- Velocity and Acceleration -
A quick review of the fundamentals
VELOCITY
Linear Velocity is the measure of the linear (straight-line) distance something moves in a specified amount of time. It is typically calculated as distance divided by time, and has units such as feet-per-second, miles-per-hour, and furlongs-per-fortnight.
Velocity, in a strict definition, is a vector quantity, meaning that it has both magnitude and direction. Technically, "speed" is the magnitude portion of a velocity. However, velocity is sometimes given in terms of magnitude only, and in many of those cases, the direction is irrelevant. In others, the direction is self-evident.
Angular velocity is the measure of rotational distance something moves in a specified amount of time. It is typically expressed in units such as revolutions-per-minute (RPM) and degrees-per-second.
For many engineering calculations, it is necessary to express angular velocity in units of radians-per-second, rather than degrees-per-second or RPM. (The explanation of "why" requires more math than is appropriate here, but suffice it to say it is necessary in order to make the numbers work out right).
A radian is an angular measurement equal to approximately 57.3 degrees. It is defined as the angle formed by an arc on the circumference of a circle, the length of which is equal to the radius of that circle. Since the circumference of a circle is the radius times 2π, then obviously the value of a radian is defined as an angle of 360 / 2π, or 57.29578 degrees.
ACCELERATION
Acceleration is the measurement of how quickly the velocity of an object is changing. If you measure the velocity of an object at a particular time (Time1), then again at a subsequent time (Time2), then the average acceleration which the object has experienced will be:
Acceleration = (Velocity2 - Velocity1) / (Time2-Time1)
Clearly, the longer the period of time over which the measurements are taken, the more that value becomes an average, and the less will be known about the instantaneous acceleration of the object.
Acceleration is a critically important value for dynamic systems, because it is the instantaneous acceleration imposed on moving (dynamic) components, along with the mass of the components, which determines the actual forces raquired or applied in order to get components within the a system to change velocity from one value to another (Newton's second law), covered previously in Force, Pressure and Friction).
Linear acceleration is typically expressed in inches-per-second-per-second and feet-per-second-per-second (velocity per unit time). Common units of angular acceleration are degrees-per-second-per-second, radians-per-second-per-second and RPM-per-second.
The acceleration value typically used in camshaft lobe design is inches-per-degree-per-degree or inches-per-degree² . This value is the acceleration which a cam lobe applies to the cam follower it is driving. In order to calculate the forces a cam applies to its mating components, the cam lobe angular velocity must be known. Using that, the lobe acceleration value can then be converted into inches-per-second-per-second, from which the forces are then calculated. ( In 2004, for some undiscernible, but most certainly politically-correct, reason, the cam design community apparently switched to metric units { mm/deg and mm/deg² }.)
