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NASA NTRS1996

Recrystallized Impact Glasses of the Onaping Formation and the Sudbury Igneous Complex, Sudbury Structure, Ontario, Canada

The origin of the Sudbury Structure and of the associated heterolithic breccias of the Onaping Formation and the Sudbury Igneous Complex have been controversial. While an impact origin of the structure has gained wide acceptance over the last 15 years, the origin of the recrystallized Onaping Formation glasses and of the igneous complex is still being debated. Recently the interpretation of the breccias of the Onaping Formation as suevitic fall-back impact breccias has been challenged. The igneous complex is interpreted either as a differentiated impact melt sheet or as a combination of an upper impact melt represented by the granophyre, and a lower, impact-triggered magmatic body consisting of the norite-sublayer formations. The Onaping Formation contains glasses as fluidal and nonfluidal fragments of various shapes and sizes. They are recrystallized, and our research indicates that they are petrographically heterogeneous and span a wide range of chemical compositions. These characteristics are not known from glasses of volcanic deposits. This suggests an origin by shock vitrification, an interpretation consistent with their association with numerous and varied country rock clasts that exhibit microscopic shock metamorphic features. The recrystallized glass fragments represent individual solid-state and liquid-state vitrified rocks or relatively small melt pods. The basal member lies beneath the Gray and Black members of the Onaping Formation and, where not metamorphic, has an igneous matrix. Igneous-textured melt bodies occur in the upper two members and above the Basal Member. A comparison of the chemical compositions of recrystallized glasses and of the matrices of the Basal Member and the melt bodies with the components and the bulk composition of the igneous complex is inconclusive as to the origin of the igneous complex. Basal Member matrix and Melt Bodies, on average, are chemically similar to the granophyre of the Sudbury Igneous Complex, suggesting that they are genetically related. Our chemical results allow interpretation of the entire igneous complex as a differentiated impact melt. However, they are also consistent with the granophyre alone being the impact melt and the nofite and quartz gabbro beneath it representing an impact-triggered magmatic body. This interpretation is preferred, as it is consistent with a number of field observations. A re-evaluation and extension of structural field studies and of geochemical data, as well as a systematic study of the contact relationships of the various igneous phases of the igneous complex, are needed to establish a Sudbury impact model consistent with all data and observations

Dressler, B. O.↗

NASA NTRS1991

Formation of Lignans(-)-Secoisolariciresinol and (-)-Matairesinol with Forsythia intermedia Cell-Free Extracts

In vivo labeling experiments of Forsythia intermedia plant tissue with [8-(C-14)]- and [9,9-(2)H2,OC(2)H3]coniferyl alcohols revealed that the lignans, (-)-secoisolariciresinol and (-)-matairesinol, were derived from two coniferyl alcohol molecules; no evidence for the formation of the corresponding (+)-enantiomers was found. Administration of (+/-)-[Ar-(H-3)] secoisolariciresinols to excised shoots of F.intermedia resulted in a significant conversion into (-)-matairesinol; again, the (+)-antipode was not detected. Experiments using cell-free extracts of F.intermedia confirmed and extended these findings. In the presence of NAD(P)H and H2O2, the cell-free extracts catalyzed the formation of (-)- secoisolariciresinol, with either [8-(C-14)]- or [9,9-(2)H2,OC(2)H3]coniferyl alcohols as substrates. The (+)- enantiomer was not formed. Finally, when either (-)-[Ar-(H-3)] or (+/-)-[Ar-(H-2)]secoisolariciresinols were used as substrates, in the presence of NAD(P), only (-)- and not (+)-matairesinol formation occurred. The other antipode, (+)-secoisolariciresinol, did not serve as a substrate for the formation of either (+)- or (-)-matairesinol. Thus, in F.intermedia, the formation of the lignan, (-)-secoisolariciresinol, occurs under strict stereochemical control, in a reaction or reactions requiring NAD(P)H and H2O2 as cofactors. This stereoselectivity is retained in the subsequent conversion into (-)-matairesinol, since (+)-secoisolariciresinol is not a substrate. These are the first two enzymes to be discovered in lignan formation.

Umezawa, Toshiaki↗

NASA NTRS1999

Integration of a Decentralized Linear-Quadratic-Gaussian Control into GSFC's Universal 3-D Autonomous Formation Flying Algorithm

A decentralized control is investigated for applicability to the autonomous formation flying control algorithm developed by GSFC for the New Millenium Program Earth Observer-1 (EO-1) mission. This decentralized framework has the following characteristics: The approach is non-hierarchical, and coordination by a central supervisor is not required; Detected failures degrade the system performance gracefully; Each node in the decentralized network processes only its own measurement data, in parallel with the other nodes; Although the total computational burden over the entire network is greater than it would be for a single, centralized controller, fewer computations are required locally at each node; Requirements for data transmission between nodes are limited to only the dimension of the control vector, at the cost of maintaining a local additional data vector. The data vector compresses all past measurement history from all the nodes into a single vector of the dimension of the state; and The approach is optimal with respect to standard cost functions. The current approach is valid for linear time-invariant systems only. Similar to the GSFC formation flying algorithm, the extension to linear LQG time-varying systems requires that each node propagate its filter covariance forward (navigation) and controller Riccati matrix backward (guidance) at each time step. Extension of the GSFC algorithm to non-linear systems can also be accomplished via linearization about a reference trajectory in the standard fashion, or linearization about the current state estimate as with the extended Kalman filter. To investigate the feasibility of the decentralized integration with the GSFC algorithm, an existing centralized LQG design for a single spacecraft orbit control problem is adapted to the decentralized framework while using the GSFC algorithm's state transition matrices and framework. The existing GSFC design uses both reference trajectories of each spacecraft in formation and by appropriate choice of coordinates and simplified measurement modeling is formulated as a linear time-invariant system. Results for improvements to the GSFC algorithm and a multiple satellite formation will be addressed. The goal of this investigation is to progressively relax the assumptions that result in linear time-invariance, ultimately to the point of linearization of the non-linear dynamics about the current state estimate as in the extended Kalman filter. An assessment will then be made about the feasibility of the decentralized approach to the realistic formation flying application of the EO-1/Landsat 7 formation flying experiment.

Folta, David C.↗

NASA NTRS2000

Enabling Spacecraft Formation Flying in Any Earth Orbit Through Spaceborne GPS and Enhanced Autonomy Technologies

Formation flying is quickly revolutionizing the way the space community conducts autonomous science missions around the Earth and in space. This technological revolution will provide new, innovative ways for this community to gather scientific information, share this information between space vehicles and the ground, and expedite the human exploration of space. Once fully matured, this technology will result in swarms of space vehicles flying as a virtual platform and gathering significantly more and better science data than is possible today. Formation flying will be enabled through the development and deployment of spaceborne differential Global Positioning System (GPS) technology and through innovative spacecraft autonomy techniques, This paper provides an overview of the current status of NASA/DoD/Industry/University partnership to bring formation flying technology to the forefront as quickly as possible, the hurdles that need to be overcome to achieve the formation flying vision, and the team's approach to transfer this technology to space. It will also describe some of the formation flying testbeds, such as Orion, that are being developed to demonstrate and validate these innovative GPS sensing and formation control technologies.

Bauer, F. H.↗

NASA NTRS2000

A Tethered Formation Flying Concept for the SPECS Mission

The Sub-millimeter Probe of the Evolution of Cosmic Structure (SPECS) is a bold new mission concept designed to address fundamental questions about the Universe, including how the first stars formed from primordial material, and the first galaxies from pre-galactic structures, how the galaxies evolve over time, and what the cosmic history of energy release, heavy element synthesis, and dust formation is. Half of the luminosity and 98% of the post Big-Bang photons exit in the sub-millimeter range. The spectrum of our own Milky Way Galaxy shows this, and many galaxies have even more pronounced long-wavelength emissions. There can be no doubt that revolutionary science will be enabled when we have tools to study the sub-millimeter sky with Hubble- Space-Telescope-class resolution and sensitivity. Ideally, a very large telescope with an effective aperture approaching one kilometer in diameter would be needed to obtain such high quality angular resolution at these long wavelengths. However, a single aperture one kilometer in diameter would not only be very difficult to build and maintain at the cryogenic temperatures required for good seeing, but could actually turn out to be serious overkill. Because cosmic sub-millimeter photons are plentiful and the new detectors will be sensitive, the observations needed to address the questions posed above can be made with an interferometer using well established aperture synthesis techniques. Possibly as few as three 3-4 meter diameter mirrors flying in precision formation could be used to collect the light. To mitigate the need for a great deal of propellant, tethers may be needed as well. A spin-stabilized, tethered formation is a possible configuration requiring a more advanced form of formation flying controller, where dynamics are coupled due to the existence of the tethers between nodes in the formation network. The paper presents one such concept, a proposed configuration for a mission concept which combines the best features of structure, tethers and formation flying to meet the ambitious requirements necessary to make a future SPECS mission a success.

Quinn, David A.↗

NASA NTRS2001

Follow That Satellite: EO-1 Maneuvers into Closed Formation With Landsat-7

As the Landsat-7 spacecraft continued NASA's historic program of earth imaging, begun over three decades ago, NASA launched the Earth Observing-1 (EO-1) spacecraft carrying examples of the next generation of Landsat-7 instruments. The validation method for these instruments was to have EO-1 fly in a close formation behind Landsat-7 on the same World Reference System path. From that formation hundreds of near coincident images would be taken by each spacecraft and compared to evaluate improvements in the EO-1 instruments. This paper will address the mission analysis required to launch and maneuver EO-1 into the formation with Landsat-7 where instrument validation was to occur plus a summary of completing the formation acquisition. EO-1 is required to operate one minute +/- 6 seconds behind Landsat-7 during the period of co-fly imaging with a cross track separation of within + 3 kilometers. This separation time can also be stated as a one minute +/- 6 seconds time difference in the Mean Local Time (MLT) at the descending nodes. Achieving the required MLT is heavily dependent on the time of launch. The EO-1 launch window, which had to accommodate the dual payloads of EO-1 and SAC-C, was very limited ranging from 0 to 22 seconds over the 16 day Landsat-7 WRS repeat cycle during which EO-1 was launched. Each EO-1 launch opportunity that occurred on a different day of a Landsat-7 16 day repeat cycle required a separate and distinct maneuver profile. These profiles varied significantly in duration and amount of onboard propellant required to achieve them. EO-1 launched on a day judged to have "medium" resource requirements for achieving the formation with Landsat-7. To phase EO-1 one minute behind Landsat-7 in the along track direction, a series of altitude adjusts separated by specific drift intervals were executed. Additional maneuvers slightly changed the EO-1 inclination to maintain the MLT requirements. Orbit maneuvers were planned and executed within errors of less than 1.5 percent and propellant usage was near nominal consuming 3.4 kilograms out of a launch and early orbit budget of 11 kilograms. The pre-launch 3 -sigma propellant budget allowed for 1+ years of EO-1 mission life. The success of the EO-1 launch and early orbit operations provided sufficient propellant for nearly 4 years of on orbit operations. Special action taken during the EO-1 maneuver period involved some maneuver re-planning to reduce concerns about a potential close approach between EO-1 and Landsat-7. The result of this re-planning was a safer close approach and improvement in future formation acquisition planning.

DeFazio, Robert↗

NASA NTRS2001

A Preliminary Formation Flying Orbit Dynamics Analysis for Leonardo-BRDF

Leonardo-BRDF is a NASA mission concept proposed to allow the investigation of radiative transfer and its effect on the Earth's climate and atmospheric phenomenon. Enabled by the recent developments in small-satellite and formation flying technology, the mission is envisioned to be composed of an array of spacecraft in carefully designed orbits. The different perspectives provided by a distributed array of spacecraft offer a unique advantage to study the Earth's albedo. This paper presents the orbit dynamics analysis performed in the context of the Leonardo-BRDF science requirements. First, the albedo integral is investigated and the effect of viewing geometry on science return is studied. The method used in this paper, based on Gauss quadrature, provides the optimal formation geometry to ensure that the value of the integral is accurately approximated. An orbit design approach is presented to achieve specific relative orbit geometries while simultaneously satisfying orbit dynamics constraints to reduce formation-keeping fuel expenditure. The relative geometry afforded by the design is discussed in terms of mission requirements. An optimal two-burn initialization scheme is presented with the required delta-V to distribute all spacecraft from a common parking orbit into their appropriate orbits in the formation. Finally, formation-keeping strategies are developed and the associated delta-V's are calculated to maintain the formation in the presence of perturbations.

Hughes, Steven P.↗

NASA NTRS2001

Networks for Autonomous Formation Flying Satellite Systems

The performance of three communications networks to support autonomous multi-spacecraft formation flying systems is presented. All systems are comprised of a ten-satellite formation arranged in a star topology, with one of the satellites designated as the central or "mother ship." All data is routed through the mother ship to the terrestrial network. The first system uses a TCP/lP over ATM protocol architecture within the formation the second system uses the IEEE 802.11 protocol architecture within the formation and the last system uses both of the previous architectures with a constellation of geosynchronous satellites serving as an intermediate point-of-contact between the formation and the terrestrial network. The simulations consist of file transfers using either the File Transfer Protocol (FTP) or the Simple Automatic File Exchange (SAFE) Protocol. The results compare the IF queuing delay, and IP processing delay at the mother ship as well as application-level round-trip time for both systems, In all cases, using IEEE 802.11 within the formation yields less delay. Also, the throughput exhibited by SAFE is better than FTP.

Knoblock, Eric J.↗

NASA NTRS2002

Results of NASA's First Autonomous Formation Flying Experiment: Earth Observing-1 (EO-1)

NASA's first autonomous formation flying mission completed its primary goal of demonstrating an advanced technology called enhanced formation flying. To enable this technology, the Flight Dynamics Analysis Branch at the Goddard Space Flight Center implemented a universal 3-axis formation flying algorithm in an autonomous executive flight code onboard the New Millennium Program's (NMP) Earth Observing-1 (EO-1) spacecraft. This paper describes the mathematical background of the autonomous formation flying algorithm, the onboard flight design and the validation results of this unique system. Results from fully autonomous maneuver control are presented as comparisons between the onboard EO-1 operational autonomous control system called AutoCon, its ground-based predecessor used in operations, and the original standalone algorithm. Maneuvers discussed encompass reactionary, routine formation maintenance, and inclination control. Orbital data is also examined to verify that all formation flying requirements were met.

Folta, David↗

NASA NTRS2003

First Results from a Hardware-in-the-Loop Demonstration of Closed-Loop Autonomous Formation Flying

A closed-loop system for the demonstration of formation flying technologies has been developed at NASA s Goddard Space Flight Center. Making use of a GPS signal simulator with a dual radio frequency outlet, the system includes two GPS space receivers as well as a powerful onboard navigation processor dedicated to the GPS-based guidance, navigation, and control of a satellite formation in real-time. The closed-loop system allows realistic simulations of autonomous formation flying scenarios, enabling research in the fields of tracking and orbit control strategies for a wide range of applications. A sample scenario has been set up where the autonomous transition of a satellite formation from an initial along-track separation of 800 m to a final distance of 100 m has been demonstrated. As a result, a typical control accuracy of about 5 m has been achieved which proves the applicability of autonomous formation flying techniques to formations of satellites as close as 50 m.

Gill, E.↗

NASA NTRS2003

Formation Flying Design and Applications in Weak Stability Boundary Regions

Weak Stability regions serve as superior locations for interferometric scientific investigations. These regions are often selected to minimize environmental disturbances and maximize observing efficiency. Design of formations in these regions are becoming ever more challenging as more complex missions are envisioned. The development of algorithms to enable the capability for formation design must be further enabled to incorporate better understanding of WSB solution space. This development will improve the efficiency and expand the capabilities of current approaches. The Goddard Space Flight Center (GSFC) is currently supporting multiple formation missions in WSB regions. This end-to-end support consists of mission operations, trajectory design, and control. It also includes both algorithm and software development. The Constellation-X, Maxim, and Stellar Imager missions are examples of the use of improved numerical methods for attaining constrained formation geometries and controlling their dynamical evolution. This paper presents a survey of formation missions in the WSB regions and a brief description of the formation design using numerical and dynamical techniques.

Folta, David↗

NASA NTRS2002

Results Of NASA's First Autonomous Formation Flying Experiment: Earth Observing-1 (EO-1)

NASA's first autonomous formation flying mission completed its primary goal of demonstrating an advanced technology called Enhanced Formation Flying. To enable this technology, a team at the Goddard Space Flight Center implemented a universal 3-axis formation flying algorithm in an autonomous executive flight code onboard the New Millennium Program's (NMP) Earth Observing-1 (EO-1) spacecraft. This paper describes the mathematical background of the autonomous formation flying algorithm, the onboard flight design and the validation results of this unique system. Results from fully autonomous maneuver control are presented as comparisons between the onboard EO-1 operational autonomous control system called AutoCon(trademark), its ground-based predecessor used in operations, and the original standalone algorithm. Maneuvers discussed encompass reactionary, routine formation maintenance, and inclination control. Orbital data is also examined to verify that all formation flying requirements were met.

Folta, David↗

NASA NTRS2003

A Fuzzy Technique for Performing Lateral-Axis Formation Flight Navigation Using Wingtip Vortices

Close formation flight involving aerodynamic coupling through wingtip vortices shows significant promise to improve the efficiency of cooperative aircraft operations. Impediments to the application of this technology include internship communication required to establish precise relative positioning. This report proposes a method for estimating the lateral relative position between two aircraft in close formation flight through real-time estimates of the aerodynamic effects imparted by the leading airplane on the trailing airplane. A fuzzy algorithm is developed to map combinations of vortex-induced drag and roll effects to relative lateral spacing. The algorithm is refined using self-tuning techniques to provide lateral relative position estimates accurate to 14 in., well within the requirement to maintain significant levels of drag reduction. The fuzzy navigation algorithm is integrated with a leader-follower formation flight autopilot in a two-ship F/A-18 simulation with no intership communication modeled. It is shown that in the absence of measurements from the leading airplane the algorithm provides sufficient estimation of lateral formation spacing for the autopilot to maintain stable formation flight within the vortex. Formation autopilot trim commands are used to estimate vortex effects for the algorithm. The fuzzy algorithm is shown to operate satisfactorily with anticipated levels of input uncertainties.

Hanson, Curtis E.↗

NASA NTRS2004

Formation and Stability of Radiation Products in Europa's Icy Shell

Spectra of Europa reveal a surface dominated by water-ice along with hydrated materials and minor amounts of SO2, CO2, and H2O2. Jovian magnetospheric ions (protons, sulfur, and oxygen) and electrons produce significant chemical modifications of the surface on time scales of a few years at micrometer depths. Our laboratory studies examine the formation and stability of radiation products in H2O-rich ices relevant to Europa. Infrared (IR) spectra of ices before and after irradiation reveal the radiation destruction of molecules and the formation of products at 86 - 132 K. In addition, spectra of ices during warming track thermal evolution due to chemical changes and sublimation processes. IR-identified radiation products in 86 - 132 K irradiated H2O + SO2 ices are the bisulfate ion, HSO4(-), sulfate ion, SO4(2-) and the hydronium ion, H3O(+). Warming results in the formation of a residual spectrum similar to liquid sulfuric acid, H2SO4, for H2O:SO2 ratios of 30:1, whereas hydrated sulfuric acid, H2SO4 4 H2O, forms for ratios of 30:1. Radiation products identified for irradiated H2O + H2S ices at 86 K are H2S2 and SO2. When irradiated at 110 and 132 K, ices with H2O:H2S ratios if either 3:1 or 30:1 show the formation of H2SO4 4 H2O on warming to 175 K. We have also examined the radiation stability of H2SO4. Addition of CO2 to H2O + SO2 ices results in the formation of CO3 at 2046 cm (sup -1) (4.89 m). This is the strongest band from a carbon-containing product in the mid-IR spectral region, and it is also seen when either pure CO2 or H2O + CO2 ice is irradiated. Experiments with CH4 added to H2O + SO2 + CO2 ices addressed the question of methane's use as a marker of methanogens in an irradiated ice environment. New results on the near-IR spectrum of pure H2O2 will be included in this presentation. Interpretations of near-IR water bands, with H2O2 present, will be discussed. Irradiations of H2O2 and H2O + H2O2 mixtures, to examine the possibility of O2 and O3 formation, are currently under investigation and new results will be discussed.

Moore, M. H.↗

NASA NTRS2004

Formation Control for the Maxim Mission.

Over the next twenty years, a wave of change is occurring in the spacebased scientific remote sensing community. While the fundamental limits in the spatial and angular resolution achievable in spacecraft have been reached, based on today's technology, an expansive new technology base has appeared over the past decade in the area of Distributed Space Systems (DSS). A key subset of the DSS technology area is that which covers precision formation flying of space vehicles. Through precision formation flying, the baselines, previously defined by the largest monolithic structure which could fit in the largest launch vehicle fairing, are now virtually unlimited. Several missions including the Micro-Arcsecond X-ray Imaging Mission (MAXIM), and the Stellar Imager will drive the formation flying challenges to achieve unprecedented baselines for high resolution, extended-scene, interferometry in the ultraviolet and X-ray regimes. This paper focuses on establishing the feasibility for the formation control of the MAXIM mission. The Stellar Imager mission requirements are on the same order of those for MAXIM. This paper specifically addresses: (1) high-level science requirements for these missions and how they evolve into engineering requirements; (2) the formation control architecture devised for such missions; (3) the design of the formation control laws to maintain very high precision relative positions; and (4) the levels of fuel usage required in the duration of these missions. Specific preliminary results are presented for two spacecraft within the MAXIM mission.

Luquette, Richard J.↗

NASA NTRS1996

Dynamics of vegetative cytoplasm during generative cell formation and pollen maturation in Arabidopsis thaliana

Ultrastructural changes of pollen cytoplasm during generative cell formation and pollen maturation in Arabidopsis thaliana were studied. The pollen cytoplasm develops a complicated ultrastructure and changes dramatically during these stages. Lipid droplets increase after generative cell formation and their organization and distribution change with the developmental stage. Starch grains in amyloplasts increase in number and size during generative and sperm cell formation and decrease at pollen maturity. The shape and membrane system of mitochondria change only slightly. Dictyosomes become very prominent, and numerous associated vesicles are observed during and after sperm cell formation. Endoplasmic reticulum appears extensively as stacks during sperm cell formation. Free and polyribosomes are abundant in the cytoplasm at all developmental stages although they appear denser at certain stages and in some areas. In mature pollen, all organelles are randomly distributed throughout the vegetative cytoplasm and numerous small particles appear. Organization and distribution of storage substances and appearance of these small particles during generative and sperm cell formation and pollen maturation are discussed.

Non-NASA Center↗

NASA NTRS2000

Kinetics of DSB rejoining and formation of simple chromosome exchange aberrations

PURPOSE: To investigate the role of kinetics in the processing of DNA double strand breaks (DSB), and the formation of simple chromosome exchange aberrations following X-ray exposures to mammalian cells based on an enzymatic approach. METHODS: Using computer simulations based on a biochemical approach, rate-equations that describe the processing of DSB through the formation of a DNA-enzyme complex were formulated. A second model that allows for competition between two processing pathways was also formulated. The formation of simple exchange aberrations was modelled as misrepair during the recombination of single DSB with undamaged DNA. Non-linear coupled differential equations corresponding to biochemical pathways were solved numerically by fitting to experimental data. RESULTS: When mediated by a DSB repair enzyme complex, the processing of single DSB showed a complex behaviour that gives the appearance of fast and slow components of rejoining. This is due to the time-delay caused by the action time of enzymes in biomolecular reactions. It is shown that the kinetic- and dose-responses of simple chromosome exchange aberrations are well described by a recombination model of DSB interacting with undamaged DNA when aberration formation increases with linear dose-dependence. Competition between two or more recombination processes is shown to lead to the formation of simple exchange aberrations with a dose-dependence similar to that of a linear quadratic model. CONCLUSIONS: Using a minimal number of assumptions, the kinetics and dose response observed experimentally for DSB rejoining and the formation of simple chromosome exchange aberrations are shown to be consistent with kinetic models based on enzymatic reaction approaches. A non-linear dose response for simple exchange aberrations is possible in a model of recombination of DNA containing a DSB with undamaged DNA when two or more pathways compete for DSB repair.

DNA Damage↗

NASA NTRS2000

Aircraft Spacings that Produce a Vortex-Free Region Below Flight Formation

Theoretical estimates are presented for the motion of vortex wakes shed by multiple aircraft flying in close formation. The purpose of the theoretical study was to determine whether the spacings between adjacent aircraft in close formations could be designed so that the lift-generated vortices being trailed would move upward rather than downward. In this way, a region below the formation is produced that is free of vortices. It was found that aircraft can be arranged in formations so that the inboard wake vortices all move upward rather than downward. The two outboard vortices travel downward at a greatly reduced velocity that depends on the number of aircraft in the formation. If the desired motions are to be produced, the lateral spacings between adjacent aircraft centerlines must be between 1.1 and 1.5 wingspans, and the vertical spacings between -0.025 and -0.15 wingspans. Since the range of acceptable spacings is small, it is recommended that the position accuracy between aircraft in the formation be kept within about + or - 0.01 wingspan of the center of acceptable spacings so that aircraft meandering do not cause unwanted vortex excursions. It was also found that, if the in-trail spacings between adjacent aircraft are more than 4 wingspans, the foregoing vertical spacings must be adjusted to allow for the additional downward travel of the vortices shed by leading aircraft.

Rossow, Vernon J.↗