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Topic: Dihedral angle

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  Angle - LoveToKnow 1911   (Site not responding. Last check: 2007-10-18)
The first concept was utilized by Eudemus, who regarded an angle as a deviation from a straight line; the second by Carpus of Antioch, who regarded it as the interval or space between the intersecting lines; Euclid adopted the third concept, although his definitions of right, acute, and obtuse angles are certainly quantitative.
A spherical angle is a particular dihedral angle; it is the angle between two intersecting arcs on a sphere, and is measured by the angle between the planes containing the arcs and the centre of the sphere.
The angle between a line and a curve (mixed angle) or between two curves (curvilinear angle) is measured by the angle between the line and the tangent at the point of intersection, or between the tangents to both curves at their common point.
www.1911encyclopedia.org /Angle   (449 words)

 Angle - ExampleProblems.com   (Site not responding. Last check: 2007-10-18)
Angles provide a means of expressing the difference in slope between two rays meeting at a vertex without the need to explicitly define the slopes of the two rays.
The degree measure of the angle is the length of the arc, divided by the circumference of the circle, and multiplied by 360.
The angle between a line and a curve (mixed angle) or between two intersecting curves (curvilinear angle) is defined to be the angle between the tangents at the point of intersection.
www.exampleproblems.com /wiki/index.php/Angle   (1442 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-18)
The dihedral angles are not all the same, because the polygons are not all identical.
Hence, dihedral angles between faces with fewer sides ought to be shallower (dihedral angle closer to 180 degrees).
So the angles we're looking for are hexagon-decagon: 142.62 degrees square-decagon: 148.28 degrees hexagon-square: 159.095 degrees It makes sense that the square/hexagon dihedral angle is is the largest, because the square and hexagon have the fewest sides, and that the hexagon/decagon dihedral angle is the smallest, by the reasoning above.
mathforum.org /library/drmath/view/64251.html   (585 words)

 Axial flow fan blade structure - Patent 5730583
Advantagously the dihedral angle decreases moving from the root to the tip over a first portion of the span of the blade, said first portion being about 50% of the total span and then stays constant for the remainder of the span of the blade.
Alternatively the dihedral angle decreases moving from the root to the tip over a first portion of the span of the blade, said first portion being about 50% of the total span and then gradually increases for the remainder of the span of the blade.
To further reduce acoustic co-incidence, the arm 141 forms an acute angle with respect to a radius of the outer ring 101, the arm 142 forms a less acute angle with a radius of the outer ring 101 and the third arm 143 is parallel to such a radius.
www.freepatentsonline.com /5730583.html   (4431 words)

 ASK DJ Aerotech Question
An angle of 74 deg., measured according to the drawing shown in the upper right corner of the Chrysalis plans, equates to an included angle of 106 degrees between the two panels.
It also equates to a dihedral angle per panel, measured from horizontal (the same way you would measure wing dihedral) of 37 degrees per side.
The dihedral angle of a V-tail is what determines how much of its authority is devoted to pitch effects, and how much to yaw effects.
www.djaerotech.com /dj_askjd/dj_questions/chrys_vtail-angle.html   (482 words)

 All Elementary Mathematics - Study Guide - Geometry - Angles. Projections. Polyhedral angles...
The plane P, perpendicular to the edge MN, gives the angle AOB in its intersection with the half-planes Q and R. The angle AOB is called a linear angle of a dihedral angle.
A linear angle is a measure of its dihedral angle.
In general case an angle between two planes P and Q (Fig.75) can be measured by an angle, formed by the straight lines AB and CD, which are perpendicular to the planes P and Q correspondingly.
www.bymath.com /studyguide/geo/sec/geo14.htm   (537 words)

 Dihedral Angle
This is the angle that is formed whenever two "planes" meet.
There are some sites that offer you a quick way to get the angle, but their calculations are based on the slope angle of the face pieces rather then the height of the pyramid.
The base angle to cut the bottom of your pieces so that when they are place the piece "stands" at the correct angle.
www.josephfusco.org /Articles/Dihedral/Dihedral.html   (495 words)

 Woodworkers Journal eZine - Web Surfer's Review
Yet to establish the dihedral angle you need to look down a pyramid from its upper point along the arris of the intersecting sides to the bottom corner and measure the angle the sloping faces of the planes form at the bottom corner.
In a pyramid where the sides lean in from the vertical at 60° the dihedral angle is 104.48° (with a miter angle of 52.24° to join them), and the angle that the triangular sides edges rise from the base line is 63.43°.
To dovetail a pyramid type structure of this type with the angles I detailed, as in a butler's tray, you have to rake the dovetails and the rake is established by the sum 180°- 104.48°= 75.52°.
www.woodworkersjournal.com /ezine/archive/126/webreview.cfm   (1179 words)

 Revolution in Understanding Weather-Singer
The angle at A is measured by the dihedral angle formed by the intersecting faces BOA and COA, the angle at B is measured by the dihedral angle formed by the intersecting faces AOB and COB, and the angle at C is measured by the intersecting faces of AOC and BOC.
The spherical angle at the intersection P (or P') is equal to the plane angle AOB which lies in the plane of the equatorial circle GABH.
The angles formed by the triangle in Figure 2-12 (which is one of the 120 triangles generated by an icosahedral pattern) has exactly 6 degrees of spherical excess, since the total of the three angles is 186°.
weather.org /singer/chapt02.htm   (2121 words)

 Hydrogene-Bonds   (Site not responding. Last check: 2007-10-18)
The position is characterized by the dihedral angle H-C-C=O. Numerical simulations enable us to calculate the partial charge on the hydrogen as a function of the dihedral angle (Graph 4.1).
Unfortunately the shape of the graphs describing the energies and the partial charge on the proton as a function of the dihedral angle depends on the types of the carbon alpha to the carbonyl.
The first atom of the dihedral angle in the second structure is a carbon, because it is smpler to describe the variation in this way.
www.ch.ic.ac.uk /motm/porphyrins/Hbond.html   (1721 words)

 WeTChe OC zmat
From the fourth atom onwards, a distance, an angle and a dihedral angle are required to define the position.
The last three numbers on each row show the definition path: for carbon 4 the distance is to atom 1, the angle is 4-1-2, and the dihedral angle 4-1-2-3.
In this case the dihedral angle is the same as what chemists call the torsion angle.
www.cmbi.kun.nl /~borkent/wetche/zmat.html   (505 words)

 Compression of graphic data normals (US5736987)
Further, a dihedral angle between each pair of adjacent triangles is determined and associated with the VRC bit.
The optimal dihedral angle is chosen so as to minimize the number of errors in predicting the nature of the transition between adjacent triangles based on the dihedral angle between the adjacent triangle.
Next, exception data are generated by comparing the dihedral angle for each pair of adjacent triangles to the optimal dihedral angle to predict a VRC bit, and noting any errors within the exception data.
www.delphion.com /details?pn10=US05736987   (584 words)

 Formula Derivations for Polyhedra
A dihedral angle is the angle of intersection of two planes.
It is the measure of an angle having its vertex on the intersecting edge and one side in each of the planes.
In the context of polyhedra, a dihedral angle is the angle of intersection of two adjacent faces.
whistleralley.com /polyhedra/derivations.htm   (1093 words)

 Experiments with LEDs in Plexiglass
(c) Dihedral angle R (right) is formed by two intersecting vertical planes, the first parallel to the longitudinal axis of the airplane, and the other at 110° to the right of the first, as viewed when looking forward along the longitudinal axis.
(b) Dihedral angle L (left) is formed by two intersecting vertical planes, the first parallel to the longitudinal axis of the airplane, and the other at 110 degrees to the left of the first, as viewed when looking forward along the longitudinal axis.
The spread is an angle from the center of the light emission pattern out to the point where the intensity is half that of the center.
ernest.isa-geek.org /Delta/Experiments/Dyke_Experiment_LED.html   (3747 words)

 Representing Proteins in Silico and Protein Forward Kinematics
This means that algorithms that operate on dihedral angles to achieve their goals will normally require a way to modify the cartesian coordinates when dihedral rotations are performed, to reflect the new atomic positions.
A more compact representation of the variables of the problem, since the dihedral angles require less space than the (x,y,z) coordinates of each atom (the protein topology requires the values of the bond lengths and angles anyway, so the total amount of numbers to store is comparable).
The two rotations are a rotation around the dihedral bond by the dihedral angle and a rotation around an axis perpendicular to the bond angle, by the bond angle.
cnx.org /content/m11621/latest   (3876 words)

 Bond-angle and dihedral angle distributions   (Site not responding. Last check: 2007-10-18)
The average bond angle found in our simulation is essentially identical to the bond angle found in the helical chain of t-Se.
Since the dihedral angle cannot be determined directly from experiment, there has been considerable controversy about the possible values of
The pair correlation functions in our simulation gives the correct peak positions beyond the second nearest-neighbor distance and thus is more plausible with respect to the dihedral angle distribution.
www.phy.ohiou.edu /~drabold/zhangthesis/node61.html   (259 words)

 Diastereomers of Butane
The dihedral angle is the angle formed by all four cabon atoms in butane.
Each molecule's dihedral angle was constrained to the appropriate degree and was then minimized to find it's proper geometry.
From manipulating the molecules to view them at a more desirable angle, we were able to discover what interactions the molecular orbitals made with each other, and how this affected the structure of the molecule and the stability of the isomer.
www.shodor.org /succeed/programs/compchem97/butane   (1138 words)

 (H-J-J-H) Coupling Constant to Dihedral Angle Converter   (Site not responding. Last check: 2007-10-18)
It is therefore dependent upon overlap, and hence upon dihedral angle.
= 9.5 are constants which depend upon the substituents on the carbon atoms and f is the dihedral angle.
2.38) to calculate the theoretical dihedral angle in the molecule to assist with molecular modelling.
www.jonathanpmiller.com /Karplus.html   (165 words)

 MAKE_RESTRAINTS -- make restraints   (Site not responding. Last check: 2007-10-18)
This constructs soft-sphere overlap restraints (lower harmonic bounds) for all atom pairs that are not in bonds, angles, dihedral angles, improper dihedral angles, nor are explicitly excluded by the
This constructs Coulomb restraints for all atom pairs that are not in bonds, angles, dihedral angles, improper dihedral angles, nor are explicitly excluded by the
are the mainchain and sidechain dihedral angle restraints.
fulcrum.physbio.mssm.edu /docs/molmod/modeller6/node113.html   (1936 words)

 Hull Design Question #1 - Dihedral Angle - Offshoreonly.com
The dihedral angle is, of course, the angle made between the outside plane of the hull and the “water line”.
A constant dihedral would be best described as, forgive me, a “true” V. A variable dihedral would be a hinged or folded V with two or more different angles to the hull.
Case A would be, say, a 24 degree angle to the first strake, then a 30 degree angle to the (last) strake and the start of the freeboard (as viewed from the back of the boat).
www.offshoreonly.com /forums/showthread.php?t=6753   (896 words)

 Dihedrals and Equal Sided Polygons.
This is the case of all equal sided or "regular" polygons where the vertex angle that is formed is not 90
This line length is needed to calculate both the side slope and the "miter gauge" angle.
Now with this information we can calculate the "Hip Angle", this is the angle that the "miter pieces" make with a level line.
www.josephfusco.org /Articles/Dihedral/Dihedral1.html   (276 words)

 R/C Soaring: Spiral Stability Augmentation by Gyro
Models with substantial dihedral such as rudder and elevator sailplanes counter this effect by their tendency to yaw outboard in circular flight.
This yaw in combination with the dihedral increases the angle of attack of the inboard wing relative to the outboard wing, countering the effect of the speed variation over the wing.
By tilting the gyro forward or aft at an angle someplace near 30 to 45 degrees it is possible to also obtain a measure of roll damping.
www.rc-soar.com /tech/spiral.htm   (1403 words)

 Presenting Input to the Program
The three internal coordinates for the atoms are the bond length, bond angle, and dihedral angle.
The dihedral angle (also referred to as the torsional or tortional angle in some cases) is defined by reference to three previously defined atoms.
(Thus an input dihedral value of 240° will be output as -120°.) It is required that the three atoms to which the dihedral of a fourth atom is referenced do not assume a straight line arrangement either as a part of the definition or as a result of the geometry optimization.
helix.nih.gov /apps/structbio/ampac/ampacmanual/input.html   (4875 words)

 Torsion or Dihedral Angle Coherency   (Site not responding. Last check: 2007-10-18)
MOPAC calculations do not distinguish between enantiomers, consequently the sign of the dihedrals can be multiplied by -1 and the calculations will be unaffected.
The dihedral angle convention used in MOPAC is that defined by Klyne and Prelog [72].
In this convention, four atoms, AXYB, with a dihedral angle of 90 degrees, will have atom B rotated by 90 degrees clockwise relative to A when X and Y are lined up in the direction of sight, X being nearer to the eye.
www.cachesoftware.com /mopac/Mopac2002manual/node580.html   (143 words)

 Overview of molecular forces: omega dihedral angle energy dependence angle
As mentioned in the main in the main dihedral angle interaction section AMBER potential energy function calculates the torsion energy for every set of four atoms bonded in a chain.
The three atoms bonded to the N atom are co-planar (all the bond angles are 120 degrees) - this also the case for the three atoms bonded to the C atom.
See Dihedral angle rotation is also restricted by steric effects in covalent interactions section.
www.cryst.bbk.ac.uk /PPS95/course/4_mol_forces/os_torg.html   (569 words)

 SYMMETRY   (Site not responding. Last check: 2007-10-18)
Symmetry data defining related bond lengths, angles and dihedrals, or x, y, and z coordinates, can be included by supplying additional data after the geometry has been entered.
Dihedral angle is set equal to the reference dihedral angle
Dihedral angle varies as the negative of the reference dihedral
www.cachesoftware.com /mopac/Mopac2002manual/node319.html   (721 words)

 R/C Soaring: Calculation of the Equivalent Dihedral Angle
The arrangement and amount of these angles determines in part the roll moment generated by the wing as a function of yaw angle.
It is the dihedral angle of a V-dihedral wing with equivalent roll moment.
The dihedral angle of a V-dihedral wing is measured from the horizon to the wing, where both wings are at the same angle to the horizon.
www.rc-soar.com /tech/spiral_eda.htm   (633 words)

 Dihedral Angle of Lens and Interfacial Tension of Air/Long Chain Alcohol/Water Systems   (Site not responding. Last check: 2007-10-18)
The dihedral angle of an alcohol lens at the air/water interface and the three kinds of interfacial tensions of air/1-octanol/water and air/1-decanol/water systems have been measured as a function of temperature from 288.15 to 313.15 K at 2.5 K intervals under atmospheric pressure.
In order to measure a dihedral angle, the new experimental apparatus was constructed and the new procedure was adopted.
By comparing the dihedral angles measured with those calculated by applying Neumann's relations to the interfacial tension values, it was concluded that the dihedral angle measurement was performed with a satisfactory accuracy.
pubs.acs.org /cgi-bin/jtext?langd5/13/i07/abs/la9605955   (180 words)

The contribution varies linearly with dihedral angle and, provided that the lift coefficient is less than 60 per cent of its stalling value, is independent of lift coefficient.
For non-rigid wings allowance must be made for the additional dihedral due to wing deflection under load and a formula is suggested to extend the use of the data to that case.
For a wing with dihedral starting at some outboard spanwise station, the contribution of dihedral to the derivative is found from the difference between the contributions for a wing with full-span dihedral (from ESDU Aero A.06.01.03) and for one with dihedral from the root to the station where dihedral starts on the real wing.
aerade.cranfield.ac.uk /subject-listing/esdu/ES73.html   (2209 words)

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