How many capybaras does it take to move a Stonehenge rock?

[enigmaticbacon]

TL;DR Summary

Struggling with how to measure the resistant force of a 25 metric ton stone with the ground.

I’m writing a presentation for younger students explaining how science can help them satiate their curiosity in a fun way. This presentation’s goal is to apply as much science as possible to a ridiculous question in hopes of promoting STEM fields. My example is, how many capybaras --the world’s largest rodent-- would it have taken to push a sarsen rock (25 metric tons) to the site of Stonehenge. Where I'm struggling is how to measure the resistant force of a sarsen stone with the ground. If the surface were rigid, I could just calculate the normal force and multiply it by a friction coefficient. But how would I know if the rock would break through the surface of the ground? If it did break through, how would I go about measuring friction at that point? Would it be a function of dirt displaced?

 

[Baluncore]

Where I'm struggling is how to measure the resistant force of a sarsen stone with the ground.

Ground traction or drag depends on the soil conditions and shear of the soil. A tractor tire has a large contact patch, so a large shear surface area is available to handle greater tractive forces. Each capybara would need to get it's spread-out claws into the soil, to provide the area of ground contact needed for traction.

It is sometimes impossible to push a rock across a soil, the rock must be pulled. That is because the pull force will have an upward component, lifting the rock, while at the same time increasing tractor downforce and so traction. A pushed rock sinks into the soil, as the rock sinks, the push force becomes more vertical and buries the rock deeper, reducing traction to zero, as it lifts the tractor off the ground.

To move a 25 tonne sarcen, two tree trunks, would be laid down as rails ahead of the rock. The rock would be moved on three or more tree trunks, used as rollers, running across those rails, over the soil.

 

[enigmaticbacon]

Ahhh so to see how much stress soil could carry without breaking, I would use the soil's shear strength? Would that also apply were the rock to be pulled?

 

[Frabjous]

I went a googling. This paper has some interesting ideas.
https://pure.uva.nl/ws/files/54547741/Liefferink2020_Article_SlidingOnWetSand.pdf

 

[enigmaticbacon]

Thanks!

 

[Lnewqban]

Dead weight can't do much.
Concrete and steel piles are driven down by huge hammers that create vibration to help.

Please, see:
https://pilebuck.com/engineering/dynamic-formulae-pile-driving/

https://onlinepubs.trb.org/Onlinepubs/hrr/1970/333/333-004.pdf

 

[anorlunda]

TL;DR Summary: Struggling with how to measure the resistant force of a 25 metric ton stone with the ground.

I’m writing a presentation for younger students explaining how science can help them satiate their curiosity in a fun way.

You have chosen a particularly difficult example that brings in physiology and numerous complications and caveats. So many complications that fatigue sets in before you get to the basic physics. Are you sure this is a wise choice?

 

[Baluncore]

Would that also apply were the rock to be pulled?

Push or pull only differ when the connection is not horizontal. If there is a vertical component to the connection, either the capybaras, or the rock will have an upward component. The rock must be lifted if it is to move, as then the capybaras will push down, which will increase their traction.

 

[jrmichler]

Ground traction or drag depends on the soil conditions and shear of the soil.

If this is your limiter, then the calculation is simple. The rock has a contact area. The capybaras feet have contact area. Divide rock contact area by capybara feet contact area, and the result is the number of capybara needed. Multiply by a factor of at least 1.1, then round up to nearest integer. Keep in mind that capybara have four feet, and can pull in spurts with all four or by walking (steady motion) with two at a time.

Need an emoticon for "only slightly tongue in cheek".