# Least Squares Method of Data Reduction: n-Sensor Pressure Probes

## Introduction

Five hole pressure probes are typically used to measure 3-D flows. They can determine the yaw and pitch angles, the statgnation and static pressure in a flow.

A typical yaw coefficient for 5-hole probe is defined as

where the pressure refer to the pressure tappings on the 5-hole probe.

A truncated pyramid 5-hole probe with side-facing pressure tappings

In use, the yaw coefficient is used to determine the yaw angle. Therefore, there must be a functional relationship between the two. The figure below shows that this is not the case at flow angles in excess of 30-40 degrees.

A problem occurs with this type of probe when the yaw

Yaw coefficient vs. flow angle (zero pitch)

However, if we examine the individual hole pressure coefficients

We see that there is a unique relationship. It is only the formation of the yaw coefficient that leads to the problem. Therefore, we use an adaptation of the Least Squares method for a 5-hole Pressure Probe. To do this, we find:

4 unknowns : *P*_{0}, *p*_{s},* a* and *b*

using 5 measurements of pressure by minimising

where

*P*_{i} is measured pressure for hole position *i*

is expected output for hole position *i*

In doing so, we find that the Least Squares method

Extends useful range of probes to maximum

Only limited by separation behaviour (Reynolds No.)

See also Least Squares Method of Data Reduction: Fast Response Probes

Papers and a thesis by Roger Dambach and Howard Hodson are available in the download section. Press here to down load papers and PhD Theses.

Howard Hodson and Roger Dambach

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