That said, let's dive into the physics behind why a ball bearing might benefit from being quenched at different temperatures.

When heated to 1000K for a long period, it loses heat slowly due to convection and radiation. However, if you quench it immediately after heating, the temperature drop is much faster because of conduction alone.

A 10-Year Backtest Reveals...

The physics problem of how a ball bearing quenched at different temperatures behaves can be simplified using ordinary differential equations (ODEs). We can model this situation as two coupled ODEs: one for the cooling due to radiation and another for the convection of heat away from the surface.

Why Most Investors Miss This Pattern

In reality, most investors would miss this pattern if they didn't have a deep understanding of the underlying physics. They might focus solely on short-term market fluctuations or assume that the ball bearing is simply losing heat due to radiation alone.

A 10-Year Backtest Reveals...

However, by considering both convection and radiation, we can see that there's more to it than just slow cooling from radiation. This phenomenon demonstrates the importance of understanding the interplay between different heat transfer mechanisms in various situations.

What the Data Actually Shows

Studies have shown that the rate at which a ball bearing loses heat due to radiation is proportional to its surface area, temperature difference, and emissivity. Conversely, the convective cooling coefficient increases with the temperature difference.

Three Scenarios to Consider

When considering scenarios like these, one might think of using a more complex model or incorporating additional factors. However, in this case, we can simplify things by assuming that the ball bearing is a lumped mass system and neglecting any non-lumped effects.

What the Data Actually Shows

By neglecting convection, we lose an important detail: the heat loss due to radiation. This simplification allows us to focus on the effect of temperature difference and emissivity on the cooling rate.

Three Scenarios to Consider

As a result, three scenarios come into play:

Quenching at 300K for a long period Quenching immediately after heating Quenching in between two different temperatures