# Vector Sum and PPV

### Background

When measuring vibration in the ground, we are actually measuring Particle Velocity.

• The vibration energy moves through the ground like a wave.
• Particle Velocity is the physical speed of a particle of soil, or ground, as it moves back and forth as the wave passes
• This is quite different to the velocity of the wave itself

Colloquial use of PPV

PPV means Peak Particle Velocity and can legitimately be used for either the peak of a single channel of a triax or the peak vector sum.

PPV has also traditionally been used to mean the Maximum Peak Particle Velocity of all of the channels of the triax.

Standards have recommended recording the Peak Vector Sum rather than a single channel peak for many years, which has often lead to the terms PPV and Peak Vector Sum being used interchangeably.

Australian Standard AS2187.2-2006

When the AS2187 was last updated, in 2006, the following terms were recommended to clear up this confusion:

• PCPV   for ‘Peak Component Particle Velocity’
• VPPV    for ‘Vector Peak Particle Velocity’

Here VPPV would explicitly be the Vector Sum, defined in AS2187:

Vector peak particle velocity (VPPV)

The peak level of the particle velocity calculated from the vector formed by the magnitude of the  three  orthogonal  components  of  the  particle  velocity  over  their  measured  time history.

PCPV is then the Peak Particle Velocity of a single component, or channel, of a triax, not necessarily the Maximum Peak Particle Velocity. In AS2187:

Peak component particle velocity (PCPV)

The peak level of the particle velocity for an individual component.

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#### Texcel Usage

Texcel uses the term Vector Sum for the Vector Peak Particle Velocity in all reports. In the Blast Report this is extended to Peak Vector Sum Velocity.

Triaxial Components

Texcel directly identifies the component peak particle velocities by their orthogonal directions to enhance the meaning of the measurement:

• Radial – Channel in Triax Pointing towards blast or vibration source
• Transverse – Channel in Triax Right Angles to blast or vibration source
• Vertical – Channel in Triax Pointing Vertically

Notes:

1. These names are consistent with AS2187.2-2006 Definitions 1.4.10
2. These meanings depend critically on correct placement of the Triaxial Sensor.
3. Channel is the same as Component with respect to the Triax.
4. Radial is sometimes referred to as Longitudinal.
5. If the velocity is reported in dB, these component names have ‘DB’ appended – see TB0015

Diagnostic Spreadsheet Reports

In Texcel’s Diagnostic Spreadsheet reports the peaks are reported by channel number:

• Pk # – Absolute Peak Value for Channel #
• Pk+ # – Positive peak for Channel #
• Pk- # – Negative peak for Channel #

These can represent Peak Particle Velocities if the sensor is measuring vibration.

Refer to Texcel Technical Bulletin – TB0015 Spreadsheet Headers for variations on these terms used in spreadsheet reports depending on the units …

#### We often get asked about the Frequency of the Vector Sum

You record the frequency of the component peaks, why not the frequency of the vector sum peak?

Consider this:

A mechanical wave is a wave that is an oscillation of matter. In ground vibration we are measuring mechanical waves.

An oscillation is the repetitive vibration of some measure about a central value. The period is the time for one complete cycle of an oscillation of a wave. The frequency is the number of periods per unit time (per second) and is typically measured in hertz

I.e. it records positive and negative values and crosses zero many times, so you can define a period and a frequency at points along the waveform (the period (and frequency) will vary along the waveform).

If you look at a peak component waveform in a typical ground vibration report, you will see that it oscillates around a rest position of zero.

This is shown in some detail in TB0019 – Texcel Zero Crossing Results.

From AS2187 J4.2 Ground Vibration:

For all limits it is necessary to measure in three orthogonal directions, one in the vertical direction and the other two in perpendicular horizontal directions. The magnitude of the vector particle velocity (Vector Sum) is the amplitude of the vector sum of three time-synchronised velocity components directly measured by an instrument.

That is for each point in the three component waveforms of a triaxial sensor we can calculate a vector sum from this equation:

The Peak Vector Sum Velocity reported in Texcel’s Blast Reports is the peak value found by computing this value for every point in the waveform and finding the maximum value.

The point to notice is that this value always has a positive result. I.e. it never goes through zero!

Because the Vector Sum Value never goes though zero, you cannot define a period to the waveform and hence it has no frequency.

• The Vector Sum does not have a frequency.