Chapter 1: The Hovering Helicopter

A curious reader from our Ukrainian channel recently posed an intriguing question: What would occur if a helicopter remains airborne for a full 12 hours?

To analyze this scenario, let's assume the pilot elevates the helicopter to an altitude of 1,000 meters and maintains that height without any maneuvers. Additionally, we’ll consider that the helicopter has sufficient fuel for the entire 12-hour duration. For simplification, we'll disregard factors like wind and other weather conditions.

So, what can we expect? Will the helicopter remain directly over the same point on Earth's surface, or will that location shift due to the planet's rotation?

It's essential to note that the atmosphere also rotates along with the Earth. If this weren’t the case, we would experience relentless hurricane-like winds. Near the surface, the air's velocity relative to the Earth's center matches the ground speed. As altitude increases, the airspeed also rises, ensuring that the angular velocity of the upper air layers aligns closely with the lower layers. The mechanics behind this phenomenon are complex, largely stemming from air viscosity and a lack of slippage.

Upon takeoff, the helicopter will share the same horizontal velocity with the ground point below. As it ascends, it will encounter air layers moving faster than itself, causing a minor drift in the opposite direction of Earth's rotation. The degree of this drift is influenced by several factors, mainly the helicopter's weight, geographic latitude, and ascent rate. Typically, this drift would only be a few meters.

Once the helicopter reaches its desired altitude and stabilizes, its horizontal speed will equilibrate with the surrounding air, effectively eliminating any drift. This is akin to how an insect remains stationary within a moving vehicle.

Over the span of 12 hours, the helicopter will hover nearly in place. However, it will experience a slight horizontal Coriolis force, resulting in a minor drift toward the equator. Conversely, this effect would not manifest at the equator itself.

Interestingly, during its descent, the helicopter will slightly advance in the direction of Earth's rotation, as it will transition into air layers with reduced horizontal speed. Without precise calculations, it's challenging to determine the exact compensation for the drift experienced during ascent.

In regions similar to our Ukrainian latitude (between 46-51 degrees), after 12 hours in the air, the helicopter is likely to land no further than 50 meters from its original takeoff point. It's crucial to note that the spot from which it ascended will not "move away" beneath it due to the Earth's rotation. The helicopter will remain airborne while the surrounding air, rotating in sync with the Earth below, will also follow suit.

This video titled "Matt has one hour to hover a helicopter" explores the challenges and dynamics of helicopter flight.

In "If I hang in the sky, will the Earth spin beneath me?" we delve into the fascinating question of hovering in relation to Earth’s rotation.

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