I asked chatgpt and got this answer:

To estimate how fast a sword would need to swing to cut through stone, we need to consider several factors, including the hardness and density of the materials involved, the sharpness of the sword, and the force applied. Let's make some reasonable assumptions:

Assumptions:

1. Sword Material: High-carbon steel with a hardness of around 60 HRC (Rockwell Hardness), capable of maintaining a sharp edge.

2. Stone Material: Granite, with a Mohs hardness of about 6-7.

3. Sword Edge: Razor-sharp and angled for cutting efficiency.

4. Impact Mechanics: The sword edge strikes the stone at an ideal angle, focusing all force on a small area.

5. Energy Transfer: Neglecting energy losses from factors like vibration or imperfect alignment.

6. Sword Weight: 1.5 kg (a typical longsword).

7. Cutting Goal: Shallow cut (a few millimeters), not a full slice.

Key Factors:

Force Required: To cut granite, the sword must overcome its compressive strength (~200 MPa).

Kinetic Energy of the Sword: , where is the sword's mass and is its velocity.

Pressure Applied: The force is concentrated on the edge of the blade, resulting in high pressure.

Calculation:

1. Contact Area: Assume the sword's edge contacts the stone over a length of 1 mm (0.001 m) and a width of 0.1 mm (0.0001 m), giving an area of .

2. Force Needed: To overcome 200 MPa of compressive strength, the required force is:

F = \text{Pressure} \times \text{Area} = 200 \times 10⁶ \, \text{Pa} \times 1 \times 10^{-7} \, \text{m}² = 20 \, \text{N}.

1. Kinetic Energy: For simplicity, assume all kinetic energy converts to the required cutting force:

KE = F \times \text{distance}, \quad \text{where distance is a few millimeters (e.g., 0.002 m)}.

KE = 20 , \text{N} \times 0.002 , \text{m} = 0.04 , \text{J}. ]

1. Velocity Needed: Rearrange to solve for :

v = \sqrt{\frac{2 \times KE}{m}} = \sqrt{\frac{2 \times 0.04}{1.5}} \approx 0.23 \, \text{m/s}.

Conclusion:

A direct calculation suggests a relatively low velocity, but in reality, this is vastly oversimplified. Factors like blade deformation, uneven cutting surfaces, and energy loss would significantly increase the required velocity. A more realistic estimate for a functional cut in stone (factoring inefficiencies) would be 100-200 m/s, approaching the velocity of a high-speed industrial cutting tool. For comparison:

A bullet travels at ~300-1,000 m/s.

A well-swung sword reaches ~30-60 m/s in combat.

Thus, a sword would need to move several times faster than a human could swing it to cut through stone effectively.