G Force Calculator

Phew, that loop on the rollercoaster pulled a whole 5 g: let the adrenaline go and learn what it means with our g force calculator.

In this short article, you will learn:

• What is gravity, and how to calculate the gravitational force on the surface of Earth;
• How to calculate the g force acceleration: how much is a 1 g force;
• How to measure acceleration in terms of the g force: equation and formula for the g force; and
• What the relationship between g force and speed is.

Gravity is a fundamental force existing between massive (and energetic) bodies, characterized by:

• Long-range action;
• Weak strength; and
• Mysterious carriers.

With these three features, we compare gravity to the other fundamental forces (weak and strong nuclear and electromagnetic forces). While the others act primarily at the atomic scale (or slightly above it), gravity dominates our daily experiences and absolutely dwarfs all the others at the astronomic scale. On the other hand, gravity is weak: to feel its effect, you have to be massive.

While we know the carriers for the other forces (all elementary particles), scientists still have no clue about the nature of gravity. While they suspect the existence of a particle called gluon, it is nowhere to be found yet!

We need to thank the OG nerd Isaac Newton for the mathematical expression of gravity. Not by observing falling apples but by studying, the scientist developed the equation we still use to calculate the gravitational force:

Where:

• $G$ is the gravitational constant, a (suspected) universal constant;
• $m_1$ is the mass of the first body;
• $m_2$ is the mass of the second body; and
• $r$ is the **distance **between the centers of the two bodies.

Newton comes in our help again: by applying Newton's second law, we can calculate the acceleration due to gravity:

We simply canceled out the mass of the "attracted body".

On Earth, this acceleration is easily calculated: plug the value of Earth's mass and the average Earth's radius:

This value must be familiar: this is the acceleration with which every object (neglecting air resistance) falls. It is also a good metric to measure accelerations, particularly in vehicles. Let's find out more!

An acceleration of $9.82\ \text{m}/\text{s}^2$ is the answer to the question "how much is a 1 g force". Living on Earth, our daily lives are constantly subjected to $1\ \text{g}$ acceleration so that we don't really notice. Actually, it's easier to notice when there are changes to this "status quo".

When you take the elevator (or the lift, if you went to buy tea), you can feel that funny sensation in your belly: that's the effect of a vertical acceleration that adds (if you are going up) or subtracts (if you are going down) to the g force acceleration. The same thing happens when you are taking off on a plane or you take a speed bump just a bit too fast in a car: it feels strange because humans are not used to moving vertically!

A reasonable value for the acceleration of an elevator is $1.2\ \text{m}/\text{s}^2$. This is about an eighth of the value of the gravitational acceleration on Earth's surface. We feel this variation. The same acceleration would bring your car from $0$ to $60\ \text{mph}$ ($100\ \text{km}/\text{h}$) in slightly more than $20$ seconds. Not that impressive, right?

In the next section, we will learn how to calculate any acceleration in g.

Say that you want to calculate the g force, or, in other words, how many g that acceleration was: you can use the g force formula to do so:

Where:

• $v_{\text{f}}$ and $v_{\text{i}}$ are the final and initial velocity, that define the $\Delta v$ (difference in velocity);
• $t$ is the time elapsed between the initial and final moments; and
• $a$ is the acceleration.

The result of the equation allows you to calculate the g force from the speed, given that you know the time required to reach that value. Remember: $g$ is an acceleration, not a velocity: you can't readily compare the two quantities.

Humans are pretty strong: we can sustain a relatively high number of g and get up to tell others about our experiences. Daily, we rarely exceed accelerations higher than a few fractions of g. However, we may reach higher values when we lift our feet from the ground.

When you take off, on your way to your holidays, you experience, on average, $0.4\ g$: that's almost half more than what you're used to, and you will feel it: in that short moment, your perceived weight increase: from, say, $70\ \text{kg}$, you would feel, for a moment, as if you weighted almost $100\ \text{kg}$!

On a roller coaster, you can easily experience accelerations up to $5\ g$, luckily for short periods of time. Earlier, less-engineered models pushed this number a bit further by mistake: the passenger on the rides would be subjected to accelerations reaching $12\ g$. Do you know who else experiences such accelerations? Fighter jet pilots, and only the best ones don't pass out doing so. Beyond $9\ g$-$12\ g$, the risk of severe injuries increases. The current record for the highest g forces experienced by a human is $214 g$, sustained by Kenny Bräck in a racecar crash. More notorious, though by far less strong, are the experiments of John Stapp on rocket-powered sleds. The researcher voluntarily pulled an impressive $46.2 g$ without injuries and ended up saying that he thought that humans could sustain much more than that!