Early Thoughts on the Jet Flap

1956 ◽  
Vol 7 (1) ◽  
pp. 45-59 ◽  
Author(s):  
B. S. Stratford
Keyword(s):  
Present State ◽  
Deflection Angle ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Quantitative Theory ◽  
The Deflection Angle ◽  
Basic Ideas ◽  
Historical Sketch

SummaryAn historical sketch shows how the basic ideas of the jet flap were evolved. The exploratory work included the prediction that lift would be induced on an aerofoil by a two-dimensional jet deflected from the trailing edge, and that the magnitude of the total lift would be of the order of four times the direct jet lift. The prediction was confirmed experimentally and a first quantitative theory evolved. Meanwhile the hypothesis was put forward that, ideally, the forward thrust on the aerofoil would be independent of the deflection angle of the jet.This paper is the first of a series of papers that will describe the development and present state of knowledge of the jet flap.

scholarly journals Static Aeroelastic Characteristics of Morphing Trailing-Edge Wing Using Geometrically Exact Vortex Lattice Method

2019 ◽  
Vol 2019 ◽  
pp. 1-15
Author(s):  
Sen Mao ◽  
Changchuan Xie ◽  
Lan Yang ◽  
Chao Yang
Keyword(s):  
Vortex Lattice ◽  
Deflection Angle ◽  
Aircraft Design ◽  
Analysis Method ◽  
Lattice Method ◽  
Trailing Edge ◽  
Vortex Lattice Method ◽  
Analysis And Design ◽  
Aeroelastic Analysis ◽  
Typical Model

A morphing trailing-edge (TE) wing is an important morphing mode in aircraft design. In order to explore the static aeroelastic characteristics of a morphing TE wing, an efficient and feasible method for static aeroelastic analysis has been developed in this paper. A geometrically exact vortex lattice method (VLM) is applied to calculate the aerodynamic forces. Firstly, a typical model of a morphing TE wing is chosen and built which has an active morphing trailing edge driven by a piezoelectric patch. Then, the paper carries out the static aeroelastic analysis of the morphing TE wing and corresponding simulations were carried out. Finally, the analysis results are compared with those of a traditional wing with a rigid trailing edge using the traditional linearized VLM. The results indicate that the geometrically exact VLM can better describe the aerodynamic nonlinearity of a morphing TE wing in consideration of geometrical deformation in aeroelastic analysis. Moreover, out of consideration of the angle of attack, the deflection angle of the trailing edge, among others, the wing system does not show divergence but bifurcation. Consequently, the aeroelastic analysis method proposed in this paper is more applicable to the analysis and design of a morphing TE wing.

scholarly journals Quantitative evaluation indexes of the spatial steering effect of directional perforation hydraulic fractures

2021 ◽  
pp. 014459872110102
Author(s):  
Lu Weiyong ◽  
He Changchun
Keyword(s):  
Quantitative Evaluation ◽  
Hydraulic Fracture ◽  
Deflection Angle ◽  
Hydraulic Fractures ◽  
Principal Stress Direction ◽  
Perforation Hole ◽  
Evaluation Indexes ◽  
Initiation Pressure ◽  
The Deflection Angle ◽  
Bending Fracture

To better evaluate the spatial steering effect of directional perforation hydraulic fractures, evaluation indexes for the spatial steering effect are first proposed in this paper. Then, these indexes are used to quantitatively evaluate existing physical experimental results. Finally, with the help of RFPA2D-Flow software, the influence of perforation length and azimuth on the spatial steering process of hydraulic fracture are quantitatively analysed using four evaluation indexes. It is shown by the results that the spatial deflection trajectory, deflection distance, deflection angle and initiation pressure of hydraulic fractures can be used as quantitative evaluation indexes for the spatial steering effect of hydraulic fractures. The deflection paths of directional perforation hydraulic fractures are basically the same. They all gradually deflect to the maximum horizontal principal stress direction from the perforation hole and finally represent a double-wing bending fracture. The deflection distance, deflection angle and initiation pressure of hydraulic fractures increase gradually with increasing perforation azimuth, and the sensitivity of the deflection angle to the perforation azimuth of hydraulic fractures also increases. With increasing perforation length, the deflection distance of hydraulic fractures increases gradually. However, the deflection angle and initiation pressure decrease gradually, as does the sensitivity.

scholarly journals OPERATOR-PRODUCT EXPANSION AND ANALYTICITY

1999 ◽  
Vol 14 (30) ◽  
pp. 4819-4840
Author(s):  
JAN FISCHER ◽  
IVO VRKOČ
Keyword(s):  
Operator Product Expansion ◽  
Deflection Angle ◽  
Vacuum Expectation ◽  
Vacuum Expectation Value ◽  
Operator Product ◽  
Coupling Constant ◽  
Expectation Value ◽  
Euclidean Region ◽  
The Deflection Angle ◽  
Class Of Functions

We discuss the current use of the operator-product expansion in QCD calculations. Treating the OPE as an expansion in inverse powers of an energy-squared variable (with possible exponential terms added), approximating the vacuum expectation value of the operator product by several terms and assuming a bound on the remainder along the Euclidean region, we observe how the bound varies with increasing deflection from the Euclidean ray down to the cut (Minkowski region). We argue that the assumption that the remainder is constant for all angles in the cut complex plane down to the Minkowski region is not justified. Making specific assumptions on the properties of the expanded function, we obtain bounds on the remainder in explicit form and show that they are very sensitive both to the deflection angle and to the class of functions considered. The results obtained are discussed in connection with calculations of the coupling constant αs from the τ decay.

Airfoil Design in Subcritical and Supercritical Flows

1979 ◽  
Vol 46 (4) ◽  
pp. 761-766 ◽  
Author(s):  
W. C. Chin ◽  
D. P. Rizzetta
Keyword(s):  
Reasonable Agreement ◽  
Relaxation Method ◽  
Supercritical Pressure ◽  
Small Disturbance ◽  
Trailing Edge ◽  
Difference Analysis ◽  
Pressure Distributions ◽  
Basic Ideas ◽  
New Formulation ◽  
Supercritical Flows

The “inverse” or “design” problem in aerodynamics, which solves for the airfoil shape that induces a prescribed chordwise surface pressure subject to additional requirements on trailing edge closure, is considered in the transonic small-disturbance limit. A new formulation for the stream function ψ is suggested which uses well-set Neumann conditions on the chordwise slit, with the degree of closure dictated by a specified jump in ψ across the downstream slit emanating from the trailing edge. The boundary-value problem is solved by a type-dependent relaxation method that automatically generates closed airfoils on convergence. Computed airfoil shapes using subcritical and supercritical pressure distributions obtained from existing finite-difference analysis codes, in the latter case, with and without shockwaves, give results in reasonable agreement with the original specified shapes, and validate the basic ideas.

The precise calculations of the constant terms in the equations of motions of planets and photons of general relativity

2021 ◽  
Vol 34 (2) ◽  
pp. 183-192
Author(s):  
Mei Xiaochun
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Deflection Angle ◽  
Constant Term ◽  
Equation Of Motion ◽  
Time Dependent ◽  
Newtonian Gravity ◽  
Newtonian Theory ◽  
The Deflection Angle ◽  
Equations Of Motions

In general relativity, the values of constant terms in the equations of motions of planets and light have not been seriously discussed. Based on the Schwarzschild metric and the geodesic equations of the Riemann geometry, it is proved in this paper that the constant term in the time-dependent equation of motion of planet in general relativity must be equal to zero. Otherwise, when the correction term of general relativity is ignored, the resulting Newtonian gravity formula would change its basic form. Due to the absence of this constant term, the equation of motion cannot describe the elliptical and the hyperbolic orbital motions of celestial bodies in the solar gravitational field. It can only describe the parabolic orbital motion (with minor corrections). Therefore, it becomes meaningless to use general relativity calculating the precession of Mercury's perihelion. It is also proved that the time-dependent orbital equation of light in general relativity is contradictory to the time-independent equation of light. Using the time-independent orbital equation to do calculation, the deflection angle of light in the solar gravitational field is <mml:math display="inline"> <mml:mrow> <mml:mn>1.7</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> . But using the time-dependent equation to do calculation, the deflection angle of light is only a small correction of the prediction value <mml:math display="inline"> <mml:mrow> <mml:mn>0.87</mml:mn> <mml:msup> <mml:mn>5</mml:mn> <mml:mo>″</mml:mo> </mml:msup> </mml:mrow> </mml:math> of the Newtonian gravity theory with a magnitude order of <mml:math display="inline"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mn>10</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> . The reason causing this inconsistency was the Einstein's assumption that the motion of light satisfied the condition <mml:math display="inline"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mi>s</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> in gravitational field. It leads to the absence of constant term in the time-independent equation of motion of light and destroys the uniqueness of geodesic in curved space-time. Meanwhile, light is subjected to repulsive forces in the gravitational field, rather than attractive forces. The direction of deflection of light is opposite, inconsistent with the predictions of present general relativity and the Newtonian theory of gravity. Observing on the earth surface, the wavelength of light emitted by the sun is violet shifted. This prediction is obviously not true. Practical observation is red shift. Finally, the practical significance of the calculation of the Mercury perihelion's precession and the existing problems of the light's deflection experiments of general relativity are briefly discussed. The conclusion of this paper is that general relativity cannot have consistence with the Newtonian theory of gravity for the descriptions of motions of planets and light in the solar system. The theory itself is not self-consistent too.

Part II: Steady aerofoil-spoiler characteristics

1987 ◽  
Vol 91 (908) ◽  
pp. 359-366
Keyword(s):  
Separated Flow ◽  
Experimental Results ◽  
Surface Singularity ◽  
Separation Region ◽  
Two Dimensional ◽  
Trailing Edge ◽  
Singularity Method ◽  
Total Head ◽  
Low Speeds ◽  
Theoretical Results

Summary A surface singularity method has been formulated to predict two-dimensional spoiler characteristics at low speeds. Vorticity singularities are placed on the aerofoil surface, on the spoiler surface, on the upper separation streamline from the spoiler tip and on the lower separation streamline from the aerofoil trailing edge. The separation region is closed downstream by two discrete vortices. The flow inside the separation region is assumed to have uniform total head. The downstream extent of the separated wake is an empirical input. The flows both external and internal to the separated regions are solved. Theoretical results have been obtained for a range of spoiler-aerofoil configurations which compare reasonably with experimental results. The model is deficient in that it predicts a higher compression ahead of the spoiler than obtained in practice. Furthermore, there is a minimum spoiler angle below which a solution is not possible; it is thought that this feature is related to the physical observation that at small spoiler angles, the separated flow from the spoiler reattaches on the aerofoil upper surface ahead of the trailing edge.

Gauging the earth

2013 ◽  
Vol 97 (540) ◽  
pp. 413-420
Author(s):  
John D. Mahony
Keyword(s):  
Approximate Formula ◽  
Deflection Angle ◽  
School Science ◽  
Science Department ◽  
Measurement Apparatus ◽  
The Earth ◽  
Interesting Discussion ◽  
Simple Measurement ◽  
The Deflection Angle

In an earlier note by W. J. A. Colman [1], the reader was treated to an interesting discussion concerning a BBC programme about the earth's radius in the context of endeavours to determine it by an 11th century Persian mathematician, Al-Biruni. At the same time a modem but approximate formula that might not have been available to the ancients was proposed for the radius and, following that account, it is the purpose here to explore just how accurately one might determine the earth's radius using this formula together with a simple measurement apparatus (not a sophisticated astrolabe) that might be constructed from materials found in the garage of any DIY handyman, or indeed, in the laboratory of any school science department. A schematic for the configuration of an observer P at a height h above the earth (of radius R) where the deflection angle to the horizon is denoted by θ, is shown in Figure 1. Also shown in the figure is a ‘sighting tube’ of length L about which more will be said later.

scholarly journals SPECIAL VEHICLE MOTION STABILIZATION SYSTEM

2021 ◽  
pp. 37-41
Author(s):  
M. V. Lyashenko ◽  
V. V. Shekhovtsov ◽  
P. V. Potapov ◽  
A. A. Shvedunenko
Keyword(s):  
Pid Controller ◽  
Deflection Angle ◽  
Angular Displacement ◽  
Dynamic Equations ◽  
Engine Torque ◽  
Special Vehicle ◽  
Vehicle Motion ◽  
Motion Stabilization ◽  
The Deflection Angle ◽  
The Mathematical Model

The system of special vehicle (SV) motion stabilization during moving on a straight surface is modeled on the base of dynamic equations of the mathematical model. The movement is stabilized by using a PID controller, the angular displacement of the mass is selected to ensure a given speed of movement, and the deflection angle is stabilized by controlling the engine torque.

scholarly journals Values estimation of deflection angle of a floating sensor for various objects (to the resistance to measuring the water surface rate)

2019 ◽  
Vol 5 (2) ◽  
pp. 181-196
Author(s):  
K. Presnyakov ◽  
G. Kerimkulova ◽  
G. Askalieva
Keyword(s):  
Water Surface ◽  
Deflection Angle ◽  
Surface Velocity ◽  
Informative Parameter ◽  
The Deflection Angle

A device is proposed for measuring the surface velocity of water, the use of which is based on the use of a new informative parameter — the deflection angle of the movable float sensor (together with the guide slide) from the vertical in the direction of the dynamic axis of the flow, allowing you to simply and reliably measure the surface velocity of water.

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