Design Guide for Pitch-Up Evaluation and Investigation at High Subsonic Speeds of Possible Limitations Due to Wing-Aspect-Ratio Variations

A design guide is suggested as a basis for indicating combinations of airplane design variables for which the possibilities of pitch-up are minimized for tail-behind-wing and tailless airplane configurations. The guide specifies wing plan forms that would be expected to show increased tail-off stability with increasing lift and plan forms that show decreased tail-off stability with increasing lift. Boundaries indicating tail-behind-wing positions that should be considered along with given tail-off characteristics also are suggested. An investigation of one possible limitation of the guide with respect to the effects of wing-aspect-ratio variations on the contribution to stability of a high tail has been made in the Langley high-speed 7- by 10-foot tunnel through a Mach number range from 0.60 to 0.92. The measured pitching-moment characteristics were found to be consistent with those of the design guide through the lift range for aspect ratios from 3.0 to 2.0. However, a configuration with an aspect ratio of 1.55 failed t o provide the predicted pitch-up warning characterized by sharply increasing stability at the high lifts following the initial stall before pitching up. Thus, it appears that the design guide presented herein might not be applicable when the wing aspect ratios lower than about 2.0

Approximating Persistent Homology in Euclidean Space Through Collapses

The \v{C}ech complex is one of the most widely used tools in applied algebraic topology. Unfortunately, due to the inclusive nature of the \v{C}ech filtration, the number of simplices grows exponentially in the number of input points. A practical consequence is that computations may have to terminate at smaller scales than what the application calls for. In this paper we propose two methods to approximate the \v{C}ech persistence module. Both are constructed on the level of spaces, i.e. as sequences of simplicial complexes induced by nerves. We also show how the bottleneck distance between such persistence modules can be understood by how tightly they are sandwiched on the level of spaces. In turn, this implies the correctness of our approximation methods. Finally, we implement our methods and apply them to some example point clouds in Euclidean space

Topological exploration of artificial neuronal network dynamics

One of the paramount challenges in neuroscience is to understand the dynamics of individual neurons and how they give rise to network dynamics when interconnected. Historically, researchers have resorted to graph theory, statistics, and statistical mechanics to describe the spatiotemporal structure of such network dynamics. Our novel approach employs tools from algebraic topology to characterize the global properties of network structure and dynamics. We propose a method based on persistent homology to automatically classify network dynamics using topological features of spaces built from various spike-train distances. We investigate the efficacy of our method by simulating activity in three small artificial neural networks with different sets of parameters, giving rise to dynamics that can be classified into four regimes. We then compute three measures of spike train similarity and use persistent homology to extract topological features that are fundamentally different from those used in traditional methods. Our results show that a machine learning classifier trained on these features can accurately predict the regime of the network it was trained on and also generalize to other networks that were not presented during training. Moreover, we demonstrate that using features extracted from multiple spike-train distances systematically improves the performance of our method

Effectiveness of Boundary-layer Control, Obtained by Blowing over a Plain Rear Flap in Combination with a Forward Slotted Flap, in Deflecting a Slipstream Downward for Vertical Take-off

The wing employed in this investigation had a 67-percent-chord slotted flap in combination with a 33-percent-chord plain rear flap equipped with a full-span blowing nozzle. The tests were conducted in a static-thrust facility at the Langley Aeronautical Laboratory. The investigation indicated that the plain rear flap alone with a low momentum coefficient for boundary-layer control provided larger turning angles than the combined slotted and plain flaps without boundary-layer control

A Notion of Harmonic Clustering in Simplicial Complexes

We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of, graph spectral clustering. The algorithm involves only sparse eigenproblems, and is therefore computationally efficient. We believe that it has broad application as a way to extract features from simplicial complexes that often arise in topological data analysis

Investigation of Interference of a Deflected Jet with Free Stream and Ground on Aerodynamic Characteristics of a Semispan Delta-Wing VTOL Model

An investigation of the mutual interference effects of the ground, wing, deflected jet stream, and free stream of a semispan delta-wing VTOL model at zero and low forward speeds has been conducted in the 17-foot test section of the Langley 300-MPH 7-by 10-foot tunnel. The model consisted of two interchangeable semispan clipped delta wings, a simplified fuselage, and a high-pressure jet for simulation of a jet exhaust. Attached to the wing behind the jet were various sets of vanes for deflecting the jet stream to different turning angles. The effect of ground proximity gave the normally expected losses in lift at zero and very low forward speeds (up to about 60 or 80 knots for the assumed wing loading of 100 lb/sq ft); at higher forward speeds ground effects were favorable. At low forward speeds, out of ground effect, the model encountered large losses in lift and large nose-up pitching moments with the model at low angles of attack and the jet deflected 90 deg or 75 deg (the angles required for VTOL performance and very low forward speeds). Rotating the model to higher angles of attack and deflecting the jet back to lower angles eliminated these losses in lift. Moving the jet rearward with respect to the wing reduced the losses in lift and the nose-up moments at all speeds within the range of this investigation