What is Deflection: Definition and 525 Discussions

The vertical deflection (VD) or deflection of the vertical (DoV), also known as deflection of the plumb line and astro-geodetic deflection, is a measure of how far the gravity direction at a given point of interest is rotated by local mass anomalies such as nearby mountains. They are widely used in geodesy, for surveying networks and for geophysical purposes.
The vertical deflection are the angular components between the true zenith-nadir curve (plumb line) tangent line and the normal vector to the surface of the reference ellipsoid (chosen to approximate the Earth's sea-level surface). VDs are caused by mountains and by underground geological irregularities and can amount to angles of 10″ in flat areas or 20–50″ in mountainous terrain).The deflection of the vertical has a north-south component ξ (xi) and an east-west component η (eta). The value of ξ is the difference between the astronomic latitude and the geodetic latitude (taking north latitudes to be positive and south latitudes to be negative); the latter is usually calculated by geodetic network coordinates. The value of η is the product of cosine of latitude and the difference between the astronomic longitude and the longitude (taking east longitudes to be positive and west longitudes to be negative). When a new mapping datum replaces the old, with new geodetic latitudes and longitudes on a new ellipsoid, the calculated vertical deflections will change, too.

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1. Deflection of partially loaded cantilever beam with non-homogeneous EI

TL;DR Summary: I have a cantilever beam with fixed end, known rectangular cross section and total length h. A uniform load is applied on the beam from a distance L from the fixed end, to the free end. The E modulus and inertia I are known, and they are two different constant values for 0<x<L...
2. I How Does Inverse Bremsstralung Affect Photon Absorption?

There are lots of diagrams showing bremsstralung as a deflection of an electron by a nucleus but none of inverse bremsstralung. Does the inverse process I.e. photon absorption only depend on the direction of the deflection by the nucleus? If not ,what determines wether the electron will absorb...
3. Simply supported beam with a spring support in the middle - deflection

Hi, I'd like to calculate the maximum deflection of a simply supported beam with spring support in the middle and UDL (uniformly distributed load) acting on the whole beam: Here's my derivation, starting from the known formula for maximum deflection of a simply supported beam with UDL and no...
4. Beam deflection and curvature radius formula doubts

Hi, I am working with leaf springs and studying the derivation of the formula for the deflection of such a structure. The derivation is shown here: My only doubt is how to obtain the following formula: $$\delta=\frac{L^{2}}{8R}$$ where: ##\delta## - deflection, ##L## - length of the beam...
5. Maximum bending moment and maximum deflection of the spring?

How can I find the maximum bending moment and maximum deflection for a spring? It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner. that's all, thank you very much.
6. I How to make the deflection equation at any point along a snow ski profile?

I am trying to figure out how to do a deflection profile for a snow ski profile at 50 mm increaments along the ski. Since the ski has different widths and heights at each crossection, the EI changes at each location making it a lot of 2nd order derivatives if I am not mistaken. I am assuming...
7. Calculate deflection of rod/axlepipe due to distributed load

Summary:: Calculate the deformation on a rod/axle/pipe due to a distributed load. I’m manually trying to calculate the deformation on a rod/axle/pipe due to a distributed load. The rod has an outer diameter of 62mm and an inner diameter of 50, is 170mm long, made from a material with an...
8. Maximum Deflection Angle In Elastic Collision

I started by writing the equation v1i + v1f = 2v and then drawing a triangle with v1i, v1f, and 2v as the three sides. Then I used the Law of Cosines to solve for cos theta but this did not lead to a solution. Could I have a hint on how to begin? Thank you!
9. How to take a moment into account for deflection of a beam

Hello! I have to calculate the deflection of a beam at at given point (C). The books says the should be a moment which plays a role in this deflection. How does this moment occur? I have drawn a FBD but couldn't find a moment? Should I divided the beam into separate parts or so? What am I...
10. Lessons with electron beam deflection tube and teltron tube

Hello, I would like to discuss with my students the deflection of electrons in electric and magnetic fields. For this purpose, I would like to perform the experiments with electron beam deflection tubes and teltron tubes. How would you implement this organizationally in the classroom? There are...
11. A How is phase velocity related to deflection angle?

Refractive index is a function of velocity in the medium. How is this related to deviation angle inside the medium? I am not asking for the known formula, but for the mechanism behind it.
12. Leaf Spring Deflection: Calculating Force & Displacement

Hi, I'm trying to calculate the deflection of a leaf spring. I've found several formulas but the one I'm currently using looks like this: $$f=k \frac{F L^{3}}{6EI}$$ where: ##k## - coefficient depending on the way leaves change their shape in the width direction (in my case it's ##1## because...
13. DART mission launches to test asteroid deflection

Um, why are we spending \$330M on a mission to (re-)prove that conservation of momentum works in space? What am I missing? https://www.cnbc.com/2021/11/23/spacex-launching-nasa-dart- spacecraft -to-crash-into-an-asteroid.html SpaceX is launching a NASA spacecraft that will crash into an asteroid
14. Spring deflection problem using energy equations

At the equilibrium position all forces are equal to 0 (they balance). So, naturally we: mg - kd = 0 d = mg/k d = 0.356 m This is the correct answer, I believe. But I want to solve it using the energy equations because I am really trying to understand energy's connection to the rest of...
15. I Maximum Angle of Deflection for Colliding Particles

When a heavier mass (or nucleus say) collides with a lighter one, it deflects through a certain angle which has a theoretical maximum. There are numerous derivations for this maximum angle of deflection ##(\sin\theta_{d_{max}}=m/M)## where m is the small mass and M the larger but none seem to...
16. Trace on the screen of a C.R.O. when a deflection coil is rotated

My answer is when the small coil is rotated, there will be change in magnetic flux in it. Initially (before rotated), the trace in c.r.o will be sinusoidal. After it is rotated, the trace will still be a sinusoidal (but I am not sure whether the amplitude will be the same). But the answer key...
17. I Base Motion and Vertical Beam - Basic Reaction Forces?

So I am trying to understand how to estimate the amount of deflection [D] the vertical beam shown above would experience if the base it is attached to is accelerating at a constant acceleration [a] of 9.81 m/s. I assume the Force [F] would be equal to weight of the vertical beam (mass x...
18. A Some questions about the derivation steps in the Gravitational deflection of light section in Schutz

In the screenshots below there are the equations (11.49) and (11.53). I don't understand how did he derive equation (11.53) from Eq.(11.49)? From (11.49) I get: ##d\phi/dy= d\phi/du du/dy = (1/b^2-u^2+2Mu^3)^{-1/2}(1+2My)##. It seems he neglected the ##2Mu^3## since ##Mu\ll 1##, so ##y\approx...
19. Ultra high energy cosmic ray deflection angle causes by magnetic field

I'm given an ultra-high energy cosmic ray with energy 10^20 eV. It is coming from a source 10 Mpc away with an extragalactic magnetic field with strength B = 10^-9 G. I am to determine the maximum angular deflection of this cosmic ray, so it hits Earth. I don't have an attempt of the solution...
20. Deflection of light passing the Sun

The book says the actual measured deflection from some experiments is about ##9\times 10^{-6}## radians, and this is double the value that a naive computation returns because of general relativity effects. So I guess my goal is to compute a number that looks like half that. If suggests to do it...
21. I Light Deflection Formula: Impact Parameter & Angle Shift

I know the basics of GR, but I'm far from an expert. I'm interested in the general formula for the angle shift experienced by a light ray in presence of a gravitational field. Light bending is topic covered in many books, of course, however the usual treatments would just not do for my purposes...
22. A500 steel tubing beam deflection

Hello, I'm looking to construct a simple rectangular 13'x17' hollow steel frame over my patio, but I'm getting conflicting beam deflection calculations. I need to determine my beam size for my long spans of 17'. My plan was to use 3.5"OD A500 structural steel. 11 gauge (.120 in) wall...

24. Engineering Determine deflection and deflection angle using Unit Load Method

relevant equations: My questions: (1)Not sure whether I did correct especially for the deflection angle (2)The limit taken for calculating defection Yc , I didn't understand why is from 0 to L/2 instead of the sum of 0 to L/2 and 0 to L, how is the limit determined? Kindly advise, thanks
25. Exploring Electron Gun Deflection: Causes and Resources for Understanding

Hi, I was wondering if anybody knows why the plate in an electron gun is tilted with respect to the electron path? Or has any resources that I could read to better understand? Thanks.
26. Engineering How to Find the First Buckling Load from the Deflection Equation?

Hi, I was working through a problem about calculating buckling loads. The problem had the following geometry (I apologise for the poor drawing skills): and the total length is ## L ##. The boundary conditions are therefore: 1. ## y(0) = 0 ## 2. ## y(L) = 0 ## My approach: After taking a cut...
27. I How do I determine I for a truncated cone in the bending of a Stylus Shaft?

So I have a Stylus as shown in above fig. Fixed at Point A, Force (F) is applied perpendicular to the stylus axis. How do we find deflection at the end of the Stylus (Made of Two Different Materials as shown in the figure)? Hand Calculations are much appreciated. Thank you.
28. Deflection of magnetic dipoles by a magnetic field

I'm reading about the Stern–Gerlach experiment and the only part that confuses me is how a magnetic field would deflect particles with magnetic dipoles instead of just rotating them. In this case the magnetic field is non-uniform, but it still seems intuitively strange to me since magnetic...
29. Deflection of a Magnet in an Inhomogenous Magnetic Field

Say I've got a magnet flying through empty space in a homogenous magnetic field. The magnet precesses and flies in a straight path. Now make that magnetic field inhomogenous. The magnet precesses and flies in a curved path. What I can't figure out is why the path is curved. It is because...
30. Deflection of a cantilever beam with applied tension at the free end

Not much to add since the question is fairly simple, but again I'm wondering if applying tension at the free end of a cantilever beam affects the deflection it would have if only itself weight is considered. Intuitively, tension should tend to straighten the beam, and if it does, how to...
31. Cantilever beam deflection with point mass and point load at the end

Hi all, I was looking for help with obtaining deflection at end of a cantilever beam with point load at end as well as point mass at the same location. I believe it would be exactly same. Is this correct? That is, I think just adding point mass at the cantilever's end wouldn't change the...
32. Understanding the deflection of a cable under tension with a force applied in the middle

With the above in mind, I have a cable of E=60GPa, cross sectional area 7e-4m^2. I want to understand the relationship between the tension applied resisting the deflection of the cable when a force is applied so that the cable will not deflect more than 0.7m in this case. Take the force as...
33. Deflection distance for an electron beam in an electric field

Have tried doing this question but I'm a bit confused on where I'm going wrong This is what I have done but get a value that doesn't match to any of the options given above? Any help would be really appreciated, Thanks!
34. New full scale deflection of an ammeter

Question: My attempt: Does 4.75 amps for the full scale deflection seem okay? Thanks for any help!
35. Stargazing Is a star's size changed due to gravitational deflection (lensing)?

Using the Sun as example, we know from the Eddington experiment that the Sun deflects light. Does light from other stars get deflected towards or away from the centre of mass, or is it a mix? Does light coming from the Sun get deflected towards or away from the centre of mass? Would this make an...
36. I How Does Elastic Collision Angle Relate to Mass Ratios?

Large mass (M) - moving - collides elastically with stationary small mass (m) as per crude diagram below. Angle θ is formed between the initial path of the large mass and the line of centres during collision. I would like to say that maximum deflection of the large mass occurs when cos(θ)=m/M so...
37. Surface speed of a strip over a deflection roll

Hello, I am trying to solve a problem at work that at first I thought was easy but has proven trickier than I originally thought: If I have a strip of material traveling in a straight line and it is tangent to a roll turning below it, the roll would need to turn at the surface speed of the...
38. A Measuring Deflection of Star Light During Eclipse: Separating Space-Time Effects

There is the famous experiment of measuring the "movement" of a star close to the sun during an eclipse. The stars position is determined before the disc of the sun moves just under it and than the position is again measured when the sun moves just "under" the star. The star will have appeared...
39. Engineering Torsion and deflection of a rectangular beam

Hello I would like some feedback about a problem. The idea is to calculate how much the angled bit of this beam moves things to account for are deflection and torsion. Did i miss anything? Underlined with red are the displacements in millimeters. In the picture the dotted line is the axis that...
40. 6061 Aluminum Angle Deflection

Hello Everyone, I'm a retired systems engineer from the aerospace industry, while working part of my job was to come up with concepts and then have great mechanical engineers implement them. Now that I'm retired I have to do both parts for myself. I'm designing a storage hoist to get heavy...
41. I really , please -- Deflection of a diving board

Here my problem: A diving board has a vertical depression of 6 inches when a 100-pound man stands 8 feet from the fulcrum. Determine the weight of a man who causes the same diving board to deflect 4 inches vertically when he stands 6 feet from the fulcrum. Show your reasoning and complete solution.
42. I E- & Ions Deflection by Earth's Magnetic Field

Do solar wind electrons turn left and positively charged ions turn right if they are interacting weakly due to long distance with Earth's magnetic field and fail to complete a loop for the electrons that are on the left of Earth and ions on the right? I assume electrons on the right and ions on...
43. Deflection of Fixed Rotated Beam

W14 x 30: d = 13.84" = 0.352 m w = 6.730" = 0.171 m tw = 0.270 = 0.00686 m tf = 0.385 = 0.00978 m 40' = 12.192 m 18" = 0.4572 m ρ = 997 kg/m3 E = 1.4*109 Calculate Weight of water: V = A*L = π*(0.4572)2/4 *12.192 = 2.0016m3 W = m*g = ρ*V*g = 997*2.0016*9.81 = 19.576kN uniformally distributed...
44. Calculate the reduction in the deflection at the free end

I can solve the deflection if only cantilever beam by deflection formula, but i have no idea for this question if calculated with a cable support arrangement.
45. Why Is the Force for T1 Doubled in the Torsional Deflection Problem?

I am confused as to why the force for T1 in the attached problem is doubled. T1 = 4000 in-lb
46. Castigliano's method for the deflection of a cantilevered beam

Hi, it may look like a homework but believe me that it's not. Castigliano's method was omitted when I was attending mechanics of materials course at my university and now I'm catching up. Another reason why I want to solve this is that I'm just curious what's the formula for the deflection of...
47. Deflection of Prismatic Beam With Fixed Ends and Single Load

I've been refreshing my mind with regards to solving statically indeterminate beam deflection problems. In an effort to achieve confidence over my solutions, I attempted to recreate the standard equations in Figure 1. In my problem, I changed it so that: a = b = L/2 Ay = R1 By = R2 etc...
48. I General Relativity and light deflection

I am a student of physics at a local Junior College in Mendham NJ and am planning on transferring to a 4 year program at the University of Alabama in a year. Iam having a bit of a difficult time understanding general relativity. Why does a photon bend twice as much under a gravitational field...
49. Calculate the sag (deflection) of a membrane

Homework Statement Not sure if this is the appropriate place to ask this question, but I didn't know where else to ask. Anyway. Let's assume that I have a film (or membrane) material that is stretched over some boundary, (lets assume a thin hollow cylinder). Then some constant force is...
50. Maximum Deflection in Columns: Fixed & Free End

How can I find maximum deflection in a column with one end fixed and other free?