### Lee-Valley Digital Angle Finder

Tuesday, July 15th, 2008**Introduction**

Low cost digital instruments are making their way into woodworkers hands. But, to avoid confusing digital precision with measurement accuracy I checked out this popular angle gauge in the Metrology Lab to see how it measured up. That’s what makes this web site different. There will be no test cuts, no plastic drafting triangles, or any other nonsense that you commonly see in other web sites and popular magazines.

They have been in metalworking catalogs for a few years but are now making their way to many of the woodworking catalogs and dealers. These digital bevel gauges are all basically identical apart from price and branding. I purchased mine from Lee-Valley Tools for about $20 plus shipping. It came with a battery and a one page instruction sheet.

Overall, the device is about 10 inches in length, the gauging surfaces measure about 8.7 inches. The main body is made from extruded aluminum and is about 2 inches wide by a little more than 3/4 Inches (0.825″) thick. The measuring arm is made from stainless steel and is about 0.075 inches thick. Flatness of the gauging surfaces on the body is about 0.003 inches and it rocked noticeably on my surface plate. The gauging surfaces on the arm are considerably better with an error of about 0.0005 inches.

Calibration is set by placing the gauge on a flat surface with the arm folded in. Holding down the “Zero ABS” button will reset the display. Pressing “Hold” will freeze the display. Pressing the “Zero ABS” button momentarily will set a temporary zero reference - pressing it again will restore the calibrated value. Momentarily pressing the “On Off” button will turn off the display. Holding down the “On Off” button will turn off the angle gauge completely.

The display is large and easy to read. There is a quadrant indicator on the far left, 3 digits to the left of the decimal, and 1.5 digits to the right of the decimal (the last digit reads 0 or 5). A locking knob can be used to fix the arm position. The arm has a window which allows the display to be read when fully closed.

**Testing**

My test setup involved using a 10 inch sine plate. This is a machinists tool used for angular inspection and setups. It consists of two hardened, precision ground, and lapped steel plates which are hinged at one end. The other end is open forming an angle between the top and bottom plates. The top plate has a cylinder fixed to it’s underside which is commonly referred to as a “roll”. The distance between the hinge and the “roll” (center to center) is precisely 10 inches (to within 0.0001″).

When fully closed, the angle between the top and bottom plates is within a few arc seconds of zero degrees. The angle is defined by gauge blocks which are placed between the top and bottom plates on the open end underneath the “roll”. Extremely accurate angle settings are possible based on the trigonometric sine function (you can see how the device gets its name).

For my testing, I wanted 45°. So, the length of the gauge blocks is calculated as 10 * sin(45), or 7.071067 inches. I have gauge blocks with increments to five micro-inches (0.000005″) so I created a stack which measures 7.071065 inches. Over a 10 inch span, the extra 2 micro-inches will hardly be noticed!

To check the accuracy of the setup, I use a Starrett Laboratory Master grade angle gauge block. When the sine plate is tilted to the proper angle, the top side of the angle block will be parallel to the surface plate. So, I place my probe directly on the top of the angle block and measure it’s surface. The 123 block under the angle block (the thing with lots of holes) is being used just to hold the angle block in position).

Here’s another view showing the use of the angle gauge block to certify the accuracy of the setup.

My gage head is electronic, and is connected to this instrument. The “dia-lectron” is an amplifier which translates movement of the gage probe to a meaningful reading on the meter. For the purposes of this test, the upper (red) scale will be used to indicate 100 millionths (0.0001″) per division. Full scale it amounts to +/-0.003 inches. Some tricks are needed to make measurements which exceed 0.006″.

Once I’m sure that the setup is accurate, it’s time to remove the angle gauge block and put the digital angle finder in its place. Error is measured in inches as a total deviation from the ideal. The procedure was as follows:

- Zero the digital angle gauge on the granite surface plate.
- Rotate the arm so that the display indicates 45.00°.
- Place the angle gauge on the sine plate.
- Measure the arm to see how far out of parallel it is with the surface plate.
- Check the reading on the digital angle finder to make sure it still read 45.00°.
- Record the measurement.

Each trial consisted of all six steps. I performed 24 trials approaching 45° from alternating directions (clockwise and counter-clockwise) and recorded the data.

**Test Data**

-0.0020 | |||

-0.0034 | |||

-0.0060 | |||

-0.0089 | |||

-0.0078 | |||

-0.0063 | |||

-0.0080 | |||

-0.0055 | Mean: | -0.0065 | |

-0.0040 | Median: | -0.0063 | |

-0.0107 | Std Dev: | 0.0026 | |

-0.0070 | |||

-0.0095 | |||

-0.0042 | |||

-0.0100 | |||

-0.0106 | |||

-0.0079 | |||

-0.0052 | |||

-0.0054 | |||

-0.0021 | |||

-0.0040 | |||

-0.0083 | |||

-0.0086 | |||

-0.0045 | |||

-0.0063 |

**Statistical analysis**

The mean and the median are very close, indicating a good normal distribution about the mean. However, the mean isn’t zero, it’s -0.0065 inches from zero. So, all the readings were skewed by an average of -0.0065 inches. The first time I did this test, I thought the data was biased by the direction I was approaching the setting from. However, this time I approached the setting equally from both directions (clockwise and counter-clockwise). So, the bias is an artifact of the measurement device - not the measurement technique. One possible cause for it would be non-parallel edges of the measurement arm. Over the 8.7 inch span the bias amounts to an angular error of 0.0428° (arc sin (0.0065/8.7)). The standard deviation is 0.0026 inches. In practical terms, it means that 68.2% of all settings will deviate from the mean by 0.0026″ or less. 27.2% of all settings will be between 0.0026″ and 0.0052″ away from the mean. And, 4.2% of all settings will be between 0.0052″ and 0.0078″ away from the mean. The remaining 0.4% of all settings will be more than 0.0078″ from the mean.

Generally speaking, 99.73% of all settings made with this digital angle finder will be within +/-0.0078 inches of the mean (-0.0065″). So, for this particular instrument, in this particular test, the settings can be off by as much as -0.0143 inches from the ideal. It translates to about 0.0941° - which is pretty close to the stated spec of 0.1°. This degree of accuracy is marginally adequate for a four sided frame with mitered corners. Using 3″ wide stock, the maximum possible error of each cut could be 0.0049 inches. Since there are 8 cuts in a four sided frame, then the total accumulated error (the gap) would be 0.0394 inches - which is a bit more than 1/32 of an inch (0.0312″). It is not likely to satisfy most people making a six sided frame with mitered corners (total gap would be 0.0591″) and just about nobody making an eight sided frame (total gap of 0.0789″ or a bit more than 1/16 inch). Since these are worst case numbers, you are likely to see better results most of the time.

My test measurements show accuracy that is pretty close to the published specs for the device (0.1°) but that includes the bias in this particular instrument. What I would really like to see is a mean and median which are both closer to zero. And, the standard deviation should be closer to 0.0152″ (for 0.1° over an 8.7 inch span). So, my sample might not be statistically significant. And, it is possible that another sample might give better or worse results.

**Summary**

Not bad for $20! But, what can you do with it? You don’t want to use it against the blade to set miter gauge angles (see the article on aligning the miter gauge). So, for a table saw it’s pretty much relegated to setting blade tilt. The gauging surfaces on the arm are really are too thin for use with dial indicators. The gauging surfaces on the body aren’t flat enough to obtain good readings. But, it can be used for sighting tiny gaps (if you are so inclined to do so). So, for machinery setup I see this product as having limited application.

Other applications include using it as a bevel gage to mark stock or check the results of cuts (if you weren’t so sure of your machine setup or you like to use high tech instruments for low tech trial and error methods). And, I suspect that this is the true intention of the device, since it is called the “Digital Angle Finder”. My preference will remain with steel angle blocks and proper machine setup but I can see how this device can come in pretty handy.

Ed Bennett

ejb@tablesawalignment.com