If you are on a carousel and throw a ball, it won't go the way you intend: discover why with our Coriolis effect calculator.

In this article, you will learn what is the Coriolis force and why it is a fictitious force. You will learn how to calculate the magnitude of the Coriolis force, the formula for the Coriolis acceleration, and much more!

What is the Coriolis force? Fictitious forces.

The Coriolis force is a fictitious force resulting from specific movements over a rotating body: its appearance is due to the presence of an acceleration (the centripetal acceleration: visit our centripetal force calculator for a refresh), which causes the reference frame of an observer moving with the rotation body to be non-inertial.

The acceleration, obvious for an observer in an inertial reference frame, is translated into a set of forces for the first observer: the Coriolis force is one of them (the centrifugal force is the other). And while the force is fictitious, it feels very much real, and without much trouble, we can learn how to calculate the Coriolis force and the equation for the Coriolis effect.

So, what is the Coriolis force? The Coriolis force is a perceived deviation of a trajectory in a rotational reference frame. While we can calculate the Coriolis effect in every rotational system, it's of the greatest relevance when considering Earth. We will explain the Coriolis force formula for our Planet: adapting the description to every other rotational motion won't be complicated.

The Coriolis effect on Earth implies that every movement in the Northern Hemisphere is deflected to the right. In contrast, every movement in the Southern hemisphere is deflected to the left — but only if you are rotating with the Earth! This happens thanks to an imbalance in the force perceived by anyone sharing the reference frame with the Planet: the forces acting are, apart from the centripetal one, the gravitational force and the one causing the motion (if you don't remember what to do with them, visit our net force calculator). From the outside, the motions would look linear.

We can calculate the Coriolis force magnitude and much more. Let's see the formula for the Coriolis force!

The formula for the Coriolis force: how to calculate the deviation due to a rotational movement

The equation for the Corolios effect is:

F=2mvωsin(α)F = 2 \cdot m \cdot v\cdot \omega \cdot \sin (\alpha)

Where:

  • FF — The Coriolis force;
  • mm — The mass of the moving object;
  • vv — The velocity of the moving object;
  • ω\omega — The angular velocity of Earth; and
  • α\alpha — The latitude at which the object is located.

The equation for the Coriolis effect only calculates the magnitude of Coriolis force. Remember the direction: right for the North and left for the South.

Notice the similarity between this equation and Newton's second law of motion (you can learn everything about it at our Newton's second law calculator). If you divide by the mass, you can find the formula for the acceleration of the Coriolis force:

a=2vωsin(α)a = 2\cdot v\cdot \omega \cdot \sin (\alpha)

The magnitude of Coriolis force depends strongly on the latitude: the maximum strength is at the poles (where the tangential speed is zero) and null at the equator. Let's see the Coriolis effect calculator in action:

How to calcualte the coriolis effect on Earth

Follow these steps to calculate the Coriolis effect. We choose, as an example, a shell of the Paris Gun, a massive howitzer used by the German Empire during WWI.

  • Gather the data required by the formula for the Coriolis force:
    • Earth rotates at a constant angular speed: ω=2π/24 h0.0000727 1/s\omega = 2\pi/24\ \text{h} \approx 0.0000727\ 1/\text{s} (visit our angular velocity calculator for a quick refresh).
    • The shell has a muzzle speed of 1640 m/s1640\ \text{m}/\text{s};
    • The shell is fired at 48.85°48.85\degree of latitude north; and
    • The mass of the shell is 1,00 kg1,00\ \text{kg}.
  • Plug these data in the equation for the Coriolis effect:
F=2mvωsin(α)=21, ⁣00 kg1, ⁣640 ms0.0000727 1ssin(48.85°)=17.96 N\begin{align*} F &= 2 \cdot m \cdot v\cdot \omega \cdot \sin (\alpha)\\ &=2\cdot 1,\!00\ \text{kg}\cdot 1,\!640\ \frac{\text{m}}{\text{s}}\\ &\cdot 0.0000727\ \frac{1}{\text{s}}\cdot \sin\left(48.85\degree\right)\\ &=17.96\ \text{N} \end{align*}

The corresponding acceleration, during the 3 minutes time of flight of the shell, would cause a deviation of almost a meter to the right (and an associated shortening of the flight path of more than 350 m350\ \text{m}).

Davide Borchia
Mass
lb
Velocity
mph
Latitude
deg
Hemisphere
Northern
Coriolis force
N
Coriolis acceleration
ft/s²
The moving body deflects to the right.
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