Page | 62
The accelerometers provide measurements of the xyz-components of the specific force acting on the tool due to gravity (Ax Ay Az). The outputs from the accelerometer allow the inclination (I) to be calculated in accordance with the following equation.
2
2
+ A A
x
y
I
=
arctan
A
z
The accelerometer outputs are also used to determine the relation between the input axis of the rate gyro at each measurement position and the high-side of the hole, often referred to as the high-side tool-face angle (TF), as follows.
A
− −
x
TF
=
arctan
A
y
Given this information, the azimuth angle ( A ) can be computed as a function of the gyro measurements, the inclination and tool-f c ngl s nd h c l compon n of E h’s us ng h follow ng qu on. ( ) − I G TF G TF cos sin cos
x
y
A
=
arctan
+ G TF G TF cos sin
I
+
sin
x
y
V
Summary : The rate gyro survey tool uses accelerometers to measure components of the specific force due to gravity; these data are used to compute borehole inclination and to determine the position of all the sensors axes with respect to the high-side of the hole. The rate gyro is used to sense and accurately measure compon n s of h E h’s sp n rate from which the azimuth can be calculated. The horizontal component of Earth’s rate always points to TRUE NORTH.
10.5 Sensor Errors
All gyroscopic sensors are subject to errors which limit the accuracy to which the angle of rotation or applied turn rate can be measured. Spurious and undesired torques (caused by design limitations and constructional deficiencies) act on the rotors of all mechanical gyroscopes. These imperfections give rise to precession of the rotor, which manifests s lf s ‘d f’ n h f nc d c ond fn dby h spn xsof h oo.Fo s n d gy oscop , . . on operating in a nulling or rebalance loop mode to provide a measure of angular rate as described in Section 3, any unw n d oqu s c opoduc ‘b s’on h m su m n of ngul . Major sources of error which arise in mechanical gyroscopes include the following: 1. Fixed bias – a sensor output which is present even in the absence of an applied input rotation; 2. Acceleration-dependent (g-dependent) bias – biases in the sensor outputs proportional to the magnitude of the applied acceleration. In this context, mass-unbalance effects are of particular concern, and are discussed further below 3. Anisoelastic (g2-dependent) bias – bias proportional to the product of accelerations applied along orthogonal axes of the sensor; 4. Scale factor errors – errors in the ratio relating the change in the output signal to a change in the input rate which is to be measured; 5. Cross-coupling/misalignment errors – errors arising because of gyroscope sensitivity to turn rates about axes perpendicular to the input axes, or is mounted in a position that is physically misaligned with respect to the required measurement axis. Each of these errors will, in general, include some or all of the following components: • fixed or repeatable terms • temperature induced variations • switch-on to switch-on variations • in-run variations
Made with FlippingBook flipbook maker