SEARCH · Engineering Papers

Results for “Collisions”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

All sources NASA NTRS DOE OSTI

NASA NTRS1999

The Use of the Satellite Breakup Risk Assessment Model (SBRAM) to Characterize Collision Risk to Manned Spacecraft

NASA uses environment models such as ORDEM96 to characterize the long-term orbital debris collision hazard for spacecraft in LEO. Occasionally, however, there are breakups of satellites or rocket bodies that create enhanced collision hazard for a period of time. This enhanced collision hazard can pose increased risks to space operations - especially those involving manned missions where the tolerance for risk is very low. NASA has developed SBRAM to simulate the enhanced debris environment in the days and weeks that follow such a breakup. This simulation provides the kind of risk probabilities that can be used by mission planners to consider if changes are warranted for the mission. Announcements of breakups come to NASA from US Space Command as soon as they are identified. The pre-breakup orbit and time of breakup are used to determine the initial conditions of the explosion. SBRAM uses the latest explosion models developed at NASA to simulate a debris cloud for the breakup. The model uses a Monte Carlo technique to create a random debris cloud from the probability distributions in the breakup model. Each piece of debris randomly created in the cloud is propagated in a deterministic manner to include the effects of drag and other orbital perturbations. The detailed geometry of each simulated close approach to the target spacecraft is noted and logged and the collision probability is computed using an estimated probability density in down-range and cross-range positions of both the target spacecraft and debris object. The collision probability is computed from the overlap of these probability densities for each close-approach geometry and summed over all computed conjunctions. Cloud propagation runs over the desired time interval are then repeated until the scale of the collision risk can be estimated to a desired precision. This paper presents an overview of the SBRAM model and a number of examples, both real and hypothetical, to demonstrate its use. In addition, a number of different examples are shown how the data can be used by decision makers on issues such as spacecraft orientation and timing of EVAs.

Matney, Mark J.↗

NASA NTRS1995

Vibrational and Electronic Energy Transfer and Dissociation of Diatomic Molecules by Electron Collisions

At high altitudes and velocities equal to or greater than the geosynchronous return velocity (10 kilometers per second), the shock layer of a hypersonic flight will be in thermochemical nonequilibrium and partially ionized. The amount of ionization is determined by the velocity. For a trans atmospheric flight of 10 kilometers per second and at an altitude of 80 kilometers, a maximum of 1% ionization is expected. At a velocity of 12 - 17 kilometer per second, such as a Mars return mission, up to 30% of the atoms and molecules in the flow field will be ionized. Under those circumstances, electrons play an important role in determining the internal states of atoms and molecules in the flow field and hence the amount of radiative heat load and the distance it takes for the flow field to re-establish equilibrium. Electron collisions provide an effective means of transferring energy even when the electron number density is as low as 1%. Because the mass of an electron is 12,760 times smaller than the reduced mass of N2, its average speed, and hence its average collision frequency, is more than 100 times larger. Even in the slightly ionized regime with only 1% electrons, the frequency of electron-molecule collisions is equal to or larger than that of molecule-molecule collisions, an important consideration in the low density part of the atmosphere. Three electron-molecule collision processes relevant to hypersonic flows will be considered: (1) vibrational excitation/de-excitation of a diatomic molecule by electron impact, (2) electronic excitation/de-excitation, and (3) dissociative recombination in electron-diatomic ion collisions. A review of available data, both theory and experiment, will be given. Particular attention will be paid to tailoring the molecular physics to the condition of hypersonic flows. For example, the high rotational temperatures in a hypersonic flow field means that most experimental data carried out under room temperatures are not applicable. Also, the average electron temperature is expected to be between 10,000 and 20,000 K. Thus only data for low energy electrons are relevant to the model.

Huo, Winifred M.↗

NASA NTRS2006

New Accurate Oscillator Strengths and Electron Excitation Collision Strengths for N1

The nonorthogonal orbitals technique in a multiconfiguration Hartree-Fock approach is used to calculate oscillator strengths and transition probabilities of N(I) lines. The relativistic effects are allowed by means of Breit-Pauli operators. The length and velocity forms of oscillator strengths show good agreement for most transitions. The B-spline R-matrix with pseudostates approach has been used to calculate electron excitation collision strengths and rates. The nonorthogonal orbitals are used for an accurate description of both target wave functions and the R-matrix basis functions. The 24 spectroscopic bound and autoionizing states together with 15 pseudostates are included in the close-coupling expansion. The collision strengths for transitions between fine-structure levels are calculated by transforming the LS-coupled K-matrices to K-matrices in an intermediate coupling scheme. Thermally averaged collision strengths have been determined by integrating collision strength over a Maxwellian distribution of electron energies over a temperature range suitable for the modeling of astrophysical plasmas. The oscillator strengths and thermally averaged collision strengths are presented for transitions between the fine-structure levels of the 2s(sup 2)p(sup 3) (sup 4)S(sup 0), (sup 2)D(sup 0), (sup 2)P(sup 0), 2s2p(sup 4) (sup 4)P, 2s(sup 2)2p(sup 2)3s (sup 4)P, and (sup 2)P terms and from these levels to the levels of the 2s(sup 2)2p(sup 2)3p (sup 2)S(sup 0), (sup 4)D(sup 0), (sup 4)P(sup 0), (sup 4)S(sup 0), (sup 2)D(sup 0), (sup 2)P(sup 0),2s(sup 2)2p(sup 2)3s(sup 2)D, 2s(sup 2)2p(sup 2)4s(sup 4)P, (sup 2)P, 2s(sup 2)2p(sup 2)3d(sup 2)P, (sup 4)F,(sup 2)F,(sup 4)P, (sup 4)D, and (sup 2)D terms. Thermally averaged collision strengths are tabulated over a temperature range from 500 to 50,000 K.

Tayal, S. S.↗

NASA NTRS2010

Reactive Collision Avoidance Algorithm

The reactive collision avoidance (RCA) algorithm allows a spacecraft to find a fuel-optimal trajectory for avoiding an arbitrary number of colliding spacecraft in real time while accounting for acceleration limits. In addition to spacecraft, the technology can be used for vehicles that can accelerate in any direction, such as helicopters and submersibles. In contrast to existing, passive algorithms that simultaneously design trajectories for a cluster of vehicles working to achieve a common goal, RCA is implemented onboard spacecraft only when an imminent collision is detected, and then plans a collision avoidance maneuver for only that host vehicle, thus preventing a collision in an off-nominal situation for which passive algorithms cannot. An example scenario for such a situation might be when a spacecraft in the cluster is approaching another one, but enters safe mode and begins to drift. Functionally, the RCA detects colliding spacecraft, plans an evasion trajectory by solving the Evasion Trajectory Problem (ETP), and then recovers after the collision is avoided. A direct optimization approach was used to develop the algorithm so it can run in real time. In this innovation, a parameterized class of avoidance trajectories is specified, and then the optimal trajectory is found by searching over the parameters. The class of trajectories is selected as bang-off-bang as motivated by optimal control theory. That is, an avoiding spacecraft first applies full acceleration in a constant direction, then coasts, and finally applies full acceleration to stop. The parameter optimization problem can be solved offline and stored as a look-up table of values. Using a look-up table allows the algorithm to run in real time. Given a colliding spacecraft, the properties of the collision geometry serve as indices of the look-up table that gives the optimal trajectory. For multiple colliding spacecraft, the set of trajectories that avoid all spacecraft is rapidly searched on-line. The optimal avoidance trajectory is implemented as a receding-horizon model predictive control law. Therefore, at each time step, the optimal avoidance trajectory is found and the first time step of its acceleration is applied. At the next time step of the control computer, the problem is re-solved and the new first time step is again applied. This continual updating allows the RCA algorithm to adapt to a colliding spacecraft that is making erratic course changes.

Scharf, Daniel↗

NASA NTRS2010

Modeling and Simulation of an UAS Collision Avoidance Systems

This paper describes a Modeling and Simulation of an Unmanned Aircraft Systems (UAS) Collision Avoidance System, capable of representing different types of scenarios for UAS collision avoidance. Commercial and military piloted aircraft currently utilize various systems for collision avoidance such as Traffic Alert and Collision A voidance System (TCAS), Automatic Dependent Surveillance-Broadcast (ADS-B), Radar and ElectroOptical and Infrared Sensors (EO-IR). The integration of information from these systems is done by the pilot in the aircraft to determine the best course of action. In order to operate optimally in the National Airspace System (NAS) UAS have to work in a similar or equivalent manner to a piloted aircraft by applying the principle of "detect-see and avoid" (DSA) to other air traffic. Hence, we have taken these existing sensor technologies into consideration in order to meet the challenge of researching the modeling and simulation of an approximated DSA system. A Schematic Model for a UAS Collision Avoidance System (CAS) has been developed ina closed loop block diagram for that purpose. We have found that the most suitable software to carry out this task is the Satellite Tool Kit (STK) from Analytical Graphics Inc. (AGI). We have used the Aircraft Mission Modeler (AMM) for modeling and simulation of a scenario where a UAS is placed on a possible collision path with an initial intruder and then with a second intruder, but is able to avoid them by executing a right tum maneuver and then climbing. Radars have also been modeled with specific characteristics for the UAS and both intruders. The software provides analytical, graphical user interfaces and data controlling tools which allow the operator to simulate different conditions. Extensive simulations have been carried out which returned excellent results.

Oliveros, Edgardo V.↗

NASA NTRS2015

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Frisbee, Joseph H., Jr.↗

NASA NTRS2017

Unmanned Aircraft Systems (UAS) Integration in the National Airspace System (NAS) Project: Advanced Collision Avoidance System for UAS (ACAS Xu) Interoperability White Paper Presentation

The Phase 1 DAA Minimum Operational Performance Standards (MOPS) provided requirements for two classes of DAA equipment: equipment Class 1 contains the basic DAA equipment required to assist a pilot in remaining well clear, while equipment Class 2 integrates the Traffic Alert and Collision Avoidance (TCAS) II system. Thus, the Class 1 system provides RWC functionality only, while the Class 2 system is intended to provide both RWC and Collision Avoidance (CA) functionality, in compliance with the Minimum Aviation System Performance (MASPS) for the Interoperability of Airborne Collision Avoidance Systems. The FAAs TCAS Program Office is currently developing Airborne Collision Avoidance System X (ACAS X) to support the objectives of the Federal Aviation Administrations (FAA) Next Generation Air Transportation System Program (NextGen). ACAS X has a suite of variants with a common underlying design that are intended to be optimized for their intended airframes and operations. ACAS Xu being is designed for UAS and allows for new surveillance technologies and tailored logic for platforms with different performance characteristics. In addition to Collision Avoidance (CA) alerting and guidance, ACAS Xu is being tuned to provide RWC alerting and guidance in compliance with the SC 228 DAA MOPS. With a single logic performing both RWC and CA functions, ACAS Xu will provide industry with an integrated DAA solution that addresses many of the interoperability shortcomings of Phase I systems. While the MOPS for ACAS Xu will specify an integrated DAA system, it will need to show compliance with the RWC alerting thresholds and alerting requirements defined in the DAA Phase 2 MOPS. Further, some functional components of the ACAS Xu system such as the remote pilots displayed guidance might be mostly references to the corresponding requirements in the DAA MOPS. To provide a seamless, integrated, RWC-CA system to assist the pilot in remaining well clear and avoiding collisions, several issues need to be addressed within the Phase 2 SC-228 DAA efforts. Interoperability of the RWC and CA alerting and guidance, and ensuring pilot comprehension, compliance and performance, will be a primary research area.

detect and avoid↗

NASA NTRS2018

A Simple, Velocity Dependent, Collision Probability Algorithm for Small Combined Hard Body Radii Close Approach Events

Over the last few years progress has been made in the velocity dependent collision probability problem. Recent progress in this problem has been approached via integration of the probability flux into the surface of the combined hard body object. The algorithm presented uses the surface flux approach and is designed to compute the collision probability rate between two objects given their time dependent states and state error covariance matrices. With regards to the computation of the collision probability (Pc) rate, two major differences exist between the development of this algorithm and the usual Pc algorithm. First, the shape of the at-risk volume is assumed to be a cube rather than a sphere. The size of the cube is chosen so that it circumscribes the usual hard body sphere chosen for the spherical Pc problem. This will result in half the length of a side of the cube being equal to the hard body radius (HBR) of the sphere. Second, it is assumed that the HBR of the cube is much smaller than the smallest combined position uncertainty (σ(sub min) > 5*HBR) at each time point of evaluation. This is necessary as the actual collision probability calculation is based on a first order, small variable expansion in the position components of the Gaussian probability density function. This leads to the collision probability rate being to second order in the combined HBR. The collision probability rate is in a concise, closed form containing exponential and error functions.

Frisbee, Joe↗

NASA NTRS2020

Projection-Based Inter-Agent Collision Avoidance in Dual Agent Systems

Inter-agent collisions can occur in otherwise dynamically-stable (i.e., Lyapunov stable) dual-agent leaderfollower systems. These inter-agent collisions between the leader and the follower happen during the transient phase of the system’s evolution, although the steady-state behavior of the system is asymptotically/exponentially stable. Therefore, to avoid such inter-agent collisions, it is essential to control the relative error trajectory between the leader and the follower during the transient phase of the system’s evolution. In this paper, we introduce a novel projection operator based modelreference control architecture that can mitigate impending inter-agent collisions by modifying the transient dynamics of relative trajectories. This controller augments the follower’s baseline controller and consists of two essential components: a collision-free reference model based on the projection operator and a model reference tracking controller to guide the follower to follow the reference-model. This paper defines the concept of transient-instability in leader-follower systems, introduces collision mitigation controller architecture, and presents an illustrative example demonstrating its effectiveness.

Bayard, David S.↗

NASA NTRS2021

Expected Collision Rates for Tracked Satellites

This analysis estimates collision risks between tracked satellites based on the statistically expected collision rate _Nc and number of collisions Nc, which are closely related to the collision probability Pc. For isolated encounters, Nc equals Pc. For multi-encounter interactions, Nc can exceed Pc and is significantly easier to approximate semi-analytically. Estimating Nc requires integrating the collision rate over time throughout an interaction, with each required _Nc value calculated as a statistical expectation value based on the uncertainty distributions of initial orbital states. The uncertainty distributions are estimated from orbit determination analyses of satellite trajectory measurements. The formulation accounts for the nonlinear orbital motion of the satellites, and derives Nc and _Nc expressions for Monte Carlo simulations as well as semi-analytical approximations for single- and multi-encounter interactions.

Collision Rates↗

NASA NTRS2017

A Fuzzy Logic Approach for Separation Assurance and Collision Avoidance for Unmanned Aerial Systems

In the coming years, operations in low altitude airspace will vastly increase as the capabilities and applications of small Unmanned Aerial Systems (sUAS) continue to multiply. Therefore, solutions to managing sUAS in highly congested airspace must be explored. In this study, a Fuzzy Logic based approach was used to help mitigate the risk of collisions between aircraft using separation assurance and collision avoidance techniques. The system was evaluated for its effectiveness to mitigate the risk of mid-air collisions between aircraft. This system utilizes only current state information and can resolve potential conflicts without knowledge of intruder intent. The avoidance logic was verified using formal methods and shown to select the correct action in all instances. Additionally, the Fuzzy Logic Controllers were shown to always turn the vehicles in the correct direction. Numerical testing demonstrated that the avoidance system was able to prevent a mid-air collision between two sUAS in all tested cases. Simulations were also performed in a three-dimensional environment with a heterogenous fleet of sUAS performing a variety of realistic missions. Simulations showed that the system was 99.98 effective at preventing mid-air collisions when separation assurance was disabled (unmitigated case) and 100 effective when enabled (mitigated case).

Verification & Validation of a Fuzzy Logic Control↗

NASA NTRS1972

Probability of satellite collision

A method is presented for computing the probability of a collision between a particular artificial earth satellite and any one of the total population of earth satellites. The collision hazard incurred by the proposed modular Space Station is assessed using the technique presented. The results of a parametric study to determine what type of satellite orbits produce the greatest contribution to the total collision probability are presented. Collision probability for the Space Station is given as a function of Space Station altitude and inclination. Collision probability was also parameterized over miss distance and mission duration.

Mccarter, J. W.↗

NASA NTRS1972

A numerical hydrodynamic study of coalescence in head-on collisions of identical stars.

The specific results reported refer to head-on collisions between identical polytropes of index 3 having solar mass and radius. If the polytropes were initially at rest at infinity, then about 5% of the combined mass is lost by ejection following collision. The volatilized mass fraction rises to about 18% for an initial relative collision velocity of 1000 km/sec at infinite separation, and to about 60% for the 2000 km/sec case. Since the initial kinetic and gravitational energies balance for a relative velocity of 1512 km/sec at infinity, it may be seen that net coalescence persists to velocities somewhat in excess of this figure. Mass ejection takes place in two ways simultaneously: (1) by a rapid sideward expulsion of fluid in a massive lateral sheet normal to the collision axis, and (2) as a result of two recoil shocks which lead momentum flows backward along this axis. The lateral effect has similarities to the expansion of gas into a vacuum i.e., shocks are not involved. However, the ejection of material from the rear colliding hemisphere due to the recoil shocks predominates at low collision velocities. As the velocity increases, both effects strengthen, but the lateral expulsion intensifies more rapidly than the recoil shocks.

Seidl, F. G. P.↗

NASA NTRS1984

Metastability of isoformyl ions in collisions with helium and hydrogen

The stability of HOC(+) ions under conditions in interstellar molecular clouds is considered. In particular, the possibility that collisions with helium or hydrogen will induce isomerization to the stable HCO(+) form is examined theoretically. Portions of the electronic potential energy surfaces for interaction with He and H atoms are obtained from standard quantum mechanical calculations. Collisions with He atoms are found to be totally ineffective for inducing isomerization. Collisions with H atoms are found to be ineffective at low interstellar temperatures owing to a small (about 500 K) barrier in the entrance channel; at higher temperatures where this barrier can be overcome, however, collisions with hydrogen atoms do result in conversion to the stable HCO(+) form. Although detailed calculations are not presented, it is argued that low-energy collisions with H2 molecules are also ineffective in destroying the metastable ion.

Green, S.↗

NASA NTRS1985

Is the Ventersdorp rift system of southern Africa related to a continental collision between the Kaapvaal and Zimbabwe Cratons at 2.64 Ga AGO?

Rocks of the Ventersdorp Supergroup were deposited in a system of northeast trending grabens on the Kaapvaal Craton approximately 2.64 Ga ago contemporary with a continental collision between the Kaapvaal and Zimbabwe Cratons. It is suggested that it was this collision that initiated the Ventersdorp rifting. Individual grabens strike at high angles toward the continental collision zone now exposed in the Limpopo Province where late orogenic left-lateral strike-slip faulting and anatectic granites are recognized. The Ventersdorp rift province is related to extension in the Kaapvaal Craton associated with the collision, and some analogy is seen with such rifts as the Shansi and Baikal Systems associated with the current India-Asia continental collision.

Burke, K.↗

NASA NTRS1990

A novel representation for planning 3-D collision-free paths

A new scheme for the representation of objects, the successive spherical approximation (SSA), facilitates the rapid planning of collision-free paths in a dynamic three-dimensional environment. The hierarchical nature of the SSA allows collisions to be determined efficiently while still providing an exact representation of objects. The rapidity with which collisions can be detected, less than 1 sec per environment object per path, makes it possible to use a generate-and-test path-planning strategy driven by human conceptual knowledge to determine collision-free paths in a matter of seconds on a Sun 3/180 computer. A hierarchy of rules, based on the concept of a free space cell, is used to find heuristically satisfying collision-free paths in a structured environment.

Bonner, Susan↗

NASA NTRS1994

O(+)-O collision frequency in high-speed flows

Throughout much of the terrestrial thermosphere and ionosphere, the motions of the neutral and ionized constituents are closely coupled and relative velocities are small, of the order of 100 m/s or less. This is particularly true at midlatitudes to low latitudes where typical velocities in the neutral gas due to tidal forcing are only 20-50 m/s. However, the solar wind-magnetosphere interaction drives a large-scale convection pattern in the polar ionosphere. When the rapid adjustment of the plasma to changes in the solar wind is combined with the slower response of the more massive neutral gas, large relative velocities on the order of 1 km/s can exist for substantial lengths of time. This will be more common during periods of high geomagnetic activity, as a result of the greater number of magnetic substorms and other particle precipitation events. When a significant relative velocity is present, the calculation of interaction parameters of the two gases passing through each other, such as collision frequency, must include that velocity. These effects are usually neglected when interpreting wind and ion drift observations. We show how the collision frequency is affected by a directed velocity between any two gases interacting with a power law or exponential potential energy curved. The directed velocity increases the collision frequency at all temperatures for most ion-neutral interactions. For certain power law potentials, such as the charge quadrupole, the collision frequency is decreased. We present an analytic solution for the high-speed collision integral using the resonance charge exchange cross section.

Pesnell, William Dean↗

NASA NTRS2004

On The Effect of Electron Collisions in the Excitation of Cometary HCN

The electron-HCN collision rate for the excitation of rotational transitions of the HCN molecule is evaluated in comets C/1995 01 (Hale-Bopp) and C/1996 B2 (Hyakutake). Based on theoretical models of the cometary atmosphere, we show that collisions with electrons can provide a significant excitation mechanism for rotational transitions in the HCN molecule. Computed values of the cross section sigma(sub e-HCN) can be as high as 1.3 x cm2, more than 2 orders of magnitude greater than the commonly assumed HCN-H2O cross section. For the ground rotational transitions of HCN, the electron-HCN collision rate is found to exceed the HCN-H2O collision rate at distances greater than 3000 km from the cometary nucleus of Hale-Bopp and 1000 km from that of Hyakutake. Collisional excitation processes dominate over radiative excitation processes up to a distance of 160,000 km from the cometary nucleus of Hale-Bopp and 50,000 km from that of Hyakutake. Excitation models that neglect electron collisions can underestimate the HCN gas production rates by as much as a factor of 2.

Lovell, Amy J.↗