I have a 1.2kg dart that is dropped from a height of 50m and penetrates into the ground to a depth of 0.09m. I can calculate (with wind resistance), the velocity, the kinetic energy at impact, the momentum at impact. Using the 0.09m penetration depth, I can also calculate the amount of work done (after impact), the impact force, the rate of deceleration and the time required to decelerate.

I am designing a tool to simulate these results which looks a lot like a mechanical fence post driver with a mast and a falling weight (with an appendage that looks like the dart). So, for a given mass and height, I can calculate (with wind resistance), the velocity, the kinetic energy at impact, and the momentum at impact. My problem is that I don’t know which of these values I should be setting equal (if any) to get the same results from the tool as I do from the dart.

Can I assume the same depth of penetration as observed with the dart? If so, I can then calculate the required combination of mass and height to get the same work and impact force from the tool. Will this then give me the same depth of penetration?

Here are some values from my calculations:

Dart

Mass: 1.2kg

Initial height: 50m

Drag factor: 1.3

Time of free-fall: 3.3897 seconds

Final Veloclty: 27.8029 m/s

Final Momentum: 33.3635 kg*m/s

Work: 463.80 Joule

Impact Force: 553.33 kg*m/s^2

Tool

Mass: 40kg

Initial height: 1.203m

Drag factor: 2

Time of free-fall: 0.4975 seconds

Final Veloclty: 4.8156 m/s

Final Momentum: 192.6239 kg*m/s

Work*: 463.80 Joule

Impact Force*: 553.33 kg*m/s^2

NOTE* Using an assumed depth of penetration of 0.09m.

In this example, the work done and the impact force have been made equal. Does this mean that I will get the same depth of penetration?

Thanks.