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A 850 GHz SIS receiver employing silicon micro-machining technology

A 850 GHz superconductor-insulator-superconductor (SIS) heterodyne receiver which uses a radiofrequency tuned niobium tunnel junction fabricated on a 1 micron thick silicon nitrate membrane, is reported. From video and heterodyne measurements, it was calculated that the niobium film loss in the radiofrequency matching network is about 6.8 dB at 822 GHz. These results are approximately a factor of two higher than the theoretical loss predicted by the Mattis-Bardeen theory in the extreme anomalous limit. The junction design and the receiver configuration are described, including the mixer block, the membrane construction and the cooled optics. The performance tests using a Fourier transform spectrometer to measure the response of the radiofrequency matching network, and the SIS simulations of the receiver response to cold and hot loads, the infrared noise contribution and the overall mixer conversion efficiency, are reported. It is concluded that the receiver response is limited by the absorption loss in the radiofrequency matching network.

Kooi, J. W.

Implicit solvers for unstructured meshes

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Venkatakrishnan, V.

Civilian Aeronautical Futures - The Responsibly Imaginable

Since 1940 Aeronautics has had an immense impact upon Global Human lifestyles and affairs - in both the Civilian and Military arenas. During this period Long distance Train and Ship passenger transport were largely supplanted by Air Travel and Aviation assumed a dominant role in warfare. The early 1940 s to the mid 1970 s was a particularly productive period in terms of Aeronautical Technology. What is interesting is that, since the mid 1970 s, the rate of Aeronautical Technological Progress has been far slower, the basic technology in nearly all of our current Aero Systems dates from the mid 70 s or earlier. This is especially true in terms of Configuration Aerodynamics, Aeronautics appears to have "settled" on the 707, double delta and rotary wing as the approach of choice for Subsonic long haul, supersonic cruise and VTOL respectively. Obviously there have been variants and some niche digression from this/these but in the main Aeronautics, particularly civilian Aeronautics, has become a self-professed "mature", Increasingly "Commodity", Industry. The Industry is far along an existing/deployed technology curve and focused, now for decades, on incremental/evolutionary change - largely Appliers vs. developers of technology. This is, of course, in sharp contrast to the situation in the early-to-later 20th century where Aeronautics was viewed as A Major Technological Engine, much the way IT/Bio/Nano/Energetics/Quantum Technologies are viewed today. A search for Visionary Aeronautical "Futures" papers/projections indicates a decided dearth thereof over the last 20 plus years compared to the previous quarter Century. Aeronautics is part of Aerospace and Aerospace [including Aeronautics] has seen major cutbacks over the last decades. Some numbers for the U.S. Aerospace Industry serve as examples. Order of 600,000 jobs lost, with some 180,000 more on the block over the next 10 years. Approximately 25% of the Aerospace workforce is eligible to retire and the average Engineer age is in the mid-50 s. Firms such as Microsoft, Intel and Walmart are individually capitalized at a factor of 4 or more than the Aerospace industry as a whole. Aerospace Research levels are in the less than 5% range in terms of overall U.S. Research Investments.

Bushnell, Dennis M.

Computations of vortical supersonic flows over a blunt-nose-cylinder at high angles of attack

Three-dimensional, viscous, and separated flows over a blunt-nose-cylinder at 20, 32, and 44-deg attack angles were computed. The approaching freestream was at a Mach number of 1.6 and a unit Reynolds number of 2 x 10 to the 6th/ft with a total temperature of 585 R. The cylinder used for the computations had a length-to-diameter ratio of 6.67 with a base diameter of 3 in. The flowfield was dominated by large-scale and multiple vortices generated by crossflow separation. The effect of turbulence on the flow structure of one case was modeled algebraically with modifications to correct the length and velocity scales in the regions of separation. The mass averaged Navier-Stokes equations were solved by an approximately factored, upwind-biased, implicit, finite volume scheme. The initialization of the flows was enhanced by a mesh sequencing strategy applied to the diagonalized form of the discretized equations. The convergence to steady-state was accelerated by a multigrid algorithm and using the block inversions for the discretized equations. Calculations were compared with experimental results.

Baysal, O.

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.

Quantum Limits of Space-to-Ground Optical Communications

For a pure loss channel, the ultimate capacity can be achieved with classical coherent states (i.e., ideal laser light): (1) Capacity-achieving receiver (measurement) is yet to be determined. (2) Heterodyne detection approaches the ultimate capacity at high mean photon numbers. (3) Photon-counting approaches the ultimate capacity at low mean photon numbers. A number of current technology limits drive the achievable performance of free-space communication links. Approaching fundamental limits in the bandwidth-limited regime: (1) Heterodyne detection with high-order coherent-state modulation approaches ultimate limits. SOA improvements to laser phase noise, adaptive optics systems for atmospheric transmission would help. (2) High-order intensity modulation and photon-counting can approach heterodyne detection within approximately a factor of 2. This may have advantages over coherent detection in the presence of turbulence. Approaching fundamental limits in the photon-limited regime (1) Low-duty cycle binary coherent-state modulation (OOK, PPM) approaches ultimate limits. SOA improvements to laser extinction ratio, receiver dark noise, jitter, and blocking would help. (2) In some link geometries (near field links) number-state transmission could improve over coherent-state transmission

laser communications

The Sun Radio Interferometer Space Experiment (SunRISE) Mission

The Sun Radio Interferometer Space Experiment (SunRISE) will provide an entirely new view on particle acceleration and transport in the inner heliosphere by creating the first low radio frequency interferometer in space to localize heliospheric radio emissions. By imaging and determining the location of decametric-hectometric (DH, 0.1 MHz–23 MHz) solar radio bursts, SunRISE will provide key information on particle acceleration mechanisms associated with coronal mass ejections (CMEs) and the magnetic field topology from active regions into interplanetary space. The SunRISE Observatory will consist of six space vehicles in a passive formation, in orbits designed to keep them within approximately 10 km of each other, and flying in a supersynchronous geosynchronous Earth orbit (GEO). Each space vehicle consists of a Solar DH-GNSS payload and a 6U form factor spacecraft. The SunRISE Observatory together with significant ground-based processing, will enable imaging of the Sun in a portion of the spectrum that is blocked by the ionosphere and cannot be observed from Earth. Key aspects that enable this mission are that only position knowledge of the space vehicles is required, not active control, and that the architecture involves a modest amount of on-board processing coupled with significant ground-based processing for navigation, position determination, and science operations. Mission-enabling advances in software-defined radios, GPS navigation and timing, and small spacecraft technologies, developed and flown on the DARPA High Frequency Research (DHFR) and the Community Initiative for Continuing Earth Radio Occultation (CICERO) have made this mission affordable and low-risk. The SunRISE mission will exploit the multiple spacecraft per aperture (MSPA) capability of NASA’s Deep Space Network (DSN), for more efficient data transfers of larger data volumes, and utilize commercial access to space, in which the SunRISE space vehicles will be carried to their target orbit as secondary payloads in conjunction with a larger host spacecraft intended for GEO.

Neilson, Tim

Assessing the difficulty of capturing the distribution function of neutrinos in neutron star merger simulations

The collision of two neutron stars is a rich source of information about nuclear physics. In particular, the kilonova signal following a merger can help us elucidate the role of neutron stars in nucleosynthesis, and informs us about the properties of matter above nuclear saturation. Approximate modeling of neutrinos remains an important limitation to our ability to make predictions for these observables. Part of the problem is the fermionic nature of neutrinos. By the exclusion principle, the expected value 𝑓 𝜈 for the number of neutrinos in a quantum state is at most 1. Any process producing neutrinos is suppressed by a blocking factor (1 −𝑓 𝜈 ). Recent simulations focused on neutrino physics mostly use a gray two-moment scheme to evolve neutrinos. This evolves integrals of 𝑓 𝜈 over momentum space, preventing direct calculations of blocking factors. Monte Carlo methods may be an attractive alternative, providing access to the full distribution of neutrinos. Their current implementation is, however, inadequate to estimate 𝑓 𝜈 : in our most recent simulations, a single Monte Carlo packet causes, in the worst cases, estimates of 𝑓 𝜈 to jump from 𝑓 𝜈 =0 to 𝑓 𝜈 ∼10 5 . While this is concerning, this brazen violation of the fermionic nature of neutrinos has been largely inconsequential, as the interactions used in simulations avoid direct calculations of 𝑓 𝜈 . We are, however, reaching a level of modeling at which this problem can no longer be ignored. Here, we discuss the relatively simple origin of this issue. We then show that very rough estimates of 𝑓 𝜈 can in theory be obtained in merger simulations, but that they will require a combination of unintuitive weighting schemes for Monte Carlo packets and smoothing of the neutrino distribution at coarser resolution than what the merger simulation uses.

79 ASTRONOMY AND ASTROPHYSICS

Transonic Navier-Stokes wing solution using a zonal approach. Part 1: Solution methodology and code validation

A fast diagonalized Beam-Warming algorithm is coupled with a zonal approach to solve the three-dimensional Euler/Navier-Stokes equations. The computer code, called Transonic Navier-Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin-layer Navier-Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method code. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000-point mesh for a NACA 0012 wing. A three-order-of-magnitude drop in the L2-norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.

Flores, J.

Transonic Navier-Stokes wing solution using a zonal approach. Part 1: Solution methodology and code validation

A fast diagonalized Beam-Warming algorithm is coupled with a zonal approach to solve the three dimensional Euler/Navier-Stokes equations. The computer code, called Transonic Navier-Stokes (TNS), uses a total of four zones for wing configurations (or can be extended to complete aircraft configurations by adding zones). In the inner blocks near the wing surface, the thin-layer Navier-Stokes equations are solved, while in the outer two blocks the Euler equations are solved. The diagonal algorithm yields a speedup of as much as a factor of 40 over the original algorithm/zonal method code. The TNS code, in addition, has the capability to model wind tunnel walls. Transonic viscous solutions are obtained on a 150,000-point mesh for a NACA 0012 wing. A three-order-of-magnitude drop in the L2-norm of the residual requires approximately 500 iterations, which takes about 45 min of CPU time on a Cray-XMP processor. Simulations are also conducted for a different geometrical wing called WING C. All cases show good agreement with experimental data.

Flores, J.

A Navier-Strokes Chimera Code on the Connection Machine CM-5: Design and Performance

We have implemented a three-dimensional compressible Navier-Stokes code on the Connection Machine CM-5. The code is set up for implicit time-stepping on single or multiple structured grids. For multiple grids and geometrically complex problems, we follow the 'chimera' approach, where flow data on one zone is interpolated onto another in the region of overlap. We will describe our design philosophy and give some timing results for the current code. A parallel machine like the CM-5 is well-suited for finite-difference methods on structured grids. The regular pattern of connections of a structured mesh maps well onto the architecture of the machine. So the first design choice, finite differences on a structured mesh, is natural. We use centered differences in space, with added artificial dissipation terms. When numerically solving the Navier-Stokes equations, there are liable to be some mesh cells near a solid body that are small in at least one direction. This mesh cell geometry can impose a very severe CFL (Courant-Friedrichs-Lewy) condition on the time step for explicit time-stepping methods. Thus, though explicit time-stepping is well-suited to the architecture of the machine, we have adopted implicit time-stepping. We have further taken the approximate factorization approach. This creates the need to solve large banded linear systems and creates the first possible barrier to an efficient algorithm. To overcome this first possible barrier we have considered two options. The first is just to solve the banded linear systems with data spread over the whole machine, using whatever fast method is available. This option is adequate for solving scalar tridiagonal systems, but for scalar pentadiagonal or block tridiagonal systems it is somewhat slower than desired. The second option is to 'transpose' the flow and geometry variables as part of the time-stepping process: Start with x-lines of data in-processor. Form explicit terms in x, then transpose so y-lines of data are in-processor. Form explicit terms in y, then transpose so z-lines are in processor. Form explicit terms in z, then solve linear systems in the z-direction. Transpose to the y-direction, then solve linear systems in the y-direction. Finally transpose to the x direction and solve linear systems in the x-direction. This strategy avoids inter-processor communication when differencing and solving linear systems, but requires a large amount of communication when doing the transposes. The transpose method is more efficient than the non-transpose strategy when dealing with scalar pentadiagonal or block tridiagonal systems. For handling geometrically complex problems the chimera strategy was adopted. For multiple zone cases we compute on each zone sequentially (using the whole parallel machine), then send the chimera interpolation data to a distributed data structure (array) laid out over the whole machine. This information transfer implies an irregular communication pattern, and is the second possible barrier to an efficient algorithm. We have implemented these ideas on the CM-5 using CMF (Connection Machine Fortran), a data parallel language which combines elements of Fortran 90 and certain extensions, and which bears a strong similarity to High Performance Fortran. We make use of the Connection Machine Scientific Software Library (CMSSL) for the linear solver and array transpose operations.

Jespersen, Dennis C.

Algorithm for Compressing Time-Series Data

An algorithm based on Chebyshev polynomials effects lossy compression of time-series data or other one-dimensional data streams (e.g., spectral data) that are arranged in blocks for sequential transmission. The algorithm was developed for use in transmitting data from spacecraft scientific instruments to Earth stations. In spite of its lossy nature, the algorithm preserves the information needed for scientific analysis. The algorithm is computationally simple, yet compresses data streams by factors much greater than two. The algorithm is not restricted to spacecraft or scientific uses: it is applicable to time-series data in general. The algorithm can also be applied to general multidimensional data that have been converted to time-series data, a typical example being image data acquired by raster scanning. However, unlike most prior image-data-compression algorithms, this algorithm neither depends on nor exploits the two-dimensional spatial correlations that are generally present in images. In order to understand the essence of this compression algorithm, it is necessary to understand that the net effect of this algorithm and the associated decompression algorithm is to approximate the original stream of data as a sequence of finite series of Chebyshev polynomials. For the purpose of this algorithm, a block of data or interval of time for which a Chebyshev polynomial series is fitted to the original data is denoted a fitting interval. Chebyshev approximation has two properties that make it particularly effective for compressing serial data streams with minimal loss of scientific information: The errors associated with a Chebyshev approximation are nearly uniformly distributed over the fitting interval (this is known in the art as the "equal error property"); and the maximum deviations of the fitted Chebyshev polynomial from the original data have the smallest possible values (this is known in the art as the "min-max property").

Hawkins, S. Edward, III

Propulsion Technology Demonstrator

NASA's Pathfinder Technology Demonstrator (PTD) project will test the operation of a variety of novel CubeSat technologies in low- Earth orbit, providing significant enhancements to the performance of these small and effective spacecraft. Each Pathfinder Technology Demonstrator mission consists of a 6-unit (6U) CubeSat weighing approximately 26 pounds (12 kilograms) and measuring 12 inches x 10 inches x 4 inches (30 centimeters x 25 centimeters x 10 centimeters), comparable in size to a common shoebox. CubeSats are a class of nanosatellites that use a standard size and form factor. The standard Cube- Sat size uses a "one unit" or "1U" measuring 4 inches x 4 inches x 4 inches (10x10x10 centimeters) and is extendable to larger sizes by "stacking" a number of the 1U blocks to form a larger spacecraft. Each PTD spacecraft will also be equipped with deployable solar arrays that provide an average of 44 watts of power while in orbit.

CubeSat

Early immune response and regulation of IL-2 receptor subunits

Affymetrix oligonucleotide arrays were used to monitor expression of 8796 genes and probe sets in activated T-cells; analysis revealed that 217 genes were significantly upregulated within 4 h. Induced genes included transcription factors, cytokines and their receptor genes. Analysis by semi-quantitative RT-PCR confirmed the significant induction of IL-2, IL-2R(gamma) and IL-2R(alpha). Forty-eight of the 217 induced genes are known to or predicted to be regulated by a CRE promoter/enhancer. We found that T-cell activation caused a significant increase in CREB phosphorylation furthermore, inhibition of the PKC pathway by GF109203 reduced CREB activation by 50% and inhibition of the PKA pathway caused a total block of CREB phosphorylation and significantly reduced IFN(gamma), IL-2 and IL-2R(alpha) gene expression by approximately 40% (p<0.001). PKC(theta) plays a major role in T-cell activation: inhibition of PKC significantly reduced the expression of IFN(gamma), IL-2 and IL-2R(alpha). Since PKC blocked activation of CREB, we studied potential cross-talk between the PKC and the PKA/MAPK pathways, PMA-stimulated Jurkat cells were studied with specific signal pathway inhibitors. Extracellular signal-regulated kinase-2 (ERK2) pathway was found to be significantly activated greater than seven-fold within 30 min; however, there was little activation of ERK-1 and no activation of JNK or p38 MAPK. Inhibition of the PKA pathway, but not the PKC pathway, resulted in inhibition of ERK1/2 activation at all time points, inhibition of MEK1 and 2 significantly blocked expression of IL-2 and IL-2R(alpha). Gene expression of IL-2R(alpha) and IFN(gamma) was dependent on PKA in S49 wt cells but not in kin- mutants. Using gel shift analysis, we found that forskolin activation of T-cells resulted in activation of AP1 sites; this increase in nuclear extract AP1 was significantly blocked by MEK1 inhibitor U0126. Taken together, these results suggest that the PKA in addition to PKC and MAPK pathways plays a role in early T-cell activation and induction of IL-2, IL-2R(alpha) and IFN(gamma) gene expression.

Non-NASA Center

Navier-Stokes Aerodynamic Simulation of the V-22 Osprey on the Intel Paragon MPP

The paper will describe the Development of a general three-dimensional multiple grid zone Navier-Stokes flowfield simulation program (ENS3D-MPP) designed for efficient execution on the Intel Paragon Massively Parallel Processor (MPP) supercomputer, and the subsequent application of this method to the prediction of the viscous flowfield about the V-22 Osprey tiltrotor vehicle. The flowfield simulation code solves the thin Layer or full Navier-Stoke's equation - for viscous flow modeling, or the Euler equations for inviscid flow modeling on a structured multi-zone mesh. In the present paper only viscous simulations will be shown. The governing difference equations are solved using a time marching implicit approximate factorization method with either TVD upwind or central differencing used for the convective terms and central differencing used for the viscous diffusion terms. Steady state or Lime accurate solutions can be calculated. The present paper will focus on steady state applications, although time accurate solution analysis is the ultimate goal of this effort. Laminar viscosity is calculated using Sutherland's law and the Baldwin-Lomax two layer algebraic turbulence model is used to compute the eddy viscosity. The Simulation method uses an arbitrary block, curvilinear grid topology. An automatic grid adaption scheme is incorporated which concentrates grid points in high density gradient regions. A variety of user-specified boundary conditions are available. This paper will present the application of the scalable and superscalable versions to the steady state viscous flow analysis of the V-22 Osprey using a multiple zone global mesh. The mesh consists of a series of sheared cartesian grid blocks with polar grids embedded within to better simulate the wing tip mounted nacelle. MPP solutions will be shown in comparison to equivalent Cray C-90 results and also in comparison to experimental data. Discussions on meshing considerations, wall clock execution time, load balancing, and scalability will be provided.

Vadyak, Joseph

Fast Near-Optimal Heterogeneous Task Allocation via Flow Decomposition

Multi-robot systems are uniquely well-suited to perform complex tasks such as patrolling and tracking, infor- mation gathering, and pick-up and delivery problems, offering significantly higher performance than single-robot systems. A fundamental building block in most multi-robot systems is dynamic task allocation: assigning robots to tasks (e.g., patrolling an area, or servicing a transportation request) as they appear based on the robots’ states to maximize reward. In many practical situations, the allocation must account for potentially heteroge- neous capabilities (e.g., availability of appropriate sensors or actuators) to ensure the feasibility of execution, and exploit predictive information concerning the likelihood of future tasks to promote a higher reward over a long time horizon. To this end, we present an efficient algorithm for predictive heterogeneous task- allocation achieving an approximation factor of at least 1/2 of the optimal reward. Our approach demonstrates that the problem can be decomposed into several homogeneous subproblems that can be solved efficiently using min-cost flow. Through simulation experiments, we show that our algorithm is faster by several orders of magnitude than a MILP-based approach.

Pavone, Marco

Eigenvalue Sensitivity Computations for Linear Stability Theory

To realize the drag reduction benefit of boundary-layer transition control strategies, it is crucial to integrate transition prediction into the vehicle design through an optimization process. The integration of transition prediction based on linear stability analysis into adjoint d design optimization requires coupling an adjoint enabled computational fluid dynamics (CFD) solver with an adjoint enabled linear stability code. In particular, the boundary-layer transition location is often predicted using the N-factor method based on linear stability theory (LST). Thus, sensitivity of the linear-stability eigenvalues constitute an essential building block for optimizing the laminar flow performance. The present paper describes an implementation of LST eigenvalue sensitivity analysis that can be easily coupled with a CFD solver. Specifically, we describe a discrete adjoint formulation for the transition location prediction based on the N-factor method. The verification of this formulation is carried out by comparing the adjoint-based sensitivity of the local growth rate of a given instability mode with respect to the disturbance frequency, and the adjoint-based sensitivity of the transition location with respect to spanwise wavenumber with those sensitivities computed using a finite-difference approximation. Finally, the adjoint LST formulation is applied to flat-plate boundary-layer flows at transonic, supersonic, and hypersonic conditions, to determine the behavior and sensitivities of the transition location with respect to a range of disturbance spanwise wavenumbers.

Boundary Layer Transition

Space Launch System (SLS) Human Factors Engineering Modeling & Analysis

The Human Systems Integration & Engineering (HSI&E) team at NASA’s Marshall Space Flight Center (MSFC) strives to advocate for the humans in the loop of Space Launch System’s (SLS) ground operations. Using assessment methods like human simulation, virtual reality, and physical mockups, both flight hardware and ground support equipment (GSE) are evaluated for human integration. Those ranging from 5th percentile female (approximately 5’2” tall) to 95th percentile male (approximately 6’2” tall) should be able to perform all SLS stacking operations. Operations include element physical mates, element electrical mates, and testing activities. The primary human simulation software used is Process Simulate Human (PSH) made by Siemens. This software supplies highly accurate human manikins that can interact with CAD models. PSH was used to evaluate the Transportation and Integration Platform’s (TIP) side opening that was designed for access to the Payload Adapter (PLA) cables. Technicians will need to access these cables for testing purposes before element stacking at Kennedy Space Center (KSC). After performing an analysis in PSH using the TIP side opening, it was found that neither a 5th percentile female or a 95th percentile male could perform the task as the designers had intended. There is a C-beam that blocks access to the cables (both physically and visually). An alternative analysis was performed using PSH to look at another access point to the PLA cables. Although this method would disrupt already established procedures and produce more work, the designers confirmed it was an option. Instead of technicians accessing the cables through the side opening in the TIP, a human simulation was performed for going through a panel opening in the bottom of the TIP. This method requires removal of a TIP panel and a stepladder of at least 36 inches for a 5th percentile female to access the cables.

human factors