This calculator will determine the shock response to a dropped 3D box with a spring and viscous damper at each corner. The box can be dropped from a specified height and angled about the x and z axes resulting in a corner drop.

The input parameters are: weight (Wt), box width in the x-direction (W), box depth in the z direction (D), box height in the y-direction (H), corner spring-rate and viscous damping (k and c), gravitational constant (G), drop height (h), tilt angle θ with right-hand rotation about the x-axis, tilt angle Φ with right-hand rotation about the z-axis, and initial velocity (V_o). All dimensional units must be consistent. Tilt angles are in degrees. The drop height is from the bottom of the box at the mid-point of the bottom surface to the ground plane.

The acceleration and displacement are charted for each corner and the box CG versus time.

A limited number of time steps are used in the solution. For large drop heights, low damping and stiff springs the drop response will be multiple low damped bounces. For smaller drop heights, moderate to high damping (>10%) and soft springs (f_n < 10-20 Hz) the drop response will be one to a few rebounds and will likely stop at the static deflection of W/k.

During free-fall the acceleration will be 0.0. The maximum acceleration would normally occur during the first drop 1/2 cycle which corresponds to the maximum spring damper displacement.

The animation shown is for a box of 50 lbs. with a drop height of 10 inches, θ and Φ tilt angles of 10 and 15 degrees and corner springs of 50 lbs/in.