# Introduction to G forces and Acceleration

As mentioned, the term G force is a misnomer and we are actually referring to acceleration. The usage is understandable given that force is related to acceleration through Newton’s second Law:

$f=ma$

$f=\text{force}\\ m=\text{mass}\\ a=\text{acceleration}$

Because mass is a constant, force and acceleration are proportional – the force that we feel is directly related to the amount of acceleration being experienced. While in later sections we will discuss forces and take into account the weight of the motorcycle and rider, this section concentrates on the longitudinal and lateral acceleration channels. The “G” part of the term stems from the usage of g, the acceleration due to gravity that is also used as a unit of acceleration – more on that later.

Longitudinal Acceleration
Acceleration in a straight line is well understood and visualized. As the motorcycle speeds up or slows down, acceleration is defined as:

$a=\frac{\Delta v}{\Delta t}$

$a=\text{acceleration}\\ \Delta v=\text{change in velocity}\\ \Delta t=\text{change in time}$

For example, if you accelerated from a stop to 60 mph in 3 seconds, your acceleration would be 20 mph/s (mph per second). Brake from 60 mph to 20 mph in 4 seconds and your acceleration is -10 mph/s. Note that braking is expressed as negative acceleration. The standard units of acceleration are ft/s2 (pronounced feet per second squared or feet per second per second) in imperial units, or m/s2 in metric. Acceleration in a straight line is sometimes referred to as longitudinal acceleration or simply acceleration.

Now to factor in the acceleration due to gravity. If you drop an anvil from an airplane, it will accelerate at a predictable rate thanks to gravity. That predictable rate is 9.8m/s2 or 32.2 ft/s2, and is referred to as 1g. If we factor that into the results above, 20 mph/s converts to .91g and -10 mph/s equates to .46g. Using g makes the numbers more easily understandable and the units much less cumbersome to deal with.

Lateral Acceleration
Lateral acceleration, or centripetal acceleration, may be less understood at times but is just as important a measure as its longitudinal counterpart. It is most commonly felt as an outward force (centrifugal force) when you are in a car that is turning a sharp corner, and is defined as:

$a=\frac{v^2}{r}$

$a=\text{acceleration}\\ v=\text{velocity}\\ r=\text{radius of turn}$

Visualize this as how quickly you are deviating from a straight-line path – at a higher speed you will move away from the straight path at a quicker rate. Likewise, turn tighter and you will move away quicker. Note that the units of lateral acceleration are the same as longitudinal acceleration: m/s2 or ft/s2. These units can also be converted to g. The usual convention is to label a right-hand turn as positive lateral acceleration, and a left-hand turn as negative.

Consider the skidpad, a circular track used to test cars for how much lateral acceleration they are capable of. The typical layout has a radius of 300 feet. If the car can drive around the pad at a speed of 60 mph (88 ft/s), the lateral acceleration is calculated as:

$a=\frac{88^2}{300}$

Which equals 25.8 ft/s2, or we can convert that to .80 g.

Both longitudinal and lateral acceleration are recorded by most data loggers. A non-GPS-based system uses internal accelerometers to record these channels, and – as we will see in a following sections – this method does not work to record lateral acceleration for motorcycles. For that, we must turn to a GPS-based system, which generates the acceleration channels from GPS data. This is what makes a GPS-based data acquisition system so valuable: The lateral acceleration data contains an abundance of useful information that is becoming more important as more is understood of motorcycle dynamics.