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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Development of Advanced Methods of Structural and Trajectory Analysis for Transport Aircraft

This paper develops a near-optimal guidance law for generating minimum fuel, time, or cost fixed-range trajectories for supersonic transport aircraft. The approach uses a choice of new state variables along with singular perturbation techniques to time-scale decouple the dynamic equations into multiple equations of single order (second order for the fast dynamics). Application of the maximum principle to each of the decoupled equations, as opposed to application to the original coupled equations, avoids the two point boundary value problem and transforms the problem from one of a functional optimization to one of multiple function optimizations. It is shown that such an approach produces well known aircraft performance results such as minimizing the Brequet factor for minimum fuel consumption and the energy climb path. Furthermore, the new state variables produce a consistent calculation of flight path angle along the trajectory, eliminating one of the deficiencies in the traditional energy state approximation. In addition, jumps in the energy climb path are smoothed out by integration of the original dynamic equations at constant load factor. Numerical results performed for a supersonic transport design show that a pushover dive followed by a pullout at nominal load factors are sufficient maneuvers to smooth the jump.

Ardema, Mark D.↗
NASA NTRS1960

An Examination of Handling Qualities Criteria for V/STOL Aircraft

A study has been undertaken to define hand-ling qualities criteria for V/STOL aircraft. With the current military requirements for helicopters and airplanes as a framework, modifications and additions were made for conversion to a preliminary set of V/STOL requirements using a broad background of flight experience and pilots' comments from VTOL and STOL aircraft, BLC (boundary-layer-control) equipped aircraft, variable stability aircraft, flight simulators and landing approach studies. The report contains a discussion of the reasoning behind and the sources of information leading to suggested requirements. The results of the study indicate that the majority of V/STOL requirements can be defined by modifications to the helicopter and/or airplane requirements by appropriate definition of reference speeds. Areas where a requirement is included but where the information is felt to be inadequate to establish a firm quantitative requirement include the following: Control power and damping relationships about all axes for various sizes and types of aircraft; control power, sensitivity, d-amping and response for height control; dynamic longitudinal and dynamic lateral- directional stability in the transition region, including emergency operation; hovering steadiness; acceleration and deceleration in transition; descent rates and flight-path angles in steep approaches, and thrust margin for approach.

Anderson, Seth B.↗
NASA NTRS1960

Flight Investigation of the Low-Speed Characteristics of a 45 deg Swept-Wing Fighter-Type Airplane with Blowing Boundary-Layer Control Applied to the Leading- and Trailing-Edge Flaps

A flight investigation has been conducted to study how pilots use the high lift available with blowing-type boundary-layer control applied to the leading- and trailing-edge flaps of a 45 deg. swept-wing airplane. The study includes documentation of the low-speed handling qualities as well as the pilots' evaluations of the landing-approach characteristics. All the pilots who flew the airplane considered it more comfortable to fly at low speeds than any other F-100 configuration they had flown. The major improvements noted were the reduced stall speed, the improved longitudinal stability at high lift, and the reduction in low-speed buffet. The study has shown the minimum comfortable landing-approach speeds are between 120.5 and 126.5 knots compared to 134 for the airplane with a slatted leading edge and the same trailing-edge flap. The limiting factors in the pilots' choices of landing-approach speeds were the limits of ability to control flight-path angle, lack of visibility, trim change with thrust, low static directional stability, and sluggish longitudinal control. Several of these factors were found to be associated with the high angles of attack, between 13 deg. and 15 deg., required for the low approach speeds. The angle of attack for maximum lift coefficient was 28 deg.

Quigley, Hervey C.↗
NASA NTRS1960

Longitudinal Aerodynamic Characteristics of a Four-Propeller Deflected Slipstream VTOL Model Including the Effects of Ground Proximity

Results are presented of a wind-tunnel investigation of the longitudinal stability, control, and performance characteristics of a model of a four-propeller deflected-slipstream VTOL airplane in the transition speed range. These results indicate that steady level-flight transition and descending flight-path angles up to 7 or 8 deg. out of the region of ground effect can be accomplished without wing stall being encountered. In general, the pitching moments out of ground proximity can be adequately trimmed by programming the stabilizer incidence to increase with increasing flap deflection, except for a relatively large diving moment in the hovering condition. The deflection of the slipstream onto the horizontal tail in proximity of the ground substantially increases the diving moment in hovering, unless the tail is set at a large nosedown incidence.

Kuhn, Richard E.↗
NASA NTRS1961

Point Return from a Lunar Mission for a Vehicle that Maneuvers Within the Earth's Atmosphere

An investigation has been made of point return of a vehicle with a lift-to-drag ratio of 1/2, returning from a lunar mission. It was found that the available longitudinal and lateral range allowed considerable tolerances in entry conditions for a point return. Longitudinal range capability for a vehicle that was allowed to skip to an altitude not exceeding 400 miles was about 3-1/2 times greater than the range capability of a vehicle that was restricted to remain in the atmosphere after entry. Longitudinal range is very sensitive to changes in both velocity and flight-path angle at the bottom of the first pull-out and at exit. An investigation showed that after a skip a vehicle could be placed in a circular orbit for a relatively modest weight penalty. A skip maneuver was found to have no effect on lateral range when the roll was initiated at a velocity near satellite speed after the vehicle had re-entered the atmosphere. However, when the roll was initiated at the earliest possible time along the undershoot boundary, lateral range was increased by a factor of about 2-1/2. The tolerable errors in time of arrival and in inclination of the orbital plane at point of entry were greater for the skip trajectory than for the no-skip trajectory.

Sommer, Simon C.↗
NASA NTRS1961

Atmosphere Entries with Vehicle Lift-Drag Ratio Modulated to Limit Deceleration and Rate of Deceleration: Vehicles with Maximum Lift-Drag Ratio of 0.5

An analysis has been made of atmosphere entries for which the vehicle lift-drag ratio was modulated to maintain specified maximum decelerations and/or maximum deceleration rates. The part of the vehicle drag polar used during modulation was from maximum lift coefficient to minimum drag coefficient. The entries were at parabolic velocity and the vehicle maximum lift-drag ratio was 0.5. Two-dimensional trajectory calculations were made for a nonrotating, spherical earth with an exponential atmosphere. The results of the analysis indicate that for a given initial flight-path angle, modulation generally resulted in a reduction of the maximum deceleration to 60 percent of the unmodulated value or a reduction of maximum deceleration rate to less than 50 percent of the unmodulated rate. These results were equivalent, for a maximum deceleration of 10 g, to lowering the undershoot boundary 24 miles with a resulting decrease in total convective heating to the stagnation point of 22 percent. However, the maximum convective heating rate was increased 18 percent; the maximum radiative heating rate and total radiative heating were each increased about 10 percent.

Katzen, Elliott D.↗
NASA NTRS1959

A Generalized Hydrodynamic-Impact Theory for the Loads and Motions of Deeply Immersed Prismatic Bodies

A theory is derived for determining the loads and motions of a deeply immersed prismatic body. The method makes use of a two-dimensional water-mass variation and an aspect-ratio correction for three-dimensional flow. The equations of motion are generalized by using a mean value of the aspect-ratio correction and by assuming a variation of the two-dimensional water mass for the deeply immersed body. These equations lead to impact coefficients that depend on an approach parameter which, in turn, depends upon the initial trim and flight-path angles. Comparison of experiment with theory is shown at maximum load and maximum penetration for the flat-bottom (0 deg dead-rise angle) model with bean-loading coefficients from 36.5 to 133.7 over a wide range of initial conditions. A dead-rise angle correction is applied and maximum-load data are compared with theory for the case of a model with 300 dead-rise angle and beam-loading coefficients from 208 to 530.

Markey, Melvin F.↗
NASA NTRS1961

Velocity Requirements for Abort From the Boost Trajectory of a Manned Lunar Mission

An investigation is made of the abort velocity requirements associated with failure of a propulsion system for a manned lunar mission. Two cases are considered: abort at less than satellite speed, which results in maximum decelerations in the following entry, and abort at greater than satellite speed with immediate return to earth. The velocity requirements associated with the latter problem are found to be substantial (several thousand feet per second) and are found to be even more severe if boost trajectories which lead to burnout at high altitudes or large flight-path angles are used. The velocity requirements associated with abort at less than satellite speed are found to be less severe than those for abort at greater than satellite speed except for nonlifting vehicles. It is found that abort rockets sufficient for abort at greater than satellite speed can be used to reduce maximum decelerations in entries following an abort at lower speeds. This reduction is accomplished by use of the abort rockets to decrease entry angle immediately prior to entry into the atmosphere.

Slye, Robert E.↗
NASA NTRS1998

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Carpenter, J. Russell↗
NASA NTRS1995

Estimates of Heat Shielding Requirements for Saturn Probe Missions

Entry trajectories, decelerations, heating and heat shielding requirements of probes entering the atmosphere of Saturn at relative entry velocities ranging from 26.5 - 33.0 km/sec were studied. Much of the Galileo Jupiter probe technology was applicable to these outer planet probes; therefore, the same configuration was used. A wide range entry flight path angles were used in the trajectory analysis in order to satisfy the complete range of arrival conditions and trajectory requirements. Various entry probe sizes and a range of entry masses from 32 - 258 kg were considered. The carbon phenolic heat shield material used on the Galileo and the successful Pioneer-Venus probes was selected. Turbulent boundary layer convection dominated the heating of the Saturn probes; radiative heating was negligible by comparison at the entry velocities considered. The peak heating rates were found to be about 4 kW per square centimeter, or approximately 17% of the Galileo probe's expected maximum value. The forebody heat shield mass fractions for the Saturn probes were found to vary from about 0.18 to 0.28. By comparison, the Pioneer-Venus probes' heat shield mass fractions ranged from 0.10 to 0.13 and the Galileo probe's forebody value is 0.43.

Wercinski, P.↗
NASA NTRS2002

Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory

This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.

Dukeman, Greg A.↗
NASA NTRS1961

A Flight Examination of Operating Problems of V/STOL Aircraft in STOL-Type Landing and Approach

A flight investigation has been conducted using a large twin-engine cargo aircraft to isolate the problems associated with operating propeller-driven aircraft in the STOL speed range where appreciable engine power is used to augment aerodynamic lift. The problems considered would also be representative of those of a large overloaded VTOL aircraft operating in an STOL manner with comparable thrust-to-weight ratios. The study showed that operation at low approach speeds was compromised by the necessity of maintaining high thrust to generate high lift and yet achieving the low lift-drag ratios needed for steep descents. The useable range of airspeed and flight path angle was limited by the pilot's demand for a positive climb margin at the approach speed, a suitable stall margin, and a control and/or performance margin for one engine inoperative. The optimum approach angle over an obstacle was found to be a compromise between obtaining the shortest air distance and the lowest touchdown velocity. In order to realize the greatest low-speed potential from STOL designs, the stability and control characteristics must be satisfactory.

Innis, Robert C.↗
NASA NTRS1960

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

An analysis is presented of supercircular entry into a planet's atmosphere giving particular attention to the corridor through which spacecraft must be guided in order to accomplish various maneuvers. A dimensionless parameter based on conditions at the conic perigee altitude is introduced for characterizing supercircular entries and conveniently pre-scribing corridor widths associated with elliptic, parabolic, or hyperbolic approach trajectories. The analysis applies to vehicles of arbitrary weight, shape, and size. Illustrative calculations are made for Venus, Earth, Mars, Jupiter, and Titan. For nonlifting vehicles having fixed aerodynamic coefficients, curves are presented of dimensionless parameters from which can be calculated the maximum deceleration, maximum rate of laminar convective heating, and total laminar heat absorbed during single-pass entry at velocities up to twice circular velocity. For lifting vehicles, curves are presented of the maximum deceleration and overshoot boundary of an entry corridor; equations are presented for estimating laminar aerodynamic heating from the maximum deceleration. It is shown that the corridor width is independent of vehicle weight, dimensions, and drag coefficient, provided these are the same at the overshoot boundary as at undershoot. The corridors of certain planets can be broadened markedly by the application of aerodynamic lift; for example, the 10-earth-g corridor width for single- pass, nonlifting, parabolic entry is increased from 0 miles for Jupiter, 7 for Earth, and 8 for Venus, to 52, 51, and 52 miles, respectively, by employing a lift-drag ratio of 1. The use of aerodynamic lift does not increase appreciably the corridors of Mars and Titan. All corridor widths decrease rapidly as the entry velocity is increased. Terminal guidance requirements on accuracy of velocity and flight path angle for successfully entering various corridors are compared with analogous requirements for putting a satellite into orbit, for hitting the moon from the earth, and for achieving ICBM accuracy. Consideration is given to the terminal guidance problem involved in using a planet's atmosphere-rather than rocket fuel-to effect orbital transfers from heliocentric to planetocentric motion, thereby converting a hyperbolic approach trajectory to an elliptic orbit about the target planet. This fuel saving maneuver appears technologically feasible for certain planetary voyages, and implies the possibility of achieving a large reduction in required Earth lift-off weight of chemical propulsion systems.

Chapman, Dean R.↗
NASA NTRS1953

A Study of the Motion and Aerodynamic Heating of Missiles Entering the Earth's Atmosphere at High Supersonic Speeds

A simplified analysis is made of the velocity and deceleration history of missiles entering the earth's atmosphere at high supersonic speeds. It is found that, in general, the gravity force is negligible compared to the aerodynamic drag force and, hence, that the trajectory is essentially a straight line. A constant drag coefficient and an exponential variation of density with altitude are assumed and generalized curves for the variation of missile speed and deceleration with altitude are obtained. A curious finding is that the maximum deceleration is independent of physical characteristics of a missile (e.g., mass, size, and drag coefficient) and is determined only by entry speed and flight-path angle, provided this deceleration occurs before impact. This provision is satisfied by missiles presently of more usual interest.

Allen, H. Julian↗
NASA NTRS2005

Simulation and Analyses of Stage Separation Two-Stage Reusable Launch Vehicles

NASA has initiated the development of methodologies, techniques and tools needed for analysis and simulation of stage separation of next generation reusable launch vehicles. As a part of this activity, ConSep simulation tool is being developed which is a MATLAB-based front-and-back-end to the commercially available ADAMS(registered Trademark) solver, an industry standard package for solving multi-body dynamic problems. This paper discusses the application of ConSep to the simulation and analysis of staging maneuvers of two-stage-to-orbit (TSTO) Bimese reusable launch vehicles, one staging at Mach 3 and the other at Mach 6. The proximity and isolated aerodynamic database were assembled using the data from wind tunnel tests conducted at NASA Langley Research Center. The effects of parametric variations in mass, inertia, flight path angle, altitude from their nominal values at staging were evaluated. Monte Carlo runs were performed for Mach 3 staging to evaluate the sensitivity to uncertainties in aerodynamic coefficients.

Pamadi, Bandu N.↗
NASA NTRS2006

JSC Orbital Debris Website Description

Purpose: The website provides information about the NASA Orbital Debris Program Office at JSC, which is the lead NASA center for orbital debris research. It is recognized world-wide for its leadership in addressing orbital debris issues. The NASA Orbital Debris Program Office has taken the international lead in conducting measurements of the environment and in developing the technical consensus for adopting mitigation measures to protect users of the orbital environment. Work at the center continues with developing an improved understanding of the orbital debris environment and measures that can be taken to control its growth. Major Contents: Orbital Debris research is divided into the following five broad efforts. Each area of research contains specific information as follows: 1) Modeling - NASA scientists continue to develop and upgrade orbital debris models to describe and characterize the current and future debris environment. Evolutionary and engineering models are described in detail. Downloadable items include a document in PDF format and executable software. 2) Measurements - Measurements of near-Earth orbital debris are accomplished by conducting ground-based and space-based observations of the orbital debris environment. The data from these sources provide validation of the environment models and identify the presence of new sources. Radar, optical and surface examinations are described. External links to related topics are provided. 3) Protection - Orbital debris protection involves conducting hypervelocity impact measurements to assess the risk presented by orbital debris to operating spacecraft and developing new materials and new designs to provide better protection from the environment with less weight penalty. The data from this work provides the link between the environment defined by the models and the risk presented by that environment to operating spacecraft and provides recommendations on design and operations procedures to reduce the risk as required. These data also help in the analysis and interpretation of impact features on returned spacecraft surfaces. 4) Mitigation - Controlling the growth of the orbital debris population is a high priority for NASA, the United States, and the major space-faring nations of the world to preserve near-Earth space for future generations. Mitigation measures can take the form of curtailing or preventing the creation of new debris, designing satellites to withstand impacts by small debris, and implementing operational procedures ranging from utilizing orbital regimes with less debris, adopting specific spacecraft attitudes, and even maneuvering to avoid collisions with debris. Downloadable items include several documents in PDF format and executable software.and 5) Reentry - Because of the increasing number of objects in space, NASA has adopted guidelines and assessment procedures to reduce the number of non-operational spacecraft and spent rocket upper stages orbiting the Earth. One method of postmission disposal is to allow reentry of these spacecraft, either from orbital decay (uncontrolled entry) or with a controlled entry. Orbital decay may be achieved by firing engines to lower the perigee altitude so that atmospheric drag will eventually cause the spacecraft to enter. However, the surviving debris impact footprint cannot be guaranteed to avoid inhabited landmasses. Controlled entry normally occurs by using a larger amount of propellant with a larger propulsion system to drive the spacecraft to enter the atmosphere at a steeper flight path angle. It will then enter at a more precise latitude, longitude, and footprint in a nearly uninhabited impact region, generally located in the ocean.

Johnson, Nicholas L.↗
NASA NTRS2004

Mars Exploration Rovers navigation results

The twin Mars Exploration Rovers, Spirit and Opportunity, were launched on June 10, 2003(dagger), and July 8, 2003, from Cape Canaveral, Florida. Spirit and Opportunity were targeted for landings at Gusev Crater (arrival on January 4, 2004) and Meridiani Planum (arrival on January 25, 2004). The primary navigation challenge was to deliver each spacecraft to the desired atmospheric entry interface point with sufficient accuracy such that each lander would touch down within a specified landing ellipse (about 70 km x 5 km) determined to be safe for landing and also judged to be scientifically interesting. In order to achieve landing within the target ellipse, precise control of the inertial entry flight path angle (FPA) at atmospheric entry was required. The maximum allowable errors in FPA following TCM-5 (trajectory correction maneuver #5) at Entry (E) - 2 days were +/-0.12(deg) (3(sigma)) for Spirit and +/-0.14(deg) (3(sigma)) for Opportunity. Achieving these entry delivery accuracies necessitated significant improvements to the interplanetary avigation system used for MER. These improvements included new processes and software for orbit determination, propulsive maneuver design, and entry, descent, and landing (EDL) trajectory simulation. The actual achieved atmospheric entry accuracies for Spirit and Opportunity significantly exceeded the requirements. At the navigation data cutoff for the TCM-5 final design, the orbit determination FPA knowledge error was +/-0.028(deg) (3(sigma) ) for Spirit and +/-0.035(deg) (3(sigma)) for Opportunity. Because of exceptionally accurate navigation performance, TCM-5 (E - 2 days) and TCM-6 (E - 4 hours) were canceled for both Spirit and Opportunity. The actual landing locations (determined from in-situ Doppler tracking between the MER rovers and the Mars Odyssey orbiter) differed from the target landing points by 10.1 km (downtrack) for Spirit and 24.6 km (downtrack) for Opportunity. The majority of the landing position offsets for both landers was primarily caused by variations in atmosphere and spacecraft aerodynamic modeling from what was predicted. The amount of the landing position offset caused by navigation-only errors was only 3.3 km (uptrack) for Spirit and 9.7 km (downtrack) for Opportunity.

Mars Exploration Rover (MER)↗
NASA NTRS2004

Mars Exploration Rovers navigation results

The twin Mars Exploration Rovers, Spirit and Opportunity, were launched on June 10, 2003, and July 8, 2003, from Cape Canaveral, Florida. Spirit and Opportunity were targeted for landings at Gusev Crater (arrival on January 4, 2004) and Meridiani Planum (arrival on January 25, 2004). The primary navigation challenge was to deliver each spacecraft to the desired atmospheric entry interface point with sufficient accuracy such that each lander would touch down within a specified landing ellipse (about 70 km x 5 km) determined to be safe for landing and also judged to be scientifically interesting. In order to achieve landing within the target ellipse, precise control of the inertial entry flight path angle (FPA) at atmospheric entry was required. The maximum allowable errors in FPA following TCM-5 (trajectory correction maneuver #5) at Entry (E) -2 days were +/-0.12 deg(3 sigma) for Spirit and +/-0.14 deg(3 sigma) for Opportunity. Achieving these entry delivery accuracies necessitated significant improvements to the interplanetary navigation system used for MER. These improvements included new processes and software for orbit determination, propulsive maneuver design, and entry, descent, and landing (EDL) trajectory simulation. The actual achieved atmospheric entry accuracies for Spirit and Opportunity significantly exceeded the requirements. At the navigation data cutoff for the TCM-5 final design, the orbit determination FPA knowledge error was 0.028 deg(3 sigma) for Spirit and 0.035 deg(3 sigma) for Opportunity. Because of exceptionally accurate navigation performance, TCM-5 (E - 2 days) and TCM-6 (E - 4 hours) were canceled for both Spirit and Opportunity. The actual landing locations (determined from in-situ Doppler tracking between the MER rovers and the Mars Odyssey orbiter) differed from the target landing points by 10.1 km (downtrack) for Spirit and 24.6 km (downtrack) for Opportunity. The majority of the landing position offsets for both landers was primarily caused by variations in atmosphere and spacecraft aerodynamic modeling from what was predicted. The amount of the landing position offset caused by navigation-only errors was only 3.3 km (uptrack) for Spirit and 9.7 km (downtrack) for Opportunity.

Mars Exploration Rover (MER)↗