and to serve as platforms for in orbit demonstrations IOD In Low Earth Orbit LEO aerodynamic forces in the. form of atmospheric drag perturb orbital trajectories sometimes in an unpredictable fashion potentially leading to. premature reentry and end of life EOL However when satellite surfaces are configured for specific angles of. incidence relative to the freestream flow particularly for sufficiently long durations near the perigee aerodynamic lift. may have an appreciable effect on preserving orbital dynamics 1 For example a stabilized disk shaped satellite may. be inclined at the same angle to the air flow at the region of perigee where aerodynamic forces are greatest for. successive revolutions As a result the resulting lift would have an appreciable effect on the orbit for perigee heights. up to 500km 2 Furthermore a spinning body in a fluid creates a nonsymmetrical flow pattern that generates an. aerodynamic lift that is commonly described as the Magnus effect This effect has been the subject of great interest in. the history of fluid physics and is named after Professor Gustav Magnus who established that a lifting force is. developed by a spinning cylinder placed in an air flow 3 For example Newton observed that a transverse force acts. on a spinning sphere moving through a fluid and Robins observed a similar effect in the trajectory of cannon balls 4 . A description of the Magnus effect was done by Lord Rayleigh who predicted that the lift was proportional to the. speed of rotation and translation Some of the earliest inventions incorporating this effect included the Flettner rotor. which was a sailboat whose sail used a rotating cylinder which produced a Magnus lift thereby generating a thrust to. push the boat forward Similarly a popular invention was the Magnus airplane where the Magnus lift was produced. by wings made of rotating cylinders However the relatively large drag induced by the cylindrical form made the. design impractical Moreover the Magnus Effect can be seen in many applications including rotary sails propeller. blades wings wind turbines and in the movement of weather systems 4 For example in hurricane formation a. hurricane will stall over open water spinning in a clockwise direction If the wind comes from the West the storm . influenced by the Magnus Effect will move rapidly north On the other hand if the wind originates from the east the. Magnus Effect will propel the rotating air mass to the south . The Magnus force is a function of geometry air density spin rate and freestream velocity and therefore as the. altitude decays atmospheric density increases thereby increasing the magnitude of this force As a result this effect. could be significant for spacecraft in the low Ionosphere Thermosphere region This added maneuverability without. using conventional thrusters could improve efforts to perform in situ atmospheric research in the low Ionosphere . Thermosphere region Likewise this effect can be used to maintain a spacecraft s altitude and could possibly be used. to perform active controlled deorbiting to improve predictions of the impact location Thus this study investigates. the feasibility of using the Magnus effect to sustain a spacecraft s orbit at a low perigee altitude of 80km . Problem Description, A spinning body creates a nonsymmetrical flow pattern above and below the body that generates a Magnus effect. that yields an aerodynamic lift As fluid flows past a rotating body streamlines on the side moving in the same. direction as the flow will converge indicating a diminished pressure 4 The streamlines on the opposite side move. against the freestream and as a result become more widely spaced indicating an increase in pressure as shown in Fig . 1 This pressure differential causes a lifting force that will displace the body in a direction normal to the freestream. flow As a result of the dependence on density the expression for the Magnus force is different for the continuum and. free molecular regime , Figure 1 Lift on a Rotating Body in a Fluid Medium. American Institute of Aeronautics and Astronautics. A continuum or free molecular regime depends on the mean free path of the fluid If the mean free path is small. in comparison with the dimensions of the body then the fluid can be considered a continuum With this assumption . the fluid s density temperature and velocity has a definite value at each point in space However many modern. engineering applications including those for spaceflight occur at high altitudes where the mean free path is not. negligible when compared with the dimension of the body and therefore the effects of the discrete character of the. fluid must be taken into account when defining its properties 5 At these two different regimes the governing physics. and interaction of the molecules are different A widely recognized parameter that determines whether a fluid medium. is a continuum or free molecular is the Knudsen number Kn which is the ratio of the mean free path and the. macroscopic length scale of the physical system In other words the local Knudsen number is a measure of the degree. of rarefaction of a gas 6 As the local Knudsen number increases free molecular effects become more pronounced. and eventually the continuum assumption breaks down As the local Knudsen number decreases as a result of the. increase in atmospheric density the Magnus lift becomes more pronounced thereby enhancing the effect of a potential. Magnus maneuver As a result the work performed in this study is restricted to a spacecraft flying at a perigee of. 80km with the objective of investigating the feasibility of the Magnus effect in sustaining the altitude The magnitude. of this force on the orbital decay will be examined by varying the altitude of apogee spin rate and mass for a spherical. spacecraft having an initial mass of 25kg and a radius of 1m Continuum and free molecular theory will be used to. formulate the appropriate force as a function of the altitude . Motivation, Potential applications that intend to also use a lift perturbation to alter the spacecraft s trajectory include satellites. or space planes which will use an airfoil in the hypersonic flow regime to maneuver in Earth s atmosphere These. airfoils can be used for orbit maintenance by providing a lift vector normal to the orbit s velocity vector Thereby . active altitude adjustments using the proposed Magnus effect on a spinning spacecraft could serve as an orbital. maneuver capability without requiring conventional thrusters For example the added maneuverability of the Magnus. force can possibly allow the spacecraft to perform a skip reentry This reentry technique involves one or more. successive skips off the atmosphere to achieve greater entry range or to reduce the velocity of the spacecraft before. final entry which helps dissipate the heat at the surface For entry vehicles with a relatively low lift to drag ratio a. known strategy since the Apollo era for achieving long downrange is to allow the vehicle to skip out of the atmosphere. 7 In addition the Magnus phenomenon could be used to maintain a low perigee orbit and aid in performing in situ. atmospheric research in the low Ionosphere Thermosphere region This could be significantly more effective for. planets with higher atmospheric densities including Venus whose atmosphere is mostly made up carbon dioxide The. scenario of perigee maintenance allows for immediate benefits for Operationally Responsive Space ORS and Space. Reconstitution SR missions 8 Significantly to perform in situ research at low perigee altitudes a substantial. propulsion system would be needed to raise and lower the perigee 9 The Magnus maneuver could meet these. requirements , Equally important the Magnus effect could be used to perform active controlled deorbiting to improve predictions. of the impact location This could benefit satellites near EOL or for systems that fail to fully demise during reentry. allowing for a controlled deorbiting capability For example several events have previously occurred that illustrate. the importance of predicting the reentry location a priori For example in the article titled Assessing the Aviation Risk. from Space Debris and Meteoroids from the Space Safety Magazine it is explained how the uncontrolled reentry of. Russia s Phobos Grunt resulted in the closing of the European airspace for two hours Most importantly a study. conducted by the FAA following the disintegration of space shuttle Columbia in 2003 found that the probability of. an impact between Columbia debris and a general aviation aircraft was one in a hundred 10 According to the. Aerospace Corporation there are about 100 large man made objects that reenter the earth s atmosphere uncontrolled. each year 10 Furthermore if the predicted risk of human casualties exceeds a specified limit typically 01 per. reentry event a controlled reentry with prescribed reentry location has to be carried out 11 Similarly for satellites. partially surviving the reentry process destruction will occur forming a debris cloud where the time to impact the. ground or to reach the airspace can be short as shown in Figure 2 Thus there exists a need for improving knowledge. of the reentry impact location to mitigate the risk of collision between space debris and other ground stations which. could possibly be achieved using the Magnus force . American Institute of Aeronautics and Astronautics. Figure 2 The risk of collision between space debris and other ground stations 12 . II Literature Review, A literature review was first conducted to examine how an aerodynamic lift perturbation affects a satellite s orbit . Ashenberg in 13 presents solutions for a flat plate satellite experiencing non constant aerodynamic coefficients by. using the Gaussian form for the Variation of Parameter VOP equations He describes that if a satellite has dominant. flat surfaces rotates at certain slow rates or has a large area to mass ratio the lift forces do not average out to zero . The lift perturbation is considered as a vector in the plane normal to the velocity pointing in any direction The. perturbations are projected in the normal direction given by hxV toward the inside of the orbit and calculations are. done assuming free molecular hyperthermal flow The orbit angular momentum is described by h whereas V is the. relative velocity of the satellite He describes how the lift acting in the orbital plane perturbs the eccentricity vector . while an orthogonal out of plane force perturbs the orientation of the orbital plane Significantly he states that since. the lifting force does not change the energy the semi major axis is perturbed by drag alone The general conclusion. is that time varying aerodynamic coefficients may cause various forms of secular orbital motion . Cook 2 explains that one can neglect the aerodynamic force for a satellite undergoing a rapid and uncontrolled. tumbling motion for most of their lifetime since the effects of the normal force to the velocity vector is averaged out. over one revolution However for satellites that remain stabilized for long intervals of time one must reexamine the. effect of the aerodynamic lift He assumes lift acts in the orbital plane and investigates two primary cases for a flat . plate satellite a constant lift to drag ratio followed by a trajectory that has a negative lift coefficient from perigee to. apogee and then a constant positive lift coefficient from apogee to perigee Similar to Ashenberg he considers the. simplest case of hyperthermal free molecule flow where the thermal accommodation coefficient 1 for which the. random thermal motion of the molecules is assumed negligible compared with the satellite s speed With complete. accommodation or with a thermal accommodation coefficient value of 1 the lift to drag ratio will be on the order of. 0 05 With no accommodation Cooke describes that the lift to drag ratio can be high as 2 3 and therefore the. importance of lift depends on the nature of the momentum exchange at the satellites surface Furthermore Cook goes. on to explain that since lift acts perpendicular to the satellite s velocity vector it can have no effect on the semi major. axis of the orbit Consequently one should only be concerned with variations of the eccentricity vector In order for. the orbital inclination to change a component of force normal to the orbital plane is required 14 For the constant. lift coefficient case Cook finds that the eccentricity remains constant and the only effect of lift is to rotate the major. axis For the discontinuous lift coefficient case Cook finds that the only secular perturbation is a decrease in the. eccentricity , Moore 15 also describes how satellites in stabilized attitudes may be subjected to steady or periodic lift giving. rise to perceptible perturbations in the orbital elements He uses the LaGrange equations of motion to study the effects. of lift and drag on the orbital elements and states that the precise determination of lift effects require either in situ. examination of the gas surface interaction or detailed analysis of orbital perturbations and spin rate data He describes. the hyperthermal free molecular flow as being where the mean free path of the molecules is very large compared with. the dimensions of the satellite and where the molecules have no random thermal motion Diffuse reflection is. American Institute of Aeronautics and Astronautics. significant at 200km 800km where atomic oxygen predominates and at higher altitudes the reflectio. Magnus Effect on a Spinning Satellite in Low Earth Orbit Sahadeo Ramjatan1 and Norman Fitz Coy2 University of Florida Gainesville FL 32611 Alvin Garwai Yew3 NASA GSFC Greenbelt MD 20771 A spinning body in a flow field generates an aerodynamic lift or Magnus effect that displaces the body in a direction normal to the freestream flow Earth

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