Helicopters have been valuable vehicles ever since their invention. Their capabilities for axial flight and hovering make them an outstanding resource. However, their complexity, directly related to their aerodynamics, makes them extremely hard to design. In today’s market competitivity resources must be optimized and accurate models are needed to obtain realizable designs. The well known Blade Element Theory was used to model helicopter rotors using the Modelica based software SystemModeler. However, it remained unverified due to the lack of experimental data available. The access to experimental data published by NASA motivated the comparison from the model to the measurements obtained during real testing to a scaled rotor. Some improvements were performed to the model obtaining unexpectedly accurate results for hover and axial flight. Two approaches based on the Blade Element Theory and related to Vortex Theory were followed: an infinite number of blades and a finite number of blades. Moreover, the model simulation speed was notice ably increased and prepared for the forward flight model development. Nonetheless, even though the model was ready for forward flight simulations, further research is needed due to, again, the lack of experimental data available. It is concluded from the present work that Wolfram’s SystemModeler can be used as a tool in early design phases of helicopters, even before CAD modeling and CFD due to its simplicity, speed, accuracy, and especially its capability for being used on simple desktop computers.

Propulsion system testing before mission operation is a fundamental requirement in any project. For both industrial and commercial entities within the space industry, complete system integration into a static test platform for functional and performance testing is an integral step in the system development process. Such a platform - if designed to be relatively safe, uncomplicated and reliable - can be an important tool within academia as well, giving researchers and students a possibility for practical learning and propulsion technology research. In this thesis, a preliminary design for a liquid-propellant rocket engine testing platform to be used primarily for academical purposes is developed. Included in the presented design is a bi-propellant Chemical Propulsion system, gas pressure fed with Gaseous Nitrogen and using Gaseous Oxygen as oxidiser and a 70 % concentrated ethanol-water mixture as fuel. The propellant assembly contains all necessary components for operating the system and performing combustion tests with it, including various types of valves, tanks and sensors. An estimation of the total preliminary cost of selected components is presented as well. Also part of the developed platform design is a small thrust chamber made of copper, water-cooled and theoretically capable of delivering 1000 N of thrust using the selected propellants. A list of operations to be performed before, during and after a complete combustion test is presented at the end of the document, together with a preliminary design of a Digital Control and Instrumentation System software. Due to time limitations, the software could not be implemented in a development program nor tested with simulated parameters as part of this thesis project.

The current trend in aircraft design is to increase the proportion of fiber composites in the structures. Since many primary parts also are constructed using metals, the number of hybrid metal-composite structures is increasing. Such structures have traditionally often been avoided as an option because of the lack of methodology to handle the mismatch between the material properties. Composite and metal properties differ with respect to: thermal expansion, failure mechanisms, plasticity, sensitivity to load type, fatigue accumulation and scatter, impact resistance and residual strength, anisotropy, environmental sensitivity, density etc. Based on these differences, the materials are subject to different design and certification requirements. The issues that arise in certification of hybrid structures are: thermally induced loads, multiplicity of failure modes, damage tolerance, buckling and permanent deformations, material property scatter, significant load states etc. From the design point of view, it is a challenge to construct a weight optimal hybrid structure with the right material in the right place. With a growing number of hybrid structures, these problems need to be addressed. The purpose of the current research is to assess the strength, durability and thermo-mechanical behavior of a hybrid composite-aluminum wing structure by testing and analysis. The work performed in this thesis focuses on the analysis part of the research and is divided into two parts. In the first part, the theoretical framework and the background are outlined.Significant material properties, aircraft certification aspects and the modeling framework are discussed.In the second part, two papers are appended. In the first paper, the interaction of composite and aluminum, and their requirements profiles,is examined in conceptual studies of the wing structure. The influence of the hybrid structure constitution and requirement profiles on the mass, strength, fatigue durability, stability and thermo-mechanical behavior is considered. Based on the conceptual studies, a hybrid concept to be used in the subsequent structural testing is chosen. The second paper focuses on the virtual testing of the wing structure. In particular, the local behavior of hybrid fastener joints is modeled in detail usingthe finite element method, and the result is then incorporated into a global model using line elements. Damage accumulation and failure behavior of the composite material are given special attention. Computations of progressive fastener failure in the experimental setup are performed. The analysis results indicate the critical features of the hybrid wing structure from static, fatigue, damage tolerance and thermo-mechanical points of view.

Trailing vortices are both a fundamental and practical problem of fluid mechanics. Fundamentally, they provide a canonical vortex flow that is pervasive in finite aspect ratio lifting bodies, practically producing many adverse effects across aeronautical and maritime applications. These adverse effects coupled with the broad range of applicability make their active control desirable; however, they remain robust to control efforts. Experimental baseline results provided an explanation of vortex wandering, the side-to-side motion often attributed to wind-tunnel unsteadiness or a vortex instability. We extracted the wandering motion and found striking similarities with the eigenmodes, growth rates, and frequencies from a stability analysis of the Batchelor vortex. After concluding that wandering is a result of a vortex instability, we applied control to the trailing vortex flow field through blowing from a slot at the wingtip. We experimentally obtained modest reductions in the metrics, but found the parameter space for optimization unwieldy. With the ultimate goal of designing control, we performed a physics-based stability analysis in the wake of a NACA0012 wing with an aspect ratio of 1.25 positioned at a geometric angle of attack of 5 degrees. Numerically computing the base flow at a chord Reynolds number of 1000, we perform a parallel temporal and spatial stability analysis three chords downstream of the trailing edge finding seven instabilities: three temporal, four spatial. The three temporal contain a wake instability, a vortex instability, and a mixed instability, which is a higher-order wake instability. The primary instability localized to the wake results from the two-dimensional wake, while the secondary instability is the mixed instability, containing higher-order spanwise structures in the wake. These instabilities imply that although it may be intuitive to place control at the wingtip, these results show that control may be more effective at the trailing edge, which would excite these instabilities that result with the eventual break up of the vortex. Further, by performing a wave-packet analysis, we found the wave packets contained directivity, coming inward toward the vortex above and below the wing, and traveling outward in the spanwise directions. We conjecture that this directivity can be translated to receptivity, with free-stream disturbances above and below the wing being more receptive than spanwise disturbances. With this, we provide two methods for instability excitation: utilizing control devices on the wing to excite near-field instabilities directly and utilizing free-stream disturbances to such as a speaker to excite near-field instabilities through receptivity. / A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2016. / April 14, 2016. / Flow control, Hydrodynamic stability, Trailing vortices, Vortex flows, Vortex wandering / Includes bibliographical references. / Louis Cattafesta, Professor Directing Dissertation; M. Yousuff Hussaini, University Representative; Peter Schmid, Committee Member; Kunihiko Taira, Committee Member; William Oates, Committee Member.

Underwater vehicles suffer from reduced maneuverability with conventional lifting appendages due to the low velocity of operation. Circulation control offers a method to increase maneuverability independent of vehicle speed. However, with circulation control comes additional noise sources, which are not well understood. To better understand these noise sources, a modal-based prediction method is developed, potentially offering a quantitative connection between flow structures and far-field noise. This method involves estimation of the velocity field, surface pressure field, and far-field noise, using only non-time-resolved velocity fields and time-resolved probe measurements. Proper orthogonal decomposition, linear stochastic estimation and Kalman smoothing are employed to estimate time-resolved velocity fields. Poisson's equation is used to calculate time-resolved pressure fields from velocity. Curle's analogy is then used to propagate the surface pressure forces to the far field. This method is developed on a direct numerical simulation of a two-dimensional cylinder at a low Reynolds number (150). Since each of the fields to be estimated are also known from the simulation, a means of obtaining the error from using the methodology is provided. The velocity estimation and the simulated velocity match well when the simulated additive measurement noise is low. The pressure field suffers due to a small domain size; however, the surface pressures estimates fare much better. The far-field estimation contains similar frequency content with reduced magnitudes, attributed to the exclusion of the viscous forces in Curle's analogy. In the absence of added noise, the estimation procedure performs quite nicely for this model problem. The method is tested experimentally on a 650,000 chord-Reynolds-number flow over a 2-D, 20% thick, elliptic circulation control airfoil. Slot jet momentum coefficients of 0 and 0.10 are investigated. Particle image velocimetry, unsteady pressure and phased-acoustic-array data are acquired simultaneously in an aeroacoustic wind-tunnel facility. The velocity field estimation suffers due to poor correlation with the unsteady pressure data, especially in the 0.10 momentum coefficient case. The prediction without slot jet blowing matches single microphone measurements within 0-10 dB over the frequency range of interest while the prediction with the jet active is quite poor and differ from measurements by as much as 35 dB. Suggestions for improvement of the proposed method are offered. Data from the acoustic array are then investigated. Single microphone spectra are obtained, and it is shown that background noise is significant. In order to circumvent this problem, beamforming is employed. The primary sources of background noise are from the tunnel collector and jet/sidewall interaction. DAMAS is employed to remove the effects of the array point spread function. Spectra are acquired by integrating the DAMAS result over the source region. The resulting DAMAS spectral levels are significantly below single microphone levels. A scaling analysis is performed on the processed array data. With a constant free-stream velocity and a varying jet velocity the data scale as M6. If momentum coefficient is held constant and free-stream velocity is varied the data scale as M7. / A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2016. / March 31, 2016. / Acoustics, Circulation Control, Experimental / Includes bibliographical references. / Louis N. Cattafesta, III, Professor Directing Dissertation; Christopher Tam, University Representative; Kunihiko Taira, Committee Member; William Oates, Committee Member.

The objective of this computational study is to examine and quantify the influence of fundamental flow control inputs in suppressing flow separation over a canonical airfoil. Most flow control studies to this date have relied on the development of actuator technology, and described the control input based on specific actuators. Taking advantage of a computational framework, we generalize the inputs to fundamental perturbations without restricting inputs to a particular actuator. Utilizing this viewpoint, generalized control inputs aim to aid in the quantification and support the design of separation control techniques. This study in particular independently introduces wall-normal momentum and angular momentum to the separated flow using swirling jets through model boundary conditions. The response of the flow field and the surface vorticity fluxes to various combinations of actuation inputs are examined in detail. By closely studying different variables, the influence of the wall-normal and angular momentum injections on separated flow is identified. As an example, open-loop control of fully separated, incompressible flow over a NACA 0012 airfoil at α = 6° and $9° with Re = 23,000 is examined with large-eddy simulations. For the shallow angle of attack α = 6°, the small recirculation region is primarily affected by wall-normal momentum injection. For a larger separation region at α = 9°, it is observed that the addition of angular momentum input to wall-normal momentum injection enhances the suppression of flow separation. Reducing the size of the separated flow region significantly impacts the forces, and in particular reduces drag and increases lift on the airfoil. It was found that the influence of flow control on the small recirculation region (α = 6°) can be sufficiently quantified with the traditional coefficient of momentum. At α = 9°, the effects of wall-normal and angular momentum inputs are captured by modifying the standard definition of the coefficient of momentum, which successfully characterizes suppression of separation and lift enhancement. The effect of angular momentum is incorporated into the modified coefficient of momentum by introducing a characteristic swirling jet velocity based on the non-dimensional swirl number. With the modified coefficient of momentum, this single value is able to categorize controlled flows into separated, transitional, and attached flows. With inadequate control input (separated flow regime), lift decreased compared to the baseline flow. Increasing the modified coefficient of momentum, flow transitions from separated to attached and accordingly results in improved aerodynamic forces. Modifying the spanwise spacing, it is shown that the minimum modified coefficient of momentum input required to begin transitioning the flow is dependent on actuator spacing. The growth (or decay) of perturbations can facilitate or inhibit the influence of flow control inputs. Biglobal stability analysis is considered to further analyze the behavior of control inputs on separated flow over a symmetric airfoil. Assuming a spanwise periodic waveform for the perturbations, the eigenvalues and eigenvectors about a base flow are solved to understand the influence of spanwise variation on the development of the flow. Two algorithms are developed and validated to solve for the eigenvalues of the flow: an algebraic eigenvalue solver (matrix based) and a time-stepping algorithm. The matrix based approach is formulated without ever storing the matrices, creating a computationally memory efficient algorithm. Based on the matrix based solver, eigenvalues and eigenvectors are identified for flow over a NACA 0015 airfoil at Re = 200, $600, and $1,000. All three cases contain similar modes, although the growth rate of the leading eigenvalue is decreased with increasing Reynolds number. Three distinct types of modes are found, wake mode, steady mode, and modes of the continuous branch. While this method is limited in the range of Reynolds numbers, these results are used to validate the time-stepper approach. Increasing the Reynolds number to Re = 23,000 over a NACA 0012 airfoil, the time-stepper method is implemented due to rising computational cost of the matrix-based method. Stability analysis about the time-averaged flow is performed for spanwise wavenumbers of β = 1$, $10π, and $20π, which the latter two wavenumbers are representative of the spanwise spacing between the actuators. The largest spanwise wavelength (β = 1$) contained unstable modes that ranged from low to high frequency, and a particular unstable low-frequency mode corresponding to a frequency observed in the lift forces of the baseline large-eddy simulation. For the larger spanwise wavenumbers, β = 10π ($L_z/c = 0.2$) and $20π ($L_z/c = 0.1$), low-frequency modes were damped and only modes with $f > 5$ were unstable. These results help us gain further insight into the influence of the flow control inputs. Flow control is not implemented in a manner to directly excite specific modes, but does dictate the spanwise wavelengths that can be generated. Comparing the unstable eigenmodes at these two spacings, the larger spanwise spacing ($\beta = 10\pi$) had a greater growth rate for the majority of the unstable modes. The smaller spanwise spacing ($\beta = 20\pi$) has only a single unstable mode with a growth rate an order of magnitude smaller than $\beta = 10\pi$. With the aid of the increased growth rate, perturbations to the flow with a wider spacing become more effective by interacting with natural modes of the flow. Taking advantage of these natural modes allows for decreased input for the wider spanwise spacing. In conclusion, it was shown that the influence of wall-normal and angular momentum inputs on fully separated flow can adequately be described by the modified coefficient of momentum. Through further analysis and the development of a biglobal stability solver, spanwise spacing effects observed in the flow control study can be explained. The findings from this study should aid in the development of more intelligently designed flow control strategies and provide guidance in the selection of flow control actuators. / A Dissertation submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2017. / April 13, 2017. / Computational Fluid Dynamics, Fluid Mechanics, Global Stability Analysis, Separation Control / Includes bibliographical references. / Kunihiko Taira, Professor Directing Dissertation; M. Yousuff Hussaini, University Representative; Farrukh Alvi, Committee Member; Louis Cattafesta, Committee Member; Shangchao Lin, Committee Member.

A satellite, with the call sign RUFS-1, will attempt in the first half of 2016 a launch into low Earth polar orbit. This feasibilitystudy shows that RUFS-1 is from an overall technical perspective capable of fulfilling its mission. This was determined by a break downof the mission requirements into a few key questions. These were answered through various means; firstly an orbital simulation,secondly a link budget and finally a risk assessment of the entire satellite project.

Today’s usage of fossil fuel leads to environmental pollution and global warming. This is not a sustainable solution since this energy source is limited. Research is being conducted by the aircraft industries to develop alternative fuels and thereby decrease the amount of carbon dioxide emissions. Green Flight Challenge was an inspiration to this and several airplane manufacturers applied for the competition. The competition purpose was to bring forth green airplanes that maximize the fuel efficiency. The rules of the competition was that every plane must fly 332km in less than 2 hours and use less energy than what is in 3,79 liter gasoline per passenger. The objective for this bachelor project was to develop a concept for a two seat airplane that will be able to fulfil the competition requirements and to win Green Flight Challenge. The execution for the concept contains calculations and design for the plane’s wings, fuselage and empennage and the aerodynamics and propulsion. A material analysis was made and the selections of the battery system and motor. The design of a sailplane has been used as a reference to reduce drag and therefor consume less energy. A research of usage of placing solar cells on the wings has been made. The results shows how fast and efficient the concept plane must fly to be able to win the contest while it meets the requirements set by the rules. / Dagens användning av fossila bränslen leder till miljöförstöring och global uppvärmning. Detta är inte heller någon slutgiltig lösning på våra energibehov då denna energikälla är ändlig. Inom flygbranschen arbetas det med att ta fram alternativa drivmedel och därigenom minska koldioxidutsläppen. Detta är temat för det här arbetet och en inspirationskälla till detta var tävlingen Green Flight Challenge som väckte entusiasmen hos flera småflygplanstillverkare. Syftet med tävlingen var att ta fram gröna flygplan som maximerar bränsleeffektiviteten. Tävlingskraven var att flygplanet måste flyga 322 km under två timmar och använda mindre energi än vad som finns i 3,79 liter bensin per passagerare. Målet med detta kandidatexamensarbete var att ta fram ett eldrivet tvåsitsflygplan som ska uppfylla tävlingskraven och vinna Green Flight Challenge. Framtagandet av konceptet innefattar beräkningar och utformningar av flygplanets vingar, kropp och stjärtparti samt aerodynamik och drivsystem. En materialanalys har gjorts samt val av batterisystem och motor. Ett segelflygplans utformning har använts som referens för att minska motståndet så mycket som möjligt för att på så sätt minska förbrukningen av energi. Användningen av solceller placerade på vingarna har även undersökts. Resultatet visar hur snabbt och hur bränsleeffektivt konceptplanet måste flyga för att vinna tävlingen då planet uppfyller tävlingskraven.

Denna rapport behandlar en konceptstudie av ett solcellsdrivet obemannat höghöjdsflygplan, förkortat HALE UAV, och innefattar bland annat en kort beskrivning av ingående delar, design och utformning, prestanda och energi beräkningar samt modeller för solstrålning och väder i atmosfären. Inspirationen till projektet gavs av det solcellsdrivna flygplanet Zephyr och har även utgjort utgångspunkten för detta arbete. Syftet med studien har varit att ta reda på hur mycket energi som krävs för att ett flygplan av denna typ ska kunna operera och hur stor del av jorden den skulle kunna täcka om den endast drivs av solceller under antagandet att ideala förhållanden råder. Utvecklingen av obemannade flygplan har gått snabbt de senaste 30 åren och i takt med de ökande miljöproblemen kommer flygplan som är mer miljövänliga att bli mer populära. Flygplan av denna typ har idag stora användningsområden och kan bland annat användas för spaning och övervakning men även som plattformar för exempelvis internet och telefoni. Med Zephyr som utgångspunkt har rimliga värden på flygplanets utformning kunnat bestämmas. Totalvikten blev 53 kg med ett vingspann på 22,5 meter och en motoreffekt på 2x450 W. Olika vingprofiler har analyserats och valet blev Wortmann FX 74-CL5-140 på grund av en hög lyftkraftskoefficient, anpassad för låga Reynolds tal samt ett mycket stort förhållande mellan lyftkraft och motstånd. Solcellerna som används för att ta tillvara på energin lagrad i solstrålningen valdes till amorfa kiselsolceller med en verkningsgrad på 20 % och batterierna för att lagra energin valdes till litium-svavel med en massa på 15,9 kg och en energidensitet på 500 Wh/kg. Beräkningar av planets prestanda har gjorts med de utdelade kompendierna som grund och de innehåller mer detaljerade beskrivningar om respektive beräkningar och lösningsgång. Olika flygfall har analyserats för att erhålla en så energisnål flygning som möjligt vilket resulterade i planflykt under dagtid och en blandning mellan glidflykt och stigning under natten. Energiåtgången beräknades till cirka 6.1 kWh under dagtid och cirka 6 kWh under natten. Den använda solstrålningsmodellen approximerar hur solstrålningen varierar under en dag samt under olika tider på året. Beräkningar för hur mycket energi som är tillgänglig vid olika latituder och höjder har gjorts och sedan jämförts med flygplanet minimala behov för att flyga. Med ett behov på minst 15 kWh per dag resulterade det i att flygplanet måste flyga på latituder under cirka 40°N i december och latituder på under 60°N i februari och oktober. Som hjälpmedel vid beräkningar och analys av vingprofiler har programvarorna MATLAB samt XFLR5 använts. / This report treats a concept study of a solar powered HALE UAV (High Altitude Long Endurance Unmanned Aerial Vehicle) and includes amongst others a short description of the parts, design, performance and energy calculations as well as a few models for solar radiation and weather/atmosphere. The inspiration was given by the solar powered airplane Zephyr, which has been the starting point for this project. The purpose of the study has been to find out how much energy is needed for this type of an airplane to be able to perform and how big area of the earth it could cover if only powered by the energy solar cells collect under the assumption of ideal conditions. The development of UAVs have been rapid during the past 30 years and considering the increasing environmental problems, environmental forms of flight will only become more and more popular. Airplanes of this type currently have many major uses, for instance they can be used for surveillance and observations as well as platforms for internet and telephony. Reasonable values of the aircraft design has been able to be determined using Zephyr as a starting point. The total weight of the airplane is set to 53 kg with a wingspan of 22.5 m using 2 motors at 450 W each. Different airfoils have been analyzed and a Wortmann FX 74-CL5-140 was chosen due to a high lift coefficient, designed for low Reynolds numbers and a very high lift to drag ratio. The solar cells used to take advantage of the energy of the suns radiation was elected to amorphous silicon solar cells with an efficiency at 20 % and the batteries used to store the energy are 15.9 kg of lithium-sulfur batteries with a specific energy at 500 Wh/kg. Calculations of the airplanes performance were conducted using mainly the distributed compendiums made by the examiner Arne Karlsson, which contain a more detailed description of the formulas. Different flight cases have been analyzed to get a clear picture of what is the most energy efficient flying schedule which resulted in level flight during the day and a mixture of glide and climb during the night. This gives an expected energy usage at approximately 6.1 kWh during the day and roughly 6 kWh during the night. A solar radiation model has been used to approximate how the energy varies in a day and during different times of the year. Calculations of how much energy there is available at different latitudes and heights were made and then compared with the minimal energy consumption the flight requires. Assuming the airplane needs 15 kWh per day to function (this is including a safety factor), the airplane needs to fly on latitudes below 40°N in December and on latitudes below 60°N in October. MATLAB and XFLR5 have been used for calculations and investigating the airfoils.

The purpose of this project is to investigate the construction and flight capacity of an environmentally friendly unmanned aerial vehicle (UAV). The airplane shall then be used for a faster transport of for example medicines or human organs. AD-150, an airplane from the producer American Dynamics Flight Systems, is a big source of inspiration for thedesign, but some new features have been added as well. New technologies and technologies under research have been used in the development of this UAV with plans of production to start in 10-15 years when these products are out on the market. The airplane has tiltrotors for easy take-off and landing, has a body made from carbon fiber to reduce the weight and is 100% environment-friendly. The UAV even charges itself during flight. Two sources of energy are used; solar cells which are placed all over the body and wings and a wind turbine in the back. The wind turbine has been thoroughly studied and as it turns out it is very profitable even though it produces a lot of drag. When the airplane started to take its final shape, different performance values were calculated for level flight with constant speed. In Sweden the maximum flight distance is 3850 km, which equals a flight of 10,5 hours at a speed of 360 km/h. The biggest disadvantage of this UAV is that for the batteries to be fully charged by only solar power,the plane has to stand outside for 87 hours. However, different solutions for this minor issue are being discussed. / Syftet med detta projekt är att undersöka konstruktionen och flygkapaciteten av ettmiljövänligt obemannat flygplan. Detta ska sedan kunna användas till snabbare transportav exempelvis mediciner eller organ. Flygplanet AD-150 från tillverkaren AmericanDynamics Flight Systems är en stor inspirationskälla för designen men en del egna inslaghar adderats. Mycket ny teknik och teknik under forskning har används i utvecklingen avdetta flygplan som planeras vara klart för produktion om 10-15 år när dessa produkterkommit ut på marknaden. Flygplanet har tiltrotorer för enkel start och landning, ett skal gjord av kolfiber för attminska vikten samt är 100 % miljövänligt och laddar sig själv under färd. De tvåenergikällorna är solceller som sitter över hela kroppen och på vingarna samt envindturbin längst bak i planet. Vindturbinen har studerats i ingående detalj och det harvisat sig att den är mycket lönsam trots det ökade motstånden den medför. När flygplanet hade börjat få sin slutgiltiga form beräknades olika prestandavärden för rakflygning med konstant hastighet. För flygning i Sverige ges då en maximal flygsträcka på3850 km vilket motsvarar en flygning på ca 10, 5 timme med en hastighet på 360 km/h.Den största nackdelen med planet är att om batterierna ska laddas fullt innan flygning medbara solenergi måste planet stå och ladda i 87 timmar. Olika lösningar på detta diskuterasdock.