Initial Altitude Research Articles

Autonomous homing control of a powered parafoil with insufficient altitude

In order to realize safe and accurate homing of a powered parafoil under the condition of insufficient initial altitude, a multiphase homing path is designed according to the flight characteristics of the vehicle. With consideration that the traditional control methods cannot ensure the quality of path following because of the nonlinear, large inertial and longtime delay existed in the system and strong disturbances in a complex environment, a homing controller, composed of the vertical and horizontal trajectory tracking controllers, is designed based on active disturbance rejection control (ADRC). Then autonomous homing simulation experiment of the powered parafoil with insufficient altitude is carried on in a windy environment. The simulation results show that the planned multiphase homing trajectory can fulfill the requirements of fixed-point homing and flare landing; the designed homing controller can overcome the influences of uncertain items of the internal and external disturbances, track the desired homing path more rapidly and steadily, and possesses better control performances than traditional PID controllers.

An active attitude control system for a drag sail satellite

The paper describes the development and simulation results of a full ADCS subsystem for the deOrbitSail drag sail mission. The deOrbitSail satellite was developed as part of an European FP7 collaboration research project. The satellite was launched and commissioning started on 10th July 2015. Various new actuators and sensors designed for this mission will be presented. The deOrbitSail satellite is a 3U CubeSat to deploy a 4 by 4m drag sail from an initial 650km circular polar low earth orbit. With an active attitude control system it will be shown that by maximising the drag force, the expected de-orbiting period from the initial altitude will be less than 50 days. A future application of this technology will be the use of small drag sails as low-cost devices to de-orbit LEO satellites, when they have reached their end of life, without having to use expensive propulsion systems. Simulation and Hardware-in-Loop experiments proved the feasibility of the proposed attitude control system. A magnetic-only control approach using a Y-Thomson spin, is used to detumble the 3U Cubesat with stowed sail and subsequently to 3-axis stabilise the satellite to be ready for the final deployment phase. Minituarised torquer rods, a nano-sized momentum wheel, attitude sensor hardware (magnetometer, sun, earth) developed for this phase will be presented. The final phase will be to deploy and 3-axis stabilise the drag sail normal to the satellite’s velocity vector, using a combined Y-momentum wheel and magnetic controller. The design and performance improvements when using a 2-axis translation stage to adjust the sail centre-of-pressure to satellite centre-of-mass offset, will also be discussed, although for launch risk reasons this stage was not included in the final flight configuration. To accurately determine the drag sail’s attitude during the sunlit part of the orbit, an accurate wide field of view dual sensor to measure both the sun and nadir vector direction was developed for this mission. The calibration results for this new Cubesat sensor (CubeSense), will also be presented.

Wind Uncertainty Modeling and Robust Trajectory Planning for Autonomous Parafoils

A key challenge facing modern airborne delivery systems, such as parafoils, is the ability to accurately and consistently deliver supplies into difficult, complex terrain. Robustness is a primary concern, given that environmental wind disturbances are often highly uncertain and time-varying. This paper presents a new online trajectory-planning algorithm that enables a large, autonomous parafoil with underactuated dynamics to robustly execute collision avoidance and precision landing on mapped terrain, even with significant wind uncertainties. This algorithm is designed to handle arbitrary initial altitudes, approach geometries, and terrain surfaces, and is robust to wind disturbances that may be highly dynamic throughout terminal approach. Real-time wind uncertainty modeling and classification are used to anticipate future disturbances, while a novel uncertainty-sampling technique ensures that robustness to future wind variation is efficiently maintained. The designed cost-to-go function enables selection of partial paths that intelligently trade off between current and reachable future states, while encouraging upwind landings. Simulation results demonstrate that this algorithm reduces the worst-case impact of wind disturbances relative to state-of-the-art approaches.

Numerical Study of Magnetohydrodynamic Flow Control Along Superorbital Reentry Trajectories

Effects of magnetohydrodynamic flow control on the aerodynamic heating of a superorbital reentry body are examined by magnetohydrodynamic numerical simulation coupled with flight trajectory analysis. The initial flight altitude and velocity are set to 75 km and , respectively. Convective wall heat flux is directly calculated in the magnetohydrodynamic numerical simulation, whereas radiative wall heat flux is calculated by a structured package for the radiation analysis using the output data from the magnetohydrodynamic numerical simulation in an uncoupled manner of flowfield and radiation. Numerical results demonstrate that magnetohydrodynamic flow control significantly mitigates a peak value of total wall heat flux during the flight duration due to a drag-enhancement effect of magnetohydrodynamic flow control, although the total wall heat flux at high altitudes is elevated by magnetohydrodynamic flow control because of a considerable increase in radiative wall heat flux.

Transport pathways from the Asian monsoon anticyclone to the stratosphere

Abstract. Transport pathways of air originating in the upper-tropospheric Asian monsoon anticyclone are investigated based on three-dimensional trajectories. The Asian monsoon anticyclone emerges in response to persistent deep convection over India and southeast Asia in northern summer, and this convection is associated with rapid transport from the surface to the upper troposphere and possibly into the stratosphere. Here, we investigate the fate of air that originates within the upper-tropospheric anticyclone from the outflow of deep convection, using trajectories driven by ERA-interim reanalysis data. Calculations include isentropic estimates, plus fully three-dimensional results based on kinematic and diabatic transport calculations. Isentropic calculations show that air parcels are typically confined within the anticyclone for 10–20 days and spread over the tropical belt within a month of their initialization. However, only few parcels (3 % at 360 K, 8 % at 380 K) reach the extratropical stratosphere by isentropic transport. When considering vertical transport we find that 31 % or 48 % of the trajectories reach the stratosphere within 60 days when using vertical velocities or diabatic heating rates to calculate vertical transport, respectively. In both cases, most parcels that reach the stratosphere are transported upward within the anticyclone and enter the stratosphere in the tropics, typically 10–20 days after their initialization at 360 K. This suggests that trace gases, including pollutants, that are transported into the stratosphere via the Asian monsoon system are in a position to enter the tropical pipe and thus be transported into the deep stratosphere. Sensitivity calculations with respect to the initial altitude of the trajectories showed that air needs to be transported to levels of 360 K or above by deep convection to likely (≧ 50 %) reach the stratosphere through transport by the large-scale circulation.

Precise science orbits for the Swarm satellite constellation

The European Space Agency (ESA) Swarm mission was launched on 22 November 2013 to study the dynamics of the Earth’s magnetic field and its interaction with the Earth system. The mission consists of three identical satellites, flying in carefully selected near polar orbits. Two satellites fly almost side-by-side at an initial altitude of about 480km, and will descend due to drag to around 300km during the mission lifetime. The third satellite was placed in a higher orbit of about 530km altitude, and therefore descends much more slowly. To geolocate the Swarm observations, each satellite is equipped with an 8-channel, dual-frequency GPS receiver for Precise Orbit Determination (POD). Onboard laser retroreflectors provide the opportunity to validate the orbits computed from the GPS observations using Satellite Laser Ranging (SLR) data. Precise Science Orbits (PSOs) for the Swarm satellites are computed by the Faculty of Aerospace Engineering at Delft University of Technology in the framework of the Swarm Satellite Constellation Application and Research Facility (SCARF). The PSO product consists of both a reduced-dynamic and a kinematic orbit solution. After a short description of the Swarm GPS data characteristics, the adopted POD strategy for both orbit types is explained and first PSO results from more than one year of Swarm GPS data are presented. Independent SLR validation shows that the reduced-dynamic Swarm PSOs have an accuracy of better than 2cm, while the kinematic orbits have a slightly reduced accuracy of about 4–5cm. Orbit comparisons indicate that the consistency between the reduced-dynamic and kinematic Swarm PSO for most parts of the Earth is at the 4–5cm level. Close to the geomagnetic poles and along the geomagnetic equator, however, the kinematic orbits show larger errors, which are probably due to ionospheric scintillations that affect the Swarm GPS receivers over these areas.

A física no salto recorde de Felix Baumgartner

<p>Em 14/10/2012 Felix Baumgartner fez seu salto recorde na atmosfera. A partir do vídeo que apresenta medidas de tempo, velocidade, altitude e aceleração durante todo o salto recorde são discutidos diversos aspectos da Mecânica envolvida no feito bem com tópicos de física da Atmosfera Terrestre, relevantes para a compreensão do movimento de descida desde a estratosfera. Além dos três recordes mundialmente reconhecidos - maior altitude inicial, maior extensão de queda e obtenção de velocidade supersônica por um paraquedista - demonstra-se quantitativamente que também ocorreu queda livre, com aceleração em acordo com o valor previsto teoricamente pela <italic>International Gravity Formula</italic>, durante mais de 20 s, por mais de 3 km, constituindo-se certamente em outro recorde. Apresenta-se também um modelo para a velocidade na etapa de descida sem paraquedas que é consistente com os dados do vídeo.</p>

Oxygen tension regulates H2S and NO bioavailability in reciprocal manner (885.3)

Nitric oxide and hydrogen sulfide modulate several physiological and cellular functions including vasodilation, cell proliferation and redox cell signaling. Production and bioavailability of either molecule may be influenced by oxygen tension; however, the relationship between H2S and NO bioavailability during hypoxia remains poorly understood. In this study, we examined plasma free H2S and nitrite levels in healthy volunteers exposed to high altitude. Plasma free H2S levels were significantly greater at sea level compared to high altitude (5260 meters) at 1 or 16 days; whereas, plasma nitrite levels were significantly higher at high altitude compared to sea level. After spending 7 or 21 days at low altitude, volunteers were tested again at 5260 m. On reascent, plasma free H2S levels were increased compared to initial high altitude exposure. Conversely, plasma nitrite levels were lower than high altitude exposure on reascent indicating reciprocal regulation between the gasotransmitters. Calculation of plasma free H2S to nitrite ratios revealed that high altitude acclimatization decreases the ratio of plasma free H2S to nitrite, and that on reascent H2S to nitrite ratios return to low altitude levels. In vitro cellular hypoxia studies using HUVEC revealed significant decreases in acid labile sulfide while increasing protein bound biochemical forms of sulfide. Interestingly, in vitro hypoxic challenge similarly decreased free H2S to nitrite ratios in HUVEC similar to high altitude exposure. These data demonstrate a unique reciprocal relationship between H2S and NO bioavailability during hypoxia.

First results of operational ionospheric dynamics prediction for the Brazilian Space Weather program

It is shown the development and preliminary results of operational ionosphere dynamics prediction system for the Brazilian Space Weather program. The system is based on the Sheffield University Plasmasphere–Ionosphere Model (SUPIM), a physics-based model computer code describing the distribution of ionization within the Earth mid to equatorial latitude ionosphere and plasmasphere, during geomagnetically quiet periods. The model outputs are given in a 2-dimensional plane aligned with Earth magnetic field lines, with fixed magnetic longitude coordinate. The code was adapted to provide the output in geographical coordinates. It was made referring to the Earth’s magnetic field as an eccentric dipole, using the approximation based on International Geomagnetic Reference Field (IGRF-11). During the system operation, several simulation runs are performed at different longitudes. The original code would not be able to run all simulations serially in reasonable time. So, a parallel version for the code was developed for enhancing the performance. After preliminary tests, it was frequently observed code instability, when negative ion temperatures or concentrations prevented the code from continuing its processing. After a detailed analysis, it was verified that most of these problems occurred due to concentration estimation of simulation points located at high altitudes, typically over 4000km of altitude. In order to force convergence, an artificial exponential decay for ion–neutral collisional frequency was used above mentioned altitudes. This approach shown no significant difference from original code output, but improved substantially the code stability. In order to make operational system even more stable, the initial altitude and initial ion concentration values used on exponential decay equation are changed when convergence is not achieved, within pre-defined values. When all code runs end, the longitude of every point is then compared with its original reference station longitude, and differences are compensated by changing the simulation point time slot, in a temporal adjustment optimization. Then, an approximate neighbor searching technique was developed to obtain the ion concentration values in a regularly spaced grid, using inverse distance weighting (IDW) interpolation. A 3D grid containing ion and electron concentrations is generated for every hour of simulated day. Its spatial resolution is 1° of latitude per 1° of longitude per 10km of altitude. The vertical total electron content (VTEC) is calculated from the grid, and plotted in a geographic map. An important feature that was implemented in the system is the capacity of combining observational data and simulation outputs to obtain more appropriate initial conditions to the ionosphere prediction. Newtonian relaxation method was used for this data assimilation process, where ionosonde data from four different locations in South America was used to improve the system accuracy. The whole process runs every day and predicts the VTEC values for South America region with almost 24h ahead.

Cloud-resolving simulations of mercury scavenging and deposition in thunderstorms

Abstract. This study examines dynamical and microphysical features of convective clouds that affect mercury (Hg) wet scavenging and concentrations in rainfall. Using idealized numerical model simulations in the Regional Atmospheric Modeling System (RAMS), we diagnose vertical transport and scavenging of soluble Hg species – gaseous oxidized mercury (GOM) and particle-bound mercury (HgP), collectively Hg(II) – in thunderstorms under typical environmental conditions found in the Northeast and Southeast United States (US). Mercury scavenging efficiencies from various initial altitudes are diagnosed for a case study of a typical strong convective storm in the Southeast US. Assuming that soluble mercury concentrations are initially vertically uniform, the model results suggest that 60% of mercury deposited to the surface in rainwater originates from above the boundary layer (> 2 km). The free troposphere could supply a larger fraction of mercury wet deposition if GOM and HgP concentrations increase with altitude. We use radiosonde observations in the Northeast and Southeast to characterize three important environmental characteristics that influence thunderstorm morphology: convective available potential energy (CAPE), vertical shear (0–6 km) of horizontal wind (SHEAR) and precipitable water (PW). The Southeast US generally has lower SHEAR and higher CAPE and PW. We then use RAMS to test how PW and SHEAR impact mercury scavenging and deposition, while keeping the initial Hg(II) concentrations fixed in all experiments. We found that the mercury concentration in rainfall is sensitive to SHEAR with the nature of sensitivity differing depending upon the PW. Since CAPE and PW cannot be perturbed independently, we test their combined influence using an ensemble of thunderstorm simulations initialized with environmental conditions for the Northeast and Southeast US. These simulations, which begin with identical Hg(II) concentrations, predict higher mercury concentrations in rainfall from thunderstorms forming in the environmental conditions over the Southeast US compared to the Northeast US. A final simulation of a stratiform rain event produces lower mercury concentrations than in thunderstorms forming in environments typical of the Southeast US. The stratiform cloud scavenges mercury from the lowest ~ 4 km of the atmosphere, while thunderstorms scavenge up to ~ 10 km.

The equivalence of gravitational potential and rechargeable battery for high-altitude long-endurance solar-powered aircraft on energy storage

Applying solar energy is one of the most promising methods to achieve the aim of High-altitude Long-endurance (HALE) flight, and solar-powered aircraft is usually taken by the research groups to develop HALE aircraft. However, the crucial factor which constrains the solar-powered aircraft to achieve the aim of HALE is the problem how to fulfill the power requirement under weight constraint of rechargeable batteries. Motivated by the birds store energy from thermal by gaining height, the method of energy stored by gravitational potential for solar-powered aircraft have attracted great attentions in recent years. In order to make the method of energy stored in gravitational potential more practical in solar-powered aircraft, the equivalence of gravitational potential and rechargeable battery for aircraft on energy storage has been analyzed, and four kinds of factors are discussed in this paper: the duration of solar irradiation, the charging rate, the energy density of rechargeable battery and the initial altitude of aircraft. This work can provide some governing principles for the solar-powered aircraft to achieve the unlimited endurance flight, and the endurance performance of solar-powered aircraft may be greatly improved by the application of energy storage using gravitational potential.

Chelyabinsk superbolide explosion in the Earth’s atmosphere: A common phenomenon or unique coincidence?

The paper analyzes the disintegration of small cosmic bodies in a planetary atmosphere and most important facts observed during the fall of the Chelyabinsk superbolide: its speed loss during passage through the upper atmosphere, its strength and the character of destruction, the altitude of its explosion, and the energy release. Detailed data are presented on the aerodynamic phenomena accompanying the supersonic atmospheric entry and destruction of the superbolide. The strength of the original meteorite is evaluated as a function of its initial disintegration altitude. Principal data obtained on the collision between comet Shoemaker-Levy 9 and Jupiter are reported.

How simulated fluence of photons from terrestrial gamma ray flashes at aircraft and balloon altitudes depends on initial parameters

Up to a few years ago, terrestrial gamma ray flashes (TGFs) were only observed by spaceborne instruments. The aircraft campaign ADELE was able to observe one TGF, and more attempts on aircraft observations are planned. There is also a planned campaign with stratospheric balloons, COBRAT. In this context an important question that arises is what count rates we can expect and how these estimates are affected by the initial properties of the TGFs. Based on simulations of photon propagation in air we find the photon fluence at different observation points at aircraft and balloon altitudes. The observed fluence is highly affected by the initial parameters of the simulated TGFs. One of the most important parameters is the number of initial photons in a TGF. In this paper, we give a semi‐analytical approach to find the initial number of photons with an order of magnitude accuracy. The resulting number varies over several orders of magnitude, depending mostly on the production altitude of the TGF. The initial production altitude is also one of the main parameters in the simulations. Given the same number of initial photons, the fluence at aircraft and balloon altitude from a TGF produced at 10 km altitude is 2–3 orders of magnitude smaller then a TGF originating from 20 km altitude. Other important parameters are altitude distribution, angular distribution and amount of feedback. The differences in altitude, altitude distribution and amount of feedback are especially important for the fluence of photons observed at altitudes less than 20 km, and for instruments with a low‐energy threshold larger than 100 keV. We find that the maximum radius of observation in 14 km for a TGF with the intensity of an average RHESSI TGF is smaller than the results reported by Smith et al. (2011), and our results support the conclusion in Gjesteland et al. (2012) and Østgaard et al. (2012) that TGFs probably are a more common phenomenon than previously reported.

燃料消費節減に効率的な降下開始地点の予測についての覚書

The aircraft descent profile has many factors, such as selected airspeed, flight weight, wind, initial altitude, and outside temperature even if fixed idle thrust was assumed. This article tries to prove a rule of thumb that "Even if the wind changes at lower altitude during descent, the flight path will converge at a lower altitude". This may be useful information for flight operation, if it is correct. In addition idle thrust descents are a useful method for fuel economy operation. This paper tries to support this rule of thumb by numerical simulations of flight paths with different wind conditions.

Simulations of High Altitude Tests for Large Area Ratio Rocket Motors

In the present study, performance characteristics of a high altitude test facility for testing large area ratio rocket engines have been investigated. Steady-state numerical simulations have been performed initially to highlight the effects of operational parameters on a high altitude test facility operation. Later, the performance of the test facility during the startup phase of the rocket motor has been analyzed. The predicted results show that during the initial high altitude test facility evacuation, the desired vacuum level is attained when the primary jet flow attaches to the ejector duct walls smoothly, thereby arresting any back flow. However, at the fully started condition of the motor, the self-ejector action of the rocket plume plays a major role in maintaining the desired vacuum condition and, hence, the ejector flow rate can be reduced significantly. The injection of water as a fine spray cools the hot gas to a sufficiently low temperature () prior to its release into the atmosphere. The transient predictions capture dynamic phenomena, such as the initial back flow of exhaust gas, and the attainment of self-ejection capability by rocket exhaust in the later stage. The predicted results compare well with in-house experimental data measured during cold and hot flow tests.

Research on characteristics of gravitational gliding for high-altitude solar-powered unmanned aerial vehicles

Gravitational gliding during night without electric power is an efficient method to enhance the endurance of high-altitude solar-powered unmanned aerial vehicles. The properties of the maximum endurance path of gravitational gliding are studied in this article. The maximum endurance path problem is formulated as the problem of the maximum endurance can be sustained by unit altitude difference with the constraints of dynamic equations and aerodynamic parameters. The maximum endurance path is generated by Gauss pseudo-spectral method, and a new way to estimate co-state variables in Hamiltonian is proposed. In order to analyze the sensitivity of initial altitude and velocity of solar unmanned aerial vehicles with its endurance performance, the lift coefficient in the interval [0.4, 1.2] and flight envelopes between 0 and 30 km are investigated. The results are as follows: first, the broad range of lift coefficients can improve solar aircrafts’ long-endurance performance; second, the lower the initial altitude, the longer the gliding endurance can be sustained by unit altitude difference; third, it is possible for a solar-powered unmanned aerial vehicle to keep aloft during the whole night just by gravitational potential energy storage, but the issues with turbulence and wind would render this mode of unlimited endurance unfeasible. Thus, gravitational gliding by potential energy storage can only be partly used instead of electric energy storage in application now.

Physical Parameters of Shock-accelerated Electron Region Estimated from Observations of Solar Metric Band-split Type II Burst

This study presents the analysis of a solar split-band type II radio burst observed on November 3, 2010 (∼ 10:17:14 UT) by CALLISTO-BR (Compound Astronomical Low frequency Low Cost Instrument for Spectroscopy and Transportable Observatory) spectrometer operating in the frequency range of 45-870 MHz. Among the physical parameters determined for the shock propagation region are: source speed of the order of 1033 km s^−1 ; electron number density of ∼ 8.6 × 10^8 cm^−3 ; Alfven speed of the order of 2007 km s^−1 ; Mach number of ∼ 1.09 − 1.33; magnetic field strength of ∼ 7 − 177 G and temperature of the order of 6.0 × 10^6 K. The outcomes, compared to those reported in the literature, are consistent, taking into account the fact we are dealing with an atypical type II radio burst, namely, one with high starting frequency, what accounts for the very high Alfven speeds estimated for the initial altitudes of propagation of the shock through the solar corona.

Effect of Spacecraft Aerodynamics and Heat Shield Characteristics on Optimal Aeroassisted Transfer

A spacecraft designed to operate in a planetary atmosphere must have an adequate heat shield to withstand the high heat fluxes and heat loads that are generated by aerodynamic heating. Very often, the mass of the thermal protection system is a significant fraction of the total mass of the vehicle. In contrast, performing maneuvers in the atmosphere, that would be very costly in terms of propellant consumption if they were performed completely outside of the atmosphere in a classic way, is a very attractive prospective technique. The advantages and disadvantages in terms of total mass spared must be determined. The mission investigated involves an aeroassisted coplanar transfer from a high to a low Earth orbit. The approach uses a combination of three propulsive impulses in space together with an aerodynamic maneuver in the atmosphere. The heat shield adopted is fully ablative, given the expected high values of the entering heat flux. The convenience of the aeroassisted maneuver and the influence of the parameters involved are evaluated in comparison to a conventional Hohmann transfer. In particular, a parametric analysis is performed by varying the following characteristics of the vehicle: aerodynamic efficiency, mass-to-surface ratio, deorbit impulse, and initial altitude of the orbit. The influence of the thermal protection system is examined by assessing the impact of the type of ablative material employed, the thermal safety factor, and the allowable temperature for the adhesive layer on the substructure. The analysis is conducted with a highly representative thermal model by coupling the dynamic and thermal analyses and using a genetic optimizer. The optimization methodology and the thermal model are completely original. The results indicate the importance of choosing low-density ablative materials, of adopting a suitable thermal safety factor, and of choosing high-performance adhesives. The optimal trajectories obtained correspond to a zero second propulsive impulse.

GPS-derived orbits for the GOCE satellite

The first ESA (European Space Agency) Earth explorer core mission GOCE (Gravity field and steady-state Ocean Circulation Explorer) was launched on 17 March 2009 into a sun-synchronous dusk–dawn orbit with an exceptionally low initial altitude of about 280 km. The onboard 12-channel dual-frequency GPS (Global Positioning System) receiver delivers 1 Hz data, which provides the basis for precise orbit determination (POD) for such a very low orbiting satellite. As part of the European GOCE Gravity Consortium the Astronomical Institute of the University of Bern and the Department of Earth Observation and Space Systems are responsible for the orbit determination of the GOCE satellite within the GOCE High-level Processing Facility. Both quick-look (rapid) and very precise orbit solutions are produced with typical latencies of 1 day and 2 weeks, respectively. This article summarizes the special characteristics of the GOCE GPS data, presents POD results for about 2 months of data, and shows that both latency and accuracy requirements are met. Satellite Laser Ranging validation shows that an accuracy of 4 and 7 cm is achieved for the reduced-dynamic and kinematic Rapid Science Orbit solutions, respectively. The validation of the reduced-dynamic and kinematic Precise Science Orbit solutions is at a level of about 2 cm.

Phugoid dynamic characteristic of hypersonic gliding vehicles

This paper focuses on the phugoid dynamic characteristic of hypersonic gliding vehicle. By regarding equilibrium glide as the fixed state of reentry trajectory, the dynamic equations are simplified and a hyper-geometric equation with a forcing function is deduced. Linearization theory is applied to analyze the characteristic of the motion, and the phugoid mode is found to be stable. An analytical solution of flight path angle as a function of speed is derived based on General Multiple Scale theory. The dynamic characteristic is analyzed, and the analytic solution is found to be in good agreement with the numerical simulation. When the initial states do not satisfy equilibrium glide condition or perturbation occurs, a damped oscillation along the equilibrium glide trajectory would occur. The damping diminishes as the speed decreases. The number of oscillations is decided by the lift-to-drag ratio, the initial altitude and the initial/final speed.