Hardhat testing with steel ball dropped from a height

[dtwitty]

Hardhats are tested by dropping a 3.63 kg steel ball (free fall) from a height of 1.52 m and allowing it to impact the top of the hardhat. Hardhats are impacted with an impact velocity of 5.5 mps. The hardhats are supported at four locations where they are connected to a circular band that tightens around a head form (i.e., I assume that the load is transferred to a head form by equally dividing it at 4 locations.) 30 hardhats are tested to determine if a particular batch passes.

If any load transferred to a head form exceeds 4450 N. maximum transmitted peak force, the test fails.

using equations of motion, x = x' + v't + 1/2 αt^2, t is determined.
t=(2*1.52/9.81)^0.5 = 0.56 sec

impulse-momentum can be used to determine max F (in theory).
F = m(v - - v)/Δt = 3.63(5.5 + 5.5)/0.55 = 71.3 N (assuming completely elastic behavior)

Either I'm missing something, or the tolerances on hardhat manufacturing are pretty crude. Any ideas?

 

[AlephZero]

Your 0.56 seconds is the time the ball is falling through the air.

The relevant time for your impulse-momentum calculation is the duration of the impact. There is no easy way to calculate that, but it will be very much smaller than 0.5 sec.

Anyway, the test is not about the force the ball applies to the hat, it is about the force the hat applies to the head. That will be reduced by the amount of energy absorbed by deforming the material of the hat, etc.

 

[dtwitty]

Its obvious once someone points it out, thx.