Point of Beginning

Web-Exclusive: Measuring with Angular Momentum

June 1, 2007
Image courtesy of William Currier, LS.

Today we have numerous tools readily available for our precision control and alignment needs. Whether it is a basic transit or a digital total station equipped with onboard RTK GPS capabilities, we venture forth confident in our ability to provide spatial expertise for our clients. In some cases, such as when working in tunnels, we are limited to a confined working space or unable to use the orbiting network of satellites we often take for granted in our day-to-day surveying activities.
Gyroscopic alignment instrumentation allows users to define an azimuth referenced to true north within a short time period, and is neither dependent upon accumulated control error or conditions of the environment. It can be a very accurate tool; some of the more sophisticated units report 1-3” of arc within minutes of setup.

Image courtesy of William Currier, LS.

Gyros in Action

The Wild GAK1 is perhaps the best-known product of this instrument line. The GAK1 gyrocompass unit sits above such instruments as the Wild T1A, T16, T2 or T1000 theodolites by a locking ring and support standards. A power supply spins an internal rotor at 20,000 rev/min, the axis of spin being held in the horizontal plane. Once the “caged” gyro has reached maximum revolutions, the locking ring is opened until the rotor spins freely or is ”uncaged.”

By virtue of its mass and velocity of spin, the rotor will define its place in space by pointing in a direction. A counterforce, primarily the mass gravity of the rotating Earth, will induce a force on the rotor to align along the axis of Earth rotation. The rotor, analogous to a clock pendulum, will oscillate either side of the true north meridian. If the rotor swings are timed and measured on either side of the true north meridian, a determination can be made of the center of swing corresponding to true north. A viewing scope attachment allows the user to read and time these swings. The axis of the spinning rotor is, in turn, related to the horizontal circle of the theodolite below and angles relative to true north are thus observed. It would make sense that the maximum angular velocity of Earth occurs at the equator, and the forces aligning the rotor axis are also at a maximum. Conversely at the pole, the rotor axis will spin freely and never come to rest-perhaps the only place in the world a surveyor can get lost for compass direction.

The principles outlined are common for all such instruments, but the measurement methods employed and possible accuracies will differ. The instrument more commonly used for higher precision jobs today is the Gyromat 2000 or 3000 model manufactured by Deutsche Montan Technologie GmbH (DMT) of Germany. The manufacturer states an accuracy of 15 mm (0.05 ft) per 1 km with 10 minutes to solution for a single reading. It can operate up to a latitude of 80 degrees to Earth poles, the maximum sensitivity being at the equator.

Andrew Wetherelt, lecturer in Mining Engineering at Camborne School of Mines at the University of Exeter in Cornwall, United Kingdom, quotes accuracies of 20 arc seconds-and even 5 arc seconds-if the Rob Smith (RSM) Micrometer Modification method is used for readings with the GAK1 gyroscope. The RSM method utilizes a fine micrometer made part of the optical graduated viewing scale. This allows for more precise reading of the angular oscillations of the gyro rotation axis. It is analogous to the reading of an etched theodolite circle by micrometers that read to seconds of arc by small interval movements of the circle itself.

In “Underground azimuth determinations using an adapted Wild GAK1,” Wetherelt discusses an adaptive electronic “eye” to automate the reading process on the GAK1, allowing comparable accuracies to the modern Gyromat instrument.

Personal Introduction to the Gyro

I was trained on the Wild GAK1 unit by Frank Prendergast, head of the Department of Spatial Information Sciences at the Dublin Institute of Technology, Ireland. “Gyros are still taught and we cover the basics,” he says. “Our instrument is still the Wild GAK1 model. Such accuracies are/were adequate for most tunneling applications in the mining environment where rock blasting is the excavation method. For more stringent accuracy requirements such as survey control in long infrastructure tunnels, and where tunnel-boring machines are required to adhere to design centerline coordinates of a few millimeters, the newer gyros are now routine. Capable of one to three arc seconds accuracy, this has revolutionized the control and minimization of orientation and breakthrough errors.”

When working in tropical West Africa, I used the Wild GAK1 for azimuth control of lines within large oil concession blocks. The dense jungle canopy and constant cloud cover prevented the sun from being used for orientation. Every four miles or so the crews would “close” the lines on transit or GPS satellite control in addition to intermediate checks with the GAK1.

The Weisbach method of using two weighted wires down a shaft is well-established for transferring accurate coordinates to the beginning of a tunnel. Modern methods will also use very coherent laser plummets to achieve the same result. The coordinates are carried forward through the tunnel using braced traverse control, and at intervals the gyro azimuth observed and checked against those carried forward by the traverse. The width and nature of the tunnel floor will dictate the spatial design of the control network. It is often a wet, cramped and high stress environment.

Image courtesy of William Currier, LS.

More Personal Experiences

For the Town River Relief Tunnel in Quincy, Mass., I used the Weisbach wire method to transfer surface GPS control down the main shaft. The Water Resources Development Act of 1986 authorized federal flood protection for the Town River in Quincy, Mass. The tunnel project included a 12-ft diameter deep rock relief tunnel approximately 4,000 ft long under the city of Quincy central business district. The most important aspects of this operation were to ensure enough weight on the thin wires to remove any residual coiled torque and to steady the oscillations of the wires themselves due to wind and vibration. An inexpensive solution and of suitable viscosity was found in two industrial-strength buckets approximately 3 ft in diameter by 2 ft deep containing Aunt Jemima’s maple syrup. Once stable, the wires provide the backsight for a conventional survey theodolite. A corrected steel tape or wire placed reflective targets for distance measurements.

In this case, two sets of vertical check boreholes corrected any tunnel traverse alignment errors further down the tunnel. Depending on the depth and overburden of a tunnel, the luxury of such drilling checks may not exist, such as is the case of the outfall tunnel in Boston Harbor where seabed and significant water depth lie overhead. In the mid-1990s I worked as an offshore survey coordinator on the outfall tunnel in Boston Harbor.

As part of the Boston Harbor cleanup, the tunnel transfers effluent from the sewerage treatment facility in Boston Harbor nine miles out to sea. A total of 55 diffuser caps and pipes connect to the tunnel below and discharge the waste to the seabed. While working with Coler and Colantonio Inc. of Norwell, Mass., I was part of a team headed by Survey Engineer Mark W. Rohde. Our responsibilities included positioning the drill rig and guiding template over the diffuser design location, measuring the verticality and final bottom coordinates of the diffuser as-built location. A static GPS survey network was observed onshore. When approximately positioned, the barge was anchored and the drill template positioned by GPS observations and a line-of-sight microwave shore network.

Once the diffuser borehole was drilled, it was the surveyor’s assignment to determine verticality, borehole bottom coordinates and elevation data. A weighted frame attached to a float was lowered down the shaft approximately 350 ft by a hand crank. When on bottom, the float would oscillate about true vertical, an inverted pendulum system, the center of oscillations defining the center of borehole.

In addition, a downhole tool manufactured by WELNAV of Tustin, Calif., allowed a vertical and horizontal profile for the borehole length. Attached to a wire, the missile-shaped tool was lowered down the shaft and held at fixed intervals. Data output included depth from the zero mark, a gyro and inclinometer fed data to a surface laptop. A caging frame matching the diameter of the borehole allowed the narrow tool to follow the center of the borehole until it hit bottom. Readings were then taken and it was raised again and held at fixed depth marks, thereby providing a data set on the return to surface.

Below the sea level at 350 ft depth, a tunnel-boring machine (TBM) was connected to all 55 diffuser boreholes. William Currier, LS, a tunnel surveyor and owner of Currier Survey, was in charge of the alignment and grade control of the 9.4-mile and 26-ft diameter tunnel.

“Since the shaft was located at the shoreline, drilling alignment holes along the centerline was never an option. Therefore, a north-seeking gyro was required,” he explains. “Initially, I utilized the Wild GAK1. This 20” instrument had been the industry standard.

“A mathematical pre-analysis assisted in determining how precise and how often gyro measurements were required to achieve the required break-through accuracies. When I reviewed the pre-analysis, I determined that the GAK1 would not give me the results I needed. I then looked at the Gyromat. There have been many advances in survey equipment during my career, including north-seeking gyros. The main difference between the two units is that the GAK1 is a 20-arc second instrument and the Gyromat is a 3-arc second instrument. The Gyromat is relatively easy to operate whereas the GAK1 requires a fair amount of skill and patience to operate. After convincing the project manager that the GAK1 would not allow us to meet the required tolerances, we ordered a Gyromat 2000 by DMT. The cost of this instrument in 1992 was about $100,000 and took seven months to fabricate and deliver.

After more than three years of mining, on Dec. 29, 1995 at approximately 3:00 a.m., we found the first diffuser on the first attempt. Much of this credit must go to Mark Rhode and his team in determining precisely where the bottom of this diffuser pipe was: ~350 feet below sea level, 8.1 miles offshore.”

After a successful completion of the Metro West Water Supply Tunnel, Currier transferred to Atlanta in 2000 to work on the Chattahoochee and Nancy Creek Tunnels as survey manager. Each of these tunnels is nine-plus miles of 18-ft diameter. Today I am involved on Atlanta’s Combined Sewer Overflow (CSO) tunnel project. This tunnel is eight-plus miles of 27-ft diameter. All of these projects are sewage conveyance and storage tunnels.

“In the tunnel, I am in the open-ended traverse business,” he explains. “Error ellipses (uncertainty of location) grow rapidly when you survey away from your ‘fixed’ monuments. I wouldn’t consider working on a large tunnel project without a Gyromat.”

The Right Tool

The need for precise alignment methods, while limited in their application, is growing as we attempt to design and place infrastructure elements to an ever-increasing degree of accuracy. At the forefront there will always be a need for creative and innovative surveyors. Large engineering projects can be time intensive and have zero tolerance for alignment errors, where GPS or conventional survey control will not suffice. The gyroscopic instruments available today allow quick setup, clear uncomplicated user interfaces for training of technical personnel and fast reading of accurate azimuth lines.

1. “Underground Azimuth determinations using an adapted Wild GAK1,” Wetherelt, Andrew, and Paul Hunt, PhD, presented at the FIGXXII International Congress, Washington, D.C. April 19-26 2002.

Gyro – from Greek gyros, a circle.

Gyrocompass – A compass consisting of a motor-driven gyroscope whose rotating axis, kept in a horizontal plane, takes a position parallel to the axis of the Earth’s rotation, and thus points to the geographic north pole instead of the magnetic pole.