Bicycle Helmet Safety Institute

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What is a "g"

Summary: The term g is based on the pull of gravity.

NASA had a definition for g in their 1965 dictionary of Technical Terms for Aerospace Use:

g or G

An acceleration equal to the acceleration of gravity, 980.665 centimeter-second-squared, approximately 32.2 feet per second per second at sea level; used as a unit of stress measurement for bodies undergoing acceleration. See acceleration of gravity; gravity.

acceleration of gravity (symbol g)

By the International Gravity Formula, g = 978.0495 [1 + 0.0052892 sin2(p) - 0.0000073 sin2 (2p)] centimeters per second squared at sea level at latitude p. See gravity. The standard value of gravity, or normal gravity, g, is defined as go=980.665 centimeters per second squared, or 32.1741 feet per second squared. This value corresponds closely to the International Gravity Formula value of g at 45 degrees latitude at sea level.

and another in a newer publication, this one still available on the web:


A dropped object starts its fall quite slowly, but then steadily increases its velocity--accelerates--as time goes on. Galileo showed that (ignoring air resistance) heavy and light objects accelerated at the same constant rate as they fell, that is, their speed (or "velocity") increased at a constant rate. The velocity of a ball dropped from a high place increases each second by a constant amount, usually denoted by the small letter g (for gravity). In modern units (using the convention of algebra, that symbols or numbers standing next to each other are understood to be multiplied) its velocity is

at the start -- 0 (zero)
after 1 second-- g meters/second
after 2 seconds-- 2g meters/second
after 3 seconds-- 3g meters/second

and so on. This is modified by the resistance of the air, which becomes important at higher speeds and usually sets an upper limit ("terminal velocity") to the fall velocity--a much smaller limit for someone using a parachute than one falling without.

The number g is close to 10--more precisely, 9.79 at the equator, 9.83 at the pole, and intermediate values in between--and is known as "the acceleration due to gravity." If the velocity increases by 9.81 m/s each second (a good average value), g is said to equal "9.81 meters per second per second" or in short 9.81 m/s2.

Got that?

In layman's terms, g is the amount of gravity the earth exerts on you when you fall. Spacemen float around at near zero g when they get up there in orbit. You experience 1 g for your whole life on earth except on those carnival rides where you float and your stomach turns upside down. Or you can encounter much, much more than one g when you fall and hit your head.

Since you fall according to gravity, and the gravity is a constant on earth, you know how hard you are going to hit when you fall from two meters with no forward speed. That's about 14 miles per hour, and that's the drop used in a lab to test bike helmets hitting flat surfaces for the US CPSC standard. (We have the speed calculations on another page.) Forward speed can add some to that, but not much if your helmet skids on the pavement the way it should and does not snag. If it snags, all bets are off, since lab tests show that the result can be more g's to the brain as well as a strain on your neck. That's why you will see us emphasize that the outside of a helmet should be round and smooth to skid well on pavement.

Without a helmet, hitting your head can transmit a thousand or more g's to your brain in about two thousandths of a second as you come to a violent, very sudden stop on the hard, completely unyielding pavement. With a helmet between you and the pavement your stop is stretched out for about seven or eight thousandths of a second by the crushing of the helmet foam. That little bit of delay and stretching out of the energy pulse can make the difference between life and death or brain injury.

Helmets do not "absorb" energy. Nothing does. The law of energy conservation says that a helmet can transform energy to work or to another form of energy, but can't absorb it. That's why we refer to helmets as "managing" impact energy rather than absorbing it.

Along with the stretching out of the impact, a helmet does change a small amount of the energy of a blow to heat as the molecules of foam move in the crushing of the foam. To test that out for yourself, take a piece of picnic cooler foam on a hard surface and hit it with a hammer. The dent the hammer makes will be warm to the touch. And crushing foam is certainly work.

So all things being equal (red flag, they never are in real life!) a thicker helmet can stop you more gradually than a thin one. It just has more distance to bring your head to a stop. (an inch, maybe, vs. a half inch). And the foam in a thinner helmet has to be firmer to work without being completely crushed right away in a hard impact. So in a softer impact it may not crush at all. For a softer landing in the full range of impacts, you want a helmet that has less dense foam and more thickness. But just try to find that on the market! Things get further complicated when the designer decides that the rider will pay more for bigger vents and a thinner helmet. Those big vents reduce the amount of foam in the helmet and require harder foam in the spots that are left. So sometimes you might get better impact protection from a cheaper helmet with thicker foam and smaller vents. But sometimes you might not, since all things are never equal in the real world.

A note on "acceleration." The hard core physics types who populate helmet labs and helmet standards committees insist on using the scientifically-correct term acceleration to describe what happens when the head hits the pavement. Not deceleration as you might expect if you speak plain English. So they will write their descriptions as g's of acceleration of the head relative to the pavement. If you are not an engineer, just translate that to deceleration. Engineers will smirk, but people will always understand you.

For more on helmet design, we have a page up on the ideal helmet.

For more on g's, see a textbook on physics.