What is the Coriolis effect?
The inertial force resulting from the rotational movement of the Earth, which rotates around its own axis from the west to the east, causes the Coriolis effect. As a result, every moving object will be subject to this rotation and thus change the direction of its movement:
- In the northern hemisphere, the direction of a moving body deflects to the right; but
- In the southern hemisphere, the direction of a moving body deflects to the left.
Coriolis effect definition
We can easily estimate the Coriolis force with the Coriolis effect definition below:
F = 2 × m × v × ω × sin(α)
where:
- F — Coriolis force;
- m — Mass of the moving object;
- v — Velocity of the moving object;
- ω — Angular velocity of the Earth; and
- α — Latitude at which the object is located.
Associated Coriolis acceleration equals:
a = F / m = 2 × v × ω × sin(α)
In our Coriolis effect calculator, we assumed that the rotating body is the Earth with angular velocity ω = 2π/24h ≈ 0.0000727 1/s (2π means 360° in radians). Change it if you want to consider some other body.
You can see from the above equation that the magnitude of Coriolis force depends on the latitude at which the object is located. The Coriolis effect is greater near the poles where α = 90° (sin(90°) = 1) and decreases to zero at the equator α = 0° (sin(0°) = 0).
Coriolis effect and airplanes
Do the Coriolis effect and airplanes have something in common? Of course, they have! Let's say that an aircraft (m = 50,000 kg) takes off from London (α = 51.50° N) and travels to North America (to the west) with the velocity v = 500 km/h. With our Coriolis effect calculator, we can compute that this airplane is subjected to the Coriolis force F ≈ 800 N, which means that it deflects to the north with the acceleration a = F / m = 0.016 m/s². It is almost 0.2% of the Earth's gravity! Pilots need to establish a constant force sideways, equal but opposite to the Coriolis force, to compensate for it. It is achieved automatically, by the autopilot, by slightly banking the airplane to keep the heading as planned.
For this example, the banking angle equals only about atan(0.002 × g/g) ≈ 0.115°, so it is too small to be perceivable by passengers. However, without this correction, the airplane may land hundreds or thousands of miles away from the destination point. It is even a possibility that it would fly around the circle, never reaching a final airport!
Example
Calculating Coriolis Effect
The Coriolis effect describes the apparent deflection of moving objects when viewed in a rotating reference frame, such as the Earth. It is a critical concept in meteorology, oceanography, and ballistics.
The general approach to calculating the Coriolis effect includes:
- Identifying the velocity of the moving object.
- Knowing the Earth's angular velocity and latitude.
- Applying the Coriolis acceleration formula.
Coriolis Acceleration Formula
The general formula for Coriolis acceleration is:
\[ a_c = 2 \omega v \sin(\phi) \]Where:
- a_c is the Coriolis acceleration (in meters per second squared, m/s²).
- \omega is the angular velocity of the Earth (approximately \( 7.292 \times 10^{-5} \) rad/s).
- v is the velocity of the object (in meters per second, m/s).
- \phi is the latitude (in degrees).
Example:
If an object moves at 50 m/s at a latitude of 30°, the Coriolis acceleration is:
- Step 1: Identify the given values: \( v = 50 \) m/s, \( \omega = 7.292 \times 10^{-5} \) rad/s, and \( \phi = 30^\circ \).
- Step 2: Compute \( a_c \): \( a_c = 2 \times (7.292 \times 10^{-5}) \times 50 \times \sin(30^\circ) \).
- Step 3: Approximate the result: \( a_c \approx 0.00365 \) m/s².
Effect on Moving Objects
The Coriolis effect influences various moving objects, such as:
- Airplane flight paths, which require adjustments to account for Coriolis deflection.
- Ballistic missiles and long-range projectiles, which experience lateral drift.
- Ocean currents, which are deflected in predictable patterns.
Impact on Weather Systems
The Coriolis effect plays a significant role in meteorology, affecting wind and storm patterns:
- Hurricanes rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.
- Trade winds and jet streams follow curved paths due to Coriolis deflection.
Real-life Applications of the Coriolis Effect
The Coriolis effect is applied in various fields, including:
- Aviation: Adjusting flight routes for Coriolis-induced shifts.
- Oceanography: Predicting current patterns and their influence on climate.
- Military Science: Correcting artillery trajectories over long distances.
Common Units of Coriolis Acceleration
SI Unit: The standard unit for Coriolis acceleration is meters per second squared (m/s²).
Common Interpretations of the Coriolis Effect
Northern Hemisphere: Moving objects are deflected to the right.
Southern Hemisphere: Moving objects are deflected to the left.
Equator: The Coriolis effect is negligible.
| Problem Type | Description | Steps to Solve | Example |
|---|---|---|---|
| Calculating Coriolis Acceleration | Finding the Coriolis acceleration of an object moving in a rotating reference frame. |
|
For an object moving at \( 50 \, \text{m/s} \) at a latitude of \( 30^\circ \), with Earth's angular velocity \( \omega = 7.292 \times 10^{-5} \, \text{rad/s} \), the Coriolis acceleration is: \( a_c = 2 \times 7.292 \times 10^{-5} \times 50 \times \sin(30^\circ) \approx 0.00365 \, \text{m/s}^2 \). |
| Effect on Moving Objects | Determining the Coriolis deflection of a projectile, airplane, or ocean current. |
|
A plane flying at \( 250 \, \text{m/s} \) at \( 45^\circ \) latitude will experience a lateral force due to the Coriolis effect, shifting its trajectory slightly to the right in the Northern Hemisphere. |
| Impact on Weather Systems | Understanding how the Coriolis effect influences wind and ocean currents. |
|
The Coriolis effect causes hurricanes to rotate counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere. |
| Real-life Applications | Applying Coriolis calculations in engineering, aviation, and oceanography. |
|
A sniper must adjust for the Coriolis effect when firing over long distances, as the bullet will be slightly deflected depending on latitude. |
