Reproducing the Velador Experiment

Selection of the support beam material and configuration is dependent on the expected self-weight deflection of the beam, thermal properties of the beam material, and the cost and workability of the beam material. 

Cost of less than $100 is preferred.  The beam should be of approximately 10ft (3m) length, light enough for a single person to lift, and be constructed of materials which can be worked to the necessary tolerances using only hand tools.  The bulk of the beam should be a single material with as uniform a cross-section as possible.

Maximum deflection of a beam under its own weight (self-weight deflection) is computed using Equations 1 and 2. 

The variables are:

δ = Deflection

θ = Angle of Deflection

W = Total Weight of Beam (Expressed as Force)

L = Length of Beam

E = Modulus of Elasticity of Beam

I = I_x = Second Moment of Inertia about x-Axis

b = Beam Width

h = Beam Height

d = Beam Diameter

For symmetric hollow beams, second moment of inertia is computed as I = I₁ – I₂.

Table 1 - Computed Beam Dimensions:

Note: Wood beam actual dimensions are as listed under each parameter, and will not equal the nominal dimensions given in the description of beam dimensions.

Table 2a - Expected Self Weight Deflections (Vertical Displacement)

All computed displacements given are in the direction of gravitational acceleration (vertical), and assumed constant.  Self-weight deflection (lateral or vertical) is initially assumed not to vary significantly with azimuthal rotation.

The predicted maximum laser beam deflection according to Osadchey’s original experiment is approximately 61μm over 180 degrees azimuthal rotation.  The maximum angle of deflection observed is 2” (two seconds of arc).  This is significantly smaller than the expected static deflections.  However, those deflections should (optimally) be roughly constant and may be compensated by adjusting the instrumentation accordingly at operating deflection.  For this reason, the angle of deflection at each end (where the instrumentation is located) is as important to calibration as displacement relative to the beam center.

Table 2b – Expected Self-weight Deflections (End Elevation)

These values of end angle deflection under the beam’s own weight are all significantly greater than the expected effect.  However, PVC is the only beam material for which the laser beam deflection will be greater than 2mm with a support beam dimension of 15 cm (6 inches) or more.  This allows the laser position to be pre-calibrated when the beam is not under load without the beam drifting completely out of the camera’s field of view as the load is applied.  Deflection of less than 2mm under the applied load allows the camera to be calibrated off of the mount and then be installed and put under load without losing the beam’s position.  Note that both end deflections are not accounted for simultaneously.  Only the camera has to move for calibration after the laser is installed.