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This fillet radius is changes. Throat depth is the distance from the root to the face, measured on an angle that bisects the joint angle, which is 45* for a lap joint or 90* t-joint. I want to create a fillet from a predefined point p of an arc A1 to a second arc A2. Familiarity has a way of increasing job costs over time, especially if they think that you are not shopping around. Includes all equations (formula). Hanover Massachusetts 02339 Tel. This task becomes more challenging when there is a curve, or radius, in the driveway. The equation has three variables (x, y and r). Weld Fillet Calculation = Minimum Fillet Weld Size (ω) = 0. The fillet weld (pronounced "fill-it") is used to make lap joints, corner joints and T joints. At corners, the suggested inside radius is 0. The directional method for design of fillet welds and partial penetration butt welds in EN 1993-1-8 clause 4. Curb to Curb Turning Radius Radius of the smallest circle inside of which the vehicle's tires can turn. 8,with D = 7 degrees, the curve's radius R can be computed. After a fillet has been applied, its radius can be edited; this is not possible with the Part Fillet. check parts availability, SKF Bearing pricing, examine remanufactured options. More Angles To calculate the radius produced at different bend angles, first find the radius and length of the arc of the bend, and then manipulate these results to factor in tensile and. In its simplest form, the equation of a circle is What this means is that for any point on the circle, the above equation will be true, and for all other points it will not. I am trying to apply fillet radius to my part for that i need formula to calculate this height and intersection point at which radius. When I come to the 90 degree reducing bends, the only information I get is the center radius of the bend. The product will be reserved for you when you. If the loads are such that a maximum sized weld isn't necessary, the flare groove doesn't have to be welded flush. A corner radius may be referring to a rounded corner at the end or on the side of a sheet of material, as like an 'L' shape. Enter length and width of the rectangle, as well as the radius of the circle that makes the corners. 1981 M34 (1980) d dT b iDT b = + 065 3 160. The effective throat, t e, for a fillet weld is taken as the least distance from the root of the weld (i. Volume and Surface Area Page 6 of 19 Example 3: Find the volume and surface area of the figure below 8 5 3 in Solution: This is a sphere. Tooth Forms for Hobs by Starcut Sales, Inc. Radius of the arc to be constructed may be set to 0, which will make a sharp corner: P Fillets an entire Polyline at the vertices. In total they probably account for around 70 to 80% of all joints made by arc welding. If your driveway has radius entrances, you will need to apply the appropriate mathematical formulas to determine the total square footage of the driveway. 05 Millimeter including IKO Bearing. • Some typical stress concentration factors for the first. The Code is divided into 50 titles which represent broad areas subject to Federal regulation. , Unlimited. This measurement assumes a curb height of 9 inches. The following is the Spandrel or Fillet Surface Area. if you know the volume you can derive the radius. Attachment 2, Minimum Fillet Weld Size for Prequalified Joints MINIMUM FILLET WELD SIZE FOR PREQUALIFIED JOINTS Base Material Thickness of the Thinner Part joined (T) Minimum Size of Fillet Weld T less than or equal to ¼ in. If this happens the solution is the same as it was in task 8 to pick specific points. The same holds true for holes and the slots. Measuring a corner radius is something that you can do by first taking a look at your diagram. Example: Find the area, if the outside radius R = 5 inches, the inside radius r = 2 inches, and ? = 72 degrees. Figure 6 - 1st Principal Stress of Bell Crank Lever with Fillet Radius 6 mm. The curved steel radius calculator from Chicago Metal Rolled Products provides an easy and effective way to find your correct curved steel measurements. 7404×105 fatigue life. Formula: r 2 = (x - h) 2 + (y - k) 2 Where, h,k - Center Points of Circle x,y - Circle Coordinates. Hello, "Fillet" is the noun, the "thing". 90 Degree & 45 Degree Long radius and short radius pipe elbow dimensions in mm as per ASME B16. Fillet Weld Moment of Inertia Equations and Calculation RTD Calibration Guide www. Make surface fillets with hold lines. The Resistance of Fillet Welds For a force per unit length, RL, applied in the direction of a fillet weld, failure is by pure shear along the throat, t, of the weld at a stress TU, giving: Ru, = t (D For a force per unit length, Rj, applied across a fillet weld, the throat is subjected to a shear stress, r, and a tension stress, tj (Fig. 20 standard varies from two to four times the wall thickness, depending on the section perimeter and wall thickness. Comparing Eqs. The segment smaller than the semi-circle is called the minor segment and the segment larger than the semi-circle is called the major segment. 5 CNC Machine G-code generator for lathes & mills, added automatic code generation for dimensional patterns, New send and recieve, Now with limited engraving, set radius and feed rate, tool nose radius, corner or fillet radius, set clockwise or. 2 involves checks of 1) combined stress and 2) direct stress on the weld throat and compares each with a different limiting stress denoted here by the general term σ L. 20 mm x 42 mm x 12 mm skf 6004 bearing 20 mm x 42 mm x 12 mm with easy-to-use 460 mm D parts graphics, giving 340 mm d you the ability to BEARING FORGE OF AMERICA CORP. Space-E Modeler is flexible modeling environment together with the surface and solid functions. Plus any size of fillet or PJP groove weld for any thicknesses or diamet er (Table 4. , Unlimited. Theoretical Throat The distance from the beginning of the joint root perpendicular to the hypotenuse of the largest right triangle that can be inscribed within the cross section of a fillet weld. 2 See thermal speed ratings in the engineering section. 3 (2) shows a profile shifted spur gear, with positive correction xm, meshed with a rack. SKF Bearing are 25 mm x 52 mm x 15 mm a few brands you will find in our inventory. Today we will take a look at How to use Fillet (or Chamfer) along the whole Polyline. 8: Simple snap-fitting hook Fig. Fillet Volume Calculation V fillet = 0,215 * r2 * 2p (0,2234 * r + a) with a = lead radius = 0,3mm r = solder pad radius minus lead radius = solder pad radius minus 0,3mm Total required paste volume with one fillet: V paste = 2 * (0,35mm 2 * h + 0,215 * r * 2π (0,2234 * r + a)) Total required paste volume with two fillets: V paste. Pyromation uses 0. Some driveways, however, have radius entrances. Small radius indicates a more compact cross-section. 787 Inch | 20 Millimeter x 1. Chamfers are more forgiving when fitting mating parts. But 3 points define a curve. Basic Gear Terminology and Calculation / Let's learn the basics of Basic Gear Technology ! Gear size, pressure angle, number of teeth…we introduce the basic terminology, measurement, and relational expressions necessary to understand basic gear technology. If the CJP groove welds are made with matching-strength filler metal, the strength of a connection is governed or con-trolled by the base metal and no checks on the weld strength are required. 4 Bending 144 3. For example, if there is only a T-section, SHAPE-THIN determines the shear area for this cross-section automatically. in any instance. It can be a rectangle, a circle even an oval, depending on how it has been cut. Equation 7. The CNC Lathe Radius Programmer G Code Generator software calculates the cnc program G Code when turning a corner radius or a fillet radius. 20 standard varies from two to four times the wall thickness, depending on the section perimeter and wall thickness. Manufacturing Service. Make one of fairly large curve and route it along the right circle (radius = bit radius - fillet radius) in the Z-axis , and it will be much more graceful to smooth out than created with a round tip. Cablofil steel wire cable tray is supplied in straight lengths from which sophisticated installations can be created without the need for additional fittings. If you have a given point of tangency and not a given fillet radius, your problem is a bit more complex. Equation 7. High performance and robust fillet creation for complex support shape -High robustness guaranteed by specifically developed own geometric engine -Variety of functions such as variable radius, chord length specification, variable radius/independent end -High flexibility realized by separated or combined running of fillet creation and merger. This page provides a set of interactive plots for common stress concentration factors. " 81188 Front Bumper Size: Front Bumper Extension: Front Wheel Type: Rear Wheel Type: Tire Brand: Page 1 of 1 10" ALUMINUM ALUMINUM MICHELIN Minimum Inside Radius 29. The geometry factor for the uncorrected gear is. Their intersection is the center of your fillet arc. Calculations on this page are valid for an internal radius up to 1 mm, and a sheet thickness up to 3 mm. 2 mmda - max. I would like more of a specific formula for accuracy and parametric designs. Re: Measuring a fillet radius Not all fillets are that hard to measure, I think the problem is where you have a fillet around a curved surface. 08 inches in the product catalog. This full radius is tangent to the involute sides A gage pin of a specific size will contact the involute sides of the spline teeth. The PartDesign Fillet is Parametric. Regardless of what’s called on the print, this setup will produce an inside bend radius in the part much greater than that of the punch nose. For example, you would need to know the depth of the recess, the width at the opening, and the width of the flat at the base of the recess. "Our mission is to provide the construction industry with a tool to save time and money through simplicity when dealing with complex formulas and calculations in the field. Familiarity has a way of increasing job costs over time, especially if they think that you are not shopping around. The plural form is radii (pronounced "ray-dee-eye"). This triangle will lie either below a flat line or above it with an arrow coming off of the flat line pointing to a. The Part Fillet becomes the parent of the object it was. If you ever need to create Chamfer Lines or Fillet Arcs, this app is a no-brainer. Also If it's easier, just finding the two points of intersection would work as well. The bigger fillet radius will results in the smaller stress concentration factor in the key seat. Click on second edge of the fillet. 1981 M34 (1980) d dT b iDT b = + 065 3 160. with generous fillet radius, or consider providing for a larger fillet radius on the shaft by relieving it into the base of the shoulder. I have 3 cases where it needs to be calculated Outside fillet Inside fillet. 20 mm x 42 mm x 12 mm skf 6004 bearing 20 mm x 42 mm x 12 mm with easy-to-use 460 mm D parts graphics, giving 340 mm d you the ability to BEARING FORGE OF AMERICA CORP. molten sulphur filter davit design and support calculation m2-334-zy-003 a/b Approx. Pilkey, Walter D. r = radius $$\theta$$ = angle of arc in radians. Stress Concentration Factor Subject. First, a terminology review: in design and machining, a chamfer is a sloped or angled corner or edge, and a fillet is a rounded corner or edge. Mechanical behaviour and failure modes of these spatial joints differ from those of planar joints. How to Calculate Bending Stress in Beams. 8,with D = 7 degrees, the curve's radius R can be computed. Fillet size typically varies from ¼” to ½”. **Please note, the D4 form must be completed, and in addition the GP must complete and sign the South Gloucestershire Council declaration form** You are required to bring the following documents with you when you attend the appointment at the licensing office and each subsequent renewal thereafter. A language can help individuals to achieve what they want, and for the larger community to achieve wonder. The directional method for design of fillet welds and partial penetration butt welds in EN 1993-1-8 clause 4. This triangle will lie either below a flat line or above it with an arrow coming off of the flat line pointing to a. Equation 7. T D a T d The maximum stress occurs on the inside of the hole, slightly below the shaft surface. Drawings often. Click the arrow to select the continuity from the list. The length of the weld is easy to measure, but if we are not cutting up welds and doing macro etches how can we calculate the throat (t)? To do this we employ basic algebra. What you need to do is find the volume of weld needed in cubic inches. 05 Millimeter IKO LRB121612 Needle Non Thrust Roller Bearings Categories in the Manufacturers Online Free. But if the radius of fillet changes it will be difficult to. Notice that you simply input the angle, tool nose radius, x drawing position, z drawing position and the fillet radius if desired and Simple Lathe Cam generates the CNC G Code for the cnc program. Space-E Modeler. 4 Bending 144 3. The fillet radius is the radius of the arc that connects filleted objects. Related video: Measuring Radius of Curvature, Chamfer and Edge Break Measuring an inside radius on a turbine blade with the 4D InSpec XL (or 4D InSpec) takes just seconds. 1) For SMAW process, only same electrode type (change from. small fillet radii need not be expensive if the part allows for using larger diameter end mills with a corner radii ground in. Referenced maximum root fillet radius rho_fPmaxref. Drawings often. Elbolet ® is used on 90° Long Radius Elbows (can be manufactured for Short Radius Elbows) for thermowell and instrumentation connections. Spur Gear Design Calculator. This is obtained by spinning the ring in the horizontal plane (around the z-axis). Nichols, H. 1 Chamfer Dimensions, Fillet Radius of. So the calculation is the load carrying capacity of the 5 identical fillet welds. 4 Stepped Bar of Circular Cross Section with a Circumferential. (mm); t is the actual thickness of. edu is a platform for academics to share research papers. The above does not apply for Base Plate Columns in tension. An interior or exterior corner, with an angle or type of bevel, is called a "chamfer". Also If it's easier, just finding the two points of intersection would work as well. Weld Fillet Calculation = Minimum Fillet Weld Size (ω) = 0. circles, lines or planes, are managed separately in ZEISS CALYPSO. Bends have a radius of curvature more than twice the diameter. Cnc mill program in a desired X and or Y direction in relation to. edu is a platform for academics to share research papers. If there is no centerline, measuring a bend radius or centerline radius requires an extra geometry. Specify fillet radius to 1, type 1 [Enter]. If you set the fillet radius to 0, filleted objects are trimmed or extended until they intersect, but no arc is created. Referenced maximum root fillet radius rho_fPmaxref. 625 Inch | 15. change, the maximum fillet radius for 14-inch column shapes 90 lbs/ft. Radius Gauges are also known for Fillet gauges. This is illustrated below. You do not need to prepare the edge and this type of joint make it easy to weld piping systems. Inverting over a small die radius (r/D ≤ 0. The fatigue life of crankshaft is depend on the proper fillet radius. Using an elliptical fillet. Hello responding to comment on joint stiffness from brab2. Beam Depth – is the height between the top and bottom flanges of the steel I-beam. The nominal shear stress is τ0 = T. (3 mm) Min. 7 Tubes 143 3. The second category covers all sharp corners that have to be broken, without actually specifying the size. 707 a a a Throat = a x cos45o = 0. Most users of vacuum brazing sheet operate at one extreme or the other, i. Command Sequence. 7" is "1 over square root of two". Curb return radius should accommodate the expected amount and type of traffic and allow for safe turning speeds at intersections. This increases the corre-sponding values for k and k 1 by 5/ 8“, and decreases the correspon-ding value of T by 11/ 4”. I have to respect two outer thickness and inner thickness for that calculation. choose r scf at the notch radius bending:. , "Peterson's Stress Concentration Factors," 3rd Edition "Roark's Formulas for Stress and Strain," 8th Edition Budynas-Nisbett, "Shigley's Mechanical Engineering Design," 8th Ed. Couplings • Hub Keyway Tolerances & Standard Fillet Radii All Types (Page 1 of 1) Nominal Bore Key Size Keyway Size. Fillet multiple pline objects? I have multiple rectangles or plines I need to fillet all at the same time (in a single user selection). Example: What is the minimum bend radius of a 1/0, 5 kV, SHD-GC cable? Answer: SHD-GC is a shielded mining cable. 03-09-2015, 10:48. According to Table 1, the minimum bend radius is found to be six times the cable's overall diameter. Thus, using the centers of the two arcs you wish to join, construct arcs that are the sum of the radius + fillet radius. This is particularly relevant in carbureted applications. Thread starter Bongo Boy; Start date Dec 3, 2004; Forums. You will need a way to measure the arc length of the inner and outer radii to calculate the radius after using the offset command. Hello responding to comment on joint stiffness from brab2. Figure 6 - 1st Principal Stress of Bell Crank Lever with Fillet Radius 6 mm. 5 Inch | 38. 0078 kg/cm 3 :. Have a surface, but need some clean toolpath. Referenced root fillet radius rho_fPref. Make a variable radius fillet on a surface. Question: A 1. mostly aesthetic with little validation to use the specified radius. If you liked this Volume of a Fillet Calculator please try some of our other Volume Calculators. Other types of failure may also occur due to poor operational conditions, such as using annealed materials, inadequate radial clearance. Space-E Modeler. Beam Depth – is the height between the top and bottom flanges of the steel I-beam. The blades can be removed through the open end if you need to use a single blade for clearance problems. A separate calc for d1 and d2 with hf1 and hf2 in the equations and with the initial 2 deleted in each equation. This page provides a set of interactive plots for common stress concentration factors. High-quality presentations are critical to most design projects. 16001 NTN 12x28x7mm fillet radius: 0. The size of the fillet weld is shown to the left of the weld. This is the intersecting set of a square with edge length a and a circle with radius a, where one corner of the square is at the center of the circle. 6 – Tooth form locator 105 Webster St. Sets the radius for one side of the fillet. 0 Some time to increase the tip width of the hob, which will also help to increase the life of the hob in such applications. Changing the fillet radius affects subsequent fillets. Scalar calculation (for two dimensions): To …. 00 mm B Find 25 mm x 52 mm x 15 mm skf 6205 bearing to BEARING FORGE OF AMERICA CORP. Select Geometry > Horizontal Curve Set > Define Curve. Plus any size of fillet or PJP groove weld for any thicknesses or diamet er (Table 4. change, the maximum fillet radius for 14-inch column shapes 90 lbs/ft. As a consequence, we find the following relation between the. Thus, using the centers of the two arcs you wish to join, construct arcs that are the sum of the radius + fillet radius. This circle must be tangent to fillet (blue) and inner circle (green) Please click on 'Graphic' to check the sketch. • The radius at the base of a boss should be ¼ of the nominal wall with a minimum radius of 0. a Distance from web face to edge of flange, inches or millimeters. A Model Parameter for the Radius of the arc – Radius; A user Parameter for the Arc Length – Arc Length; A User Parameter to convert Degrees into Radians – Radians; The Formula is: Radius * ( Radians / 1 rad ) To Drive the Length of an Arc. Learn more. A circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the center. 9 Shear stress versus torque for D/d is equal to 1. Make a variable radius fillet on a surface. (1–3) and (1–4), we see that tan 2ϕs is the negative reciprocal of tan 2ϕp. Kent Reece Van Gerpen-Reece Engineering, Cedar Falls, IA One of the most frequently neglected areas of gear design is the determination of "form diameter': Form diameter is that diameter which specifies the transition point between the usable involute profile and the fillet of the tooth. A bigger radius should be used if part design allows. Outside fillet. I have a: radius (fillet between 2 lines) with R80mm (blue color) circle tangent to this fillet with diameter 35mm (green color) What I need: I need to calculate the red circle, that also has diameter 35mm. Add setback parameters to the surface fillets. A fillet weld with a flat face forms a right triangle. 1 kNBasic static load rating (C0)2. 38 Corner Joint Welds (Fig. (refer to Fig. A submerged arc fillet weld is first made on the inside corner of the joint and a square groove butt weld is then made on the reverse side of the joint. Added a Thread Milling Calculator / Programmer. The amount of fillet radius that a hob will produce is normally different from the radius on the tip of the hob. We sell GenuineIKO Bearing at discount 5500 N Basic Static Radial Load Rating Co. The second category covers all sharp corners that have to be broken, without actually specifying the size. The allowable shear stress is 15,000 psi and the load T = 4800 1b-in. Nose radius suitable for fillet milling, also tangential form radius fit composite blade surface machining. 38 Corner Joint Welds (Fig. l (Structural Welding Code ― Steel) specifies the minimum fillet weld size for each base metal thickness: e. Need to 3D a radius on to an ever chaning edge (varies in z depth constantly). High-quality presentations are critical to most design projects. xxx Enter consistent dimensions(i. Our target is to create an UDF, which can be used for measuring bend radius, center line radius and bend angle of a dead geometry of a tube. See the reference section for more details. Form Diameter 0 1£ Gears Harlan Van. The fillet radius r n at the bottom of the cylinder is the fillet radius r p of the deep drawing die of this process. First, a terminology review: in design and machining, a chamfer is a sloped or angled corner or edge, and a fillet is a rounded corner or edge. 468 mm, we will take the 3mm as the weld size for this example problem. In other words, external radius = internal radius + thickness. You will get solution with step-by-step explanation. Changing the fillet radius affects subsequent fillets. by default calculation of volume will be selected, but we can change to other calculation, like mass, surface area, weight and of course radius of gyration, we will see new axis with symbol Zp,Xp and Yp, yest, there is position of radius of gyration, exact position also can see on box that appear, it's distance from the center. Measuring a corner radius is something that you can do by first taking a look at your diagram. Inputs: circle radius: circle center to chord midpoint distance: Sector of a Circle. Tangents B-C and C-D highlight. beff tfb tfc twc rc σ Figure 3. Corner chamfer end mills have an angled cutting edge and are used where a specific radius size is not required. Analytical solution for shear area calculation:. I want to create a fillet from a predefined point p of an arc A1 to a second arc A2. The centre distance that the calculator returns is for the two gears in tight mesh. 05 Millimeter x 1 Inch | 25. Familiarity has a way of increasing job costs over time, especially if they think that you are not shopping around. Regardless of what’s called on the print, this setup will produce an inside bend radius in the part much greater than that of the punch nose. even if there are inaccuracies in a chamfer mating parts might fit together. Type R and press Enter to set the fillet radius. IIRC, I had a small lisp program that gave me arc lengths. The basic rack fillet radius must be reduced for teeth with a 25-degree pressure angle having a clearance in excess of 0. 8: Simple snap-fitting hook Fig. However, the fillet radius of the key seat corner cannot be very big because the key must be assembled properly in the key seat. The effective throat shall be the shortest distance from the joint root to the weld face of the diagrammatic weld (see Annex I). external circlip dimensions for shafts (metric - din 471) External circlips are retaining rings for holding structural parts (e. sketching the arc in sketch will allow you to place the tangent constraints and concentric constraints to define the fillet without requiring a radius. For spur and helical gears, the root fillet geometry cut by a rack with and without cutter tip radius is discussed. How is the formula to determine every corner radius for the innerBorder element. Short Radius and Long Radius. 875 Millimeter is your source BEARING PRECISION AXLE CORP. This is a male radius on an external edge,. This creates a circular cut-out style of fillet, the circles will be created with the Radius specified. change, the maximum fillet radius for 14-inch column shapes 90 lbs/ft. and apply all rules which required in this paragraph and the next paragraphs, then compare between the size of fillet weld which you calculated and the values in table 4. This fillet radius is changes. Four-Row Tapered Roller Bearings TQITS Nachi Gear Pump Four Row Tapered Roller Bearings. Radius router bit for roundover fillet? If this is your first visit, be sure to check out the FAQ by clicking the link above. Fillet Radius Pad. and apply all rules which required in this paragraph and the next paragraphs, then compare between the size of fillet weld which you calculated and the values in table 4. Peterson, Stress-Concentration Factors, Wiley, New York, 1974, pp. 8 Stepped Pressure Vessel Wall with Shoulder Fillets 143 3. The plane along path should work to get a plane perpendicular to the fillet. Learn more. LAB 5 - Horizontal Alignments Labs for InRoads V8i SS2 1. As another example, say you’re working with 0. A value of 0 sets Kn and Kb to 1. The radius of a circle is the straight-line distance from the very center of the circle to any point on the circle. SKF Bearing are 25 mm x 52 mm x 15 mm a few brands you will find in our inventory. The radius of a circle is the length of the line from the center to any point on its edge. Fillet geometry, when on an interior corner is a line of concave function, whereas a fillet on an exterior corner is a line of convex function (in these cases, fillets are typically. Shaft Stress Calculations. Added a CNC Mill Program Shifter that calculates and moves a. individual dimensional and geometrical tolerances, fillet radii, tolerances and individual machining allowances; NOTE Because the dimensional and geometrical accuracy of a casting is related to production factors, tolerance grades which can be achieved for various methods and metals are described in Annex A. When the directional strength enhancement factor is not included in the strength calculation of fillet welds to HSS, the equations in AISC 360 can be used with adequate safety level being achieved. Kent Reece Van Gerpen-Reece Engineering, Cedar Falls, IA One of the most frequently neglected areas of gear design is the determination of "form diameter': Form diameter is that diameter which specifies the transition point between the usable involute profile and the fillet of the tooth. We are given that the diameter of the sphere is 8 5 3 inches. com Methods for the calculation of fillet weld sizes are explained here. This tool is made to make it easy for you to calculate arcs. the Apply button. Kent Reece Van Gerpen-Reece Engineering, Cedar Falls, IA One of the most frequently neglected areas of gear design is the determination of "form diameter': Form diameter is that diameter which specifies the transition point between the usable involute profile and the fillet of the tooth. beff tfb tfc twc rc σ Figure 3. The first two tangents A-B and B-C highlight. Punching force calculation pdf. Free Circle calculator - Calculate area, circumferences, diameters, and radius for circles step-by-step This website uses cookies to ensure you get the best experience. Important note: The methods described below is based on the simple method of calculation of weld stress as identified in BS 5950- clause 6. In mechanical engineering, a fillet / ˈ f ɪ l ɪ t / is a rounding of an interior or exterior corner of a part design. More Angles To calculate the radius produced at different bend angles, first find the radius and length of the arc of the bend, and then manipulate these results to factor in tensile and. Nuclear Regulatory Commission. I would try some different shops, as it may be that they have grown too comfortable with your business. 149 mmra - max. However, applying a chamfer on an inside pocket is not a popular practice, explained Eng-Tips Forums user AJACK. 0-98, Standard Methods for Mechanical Testing of Welds, but is included for information purposes only. (v) Finally, a convenient formula is proposed that is useful for any dimensions of fillet in a round bar. Using a number of small notches rather than a long one, if a notch is unavoidable. Fillet definition at Dictionary. I work as an AutoCAD drafter for a wastewater/water engineering company. 3D Electromagnetic Field Simulator for RF and Wireless Design. Please consider: The online calculator has been coded with greatest care and results have been verified. Theoretical Throat The distance from the beginning of the joint root perpendicular to the hypotenuse of the largest right triangle that can be inscribed within the cross section of a fillet weld. RE: fillet radius not working Right now, I am trying surface approach (see attached image). 707a Failure Plane L Shear stress in fillet weld of length L subjected to load P = fv = 0. For this you can use calculator above by entering arbitrary angles those sum is 180. Peterson, Stress-Concentration Factors, Wiley, New York, 1974, pp. The built-up shaft is designed to rotate at 540 rpm. By starting the calculation under 'Calc' you confirm that you have read this article and agree with the content. Property #1) A tangent intersects a circle in exactly one place Property #2) The tangent intersects the circle's radius at a 90° angle, as shown in diagram 2. 707 a a a Throat = a x cos45o = 0. - 1st Principal Stress of Bell Crank Lever with Fillet Radius 4 mm. The convexity in convex fillet welds serve as reinforcement, which is believed to provide additional strength. At PI/2, the circle is vanishingly small. RE: Fillet radius of Stepped-down shaft stanlsimon (Mechanical) 21 Mar 08 00:58 Looking at the situation from the aspect of the lathe operator the minimum inside corner radius would be the smallest radius on the carbide cutter insert that is available. Calculate the volume, surface area, circumference, diameter and radius of a sphere from any starting point e. The idea is self-explanatory: "Variable fillet corners" would be similar to the existing "Fillet corners" tool (which is ideal for pre-selecting of multiple curve shapes to apply the same fillet radius everywhere), but with one notable difference - the ability to apply different radius for the fillet depending on the angle between curves. During a long process, many global experts created a new thermowell calculation method ASME PTC 19. You will need a way to measure the arc length of the inner and outer radii to calculate the radius after using the offset command. Calculating Radius of a Curve Two points define a straight line. When designing a three-edge inside corner, one of the inside edges must have the radius of the end mill. The size of a fillet weld should be calculated by the designer of the welded structure, based on the nature and magnitude of applied loads, on the material and on the design basis. 2 (a), while the values in Table 11. In the geometry only changes the fillet radius and other boundary conditions are same. Add to Cart. A Tangent of a Circle has two defining properties. Dimension tolerance for the piping elbow. Calculate area, circumference and radius of a circle. Input in inches and it'll output in inches. 1875” Circle A Fig. Other types of failure may also occur due to poor operational conditions, such as using annealed materials, inadequate radial clearance. A Keyway is a slot of some kind that is used to align the part […]. 1 Effective Throat 2. Area of an elliptical sector. The bigger fillet radius will results in the smaller stress concentration factor in the key seat. 75 Inch | 19. Attachment 2, Minimum Fillet Weld Size for Prequalified Joints MINIMUM FILLET WELD SIZE FOR PREQUALIFIED JOINTS Base Material Thickness of the Thinner Part joined (T) Minimum Size of Fillet Weld T less than or equal to ¼ in. The curved steel radius calculator from Chicago Metal Rolled Products provides an easy and effective way to find your correct curved steel measurements. where R is the radius of the inner arc segment, and t is the angle In both cases, the radius of the circle is equal to its x coordinate. Area of a hyperbolic sector. 5 mm is used to connect the shafts at B. 14 and round the decimal point to your answer of approximately 2. Nose radius suitable for fillet milling, also tangential form radius fit composite blade surface machining. It assumes a symmetrical, mitre, fillet. Then, the least-squares method is applied for calculation of K t /K td and K t /K ts. Design For Manufacturability – Sheet Metal Guidelines Bends For the ease of manufacturing, multiple bends on the same plane should occur in the same direction. Using a number of small notches rather than a long one, if a notch is unavoidable. Once you determine the radius at the nut and the spread of the strings, the radius at the bridge is determined by those values. Inputs: circle radius: circle center to chord midpoint distance: Sector of a Circle. The idea is self-explanatory: "Variable fillet corners" would be similar to the existing "Fillet corners" tool (which is ideal for pre-selecting of multiple curve shapes to apply the same fillet radius everywhere), but with one notable difference - the ability to apply different radius for the fillet depending on the angle between curves. Measuring radius variations along an edge can be done efficiently in PolyWorks|Inspector™ using profile gauges, whether you are inspecting sheet metal bending radii, rounds and fillets on machined parts, or design lines on car bodies. E: Desired result (done using sketch fillets on a thin extrude, but this is not always possible. Inputs: circle radius: circle center to chord midpoint distance: Sector of a Circle. High-quality presentations are critical to most design projects. The outer surface of the LPD shall be smooth, and so far as possible continuous from front to rear; adjacent parts may however overlap provided that the overlapping edge faces rearwards or downwards, or a gap of not more than 25 mm measured longitudinally may be left, provided that the rearward part does not protrude outboard of the forward part; domed heads of bolts or rivets may protrude. Tooth Forms for Hobs by Starcut Sales, Inc. Re: Measuring a fillet radius Not all fillets are that hard to measure, I think the problem is where you have a fillet around a curved surface. A segment is a portion of a circle which is cut off by a straight line not passing through the center. Consider the drawing below. Radius Gage Calibration Purpose The purpose of this procedure is to provide general instructions for the calibration of radius gages. 20 standard varies from two to four times the wall thickness, depending on the section perimeter and wall thickness. Our surface modeling is the best in the Japanese market and will enable creation and edit of complex free form shape for automotive and home electronics parts. This publication is a compilation of equations for moments of centroidal dis tances, radii of gyration, other mathematical properties related to solids, thin shells, thin rods, plane areas, and ogival shapes. I would like more of a specific formula for accuracy and parametric designs. This course is primarily intended for complete design studying components like design of shafts, springs and flywheels and design of Ic engine parts and design of machine components against static and variable loading. Without the basic dimensions, the fillet cannot be calculated. - 1st Principal Stress of Bell Crank Lever with Fillet Radius 4 mm. A stress concentration factor is an intensification multiplier by which stress rises due to a discontinuity, which may be a notch, hole, groove or a change in material. RE: fillet radius not working Right now, I am trying surface approach (see attached image). For tools with an edge radius, a wear-min-. The Resistance of Fillet Welds For a force per unit length, RL, applied in the direction of a fillet weld, failure is by pure shear along the throat, t, of the weld at a stress TU, giving: Ru, = t (D For a force per unit length, Rj, applied across a fillet weld, the throat is subjected to a shear stress, r, and a tension stress, tj (Fig. Curb return radius should accommodate the expected amount and type of traffic and allow for safe turning speeds at intersections. The maximum exterior corner radius permitted by the G40. For example, Figure 5 shows a central angle of 1° in a circle of radius 1,800 feet, along with the arc and chord cut off by 1°. 756 Inch | 70 Millimeter x 4. High flexibility Separate or combined running of fillet. If your driveway has radius entrances, you will need to apply the appropriate mathematical formulas to determine the total square footage of the driveway. Solution to Example 7. It's is available for download on Google Play. First, a terminology review: in design and machining, a chamfer is a sloped or angled corner or edge, and a fillet is a rounded corner or edge. Also shown below is how a separate hole can serve to allow relief for a male ninety-degree corner to fit. Question: A 1. Keyway, Key, & Keyseat Work with Keyseat Cutters Whenever we need to affix a part to a shaft, such as a gear or pulley, keyways, keys, and keyseat work comes into play. Determining how much concrete is necessary for a straight driveway is a fairly simple task. where a stress concentration, K, of 2. Inverting over a small die radius (r/D ≤ 0. Also, the pitch line of the rack has shifted outward by the amountxm. The initiation period in the presence of a larger toe radius, R= 1 mm lasts longer and is more. Then the least squares method is applied for calculation of K t /K td and K t /K ts. Figure 6 - 1st Principal Stress of Bell Crank Lever with Fillet Radius 6 mm. Outside fillet. Shaft 1 (Diameter=3/8”) Material: 1045 Steel, Yield Strength (Sy)= 530 MPa, Ultimate Strength= 625MPa. By starting the calculation under 'Calc' you confirm that you have read this article and agree with the content. By using this website, you agree to our Cookie Policy. insertion length + leg dimension of the fillet weld at the backface of a loose flange, and insertion length + leg dimension of the fillet weld + 13 mm for integral flanges respectively. Fillet Weld Moment of Inertia Equations and Calculation RTD Calibration Guide www. 35 kg Mass adapter sleeve assembly SEARCH - BEARING BOWER CORP. Click on first edge of fillet. Example: Find the area, if the outside radius R = 5 inches, the inside radius r = 2 inches, and ? = 72 degrees. Appendix C) c. 125-in fillet radius at the diameter increase shown in the detail view on the far right. The segment smaller than the semi-circle is called the minor segment and the segment larger than the semi-circle is called the major segment. The spur gear hasa larger pitch radius than standard, by the amount xm. "Our mission is to provide the construction industry with a tool to save time and money through simplicity when dealing with complex formulas and calculations in the field. 707 a Lw P If the ultimate shear strength of the weld = fw Rn = fw ×0. By starting the calculation under 'Calc' you confirm that you have read this article and agree with the content. The fillet root side fit spline exhibits a full radius in the trochoid area between the teeth on both members. 1) necessary for normal stresses determination for different values of tooth root fillet radius ρF. 270/P for a 25-degree pressure angle rack for a clearance of 0. 019 KgBasic dynamic load rating (C)5. The radius of gyration for an infinitely thin circular ring of radius R is Rgz 2 = R2. If you liked this Volume of a Fillet Calculator please try some of our other Volume Calculators. A separate calc for kf1 and kf2 based on d1 and d2 ( and possible using separate E values (Ef2 an. Horizontal Curve Formulas. 16001 NTN 12x28x7mm fillet radius: 0. Correct placement of the blowing angle can help optimize performance, reduce noise levels and improve efficiency. Electronic Radius Gage (1) Inside Radius Gauge (1) Outside Radius Gauge (1) Radius Gage (5) Radius Gage Set (17) View All. Related video: Measuring Radius of Curvature, Chamfer and Edge Break Measuring an inside radius on a turbine blade with the 4D InSpec XL (or 4D InSpec) takes just seconds. 1 of AWS D1. So, let's begin by getting our terminology straight. Variable radius/ independent end conditions/ arbitrary stop position, etc. The length of the arc and the angle subtended by the arc (not shown in figure) are also calculated. 5% Moisture. Theoretical Throat = 0. The fillet shape is classified into several groups according to the fillet radius and fillet depth. It can be visualized as the amount of paint that would be necessary to cover a surface, and is the two-dimensional counterpart of the one-dimensional length of a curve, and three-dimensional volume of a solid. The one you show there is like a sweep - it's not a connection between 2 existing surfaces, and since the output is only polygons there is no kind of. Attachment 2, Minimum Fillet Weld Size for Prequalified Joints MINIMUM FILLET WELD SIZE FOR PREQUALIFIED JOINTS Base Material Thickness of the Thinner Part joined (T) Minimum Size of Fillet Weld T less than or equal to ¼ in. The fillet is the inside curve where Radius is the outside curve. 1: Fillet radius calculated based on the figure 3. The calculation of shear areas for simple cross-sections is thus very easy. Once a fillet weld size has been calculated, it should be reported on the technical drawing(s), using the appropriate welding symbols or provided in a technical specification. Riveted Steel Structures Steel structural members are riveted in the shop where they are fabricated to the extent allowed by shipping conditions. BEARING PRECISION AXLE CORP. To determine a force’s moment, you use one of two different calculations, as you can see in the following list. Is there any way I. Area of a circular sector. A fillet radius improves the ability for the pattern to shed air bubbles as the slurry is applied thus reducing the propensity of casting to exhibit positive metal. , Mg levels around 0. DESIGN OF SHAFTS AND HOUSINGS Housing r a r a h h Fig. Fillet Weld Moment of Inertia Equations and Calculation RTD Calibration Guide www. Referenced Addendum h_aPref. (refer to Fig. So if we are given the radius r, and an x coordinate, we can find y by rearranging the equation: Notice how this has two answers, due to the plus/minus. The numerical results agreed well with the. Calculate them for the section at the fillet radius if 80. Field Formulas. R = Do/2 - (tr - Ca) + Ut = working radius. This is a male radius on an external edge,. A circle is the set of all points in a plane at a fixed distance, called the radius, from a given point, the center. 125-in fillet radius at the diameter increase shown in the detail view on the far right. Root radius r mm Depth between fillets d mm Ratios for local buckling Flange B/2T Ratios for local buckling Web d/t Second moment of area Axis X-X cm4 Second moment of area Axis y-y cm4 Radius of gyration Axis X-X cm Radius of gyration Axis y-y cm Elastic modulus Axis X-X cm3 Elastic modulus Axis y-y cm3 Plastic modulus Axis X-X cm3 Plastic. 75 Millimeter x 1. 25 Inch | 31. 5 Inch | 38. Type R and press Enter to set the fillet radius. The outer surface of the LPD shall be smooth, and so far as possible continuous from front to rear; adjacent parts may however overlap provided that the overlapping edge faces rearwards or downwards, or a gap of not more than 25 mm measured longitudinally may be left, provided that the rearward part does not protrude outboard of the forward part; domed heads of bolts or rivets may protrude. Referenced maximum root fillet radius rho_fPmaxref. 75 Inch | 19. Code to add this calci to your website. This measurement assumes a curb height of 9 inches. Volume and Surface Area Page 6 of 19 Example 3: Find the volume and surface area of the figure below 8 5 3 in Solution: This is a sphere. Area of a circular sector. This tool is made to make it easy for you to calculate arcs. Input in inches and it'll output in inches. Command: DIMRADIUS Select arc or circle: (pick the circumference P2). Added a Ball Endmill Surface Roughness Calculator. 8' Wheelbase: Body Width:. 5 times the material thickness. Note: Product availability is real-time basis and adjusted continuously. Read Full article here. Enter the fillet radius between the pad and the vessel shell. and heavier has increased by 5/ 8“. RE: Fillet radius of Stepped-down shaft stanlsimon (Mechanical) 21 Mar 08 00:58 Looking at the situation from the aspect of the lathe operator the minimum inside corner radius would be the smallest radius on the carbide cutter insert that is available. So the calculation is the load carrying capacity of the 5 identical fillet welds. Optimizing the turning radius of a vehicle using symmetric four wheel steering system V. Consider the drawing below. By starting the calculation under 'Calc' you confirm that you have read this article and agree with the content. you must first calulate the fillet weld size according to Para. To find the radius of a circle or arc, you can use the Radius Inquiry tool. Ideally when detailing the design, you make the radius to the point where its just bridged by the chamfer without interference, you seat the inner race to the hard shoulder, and things go as planned. Fillet the two new lines with zero radius to join them as shown in fig TSK 23. A language can help individuals to achieve what they want, and for the larger community to achieve wonder. Input in inches and it'll output in inches. This page provides a set of interactive plots for common stress concentration factors. The convexity in convex fillet welds serve as reinforcement, which is believed to provide additional strength. Using high school math we can see that a right triangle with ¼" legs would have an area of ½ x base x. Profile: Sets the profile type to fillet. Shaft Stress Calculations. 9 allows calculation of the curve's length L, once the curve's central angle is converted from 63o15'34" to 63. 5 Create the Base Circle Radius = PD/8 Radius = 1. Most users of vacuum brazing sheet operate at one extreme or the other, i. The AGMA approximates the fillet curvature with a constant radius on its layout procedure whereas this paper evaluates bending stress in gear taking actual Trochoidal fillet generated by the rack cutter. The radius of a sphere is half of its diameter. How to Select the I-Beam. 4 Maximum housing fillet radius that bearing corners will clear. VINTAGE BROWN& SHARPE NUMBER 627A FILLET AND RADIUS GAGE 1/32" TO 1/4" RADII: This sale is for a nice vintage Brown and Sharpe number 627A fillet and radius gage. Calculations at a round corner, or rather in a quarter circle, the most simple form of a round corner. For a right circular cone calculator click here. The range of t is between some minimum angle and PI/2. 05 Millimeter x 1 Inch | 25. Basic Gear Terminology and Calculation / Let's learn the basics of Basic Gear Technology ! Gear size, pressure angle, number of teeth…we introduce the basic terminology, measurement, and relational expressions necessary to understand basic gear technology. Different modelling techniques using. If the CJP groove welds are made with matching-strength filler metal, the strength of a connection is governed or con-trolled by the base metal and no checks on the weld strength are required. Some allowance will have to be made for backlash. Inverting over a small die radius (r/D ≤ 0. A bigger radius should be used if part design allows. Square Groove Corner Joint (See Fig. 9 Shear stress versus torque for D/d is equal to 1. , "Peterson's Stress Concentration Factors," 3rd Edition "Roark's Formulas for Stress and Strain," 8th Edition Budynas-Nisbett, "Shigley's Mechanical Engineering Design," 8th Ed. Measure a corner radius with help from an experienced math professional in this free video clip. The Part Fillet becomes the parent of the object it was. Spandrel or Fillet / Tube Surface Area Equation: Area Equation and Calculation Menu. I have two filleted corners that are not at 90deg on an aluminium part. The fillet radius is the radius of the arc that connects filleted objects. Referenced maximum root fillet radius rho_fPmaxref. In Autodesk® AutoCAD® there is the existing _Fillet command, which even has the _Polyline option, i. Determine the maximum shear stress in the shaft. The AGMA approximates the fillet curvature with a constant radius on its layout procedure whereas this paper evaluates bending stress in gear taking actual Trochoidal fillet generated by the rack cutter. The number you type will be the radius of the arc that joins the two lines. 5-in-diameter bar has been machined from an AISI 1050 cold-drawn bar This part is to withstand a fluctuating tensile load varying from 0 to 18. Fillet radius might be referring to fillet welds. 5 in, and a full quarter-circular fillet. The fillet will have a 1/4 inch radius (thickness) on both sides and will run along the angle for 4 inches. Make fillets between two surfaces, or face fillets. The radius of the fillet is called the fillet radius (not always provided) Structural Angle is a steel bar that has an L-shaped cross section. Among our handy steel section tables you can find standard beam and channels dimensions, weights, steel hollow sections tables and other steel profiles tables. This option should be used if the slot width and the tool are similar in size so the slot can grow out to the side to ensure there is space for them to fit. When designing a three-edge inside corner, one of the inside edges must have the radius of the end mill. Corrective measures are taken to avoid tooth damage by introducing profile modification in root fillet. Тип шлицов. Stress concentrations occur when there are irregularities in the geometry or material of a structural component that cause an interruption to the flow of stress. The spur gear has a larger pitch radius than standard, by the amount xm. 5x of the wall thickness with a recommended minimum of. 05 Millimeter IKO LRB121612 Needle Non Thrust Roller Bearings Categories in the Manufacturers Online Free. Fillet geometry, when on an interior corner is a line of concave function, whereas a fillet on an exterior corner is a line of convex function (in these cases, fillets are typically referred to as rounds). Also, the pitch line of the rack has shifted outward by the amount xm.
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# Proof Theory - Katalin Bimbo - Bok 9781466564664 Bokus

Wordlist Plants Nature - Scribd

Request PDF | Natural Deduction and Sequent Calculus | The propositional rules of predicate BI are not merely copies of their counterparts in propositional BI. Each proposition, φ, occurring in a 2017-08-25 · Sequent calculus makes the notion of context (assumption set) explicit: which tends to make its proofs bulkier but more linear than the natural deduction (ND) style. The two approaches share several symmetries: SC right rules correspond fairly rigidly to ND introduction rules, for example. 2010-09-10 · Natural deduction and sequent calculus - united in a polarized linear framework In the last post I talked a little bit about what it means to give atomic propositions in a logical framework polarity . Se hela listan på plato.stanford.edu A SIMULATION OF NATURAL DEDUCTION AND GENTZEN SEQUENT CALCULUS Abstract. We consider four natural deduction systems: Fitch-style sys-tems, Gentzen-style systems (in the form of dags), general deduction Frege systems and nested deduction Frege systems, as well as dag-like Gentzen-style sequent calculi.

naturalised. naturalism. naturalist sequent. sequential. sequentially. sequestered.

## Logic: The Laws of Truth - E-bok - Nicholas J.J. Smith - Storytel

Moreover, we arrange all the We choose natural deduction as our deﬁnitional formalism as the purest and most widely applicable. Later we justify the sequent calculus as a calculus of proof search for natural deduction and explicitly relate the two forms of presentation.

In natural deduction the flow of information is bi-directional: elimination rules flow information downwards by deconstruction, and introduction rules flow information upwards by assembly. In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem.

naturalisation. naturalise. naturalised. naturalism. naturalist sequent.

SILVIA GHILEZAN.

§1. Sequent calculus (   Sequent calculus systems for classical and intuitionstic logic were introduced by Gerhard Gentzen [171] in the same paper that introduced natural deduction  To obtain a Hilbert-style proof system or sequent calculus, we proceed in the same way as we did for first-order logic in Chapter 8. Semantics. We begin  Gentzen had a pure technical motivation for sequent calculus.
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### Structural Proof Theory CDON

2021-1-24 · Then, using a general method proposed by Avron, Ben-Naim and Konikowska (\cite{Avron02}), we provide a sequent calculus for $\cal TML$ with the cut--elimination property. Finally, inspired by the latter, we present a {\em natural deduction} system, sound and complete with respect to the tetravalent modal logic.

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fonder premiepension systemet

### sequent: Översättning till svenska, uttal, synonymer

In: The Semantics and Proof Theory of the Logic of Bunched Implications. Applied Logic Series, vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0091-7_12.

## From storm at cwi.nl Sat Jan 2 07:27:36 2016 From: storm at

calcutta deductible. deducting. deduction.

Definitions 0.2 A sequent calculus is given in which the management of weakening and contraction is organized as in natural deduction. The latter has no explicit weakening or contraction, but vacuous and multiple discharges in rules that discharge assumptions. I don't understand some rules of natural deduction and sequent calculus. (red) The rule makes sense to me for ND but not for SC. In SC it says "if $\\Gamma,\\varphi$ proves $\\Delta$ then \$\ eg\\varphi,\\ The result was a calculus of natural deduction (NJ for intuitionist, NK for classical predicate logic). [Gentzen: Investigations into logical deduction] Calculemus Autumn School, Pisa, Sep 2002 Sequent Calculus: Motivation Gentzen had a pure technical motivation for sequent calculus Same theorems as natural deduction In this paper we present labelled sequent calculi and labelled natural deduction calculi for the counterfactual logics CK + {ID, MP}. As for the sequent calculi we prove, in a semantic manner, that the cut-rule is admissible. As for the natural deduction calculi we prove, in a purely syntactic way, the normalization theorem. Curry-Howard isomorphism for natural deduction might suggest and are still the subject of study [Her95, Pfe95].

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# Math Help - integrals with trig

1. ## integrals with trig

Help with this integral:
integral of tcost - sin^2t + cost dt

2. Mostly I just don't understand the tcos(t) part. How do you take the integral of that.. the rest I understand.

3. So that's:

$\int tcostdt - \int sin^2tdt - \int costdt$

Try integration by parts for the first integral and a half-angle identity for the second.

Parts:

$\int udv = uv - \int vdu$

4. Originally Posted by s7b
Help with this integral:
integral of tcost - sin^2t + cost dt
The integral can be split into 3 separate integrals: $\int t \cos{t}~dt - \int \sin^2{t}~dt + \int \cos{t}~dt$

The first integral is easily done by parts: $\int t \cos{t}~dt = \int t (\sin{t})' dt = t\sin{t} - \int \sin{t}~dt = t\sin{t} + \cos{t}$

5. Originally Posted by s7b
Mostly I just don't understand the tcos(t) part. How do you take the integral of that.. the rest I understand.
Integrate by parts

$u=t \implies du= dt$ and

$dv=\cos(t)dt \implies v=\sin(t)$

don't forget that the formula is

$uv -\int vdu$

6. integrate tcos(t) by parts---do you know the integration by parts formula?

If not use a table of integrals the integral is tsin(t) + cos(t)


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### astAxNorm

Normalise an array of axis values

#### Description:

This function modifies a supplied array of axis values so that they are normalised in the manner indicated by parameter " oper" .

No normalisation is possible for a simple Frame and so the supplied values are returned unchanged. However, this may not be the case for specialised sub-classes of Frame. For instance, a SkyFrame has a discontinuity at zero longitude and so a longitude value can be expressed in the range [-Pi,$+$PI] or the range [0,2$\ast$PI]. See the " Applicability:" section below for details.

#### Synopsis

void astAxNorm( AstFrame $\ast$this, int axis, int oper, int nval, double $\ast$values, int $\ast$status )

#### Parameters:

##### this
Pointer to the Frame.
##### axis
The index of the axis to which the supplied values refer. The first axis has index 1.
##### oper
Indicates the type of normalisation to be applied. If zero is supplied, the normalisation will be the same as that performed by function astNorm. If 1 is supplied, the normalisation will be chosen automatically so that the resulting list has the smallest range.
##### nval
The number of points in the values array.
##### values
On entry, the axis values to be normalised. Modified on exit to hold the normalised values.

#### Applicability

##### SkyFrame
If " oper" is 0, longitude values are returned in the range [0,2$\ast$PI]. If " oper" is 1, longitude values are returned in either the range [0,2$\ast$PI] or [-PI,PI]. The choice is made so that that the resulting list has the smallest range. Latitude values are always returned in the range [-PI,PI].
##### All other classes of Frame
The supplied axis values are returned unchanged.


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Journal article Open Access

# Analysis of the Marshall Islands Fireball of February 1, 1994

Tagliaferri, E.; Spalding, R.; Jacobs, C.; Ceplecha, Z.

### Dublin Core Export

<?xml version='1.0' encoding='utf-8'?>
<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
<dc:creator>Tagliaferri, E.</dc:creator>
<dc:creator>Spalding, R.</dc:creator>
<dc:creator>Jacobs, C.</dc:creator>
<dc:creator>Ceplecha, Z.</dc:creator>
<dc:date>1995-01-01</dc:date>
<dc:description>On February 1, 1994, a large meteoroid impacted over the Pacific Ocean at 2.6° N, 164.1° E. The impact was observed by space based IR sensors operated by the US Department of Defense and by visible wavelength sensors operated by the US Department of Energy. During entry the object broke into several pieces, one of which detonated at 34 km and another at 21 km altitude. The entry velocity of the object is estimated to be 24–25 km/sec. Based on the visible wavelength data, the integrated intensity of the radiated energy of the fireball was approximately 1.3 × 1013 joules. Assuming a 6000 K black body and a 30% efficiency for the conversion of the kinetic energy of the body into visible light, we estimate the mass of the body to be between 1.6×105 kg and 4.4×106 kg, and to have a diameter of between 4.4 and 13.5 meters. The object entered at a 45° angle, traveling on a heading of approximately 300°, i.e. from the southeast to the northwest. Calculations using a gross-fragmentation model indicate that the body was most likely a stony object larger than 10 m with an Apollo orbit prior to impact.</dc:description>
<dc:identifier>https://zenodo.org/record/1232448</dc:identifier>
<dc:identifier>10.1007/bf00671553</dc:identifier>
<dc:identifier>oai:zenodo.org:1232448</dc:identifier>
<dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
<dc:rights>https://creativecommons.org/publicdomain/zero/1.0/legalcode</dc:rights>
<dc:title>Analysis of the Marshall Islands Fireball of February 1, 1994</dc:title>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>publication-article</dc:type>
</oai_dc:dc>

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# Windows 10

If you're using Windows 10, you can use Bash On Ubuntu on Windows to get going in an easy way.

Once you have installed Bash on Ubuntu on Windows, simply follow the [Linux instructions]. You'll also need the grub-pc-bin package.

Finally, you'll need an "X server"; this will let us run intermezzOS in a graphical window. Any will do, but we've tried xming and it works well.

Finally, you'll need to run this:

\$ export DISPLAY=:0

You can put it in your ~/.bashrc file to have it automatically work on each session.

## Other Windows Versions

I hope to have better instructions for Windows soon; since I don’t have a computer that runs it, I need to figure it out first. If you know how, this would be a great way to contribute.


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• MITESH CHAKRABORTY

Articles written in Pramana – Journal of Physics

• Theoretical study of diaquamalonatozinc(II) single crystal for applications in non-linear optical devices

The aim of the present paper is to employ theoretical methods to investigate the zero field splitting (ZFS) parameter and to investigate the position of the dopant in the host. These theoretical calculations have been compared with the empirical results. The superposition model (SPM)with themicroscopic spin-Hamiltonian (MSH) theory and the coefficient of fractional parentage have been employed to investigate the dopant manganese(II) ion substitution in the diaquamalonatozinc(II) (DAMZ) single crystal. The magnetic parameters, viz. $g$-tensor and $D$ tensor, has been determined by using the ORCA program package developed by F Neese $\it{et al}$. The unrestricted Kohn–Sham orbitals-based Pederson–Khanna (PK) as the unperturbed wave function is observed to be the most suitable for the computational calculation of spin–orbit tensor ($D^{SO}$) of the axial ZFS parameter $D$. The effects of spin–spin dipolar couplings are taken into account. The unrestricted natural orbital (UNO) is used for the calculation of spin–spin dipolar contributions to the ZFS tensor. A comparative study of the quantum mechanical treatment of Pederson–Khanna (PK) with coupled perturbation (CP) is reported in the present study. The unrestricted Kohn–Sham-based natural orbital with Pederson–Khanna-type of perturbation approach validates the experimental results in the evaluation of ZFS parameters. The theoretical results are appropriate with the experimental ones and indicate the interstitial occupancy of $\rm{Mn}^{2+}$ ion in the host matrix.

• Investigation on the electrical and optical properties of some zinc titanate ceramics

The ceramics of spinel zinc orthotitanate (SZT) and perovskite zinc metatitanate (PZT) sintered at $800^{\circ}$C have been prepared using the high-energy ball milling technique. The structural and optical characterisation of the prepared samples has been performed using X-ray diffraction and Fourier transformation of infrared (FT-IR)spectroscopy analysis. The measurements of frequency-dependent dielectric constant of the PZT and SZT ceramics sintered at $800^{\circ}$C have been performed in the $(50−600)^{\circ}$C temperature range. Impedance spectroscopy studies have been reported for the prepared nanocrystalline ceramics. The empirical vibrational frequencies observed from the FT-IR spectra have been compared using the computational method of ORCA program package. Constraints for symmetry, bonds, angles or dihedral angles have not been applied in the geometry optimisation calculations. Hybrid three-parameter exchange-correlation functional of Becke, Lee, Yang, Parr with 20% amount of exact exchange and Ahlrichs triple-zeta valence (def2-TZVP) basis set with polarisation function have been investigated for all atoms without considering the relativistic effects.

• # Pramana – Journal of Physics

Current Issue
Volume 93 | Issue 5
November 2019

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019


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# infragram-conversion infragram-conversion

Author Comment Last activity Moderation
warren "I also updated http://publiclab.org/wiki/infragram#Filters with red/blue filter information. I believe all webcams are CMOS sensors so I'm not actu..." | Read more » over 8 years ago
warren "The blurry photo looks interesting though... " | Read more » over 8 years ago
warren "Hi natalie- it looks like the focus is a bit off... You actually don't have to remove the lens or anything to test this, you can just tape some red..." | Read more » over 8 years ago
warren "Hm, interesting. Sometimes the glues they use will melt when you heat them with a hair dryer, which could be worth a try. If you manage to convert ..." | Read more » over 8 years ago
daddyboomalati "No, it actually looks a lot like camera one above. I have been reading about light leakage in the other cheap cameras, so I will probably bite the ..." | Read more » over 8 years ago
warren "Sorry, do you mean Mobius action cam? @cfastie did a great conversion of one of those, here: http://publiclab.org/notes/cfastie/04-22-2014/mobius-i..." | Read more » over 8 years ago
daddyboomalati "I have an Emerson Action Cam that looks a lot like the camera in your first photo. The lens appears to be glued irreversibly in place with cyanoacr..." | Read more » over 8 years ago
ttaylor "Many thanks to Ned and the other conversion pioneers. On my second try I followed these instructions and successfully converted an A2200. On my fi..." | Read more » over 8 years ago
cfastie "I guess it depends which camera and spectrometer you want to connect. A good approach might be to make a 3D printable Ebert. That could work with m..." | Read more » over 8 years ago
warren "Wow cool Chris. I wonder if we could design a 3d printed adaptor between the camera and a spectrometer. " | Read more » over 8 years ago
cfastie "Thanks for the link. For my ghost hunting, I have been buying PowerShot A590s for $20-$40, plus a $5 filter tube that snaps on, plus an$8 IR filte..." | Read more » over 8 years ago
PlanetenPaultje "Took me a while to find the URL again: http://www.angelsghosts.com/store/viewitem.php?productid=16 I think the price has gone up a bit, I paid jus..." | Read more » over 8 years ago
cfastie "Do you have a link for those IR filters? " | Read more » over 8 years ago
PlanetenPaultje "Forgot to mention: There are IR pass filters to be had specifically for this type of camera. They come with glue buds and they fit perfectly on the..." | Read more » over 8 years ago
warren "I just followed these instructions and converted an A2200 -- thanks! " | Read more » over 8 years ago
warren "...the plant pixels will have the biggest values for both R and B and the difference between them is therefore likely to be bigger. Yeah, the idea..." | Read more » almost 9 years ago
PeeBee "Thanks cfasie. I understand now the exposure issue you raise. But you seem to assume the different exposures are an unknown, which it strikes me ..." | Read more » almost 9 years ago
cfastie "To compute NDVI, you have to know the relative amount of light in a visible and an NIR band being reflected from plant leaves. The difference betwe..." | Read more » almost 9 years ago
air_maiden "I too am interested to see whether a non-modified camera and a camera with the IR filter removed can be used to calculate NDVI. Could you please cl..." | Read more » almost 9 years ago
cfastie "That's a really clever idea, and I think it might work. However, it assumes that: The photos must be simultaneous if anything in the scene is cha..." | Read more » almost 9 years ago
PeeBee "Thanks cfastie. I don't think I understand the need for the Wratten filter. My understanding is: A camera with just the IR filter removed (i.e. n..." | Read more » almost 9 years ago
zorn "Ah, thanks for the answers! Makes it much clearer now.... As i told before, i want to have the possibility to tae normal Pics and pure NIR.... I ..." | Read more » almost 9 years ago
cfastie "I see what you mean when you say that the difference between the blue and red channels is correlated with the presence of plants. Your monochrome i..." | Read more » almost 9 years ago
cfastie "Zorn, If you remove the IR block filter, the camera will take very strange photos because all three color channels (RGB) will have lots of NIR ligh..." | Read more » almost 9 years ago


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# Intuitively, what exactly does the ellipse equation mean?

I get how to derive the ellipse equation, but I'm struggling to understand what it means intuitively.

You see, a circle equation can be understood very intuitively. The circle equation models how the radius of the circle can be represented using the Pythagorean theorem. But I don't understand what the ellipse equation means at such a level. Does it model how an ellipse can be drawn out using a stretched rope? What exactly does it model? Can someone please explain?

Can you please explain it as simply as possible, as I'm still a beginner?

• Which ellipse equation are you asking about? There are quite a few to choose from. – amd Jun 23 '18 at 5:27
• a circle equation can be understand very intuitively Then think of it the other way around. An ellipse is what a circle looks like if "dilated" along the axes. The canonical circle equation $\,x^2+y^2=r^2\,$ then becomes something like $\,\lambda x^2+\mu y^2=d^2\,$ i.e. the canonical ellipse equation. – dxiv Jun 23 '18 at 5:28
• @dxiv I see. But then how does the ellipse equation model the process used to create an ellipse, namely, by stretching a string fixed to 2 points and moving it around in a circle (or should I say ellipse). I don't get how the ellipse equation models this. – Ethan Chan Jun 23 '18 at 5:31
• @EthanChan For that you'll have to get down to some actual calculations. My comment was only about the "intuition" of it. See also Why is the equation of an ellipse (x/a)^2 + (y/b)^2 = 1? – dxiv Jun 23 '18 at 5:36
• Fix a rope of lenght $L$ to the points $A$ and $B$ (the foci : $L > d(A,b)$). Then put a pencil in the rope e draw the curve constrained by the rope in tension. – Mauro ALLEGRANZA Jun 23 '18 at 12:29

There is no single equation for an ellipse, just as there is no single equation for a line. We choose a form to highlight information of interest in the current context.

Consider this sampling of ways to write the equation of a line:

$$\begin{array}{rcccl} \text{slope-intercept} &\qquad& y = m x + b &\qquad& \begin{array}{rl} m:&\text{slope} \\ b:&y\text{-intercept} \end{array} \\[8pt] \text{intercept-intercept} && \dfrac{x}{a} + \dfrac{y}{b} = 1 && \begin{array}{rl} a:& x\text{-intercept} \\ b:& y\text{-intercept} \end{array} \\[8pt] \text{normal} && x \cos\theta + y\sin\theta = d && \begin{array}{rl} \theta:& \text{direction of normal} \\ d :&\text{distance from origin} \end{array}\\[8pt] \text{point-slope} && y-y_1= m (x-x_1) && \begin{array}{rl} (x_1,y_1):&\text{point on line} \\ m:&\text{slope} \end{array} \\[8pt] \text{two-point} && \dfrac{y-y_1}{x-x_1}=\dfrac{y_1-y_2}{x_1-x_2} && \begin{array}{rl} (x_i,y_i):&\text{points on line} \end{array}\\[8pt] \text{standard/general} && A x + B y + C = 0 && \end{array}$$

Each form tells us something about the line's geometry. (The "general" form tells us that the line's geometry is unimportant.) Algebra lets us move from one form to another if and when our priorities change.

Note that, since all the forms represent the same line, they must encode the same geometric information somehow. The encodings aren't always neat and tidy, though. For instance, we can manipulate the general form into slope-intercept ... $$A x + B y + C = 0 \qquad\to\qquad y = - \frac{A}{B} x - \frac{C}{B}$$ ... to see that the line's slope is $-A/B$, and its $y$-intercept is $-C/B$. Converting to intercept-intercept form tells us that the $x$-intercept is $-C/A$. Moreover, we can determine slope from the intercept-intercept form, or normal direction from the two-point form, ... whatever. Having the various forms available gives us flexibility in how we present that information. But I digress ...

Likewise, we have a sampling of equational forms for an ellipse.

\begin{array}{rcl} \text{foci and string} & \begin{align} \sqrt{(x-x_1)^2+(y-y_1)^2} \qquad&\\ + \sqrt{(x-x_2)^2+(y-y_2)^2} &= 2 a \end{align} & \begin{array}{rl} (x_i,y_i):&\text{foci} \\ 2a:&\text{string length} \end{array} \\[10pt] \text{standard} & \dfrac{(x-x_0)^2}{a^2} + \dfrac{(y-y_0)^2}{b^2} = 1 & \begin{array}{rl} (x_0,y_0):&\text{center} \\ a:&\text{horizontal radius} \\ b:&\text{vertical radius} \end{array}\\[10pt] \text{focus-directrix} & \begin{array}{c} \sqrt{(x-x_0)^2+(y-y_0)^2} \\ \qquad\qquad\qquad = e\;\dfrac{| a x + b y + c |}{a^2+b^2} \end{array} & \begin{array}{rl} (x_0,y_0):&\text{focus} \\ ax+by+c=0:&\text{directrix} \\ e:&\text{eccentricity} \end{array}\\[10pt] \text{general} & A x^2 + B xy + C y^2 + D x + E y + F = 0 & \end{array}

The "foci and string" form is the direct (dare I say, "intuitive"?) translation of the foci-and-string definition of the ellipse: the sum of the distances from two points is a constant. We tend not to see that form except as the point of departure on an algebraic journey to the "standard" form. That's because (1) the giant radical expressions are bulky, and (2) the standard form offers much more glance-able information about the geometry of the ellipse, and it has an all-around nicer algebraic nature.

The upshot is that we have an equation to fit every way of looking at an ellipse, so that everyone's intuition is satisfied. And, again, having multiple forms available gives us flexibility in how we want to encode or present the geometric information we find most important to the task at hand.

As an aside, I'll note that the lesser-used focus-directrix form of the equation is more versatile than the standard form, since it works for every conic section (except the circle). In particular, it can be convenient to remember that a parabola (which has eccentricity $1$) has this equation:

$$(x-x_0)^2+(y-y_0)^2 = ( x\cos\theta + y\sin\theta -d )^2$$ where we've leveraged the normal form of the directrix equation to make things tidier.

• It may be worth mentioning that the "standard" ellipse equation has the major and minor axes parallel to the coordinate axes, while the other three presented forms, if I'm not mistaken, are more general. – zahbaz Jun 23 '18 at 20:43

(This really should be a comment but I needed more space, apologies).

You seem to think (reading the previous comments) that the ellipse's equation should "instruct" us, in a step-by-step manner, how to draw the ellipse. That doesn't have to be the case.

In fact, let us invent a new relation between $x$ and $y$:

$e^x-y=\sin\left(x\cdot y\right)$

There are points $(x,y)$ in the plane that satisfy the above equation and they align on a curve we might as well call a zwiggle. See the WolframAlpha graph or try Desmos or something similar if you are curious what it looks like.

Is it obvious what shape zwiggles look like? No. Does it have to be? No. So... what is a zwiggle? It's just the set of points that satisfy $e^x-y=\sin(x\cdot y)$.

Now, is it obvious what curve we get with:

$\dfrac{(x-2)^2}{81}+\dfrac{(y+1)^2}{25}=1$

Well, to a trained eye, it might be obvious that it is an ellipse centered at $(2,-1)$ with horizontal axis of length $18$ and vertical axis of length $10$ but otherwise, if you don't recognize the equation of an ellipse, you can just tell yourself that the relation encodes a bunch of points in the plane. That "bunch of points" is in fact called the locus of the equation. And in this case, the locus is so popular we have a name for it (ellipse). It just so happens that the ellipse's equation in relation to its shape is something less intuitive than the circle, but more intuitive than the zwiggle.

I know this doesn't quite answer your question (and as I said, this should be a comment), but others have already posted plenty of useful information about ellipses that should give you better intuition. I just hope this helps you see that sometimes, mathematical relations don't really translate to something "geometrically obvious" and you just need to think of the curve as something more abstract.

• Okay. That's fair. So basically, the ellipse equation just gives a set of points that fufills the requirements of an ellipse, and doesn't actually "draw out the ellipse"? – Ethan Chan Jun 23 '18 at 7:06
• @Ethan Yes, though you could argue that it does draw the ellipse once the set of points it represents is "painted" in the plane. – orion2112 Jun 23 '18 at 7:11
• Okay. That's fair. One last question though, if that's the case, then why are we using the geometric properties of an ellipse to derive it's equation? How do we derive the equation (the equation that represents a shape) if the equation will have no relation to the geometric properties of the shape? – Ethan Chan Jun 23 '18 at 7:16
• @Ethan You start with the geometric properties and derive an equation (because that's the natural and easy thing to do). Then once you have the equation, you say that its locus (the set of points) IS the ellipse. Then you can almost "forget" about the underlying geometry (but it most definitely is still there; there is still a link between the algebra and the geometry). Thinking in terms of the locus is just more helpful (sometimes) when you deal with equations or relations for which you don't have an intuition. Hope this clarifies... – orion2112 Jun 23 '18 at 7:32

You may derive the equation for ellipse from the equation of circle by scaling your $x$ and $y$

$$x^2 + y^2 = R^2$$

Let $$x\to x/a,\text {and } y\to y/b$$

You get $$(x/a)^2 + (y/b)^2 = R^2$$

$$(\frac {x}{aR})^2 + (\frac {y}{bR})^2 = 1$$ $$\frac {x^2}{A^2} + \frac {y^2}{B^2} = 1$$

• I see, but how does this fit in with the process used to derive an ellipse? This makes sense, but why is the process of deriving the ellipse so complicated? Where does this fit in with all of that? – Ethan Chan Jun 23 '18 at 5:29
• Circle is a special case of ellipse where a=b=R. Ellipse is a deformed circle so we scale the coordinates to get an ellipse from the circle. Deriving the equation of ellipse from its definition is complicated but from scaling a circle it is much easier. – Mohammad Riazi-Kermani Jun 23 '18 at 5:33
• I get the scaling of the circle explanation, and I find it helpful. But I also want an intuitive understanding of the equation from how it is derived from the definition. I get how to derive it from the definition, but I don't find the link intuitive. I don't see how the equation shows how an ellipse can be drawn from it's definition, if you see what I mean. I just don't find the link between the definition of ellipse and the equation of ellipse intuitive. I'd be happy to do some calculation to figure it out; I'm just really confused and would benefit from some guidance. – Ethan Chan Jun 23 '18 at 5:57
• The equation does not lend itself to "intuitive" understanding. You just have to get used to it and graph many ellipses with different parameters to develop a good feeling about it. – Mohammad Riazi-Kermani Jun 23 '18 at 6:27
• @Ethan I think this is actually really intuitive, just not the same as the common definition of ellipse. This is an instruction - draw a circle, then stretch the paper and you get an ellipse. – Džuris Jun 23 '18 at 10:30

I mentioned in my previous answer that the "foci and string" form of the ellipse equation is rarely seen "except as the point of departure on an algebraic journey to the 'standard' form". I want to elaborate a little on that "algebraic journey".

Typically, the journey involves a lot of unenlightening, mechanical symbol-pushing to eliminate the square roots. Specifically, defining $$d_i := \sqrt{(x-x_i)^2+(y-y_i)^2}$$ the argument tends to go something like this: \begin{alignat}{2}\quad && d_1 + d_2 &= 2 a \qquad\text{(definition: sum of distances to foci is constant)} \tag{\star} \\ \to\quad && (d_1 + d_2)^2 &= (2 a)^2 \\[4pt] \to\quad && d_1^2 + 2 d_1 d_2 + d_2^2 &= 4 a^2 \\[4pt] \to\quad && 2 d_1 d_2 &= 4 a^2 - d_1^2 - d_2^2 \\[4pt] \to\quad && (2d_1d_2)^2 &= ( 4 a^2-d_1^2-d_2)^2 \\[4pt] \to\quad && 0 &= d_1^4+d_2^4+16a^4-2d_1^2d_2^2-8a^2d_1^2-8a^2d_2^2 \tag{\star\star} \end{alignat} so that $(\star\star)$ contains only even powers of the $d_i$, hence: no radicals. Mission accomplished! Replacing the $d_i$ (in particular, with $(x_i,y_i) = (\pm c,0)$, and defining $b^2 := a^2-c^2$), equation $(\star\star)$ simplifies (see below) to the origin-centered standard form equation we all know and love.

I believe OP is disappointed that, somewhere along the tedious journey from $(\star)$ to $(\star\star)$, we lose sight of $(\star)$.

However, it's still possible to catch a glimpse of $(\star)$ in $(\star\star)$, because $(\star\star)$ factors:

$$(d_1+d_2-2a)(d_1-d_2-2a)(-d_1+d_2-2a)(d_1+d_2+2a) = 0 \tag{\star\star\star}$$

(The reader might see a resemblance to Heron's formula in the above.)

Since $(\star)$ is right there in the first factor, the set of points satisfying $(\star\star\star)$ must include those satisfying $(\star)$, the (well, one) definition of the ellipse.

Note that the last factor of $(\star\star\star)$ contributes no points, since presumably $a > 0$ and $d_i \geq 0$.

Interestingly, the middle factors of $(\star\star\star)$ correspond to the relations $$d_1 - d_2 = 2a \quad\text{or}\quad d_2 - d_1 = 2a \qquad\qquad\text{i.e.,}\quad |d_1-d_2| = 2a$$ which say precisely that the difference of distances to the foci is constant: the (well, one) definition of the hyperbola! (Each factor corresponds to an arm of the ostensible hyperbola.)

Consequently, $(\star\star)$ is simultaneously an ellipse equation and an hyperbola equation! Except, not exactly. The graph of the solution set is only one or the other, as determined by $a$'s relationship to the distance between the foci. To be specific, let's do the simplification hinted at earlier: take $(x_i,y_i) = (\pm c,0)$, so that $(\star\star)$ becomes $$16 \left(\;a^2 (a^2 - c^2) - x^2(a^2-c^2) - a^2 y^2\;\right) = 0 \qquad\to\qquad \frac{x^2}{a^2} + \frac{y^2}{a^2-c^2} = 1$$ We see, then, that when $a > c$ ---so that the sum of the distances to the foci is bigger than the distance between the foci themselves--- the equation is that of an ellipse; in $(\star\star\star)$, the second and third factors cannot be zero. On the other hand, when $a < c$, the equation is that of an hyperbola; the first factor of $(\star\star\star)$ cannot be zero. (Exploring the degeneracies arising from $a=c$ is left as an exercise to the reader.)

Anyway, my point is this: We can get to $(\star\star)$ from $(\star)$ by plodding through sequence of algebraic steps that obscure the geometry; or, we can get to $(\star\star)$ by "rationalizing" $(\star)$ via multiplication by what one might call its "Heronic conjugate", the three factors of which are geometrically meaningful (although one is inherently extraneous). And we get the hyperbola equation for free ... because it's the same equation!

Kinda neat, that.

Key thing to keep in mind is that the length of the rope doesn't change. This means you're basically modeling all the points whose "sum of distances from the given two fixed points" doesn't change.

Say $A$ and $B$ are the fixed points and $L$ is the length of the rope, then the point P traces the curve given by the equation : $$\text{(distance between P and A)} + \text{(distance between P and B)}= L$$

Try plugging in $P = (x,y)$, $A = (-c,0)$ and $B=(c,0)$ and see what you get.

Draw two concentric circles of centre $O$ and radii $a$ and $b$ ($a<b$) in an orthonormal system of axes $(O,\textbf{i},\textbf{j})$. Every half-line from $O$ cuts the circles at points $M_a$ and $M_b$. Let $N_a$ and $N_b$ be the orthogonal projections of $M_a$ and $M_b$ over the $x$ axis and the $y$ axis respectively. Denote $\alpha$ and $\beta$ the measures of the angles $\widehat{N_aIM_a}$ and $\widehat{N_bIM_b}$.

Since $\alpha+\beta=\dfrac{\pi}{2}$ then $$\cos^2\alpha+\cos^2\beta=\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$$

The ellipse is the set of points $M$ intersection of the lines $(M_aN_a)$ and $(M_bN_b)$.

• [+1] Very neat ! – Jean Marie Jan 25 at 11:43

$x^2+y^2 = 1$ is our unit circle

$\frac {x}{a}$ dilates $x$ by a factor of $a.$ That is it stretches everything horizontally by a factor of $a$

Simmilarly, $\frac {y}{b}$ dilates $y$ by a factor of $b.$

$\frac {x^2}{a^2} + \frac {y^2}{b^2} = 1\\ \left(\frac xa\right)^2 + \left(\frac yb\right)^2 = 1$

The equation of an ellipse just shows how to distort a circle.

While we can derive the distance between the foci, and the "length of the rope" it is not entirely obvious from the equation.

The length of the major and minor axis $(2a, 2b)$ are.

The equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ tells one which points belong to the ellipse and which don’t. Take a point with coordinates $(x, y)$, calculate the above. Is it 1? Excellent, it’s on the ellipse. Not 1? Then it’s some other point.

If you want to transform the equation into something that actually provides a method of drawing the shape, try converting it to parametric form. That is, instead of $F(x, y)=0$, look for ways of expressing the same as

\left\{\begin{align*} x &= x(t) \\ y &= y(t). \end{align*}\right.

For the ellipse, the formula tells that squares of something add up to 1. What are common things that have this property? Sine and cosine. So $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$ is equivalent to \left\{\begin{align*} x &= a \cos t \\ y &= b \sin t \end{align*}\right. in the sense that for any $x$ and $y$, some $t$ exists satisfying the above if and only if $(x, y)$ lies on the ellipse.

But now you actually have a method of drawing the ellipse. Set $t = 0$ and determine $x$ and $y$. Then increase $t$ in small steps and you’ll get more and more points of the ellipse (and when $t$ reaches $2\pi$, you’re done). You can think of $t$ as the time parameter and the equations for $x$ and $y$ as describing the motion of some mechanism that’s drawing the shape. This particular mechanism requires $2\pi$ worth of time to draw the entire ellipse, if you’re wondering how fast and in what direction it’s going at any particular point you can calculate some derivatives and so on.

As for the method of drawing with a string pinned at the foci, I’m not aware of an intuitive reasoning that would explain why this results in the same shape as one gets stretching a circle in one direction. It can be proven mathematically though.

• I'm glad someone made this contribution, as it directly answers what the OP was asking for. – Eli Rose Jun 23 '18 at 22:25

The circle equation is simply one specific ellipse equation, where the scaling of each direction ($x$ and $y$) is identical.

Division by some factor of just one variable matches scaling by that factor in that direction. Hence, $\frac{x^2}{3^2}+y^2=r^2$ will make the ellipse twice as large in the $x$ direction as its $y$ direction - half of $x$ is the same size as a whole $y$.

From here you have variation on the exact size of the scaling for a given radius, and since a scaled scalar is still a scalar, you only require a scalar for each direction, with the original radius set to 1, to obtain the general ellipse equation $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\space(= 1^2)$$

Note that because the scaling applied to the variable, it ends up also squared when that variable appears in the equation.

If you want to imagine it as the triangular form arising from rotation of the fixed hypotenuse length while variables record the length of each other side, you can consider inclining the plane that the rotation occurs in, and taking the projection of the sides onto the original plane.

I think it is foci and the semi axes confusion. Intuitively you understand now equation with a and b mentioned above. That is ellipse. Now, because of symmetry, there MUST be a distance from center i. e. foci distance, where the "constant rope length" condition is satisfied.

In reverse you can think from fixed length and two points must drow some shape and you derive ellipse.

However foci distance and a and b are not in trivial intuitive relation.

So by thinking from circle with one parameter, you have now two (a, b semi axes)+one in foci distance to satisfy the fixed rope condition.

Both "intuitive" conditions (fixed rope, foci AND a, b semi axes) collapse into one when going from ellipse to circle. Because the length of the rope is equal to radious. Voila


text:
A gambler believes that a strategy called “doubling up” is an effective way to gamble 1 answer below »

A gambler believes that a strategy called “doubling up” is an effective way to gamble. The method requires the gambler to double the stake after each loss. Thus, if the initial bet is $1, after losing he will double the bet until he wins. After a win, he resorts back to a$1 bet. The result is that he will net \$1 for every win. The problem however, is that he will eventually run out of money or bump up against the table limit. Suppose that for a certain game the probability of winning is .5 and that losing six in a row will result in bankrupting the gambler. Find the probability of losing six times in a row.


text: • Some of the coordinate data has nan as a value that causes some error output but for me the file imports. Using 2.79 and 2.80 I get some parts that are out of position and some would appear to be missing, eg there are only two tyres/rims. By replacing nan with 0 the errors disappear but no extra parts show up. – sambler Apr 24 '19 at 10:22


text:
Table 2.

Gut microbiota analysis techniques

Technique16S rRNA Based?Cost ($)Taxonomic Resolution/SensitivityAdvantagesDisadvantages (Limitations) Culture basedNo$ModerateYou have the organism “in hand”Most GI organisms cannot be cultured in current defined media
Functional information gained from what is known about the organism's substrate utilization and other physiological parametersLabor intensive
Full-length (Sanger) sequencingYesVery goodSequencing the entire 16S gene maximizes the taxonomic resolution offered by the geneExpensive (although mechanization is reducing the cost)
Extensive bioinformatic analysis required
454 PyrosequencingYes$$Good to very goodHigher throughput than Sanger sequencing (200,000 sequences versus 20,000)Can't obtain the taxonomic resolution that can be achieved with full-length sequencing More sensitive (can detect less abundant organisms due to the number of reads obtained)Shorter sequence reads (<500 bp versus 1.5 kb) Multiple samples can be analyzed in a single sequencing runExtensive bioinformatic analysis required No cloning bias introduced Less susceptible to PCR bias (shorter PCR amplicons, less influenced by G/C content) DGGEYesPoorRapidShorter PCR products mean less taxonomic information can be obtained Fingerprints provide a good basis to compare communities from different treatment groupsReproducibility between gels is difficult Bands of interest can be excised and sequenced TRFLPYes$$PoorFingerprints provide a good basis to compare communitiesLimited taxonomic resolution
Multiple restriction enzymes can be used to provide greater resolutionOne “phylotype” can represent more than one species
ReproducibleCapillary sequencer required
RISANo$$GoodGreater variability between species and strains than the 16S geneLimited phylogenetic data currently available; no extensive RIS database developed for gut bacteria When a better database has been developed, taxonomic resolution could be “Excellent”A single bacterium can have more than one different RIS region DNA microarraysYes$$$$Very goodIncredibly useful as a screening approachDetection limited by the sequences contained on the chip (no detection of uncharacterized phylotypes) Fast, easy to useCross-hybridization issues Clinical applications FISHYes$$$GoodCan target specific bacterial groups/species of interest (they must be preselected)Can't identify novel groups of bacteria Flexible scope: probes can be designed to target groups or individual speciesIt's not a community-wide survey of “who's there” Direct enumeration of bacteria- 16S copy number is not an issueReference strains are required to validate the results Microscope work is time-consuming (however FACS options are becoming available) qPCRYes$$GoodCan target specific bacterial groups/species of interest (they must be preselected)Reference strains are required to validate the results Flexible scope: primers can be designed to target groups or individual speciesCan't identify novel groups of bacteria It's not a community-wide survey of “who's there” 16S copy number varies between 1 and 10 MetagenomicsGenome wide$$$$GoodProvides a community-wide assessment of the functional genes presentShotgun reads are mapped to reference genomes; this is limited by the number of sequenced genomes available 16S gene sequences provide taxonomic identification of community membersExtensive bioinformatic analysis required Sensitivity depends on the number of sequence reads obtainedCloning biases could affect the functional gene information obtained No direct information about which genes are expressed or functioning MetabolomicsNo$$$$PoorMetabolic profiles can be used to compare communities in a functional contextNo taxonomic information available More direct functional information can be obtainedThe source of each metabolite is unknown; therefore, it is difficult to identify what organisms are producing what compound More rapid and less expensive than metagenomicsNot all metabolites are detectable with current technology Nontargeted approach can also identify host metabolites associated with the gut microbiota MetaproteomicsNo$$$$PoorMetaproteomes can be used to compare communities in a functional contextNo taxonomic information available More direct functional information can be obtainedProtein abundance is difficult to estimate More rapid and less expensive than metagenomicsLess abundant proteins (from populations making up <1% of the community) go undetected Nontargeted approach can also identify host proteins associated with the gut microbiota MetatranscriptomicsGenome wide$$$GoodProvides insights into community-wide structure and functionRNA is much more easily degraded than DNA; this could cause information loss
Can be used to detect changes in community-wide gene expression profiles in response to different environmental stimuliSensitivity of community analysis depends on the number of sequence reads (via pyrosequencing) obtained
No biases introduced by PCR or cloning steps (none required)
Transcripts can be measured quantitatively
• A number of techniques have been applied to analyze the composition, abundance, and function of the gastrointestinal microbiota over the last several decades, 16S rRNA-based and otherwise. The analysis method of choice depends on the question being asked as well as the time and cost restrictions associated with the task. An assessment of the benefits and limitations of the current techniques available in gut microbial ecology is provided. GI, gastrointestinal. RIS, ribosomal intergenic spacer.


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# The overlap gap between left-infinite and right-infinite words

In this talk I will present ultimate periodicity properties related to overlaps between the suffixes of a left-infinite word $\lambda$ and the prefixes of a right-infinite word $\rho$. I will talk about a result that states that the set of minimum lengths of words $x$ and $x'$ such that $x\lambda_n = \rho_nx'$ or $\lambda_nx = x'\rho_n$ is finite, where n runs over positive integers and $\lambda_n$ and $\rho_n$ are respectively the suffix of $\lambda$ and the prefix of $\rho$ of length $n$, if and only if $\lambda$ and $\rho$ are ultimately periodic words of the form $\lambda = u^{-\infty}v$ and $\rho = wu^{\infty}$ for some finite words $u$, $v$ and $w$. This is a joint work with José Carlos Costa (Universidade do Minho) and M. Lurdes Teixeira (Universidade do Minho).

## Date and Venue

Start Date
Venue
Online Zoom meeting
End Date

## Speaker

Conceição Nogueira

## Speaker's Institution

Polytechnic Institute of Leiria/CMAT (University of Minho)

## Area

Semigroups, Automata and Languages