Unmanned High-Altitude Solar-Powered Airplane
In recent years the development of High Altitude/ Long Endurance (HALE) solar-powered unmanned aerial vehicles (UAVs) has been gaining importance. Such aircrafts could serve as “pseudo satellites”, with the advantages of being closer to the ground, more flexible and less expensive when compared to common satellites. Using a combination of a solar array and batteries and without requiring sophisticated assisted take-off systems these UAVs could potentially cover a 1,000 km diameter area and process about 425,000 cell phone conversations while sustaining long endurance flights. ## Challenge
Stability and control are critical issues in any aircraft design, more so in this case particular care was paid to this problem especially considering that the airplane flies at altitudes of up to 17km. Another concern is how to identify the best setup of battery packs and power system in order to comply with aircraft standards and regulations. The researchers of the Brazilian Instituto Tecnológico de Aeronáutica worked on the enhancement of a light-weight solar-powered UAV model, featuring a rectangular wing with a conventional tail connected to the wing by means of a boom and two engines located on the inner wing. The baseline airplane gross weight was 30.1 kg and the battery fraction, impacting the overall weight, was very high. With this in mind, the researchers sought the best configuration of selected parameters - geometry, aerodynamics, structures, stability, weight and systems. The multi-objective optimization was concerned with
maximizing the available electrical power while reducing the gross weight of the airplane configuration. ## Solution
The multi-disciplinary workflow built with modeFRONTIER took into account the stability constraints and the area of solar panels, which could not exceed the dedicated portion of the wing. The objective of the optimization was to minimize weight and maximize the power surplus. The wing area range could vary between 30 and 60 m2, and after 40 generations with 30 individuals each, the MOGA-II algorithm returned a group of feasible designs. The best configuration featured a 50% expansion in wing area, admitting a larger solar panel resulting in a considerably higher power availability with a slight increase in aircraft weight. ## Benefits
The choice of modeFRONTIER as the multi-objective optimization tool provided researchers with a large variety of configurations in less than one day’s computation. For each design solution, engineers identified the strengths, weaknesses and typical values of the variables in order to introduce the improvements sought. “The disciplines of aerodynamics, structures, stability, weight, and systems were all considered and integrated in a modeFRONTIER workflow, capable of providing a relatively simple resizing, but highly realistic airplane”, said Bento Silva de Mattos of the Instituto Tecnológico de Aeronáutica. This case study clearly demonstrates the added value achieved by combining optimization and simulation. With only a few semi-empirical mathematical models and data obtained with the computations and the application of simple theories, it was possible to reach the optimal design and verify the consistency of the solution.