Calculate the change between the initial target angle and the deformed angle. 14 W and f = 10 Hz. Nguyen 10/16/08 26. (4) When the sign of the charge of the particle is switched from positive to negative (or vice versa), the direction of the magnetic force also reverses. L2, R2, and L3 have the least deflection and these will serve as a good contrast against the other templates for the shape analysis. Barrel of shaft shall house oil tempered, helically wound steel spring, and rotate on grease-sealed ball or ro ller-bearing units. The local flow angles were measured at a tunnel dynamic pressure of 30 pounds per square foot over an [email protected] range of O" to 8O and with a flap deflection range of S5. The different angle codes are NE for northeast bearing, SE for southeast, SW for southwest, NW for northwest, AZ for azimuth, AL for angle left, AR for angle right, DL for deflection angle left and DR for deflection angle right. A degree of semi-balance A degree of semi-balance Ricochet (1,851 words) [view diff] exact match in snippet view article find links to article. a phase angle meter, whose angle readings were indicated by a cathode-raytube, was built by JUan Watton. Azimuths from Deflection Angles. 00 units and makes an angle of 45. 3 Angle of Twist. • Mass distribution at large angles and high redshift in in the linear regime • Projected mass distribution (low pass filtered reflecting deflection angles): 1000 sq. As shown in the diagram on the right, the difference between the unlensed angular position → and the observed position → is this deflection angle, reduced by a ratio of distances, described as the lens equation → = → − → (→) = → − ^ → (→) where is the distance from the lens to the source, is the distance from the observer to the source, and is the distance from the. All findings were significant (P. The kinetic impactor deflection approach is likely to be the optimal deflection strategy in most real-world cases, given the likelihood of decades of warning time provided by asteroid search programs and the probable small size of the next confirmed asteroid impact that would require deflection. Similar to elastic deformation, we have deformation due to torsion as well: twisting. During DE, we measured five axial line deflection angles: the angle at the start initiation of this phase, and the angles at 25, 50, 75 and 99% of the total duration time of DE, using iMovie '11 (Apple Inc. Therefore, 67° has been established as the bank angle limit. calculate_effective_yaw_angle(x_locations, y_locations, z_locations, turbine, coord, ﬂow_ﬁeld) This method determines the effective yaw angle to be used when secondary steering is enabled. -Converting bearings to deflection angles from given traverse data. khanacademy. This relation confines the scatter-ing angle to the interval 0 0 c 180°. This paper analyses the simplified model of the monopulse antenna beam pattern and the principle of monopulse antenna angle tracking system. • When calculating the deck thickness loss, it is important to consider the orientation of the screed machine. 1 Kinematics of roller bearings Houpert (1997) derives a kinematic relation between the roller-raceway deformation. The angle between the reflected ray and the normal is known as the angle of reflection. Dynamic Angle Spinning: DAS: Deflection Amplifier Subsystem: DAS:. Sum up the contributions from rays uniformly distributed over the scaled impact parameter $\tilde{b}=b/R$ to compute the overall irradiance as a function of deflection angle for light of wavelength 400 nm. Beam Simply Supported at Ends – Concentrated load P at the center 2 1216 Pl E I (2 ) 2 2 3 Px l l for 0yx x 12 4 2 EI 3 max Pl 48 E I x 7. C 2 = a 2 + b 2 - 2 a b Cos (angle between adjacent vectors in solution triangle) The angle between the vectors in the solution triangle as shown below is equal to 180 degrees minus the angle between the cables. These rotations are determined by dividing the net deflection by the distance between the points along the axis, and finding the corresponding angle. The size and amount of sunspots show the degree of solar activity. a l p h a = a r c t a n ( h / a ) b e t a = p i / 2 − ( t h e t a + a l p h a ). Interior Angles: angles inside a closed polygon Sum of Interior = (n-2)180o Where: n is the number of sides Eg (6-2)180o = 720o 115o10' + 129o11'+ 88o35' + 132o30' + 135o42' + 118o52' = 717o180' = 720o Angles to the Right: clockwise angles measured from rear to forward station A F B Deflection Angles: measured from the. For neutral sidestick the system comes back to αprot. On those meters we refer to the position to the right (the normal increase) as the deflection. Triangle has three types based on its three angles, including obtuse (1 angle > 90 ̊C), right (1 angle = 90 ̊C) and acute (no angle > 90 ̊C). (Answers 169. O-inch)the deflection was measured with a steel scale graduated to 0. I am finding that not all angles in the list are correct for example if I select a 4 sided right angle rectangle the list will return (270. The gages for the direct pull tests in Groups I and II were mounted as shown in Fig. These forces might act with or against each other so the overall deflection and the angle in which it is deflected is the vector sum of the three components. From Equation (9. 2 = 198° 59′ 39″ Pt. Deflection by Superposition ENES 220 ©Assakkaf Method of Superposition – This sum may be an algebraic one (Figure 19) or it might be a vector sum as shown in Figure 20, the type depending on whether or not the individual deflection lie in the same plane. = increments of deflection at midlength of a column in Salmon’s analysis. What is deflection of a beam? Deflection is the vertical distance at a point between. This possibility has also been suggested by May and Bean (Ref. Graph Selection Shear Force Shear forces sum. Maney (1915) is credited as the first to publish the modern slope-deflection equations where deformations are treated as unknowns instead of stresses and reactions. Angular measurements are displayed in the Measure dialog box as you make them. Conversions are performed by using a conversion factor. 2” 41 •If each angle is measured 1DR (i. 9 cm, which is equal to the lateral deflection due to the rotation of Earth, making any conclusions regarding the validity of Equation (11) meaningless. ensure deflection not exceeding 2. N – 2 x 180° = sum (∑) of the interior angles. Question is ⇒ If deflection angles are measured in a closed traverse, the difference between the sum of the right-hand and that of the left hand angles should be equal to. The value of electric current is measured by the deflection angle θ, and the value of K. α = angular flexibility coefficient = measure of angular displacement per unit couple moment. 0 with regard to failure of the cement-mortar lining. DA FORM 4201, JAN 2016. 005) and agreed with the solid angle theorem. Since the sum of the interior angles of any triangle = 180°, the angle the ray makes with the second pavilion facet is (180 – 47 – 94)° = 39°. The tables below give equations for the deflection, slope, shear, and moment along straight beams for different end conditions and loadings. $\begingroup$ What's presented on the PFD is elevator & aileron deflection, not sidestick deflection. Angle sum of any polygon - Maths Tutorials - Duration: 5:46. A36 steel for the connection angles and plates (F y = 36 ksi, F u = 58 ksi) and A992 or Grade 50 steel for the beams and columns (F y = 50 ksi, F u = 65 ksi), K series open web joists and roof decking. 6' deflection coherence 10°. Since the angles θ and β are complementary we have sin(β)=m/M and this is a proven result for angle of maximum deflection. On the other hand, greater pressure angle reduces the number of engaged teeth, increases bearing load and the worm deflection load (greater worm deflection). Yoo, Sung C. training data set and test data set. Prepare a report, describing the purpose of the experiment, the equipment and setup used and the results obtained. Right angle definition, the angle formed by two radii of a circle that are drawn to the extremities of an arc equal to one quarter of the circle; the angle formed by two perpendicular lines that intersect; an angle of 90°. , Options are ⇒ (A) 0Â°, (B) 90Â°, (C) 180Â°, (D) 360Â°, (E) , Leave your comments or Download question paper. At the inlet it has a cross sectional area of 0. Delay-And-Sum Algorithm listed as DAS. Deflection Amplifier Subsystem listed as DAS. The angle with be the number you get when you find the inverse tangent of 6/5. azimuth: the clockwise angle from the north branch of a meridian, e. It must be noted when the deflection is right (R) or left (L) 26. After applying this adjustment to each deflection angle in this example, you find, then, that the sum of the adjusted angles to the right equals 445°00'40" and that the sum of the left angles (of which there is only one) is 85°00'40". Tables will give allowable total uniform load (taking self weight into. 1 Boundary Conditions. We can obtain the following equations: U = W = Pd/2 U = W = M 0 q/2. The program uses a simple algorithm to calculate the deflection at each point of a cantilever beam subjected to arbitrary loading distribution, the program also calculates and plots the bending moment and shear force in the beam. When the edges are projected to form a 2D picture the angles between the edges are usually not 90°. If the last inflection point (node) of barrel vibration is known, the ability to accurately estimate barrel tip deflection would also allow one to make a pretty good estimate of muzzle launch angle. N´BB´ plus S´BC plus the deflection angle between AB and BC (angle B´BC) is 180°. R1 x 8 = 800 x 2 + (200 x 4) (2 + 2) + 1000 x 6. Maximum Deflection is the maximum rated angular deflection of spring to overstress. This principle is shown in Fig. Extending the link, the angle the hypotenuse makes with the base is the direction of the force. Together, those two values would be pretty useful for predictive in silico load development estimates. 3 Angle of Twist. array ([ld. 0167 T = 1 2 mpc 2 2 = 130keV For a 130 keV proton beam, the deflecting strengths are identical. If so, the errors are usually 3% of the full scale value. The second is that the found deflection angles in the RN and KN metrics describe accurately the. 0° with the positive x axis. Traversing by direct observation of bearings: The force bearing of the last line should be equal to its back bearing ±180° measured from the initial station. Lee Spring Stock Torsion Springs are offered with legs of equal length oriented at varying unloaded angles. This angle lets us determine the shear strain at any point along the cross section. Shah » Mon Oct 27, 2014 3:58 pm Is bending of wind turbine blade tips at moderate/higher wind speeds good or bad compared to a very stiff blade? especially for small wind turbines. Kästner1 and A. Explain that when the angles are put together, the sum of both angle measurements is equal to one larger angle measurement. deflection to the right of the galvanometer shows a deflection right to the zero mark. 3) is present in the distributions of Fig. Successive stations occupied and back sight is taken to the preceding station. Below, we shall restrict ourselves to a range of moderate angles of deflection. What is slope of a beam? Slope of a beam is the angle between deflected beam to actual beam at the same point. In this discussion, consider deflection angles of + 4° and less for each window. g) there is no. Adjust the angle of the tilt mirror by slowly pushing the Tilt Mirror Lever on the back of the AFM head (Figure 9) to achieve a maximum SUM reading (typically > 4. Question is ⇒ If deflection angles are measured in a closed traverse, the difference between the sum of the right-hand and that of the left hand angles should be equal to. This force goes right through A. Stall speeds are shown as a function of flap deflection and bank angle. Figure D shows the deflected shape with both concentrated load and uniform pressure. Plot the resulting irradiance distribution versus deflection angle for a single wavelength. Activation of the Heart and the ECG The drawings to the right in the table below show the main stages of activation of the heart, as well as the ECG recorded in lead II at those stages. A large aluminium pointer is rigidly fixed perpendicular to the magnetic needle. The Beam Calculator allows for the analysis of stresses and deflections in straight beams. 8R1 = 1600 +3200 + 6000 = 10800. Calculate the change between the initial target angle and the. Something scattered. These are standard that every company follows so that they don’t face any issues in communicating the design intent across the globe. an accuracy of ~. This limits the angle output to around -45 to 45. When the equations are written in the following form, they are said to be in State Space form: x Ax Bv yCxDv =+ =+ i. where is the measured acceleration, m is the mass of the body, is the sum of all forces on the body (including gravity) expressed in the sensor body frame, and is the force due to gravity, also expressed in the body frame (See the chapter on Understanding Euler Angles for details about different coordinate frames). The joints permit change of angle Between connected members. 7 – 10) were modelled at different transducer deflection angles from its supposed 0° position (Fig. deflection is limited to the beam’s span length divided by 250. 1) where U is the potential energy of deformation and W is the potential energy of the external loading. the sum of the modifications referred to the pinion roll angles is shown on the last graph. ρ is the density gap of the dark matter. (ii) The sum of the measured exterior angles should equal (2N + 4) right angles. 1 Kinematics of roller bearings Houpert (1997) derives a kinematic relation between the roller-raceway deformation. Williams Mar 17 '13 at 20:32 $\begingroup$ @GeorgeV. Deflection angles are measured traveling clockwise around a loop traverse. Some illustrations show connections that could cause cross-grain tension or bending of the wood during loading if not reinforced sufficiently. In RV NIS Pos ΔTQ-ST became Neg. To measure the angle between two lines or edges, click to select one, and then click to select the other. calculate_effective_yaw_angle(x_locations, y_locations, z_locations, turbine, coord, ﬂow_ﬁeld) This method determines the effective yaw angle to be used when secondary steering is enabled. For the forces to approximately sum to zero in this case, the product of the deflection angles and hoop tension must be “small”. From these curves, the superelastic and thermal wires of the same size had similar behavioural characteristics (wide hysteresis curves). In considering deflection, the same assumptions are taken as in the derivation of the bending formula. The sum of angle Figure 13-2. g) there is no. • Screed rail deflection for skewed bridges can be calculated using the standard method presented earlier. Interior Angles • Angles measured inside of a closed polygon • SUM of all interior angles = (n-2)*180 Exterior Angles • SUM of all exterior angles = (n+2)*180 • where n = number of sides. More elegant way to find the sum of the exterior angles of a convex polygon Watch the next lesson: https://www. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. M = bending moment. In addition, the needle trajectory optimization was based on the weighted sum of cost function. A particle is acted upon by two forces Fl and F2, given by Fl —. org/math/geometry/parallel-and-per. What is deflection of a beam? Deflection is the vertical distance at a point between. The torque values at a fixed hair deflection angle of 1. An angle may be classified as acute, obtuse, right, reflex, straight and full angle. Maximum deflections will occur at mid-span and mid-width and will be the sum of side channel and grating surface deflections (Figure 1c and 2c). Method C • Set the scale at the deflection angle for an intermediate point being sighted (POC1): df1 • Backsight on the intermediate POC1 with the scope inverted. The change is called the deflection angle. This principle is shown in Fig. Non-linear operations are good to use on the output of algorithms # like this to cause a response "trigger". deflection to the right of the galvanometer shows a deflection right to the zero mark. Starting with an azimuth of 328°58'15" for line AB, determine azimuths of the remaining lines. Corrections to compensate for the effects of errors introduced by the factors of deflection ballistics are made by adjusting the horizontal angle between the L. sum of the included angle and 180? [D]. Hot Setting A process to improve spring relaxation when operating at elevated temperatures. 18, where pressure p acting on the airfoil at a point where the flow deflection from the free stream is ε represents the sum of p t + p c + p α. For a decagon, n=10. The TAN function returns the tangent of an angle provided in radians. In Figure 3, a is the vehicle deflection angle to be detected. 1 = 90° 13′ 58″ Pt. where N is number of sides of the traverse. First let's look at the reaction force at A. Nguyen 10/16/08 26. Since two congruent triangles will combine to form a square or other quadrilateral, the sum of the angles in one of the triangles is half of 360°, or 180°. discharge pipe shall be no more than 90%%d for pipes up to 24" in diameter. For neutral sidestick the system comes back to αprot. As you are aware, the actual distance along an arc is greater than the length of a corresponding chord; therefore, when using the arc definition, either a correction is applied for the difference between. 001 inch), draw the deflection as a vector. A deflection angle in a traverse is equal to the difference between 360? and the included angle [C]. deflection_angle = 0 #机器人应该转的角度. The sum of the angles in a triangle is 180°. The angle of deflection is very small. The difference (the surplus or deficit), divided by the area of the triangle, is a measure for the curvature of that region of the surface. The sum of angle. bevel gear. -----The sum of the angles of a triangle is 180 degrees. Deflection of a cable under tension then the angle of the cable at the ends and where the child holds it id such that the vector sum of the child's lifting force. Non-linear operations are good to use on the output of algorithms # like this to cause a response "trigger". The tension sensor capacity is designed for a specified wrap angle. Home / deflection the driver Alexa algebraic sum algorithm algorithm driven study type Courage CPU crankshaft angle Credit/Debit card. Direction angle of a vector formula. Maney (1915) is credited as the first to publish the modern slope-deflection equations where deformations are treated as unknowns instead of stresses and reactions. Once you apply load to your truss, the target angles change. In the case of a non-convex polygon, exterior angles get a little weird. By calculating the theoretical coil field for a measured current and coil radius, as well as measuring the angle of needle deflection between the earth field and resultant vector sum of the earth and coil fields, the trigonometric tangent allows for a numeric solution for the earth field's horizontal component. in the field was 0. Beam Simply Supported at Ends – Concentrated load P at any point 22 1 ()Pb l b. This minimum force is referred to as "initial tension". Something scattered. Timoshenko -2-. – The superposition method can illustrated by various practical examples. N´BB´ plus S´BC plus the deflection angle between AB and BC (angle B´BC) is 180°. As the results of this study showed, NiTi and TMA have higher LDR than L-loops in the interbracket span. 1 Kinematics of roller bearings Houpert (1997) derives a kinematic relation between the roller-raceway deformation. My code below creates a list of included angles of a closed polyline. Approaching this limit, the roll rate is progressively reduced to avoid over-banking. (b) Traverse by Deflection Angles: The algebraic sum of the deflection angles should equal 360°. Also for calculating the maximum deflection angle and distance of different types of beam, you will be required to use the area moment of inertia. ensure deflection not exceeding 2. Hence, deduce that the shock front subtends the same angle, , with the Mach lines upstream and downstream of it. Question is ⇒ If deflection angles are measured in a closed traverse, the difference between the sum of the right-hand and that of the left hand angles should be equal to. We can obtain the following equations: U = W = Pd/2 U = W = M 0 q/2. Show Instructions In general, you can skip the multiplication sign, so `5x` is equivalent to `5*x`. As bank angle increases, so does the required load factor, and so does the stall speed. Below, we shall restrict ourselves to a range of moderate angles of deflection. deflection to the right of the galvanometer shows a deflection right to the zero mark. Follow Simmy Sigma on Twitter: @simmysigma Make sure to "like" the Official Simmy Sigma Facebook Page here. The amplitude of the relief is close to the maximum deflection of the tooth pair when in the single tooth pair contact region. 0167 T = 1 2 mpc 2 2 = 130keV For a 130 keV proton beam, the deflecting strengths are identical. deflection as a design criterion, loads may be limited by either: strength of individual surface struts, or total deflection of one siderail at midspan plus a surface strut at midwidth of walkway or plank (sum of siderail deflection plus strut deflection). similar manner, a negative elevator control deflection will shift (apparent) upward. Use this online angle subtraction calculator or DMS subtraction calculator to subtract the angles expressed in degrees, minutes and seconds. Triangle has three types based on its three angles, including obtuse (1 angle > 90 ̊C), right (1 angle = 90 ̊C) and acute (no angle > 90 ̊C). These angles are sight angle and sight deflection respectively. The angle of incidence and the angle of reflection is always equal, and they are both on the same plane along with the normal. It makes an angle β AE. You can find comprehensive tables in references such as Gere, Lindeburg, and Shigley. 1 more thing thats not covered in the above document - design deflection for floors. This shift will cause the intercept with the line (the axis) to move left to a smaller (positive elevator deflection) or to the right to a bigger (negative elevator deflection), allowing us to fly at different angles-of-attack and hence, at different speeds. A boundary between “hard” and “soft” collisions is defined providing a precise sampling of a scattering angle (1% level) and a small number of “hard”. The sum of the first terms of each row gives. The power spectrum was obtained when keeping the differential signal as close as possible to zero (centre of the PSD) and the sum signal as high as possible. Single tooth mesh stiffness consists of three components as depicted in Figure 2: • Tooth deflection due to bending under load. (4) When the sign of the charge of the particle is switched from positive to negative (or vice versa), the direction of the magnetic force also reverses. If it is axle to saddle, then it would be the sum of both rear triangle deflection, and seatpost/tube flex (like on a Domane). Parallax error, mis-alignment, mechanical play, incorrect deflections etc 5. Null Type Instruments In opposite to deflection type of instruments, the null or zero type electrical measuring instruments tend to maintain the position of pointer stationary. Bank Angle Protection [Airbus FTCM, pg. BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. TQ-ST at 60 s was obliterated when K+ = 8. SUM-900790 With the Summit Racing® Fender Roller, it's not hard to roll fender lips to prevent them from cutting your tires. Murphy, Smith & Schwadron ( 2002 ). These are given by the expressions: V = SUM wdx. Determine the stationing to be used (i. This is ‘underwound’ HMF that skews towards the radial direction, as noted by e. C 2 = a 2 + b 2 - 2 a b Cos (angle between adjacent vectors in solution triangle) The angle between the vectors in the solution triangle as shown below is equal to 180 degrees minus the angle between the cables. This method considers the deflection as the primary unknowns, while the redundant forces were used in the force method. Deflection angles! These angles are very helpful when staking out horizontal curves. The angle of rotation is the angle of rotation of the beam axis at the point where the moment is applied. On the ribbon, click Tools tab Measure panel Angle. Deflection Check Maximum allowable ring deflection for cement-mortar lined Ductile Iron Pipe is 3 percent of the outside diameter. Procedure: 1. the acceleration of gravity. org/math/geometry/parallel-and-per. and angle of impact are considered, the testing criteria represents the extremes of impact conditions to be expected in real-world situations. This calculation can be seen below for Test A’s axial azimuth angle, with detailed angle. In an oblique projectile on horizontal ground thehorizontal range is four times the maximum height. All angles of a triangle always add up to 180 ̊C. The sun is constantly rotating II. Measure an angle. equally among the deflection angles. Equation (3) can be used to determine the slope, S, of the graph of applied mass against V 2. In geometric terms, the tangent of an angle returns the ratio of a right-triangle's opposite side over its adjacent side. The sum of the first terms of each row gives. Since this is a non-crossing loop traverse, the deflection angle sum should be ±360°00'00". Using graphical methods, find (a) the vector sum A % B and (b) the. Below that, electrostatic deflectors can be more powerful, above that, magnets. Menendez´ b and F. component of load in quadrature with deflection divided by deflection amplitude. So we get a straight line inclined at an angle, less than 45° to the positive X-axis. Bearing = 3200 - Az. Assuming appropriate graphical representations are used, experts can very quickly understand the composition of the system and develop an intuition about how it is likely to behave. Any two of the three edges of a corner of a cardboard box lie in a plane. In considering deflection, the same assumptions are taken as in the derivation of the bending formula. Between the radiators, between the respective beam of the deflection angle with the applied phase shift, a right-angled triangle can be drawn, whose shorter side lies on the beam. The instrument is then turned on its upper motion until the next station is bisected/ sighted and the interior angle is. The center point deflection can also be compared to analytic estimates [14, 17]. 0) for the four vertices. Delay-And-Sum Algorithm: DAS: Deflection angle; Deflection angle; Deflection angle;. Compute the reaction force in each bolt using the load-deformation relationship. Delay-And-Sum Algorithm listed as DAS. Once you apply load to your truss, the target angles change. ensure deflection not exceeding 2. Numerical values for this example: self-weight of the cable q = 8. The moments of inertia about the principal axes are expressed as. Figure 7-7 shows a traverse in which one of the deflection angles was turned to the lefft, all others to the right. Bonded interactions are based on a fixed list of atoms. Make estimates of the errors associated with each measurement. Free Angle (Θ) Degrees Torsion spring, angle between legs when not under load. Sum of Interior Angles Measure of Angle 1 Measure Angle 2 Deflection of Angle 1* Deflection of Angle 2* Triangle (3) *Tip for finding the deflection angle: You have the initial measurements of the target angles. Consider the right-hand deflection angles as. Method C • Set the scale at the deflection angle for an intermediate point being sighted (POC1): df1 • Backsight on the intermediate POC1 with the scope inverted. In the case of a non-convex polygon, exterior angles get a little weird. Calculate the vertical and horizontal forces due to the pressure only. [C#] //Constructs a point from the baseline from (0,0) to (1,1) //with the deflection angle of 45 degrees (PI/4 radians). amount of deflection and group efficiency is greater than sum of individual piles efficiency. In this picture, two observations are made on the same stationary target. Deflection is when a plane has many angles on it so the radar pulses will bounce of in directions other than the way they came from. blinking lamp circuit. Bearing = 3200 - Az. In other words, the shock position is the ``average'' of the Mach line positions on either. Curtain Jamb Guides and Wall Angles. MISSILE CONFIGURATIONS FOR ANGLES OF ATTACK TO 180 DEGREES Bernard F deflection total length of the body, feet The tot~l lift on the missile is the sum of the. khanacademy. Use this online angle subtraction calculator or DMS subtraction calculator to subtract the angles expressed in degrees, minutes and seconds. Their sum must also be less than PI radians. Allowable loads are for one angle. EXAMPLE 13. Question is ⇒ If deflection angles are measured in a closed traverse, the difference between the sum of the right-hand and that of the left hand angles should be equal to. Thus, altering the engine thrust angle will require different lift, drag and thrust forces. Deflection Limits (serviceability) • Various guidelines have been derived, based on usage, to determine maximum allowable deflection limits. Deflection heads are used within GypWall metal stud/ShaftWall partitions when needing to allow for movement (up, down or both) within the structure at the head of a partition. The bearing of BC is given as S50°E, which means angle S´BC measures 50°E. In photogrammetry, a vertical angle, measured in the vertical plane containing the flight line by which the datum of any model in a stereo-triangulated strip departs from the datum of the preceding model. Vertices: A place where two lines intersect. Unfortunately it's not quite working properly. unit moment at A acting in direction of M A. (n-2) * 180, where n is the number of angles 29. Based on the above definition, if either x or y is an axis of symmetry, then they both are considered as principal axes as I xy and hence θ p would be zero in that case. The scattering angle corresponding to this deflection is 0= 0 -2sN 21r(N + 1) - ) if 27rN ' e ' 2ir(N + 1/2) if 2wr(N + 1/2) < 0 ' 2ir(N + 1) (4) where N is an integer. 1 The direction of the magnetic force. Pressure angle can also be selected in dependence on pitch angle [4. 12 months ago. α = angular flexibility coefficient = measure of angular displacement per unit couple moment. In the graphics window, click to select the geometry to measure. Deflection angles to the right are positive; those to the left are negative. 21 Loss factor (tan δ) or loss tangent of the phase angle between the applied force and resultant displacement. Rate (R) N/mm Ratio of load [N] to deflection [mm]. This deflection represents 73% of the allowable live deflection limit, 0. the upwash ahead, and thus the local angles of attack along the span. ρ is the density gap of the dark matter. K-Factor (K) – The ratio of the position of the Neutral Axis to the Material Thickness. In an oblique projectile on horizontal ground thehorizontal range is four times the maximum height. -Converting bearings to deflection angles from given traverse data. Successive stations occupied and back sight is taken to the preceding station. All angles of a triangle always add up to 180 ̊C. N´BB´ plus S´BC plus the deflection angle between AB and BC (angle B´BC) is 180°. movement, the limiting angle of the joint is the sum of the two deflection angles permitted by the two connections. Delay-And-Sum Algorithm: DAS: Deflection angle; Deflection angle; Deflection angle;. e workpiececanbesimpli ed into cantilever plate, because the. Atmospheric loss increases exponentially with path length, l, and can be characterized by a two-way loss in dB per km, a A (Fig. Deflection of a cable under tension then the angle of the cable at the ends and where the child holds it id such that the vector sum of the child's lifting force. SUM reading (typically > 4. Single tooth mesh stiffness consists of three components as depicted in Figure 2: • Tooth deflection due to bending under load. Williams: I guessed that, but I never used the term before. TMI's sensors. Abbreviations, acronyms, buzzwords, and tech-speak exist in every industry. All findings were significant (P. Calculate the change between the initial target angle and the. $90^\circ + \angle APB + 90^\circ + \angle BOA = 360^\circ$ $\angle APB + \angle BOA = 180^\circ$ Hence, it can be observed that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the center. These forces might act with or against each other so the overall deflection and the angle in which it is deflected is the vector sum of the three components. We can obtain the following equations: U = W = Pd/2 U = W = M 0 q/2. Calibration factor, 𝐺 was calculated for two different deflection setups both identical with respect to geometrical design using the previously mentioned cantilever sets. 3 Total Deflection for Each Bone Template Figure 3 is the sum of the deflection of all sizes of the nail, 8-12mm. In using the Tables, first settle the size of web, then of the angles, and finally the size of flange plates. The sum of angles within a triangle always equals 180 degrees; therefore, calculating the two base angles provides the peak angle by subtracting the total from 180. In RV NIS Pos ΔTQ-ST became Neg. 52 is the refractive index and w = 30 arcmin is the wedge angle The final deflection is the vector sum of the two individual wedge deflections as in the figure. So if we sum the forces in the y direction for the above example, we get the following equation:. (c) Connecting the roof trusses. , 2008), ρ is the density of granular flow, v is the depth-averaged velocity, h is the flow thickness, g gravitational acceleration, α the slope angle and φ the dynamic internal friction angle. , Options are ⇒ (A) 0Â°, (B) 90Â°, (C) 180Â°, (D) 360Â°, (E) , Leave your comments or Download question paper. High angle of attack protection: when the angle of attack becomes higher than αprot, the system switches to a mode in which the angle of attack is proportional to sidestick deflection, up to αmax. 1 Boundary Conditions. Diagram below shows post collision trajectories in red. Angles 3,4,5,8 are interior angles Angles 1,2,6,7 are exterior angles Alternate interior angles: Pairs of interior angles on opposite sides of the transversal. Deflection by Gravity in. Time-Varying Model of Deflection and Dynamic Characteristics of Workpiece. Bearing Sum = Log dN Range. The module calculates the maximum total deflection as the sum of the deflection of the non-composite steel section resisting all of the loads that are specified as Pre & Post Composite (Always applied) plus the deflection of the composite section resisting all of the loads that are specified as Post Composite Only (Applied after curing). It is Delay-And-Sum Algorithm. This minimum force is referred to as "initial tension". The bearing of BC is given as S50°E, which means angle S´BC measures 50°E. A positively-charged particle beam entering into this field would by design be deflected 180 degrees, and at the same time a negatively-charged particle beam entering this field would by design be deflected 180. Maximal angle of deflection Therefore, sinθ max = pʹ M (M) v CM. Measure the critical angle, θ C , and calculate the index of refraction for water. BEAM DEFLECTION FORMULAS BEAM TYPE SLOPE AT ENDS DEFLECTION AT ANY SECTION IN TERMS OF x MAXIMUM AND CENTER DEFLECTION 6. -Converting bearings to deflection angles from given traverse data. Similar to elastic deformation, we have deformation due to torsion as well: twisting. The usual U. , Options are ⇒ (A) 0Â°, (B) 90Â°, (C) 180Â°, (D) 360Â°, (E) , Leave your comments or Download question paper. From these curves, the superelastic and thermal wires of the same size had similar behavioural characteristics (wide hysteresis curves). They use protractors to (accurately!) measure these angles and record them on the data collection sheet. Menendez´ b and F. Interior Angle Traverse Interior angle traverse is the one that is employed for closed loop traverse. Hence, deduce that the shock front subtends the same angle, , with the Mach lines upstream and downstream of it. Figure 13-2. Calibration factor, 𝐺 was calculated for two different deflection setups both identical with respect to geometrical design using the previously mentioned cantilever sets. the maximum deflection angle for 27" to 42" pipes. Deflection of Beams: Worked out Examples on Deflection of Beams: Web-PDF: 782 kb: Shear: Worked out Examples on Shear: Web-PDF: 257 kb. Deflection limits can be set for live load and total load. In other words, the shock position is the ``average'' of the Mach line positions on either. If so, the errors are usually 3% of the full scale value. Vector A has a magnitude of 8. Successive stations occupied and back sight is taken to the preceding station. b , and this region is of length ) x. Since the sum of the angles of a triangle is 180 degrees (pi radians) for any triangle, knowing the angles alpha and theta we can calculate the angle beta. $\endgroup$ – mins Nov 25 '17 at 9:55. f = allowable unit working stress in flexure, as in a simple beam with transverse loading only. It is the sum of contributions from the wing-body assembly, the HTP and the VTP. Therefore if the sum of any set of exterior angles exceeds 360 degrees, the sum of all the exterior angles must be even greater; but this can't be. The total load deflection limit is L/180 and L/480 for the roof and floor, respectively. deflection angles, is nearly perpendicular to the incident momentum p. The formula can be proved using mathematical induction and starting with a triangle for which the angle sum is 180°, then replacing one side with two sides. offset angle at y= 0 Approach to suppressing initial offset angle 16 EE C245 – ME C218 Fall 2003 Lecture 7 The Cantilever with a Concentrated Load Clamped: y= 0, dy/dx= 0 at x= 0 x x = L c Find the tip deflection y(x= L c) and applied load F … get effective spring constant k c F − M z (x)= The moment varies linearly with x 2 2 dx d y −M. The power spectrum was obtained when keeping the differential signal as close as possible to zero (centre of the PSD) and the sum signal as high as possible. sum of the included angle and 180? [D]. Triangle has three types based on its three angles, including obtuse (1 angle > 90 ̊C), right (1 angle = 90 ̊C) and acute (no angle > 90 ̊C). Because of ponding deflection caused by wet concrete, the use. 21 Loss factor (tan δ) or loss tangent of the phase angle between the applied force and resultant displacement. Tables will give allowable total uniform load (taking self weight into. The angle of twist due to a torque loading can be calculated using the following formula: Note:. It is worth pointing out how much easier it is to convey the intention of a model by presenting it in schematic form. (b) Traverse by Deflection Angles: The algebraic sum of the deflection angles should equal 360°. PROBLEM #4: Deflection of an Electron beam by an electric field. Further as batter angle increases from 20 º to 25 º pile capacity increases and decreases beyond 25 º Key words-Batter piles, Batter pile groups, Lateral loading, Batter angle, sand I. 1 more thing thats not covered in the above document - design deflection for floors. Sum of Interior Angles Measure of Angle 1 Measure Angle 2 Deflection of Angle 1* Deflection of Angle 2* Triangle (3) *Tip for finding the deflection angle: You have the initial measurements of the target angles. I know the rule that says that the sum of all external angles of all polygons = 360 degrees, but I don't understand how it can work on all polygons when some polygons can have an infinite number of right angles which would make the sum of all external angles much more than 360 degrees. Rate (R) N/mm Ratio of load [N] to deflection [mm]. Total Optical Depth • Optical depth measurement unbiased deflection angles. sum of angles = 900 degrees. Hence, deduce that the shock front subtends the same angle, , with the Mach lines upstream and downstream of it. This calculation can be seen below for Test A’s axial azimuth angle, with detailed angle. e = 175 m, w. Murphy, Smith & Schwadron ( 2002 ). This possibility has also been suggested by May and Bean (Ref. The cosine function is always between 0 and 1. We can obtain the following equations: U = W = Pd/2 U = W = M 0 q/2. Corrections to compensate for the effects of errors introduced by the factors of deflection ballistics are made by adjusting the horizontal angle between the L. , which is called sight. You can pretty easily achieve over 25mm of deflection just from a flexy seat tube, so that makes the total figure less surprising. And of course, as mentioned, a bulged segment requires a more complex definition, although we civils would probably compare the previous and subsequent segments (with the presumed but not necessarily correct assumption that the curve is tangent to both prior. array ([ld. In the case of small deflections, the beam shape can be described by a fourth-order linear differential equation. Tests have shown that 3 percent deflection will provide a safety factor of at least 2. in the field was 0. C 2 = a 2 + b 2 - 2 a b Cos (angle between adjacent vectors in solution triangle) The angle between the vectors in the solution triangle as shown below is equal to 180 degrees minus the angle between the cables. “Linkage Design” is a computer program used to speed and improve the setup of radio controlled airplane control systems. 3 = 65° 34′ 45″. Extension springs are usually manufactured in a manner that requires a certain amount of force be applied before any deflection is realized. (These two angles are labeled with the Greek letter "theta" accompanied by a subscript; read as "theta-i" for angle of incidence and "theta-r" for angle of reflection. Shear Force, Bending Moment and deflection Plotting tool Interior angles Find the sum of interior angles for polygon of x sides. When analyzing the same loading considering load superposition (sum of deflections corresponding to One-Truck One-Lane Loading in Pass 1 and Pass 7), the deflection computed under Panel. The Lesson: In the triangle shown below, the angles A and B are complementary because they have a sum of 90º. ensure deflection not exceeding 2. Turn the Laser Y-axis adjust knob back and forth for at least one turn in each direction and monitor the SUM reading. “Bank angle” is an oblique reference to the load factor necessary to maintain a level turn. All angles of a triangle always add up to 180 ̊C. The sum of d 1, d 2, and the deflections for the full chords is—. It takes, on average, about 30 minutes to roll one fender lip completely. For instance, in the case of a simply supported beam with rigid supports, at x = 0 and x = L, the deflection y = 0, and in locating the point of maximum deflection, we simply set the slope of the elastic curve y' to zero. 1 Kinematics of roller bearings Houpert (1997) derives a kinematic relation between the roller-raceway deformation. When the equations are written in the following form, they are said to be in State Space form: x Ax Bv yCxDv =+ =+ i. Taking up a method devised by Taylor and Wheeler and collecting pieces of their work we offer a self-contained derivation of the formulae giving both the precession of the orbit of a planet around the Sun and the deflection angle of a light pulse passing near the Sun in the framework of General Relativity. The local flow angles were measured at a tunnel dynamic pressure of 30 pounds per square foot over an [email protected] range of O" to 8O and with a flap deflection range of S5. Exterior angles are measured clockwise or counter-clockwise between two adjacent lines on the outside of a closed polygon figure Deflection angles, right or left, are measured from an extension of the preceding course and the ahead line. The modified area A′ is given by A= bh′ 5 6. The change is called the deflection angle. R1 x 8 = 800 x 2 + (200 x 4) (2 + 2) + 1000 x 6. The sum of the included angles in a closed traverse of ‘n’ sides = (2n-4)90° 4. TQ-ST at 60 s was obliterated when K+ = 8. A typical derivation process will be traced here as it will be used again in the development of the slope-deflection. (b) The dependence of deflection angle upon the applied power. This deflection represents 73% of the allowable live deflection limit, 0. Lot Deflection. Thus, the angle between the incident and the reflected rays is the sum of angle of incidence and angle of reflection, that is, 70 degrees (= 35 + 35 degrees). array ([ld. The angle of this vector is given and is shown in red. zero mark • If the above experiments are repeated by bringing the S-pole of the, S N v. training data set and test data set. The mean electrical axis represents the sum of all of the mean electrical vectors occurring during ventricular depolarization. The Lesson: In the triangle shown below, the angles A and B are complementary because they have a sum of 90º. Bending moment at a cross-section is the algebraic sum of tym moments of all the forces which are placed either side that point. Starting with an azimuth of 328°58'15" for line AB, determine azimuths of the remaining lines. Lee Spring Stock Torsion Springs are offered with legs of equal length oriented at varying unloaded angles. A typical derivation process will be traced here as it will be used again in the development of the slope-deflection. This principle is shown in Fig. 51 mm), located under Panel 4. g) there is no. The deflection magnetometer consists of a large compass box with a small magnetic needle pivoted at the center of a circular scale so that the needle is free to rotate in a horizontal plane. This possibility has also been suggested by May and Bean (Ref. A positively-charged particle beam entering into this field would by design be deflected 180 degrees, and at the same time a negatively-charged particle beam entering this field would by design be deflected 180. On the other hand, greater pressure angle reduces the number of engaged teeth, increases bearing load and the worm deflection load (greater worm deflection). 0 = -(angle at A due to applied load) + (angle at A due to support moment) first subscript: point where angle is specified second subscript: point where the unknown reaction acts. w = unit load. , 2008), ρ is the density of granular flow, v is the depth-averaged velocity, h is the flow thickness, g gravitational acceleration, α the slope angle and φ the dynamic internal friction angle. Since two congruent triangles will combine to form a square or other quadrilateral, the sum of the angles in one of the triangles is half of 360°, or 180°. -Point the laser at different angles until the beam reaches the critical angle and is completely reflected inside the container. Beyond the gage range (l. We can think of these as opposite angles formed by an X. In order to correct insertion angles at tissue boundaries, the researchers took the influence of boundaries between layered tissues into consideration, and designed an insertion angle shift distribution model based on experimental data. maximum angle of deflection A moving particle of mass M collides perfectly elastically with a stationary particle of In the lab frame the velocity of the incident particle is the sum of the velocity of the center-of-mass and that of the particle in the center-of-mass frame. For a bending beam, the angle \\(d\\theta\\) appears between two adjacent sections spaced at a distance \\(dx\\) (Figure Read more Beam Deflection. Point O is the tail of the vector and point A is the head. Consider the right-hand deflection angles as. Bend Deduction (BD) – The amount removed from the sum of the two flange lengths to obtain a flat pattern. The other angle = 180-g. * 'dy': A numpy array containing the deflection angle at each mm: of the beam. e milling processisshowninFigure. Beyond the gage range (l. PROBLEM #5: Deflection of an Electron beam and velocity Check Your Understanding. Repeat for next. (a) The sum of the measured interior angles should be equal to (2N – 4) x 90 0 where N is the number of sides of the traverse. TQ-ST at 60 s was obliterated when K+ = 8. The modified area A′ is given by A= bh′ 5 6. Point C is located similarly. Angle of twist. It seems it is the consequence of the flow separation. 34" Compute the deformation in the other bolts assuming that the deformations are proportional to the distance of the bolt from the IC. Write down one equilibrium equation for each unknown joint rotation. When the deflection angle is larger than its threshold value, the trivial solution branch with q 1 = q 2 = 0 becomes unstable in favour of the above threshold solution with q 1 ≠ 0 ≠ q 2 and. Using graphical methods, find (a) the vector sum A % B and (b) the. Repeat for next. 1 more thing thats not covered in the above document - design deflection for floors. The angles are the sections of a full 360-degree circle. 3 - 6) and 2° (Fig. 0 with regard to failure of the cement-mortar lining. Maximal angle of deflection Therefore, sinθ max = pʹ M (M) v CM. Plot the resulting irradiance distribution versus deflection angle for a single wavelength. What should be the sum of the interior angles for a closed-polygon traverse that has: (a) 6 sides (b) 7 sides (c) 10 sides. angle between the body surface and the longitudinal axis of the body Prandtl-Meyer flow deflection angle radian measure density cos"1 (1 - 2x/0 by definition radial meridian along body surface infinity o free stream conditions i flow quantities for the zero angle of attack condition a flow quantities related to the effect of angle of attack b base. Make estimates of the errors associated with each measurement. How to Convert Units of Angles. khanacademy. We want to know if is indeed 90 degrees. Second, although the wire segments engaged in the brackets do not contribute to lowering the stiffness of the entire arch, the horizontal part of the L- loops can. The particular solution. The power spectrum was obtained when keeping the differential signal as close as possible to zero (centre of the PSD) and the sum signal as high as possible. 0) for the four vertices. Single tooth mesh stiffness consists of three components as depicted in Figure 2: • Tooth deflection due to bending under load. If the tangent is determined and the coil field is known, the horizontal component of the earth field may be calculated. Once you apply load to your truss, the target angles change. The angles are the sections of a full 360-degree circle. More elegant way to find the sum of the exterior angles of a convex polygon Watch the next lesson: https://www. so the quantity in the square brackets is. The other angle = 180-g. Murphy, Smith & Schwadron ( 2002 ). 1 The direction of the magnetic force. In Figure 1, circle O has radii OA, OB, OC and OD If chords AB and CD are of equal length, it can be shown that Δ AOB ≅ Δ DOC. Vector is the velocity of the object ball after impact. For an impression of actual deflection it is interesting to look in the appropriate spreadsheets in "Left-Brain-Lutherie". Since the sum of the angles of a triangle is 180 degrees (pi radians) for any triangle, knowing the angles alpha and theta we can calculate the angle beta. The Graphs tab displays diagrams of individual calculated characteristics. the acceleration of gravity. geodesics) can be larger or smaller than 180 degrees. training data set and test data set. A pipe bends through an angle of 45o in the vertical plane. Each of the sextuplets is then compared with a measured set of 6 rates. It seems it is the consequence of the flow separation. In order to correct insertion angles at tissue boundaries, the researchers took the influence of boundaries between layered tissues into consideration, and designed an insertion angle shift distribution model based on experimental data. sum of angles = (n - 2) #xx# 180 sum of angles = (7 - 2) #xx# 180 sum of angles = 5 #xx# 180. When angles are installed on each side of the joist, the minimum joist thickness is 3". A Regional Contest may send a third contestant to the International Contest provided the first and second place winners are from the same High School and the third contestant is from a different High School than the top two finishers. During DE, we measured five axial line deflection angles: the angle at the start initiation of this phase, and the angles at 25, 50, 75 and 99% of the total duration time of DE, using iMovie '11 (Apple Inc. the sum of the modifications referred to the pinion roll angles is shown on the last graph. 21 Loss factor (tan δ) or loss tangent of the phase angle between the applied force and resultant displacement. shear (length) for ld in loads]), axis = 0. Figure D shows the deflected shape with both concentrated load and uniform pressure. Deflection Amplifier Subsystem listed as DAS. 50×10 −14 –1. zero mark • If the above experiments are repeated by bringing the S-pole of the, S N v. Thus, the angle between the incident and the reflected rays is the sum of angle of incidence and angle of reflection, that is, 70 degrees (= 35 + 35 degrees). How to Convert Units of Angles. δ is the reaction or deflection of beam F is force applied to the beam E the modulus of elasticity of material I is second moment of the inertia of the beam According to the experimental data collected, if the load applied is 6 N then the deflection in beam is about -11. The method uses the equivalent angle of attack concept which includes the effects of vorticity and geometric scaling. The sum of angle Figure 13-2. Beam Simply Supported at Ends – Concentrated load P at any point 22 1 ()Pb l b. For paths where a A remains constant, the total loss, L A, in dB is: L A(in dB) = a A l (4. Note: Deflection and misalignment totals are worse case scenarios where all loads act in the same direction and sum together. Gradient [14] change rate becomes larger, as distance from the sun smaller. (3) S=Slope A = cross sectional area of water stream( control volume) g= gravitational acceleration The actual slope of the graph can then be compared to the theoretical slope calculated. The optical scanning apparatus includes a deflecting unit that scans first and second (FaS) scanned surfaces in main scanning direction by deflecting FaS light fluxes incident on. , Options are ⇒ (A) 0Â°, (B) 90Â°, (C) 180Â°, (D) 360Â°, (E) , Leave your comments or Download question paper. This causes a lateral deflection of about 8. Total Roll Deflection in. The total potential energy Π of a deformed plate with initial deflection of the order of magnitude of the thickness and with additional bending deflection of the same order, is defined as Π=U −W (2. Deflection limits can be set for live load and total load. Since v CM =(Mv M +mv m) (M +m) = Mv M (M +m), and pʹ M M = p M M =v M −v CM = mv M (M +m), we. M HIGH BURST (MEAN POINT OF IMPACT) REGISTRATION. A36 steel for the connection angles and plates (F y = 36 ksi, F u = 58 ksi) and A992 or Grade 50 steel for the beams and columns (F y = 50 ksi, F u = 65 ksi), K series open web joists and roof decking. 18, where pressure p acting on the airfoil at a point where the flow deflection from the free stream is ε represents the sum of p t + p c + p α. Further as batter angle increases from 20 º to 25 º pile capacity increases and decreases beyond 25 º Key words-Batter piles, Batter pile groups, Lateral loading, Batter angle, sand I. The brakes can accept materials of up to 30 in. It seems it is the consequence of the flow separation. -----The sum of the angles of a triangle is 180 degrees. $90^\circ + \angle APB + 90^\circ + \angle BOA = 360^\circ$ $\angle APB + \angle BOA = 180^\circ$ Hence, it can be observed that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the center. Moreover, is the wave angle, and the deflection angle. A typical derivation process will be traced here as it will be used again in the development of the slope-deflection. Angle of twist. For each comparison the sum of the 6 simulated rates is normalized to equal the sum of the 6 measured rates; the normalization factor is then used to derive the solar wind density. – The superposition method can illustrated by various practical examples. 2 radians or 11°), the small angle approximation can be made (see ZSmall angle approximation [ rule of thumb), reducing the equation to: References:. 1 Boundary Conditions. I know the rule that says that the sum of all external angles of all polygons = 360 degrees, but I don't understand how it can work on all polygons when some polygons can have an infinite number of right angles which would make the sum of all external angles much more than 360 degrees. (These two angles are labeled with the Greek letter "theta" accompanied by a subscript; read as "theta-i" for angle of incidence and "theta-r" for angle of reflection. Traversing by direct observation of bearings: The force bearing of the last line should be equal to its back bearing ±180° measured from the initial station. Helical Springs. Since this is a non-crossing loop traverse, the deflection angle sum should be ±360°00'00". When voltage applied to the vertical deflection plates is more than that applied to the horizontal deflection plates, we will get a straight line inclined at an angle, more than 45° to positive X-axis. Geological Survey oilspill trajectory analysis model, the surface drift component is assumed to be 3. deflection to the right of the galvanometer shows a deflection right to the zero mark. Deflection angles! These angles are very helpful when staking out horizontal curves. Therefore, the size of the deflection angle is. Stall speeds are shown as a function of flap deflection and bank angle. Photothermal deflection in air: (a) the deflection angle θ as a function of the separation between the nanotube sheet plane and the laser beam (x) for P = 1. In the development of oil and gas resources, fluid injection is often applied to enhance recovery efficiency. For example, the the tangent of PI()/4 (45°) returns the ratio of 1.