The Traffic Accident Reconstruction Origin -ARnews-
Information on the British Pendulum can be obtained through the American Society for Testing and Materials. ( http://www.ASTM.org ) The ASTM Standards are generally available in major libraries.
The standard was updated in 1993: ASTM E303-93 - Standard Test Method for "Measuring Pavement Surface Frictional Properties Using the British Portable Tester".
The Test Method can be ordered directly from the ASTM web site.
For example, to continue this discussion look for a thread titled
Pendulum Drag Tester
If this thread does not exist in the current archive, you can begin another one by using that title.
Repeatability errors can also be present in conventional skid testing. Say the person running the skid tests was reading a speedometer to determine his skid test speed. Some analog speedometers are hard to read. If he was 1M/H, slow on this test, .5M/H fast on the next, and 1 M/H fast on the third, repeatability errors would arise when calculating for the drag factor. Digital speedometers help a little but still don't tell the entire story. Is an indicated 34 M/H 34.0 or 34.99? Notice that this person could test forever and would never have his test results settle on a particular value. These types of errors involve repeatability.
Any time you are presented with a number you should be aware of the accuracy involved. Knowing it is 6:15 AM with an accuracy of plus or minus 5 minutes is probably good enough to get you to work on time. On the other hand, this same accuracy may not be good enough if you are scheduling the launch of a spacecraft. It is also worth noting that increased accuracy generally costs money.
The next question one needs to think about is the nature of what we are measuring. Is the quantity we are interested in constant? In the rifle-sighting example, the site and bulls-eye remained fixed. Given an accurately calibrated scale (low bias) we could determine the distance away the bullets hit resulting in a measure of the accuracy of your the rifle's sight. The problem gets more complex if the quantity measured is changing. Another example will help illustrate.
Imagine yourself standing in your kitchen in front of your refrigerator. You have in your hand a 12" patio thermometer. Looking at the thermometer you can see it is 80 degrees (27 C) in the kitchen. Next, you open the freezer door put the thermometer inside and quickly slam the door. You wait 10 seconds, open the door and read the thermometer. It still reads 80 degrees.
The problem here is obvious and the solution intuitive. The thermometer just hasn't had a chance to respond to the temperature change. If we repeated the experiment and waited a minute this time, chances are the thermometer would read less that 80. Wait 5 minutes more and the temperature will be lower still. Wait half an hour and the thermometer will be reading less than that, say 20 degrees (-7 C). Is the thermometer reading the accurate temperature of the freezer after 30 minutes? It would be difficult to tell without more information on the behavior of the thermometer. One way to be sure would be to continue to watch until the reading doesn't change any more. When the reading has stopped changing we can presume it has settled on the temperature in the freezer. Issues of bias and repeatability remain but we can feel confident that we at least have a measurement.
This type of measurement system is called a first order system. The behavior of first order systems can be characterized just like the thermometer from the example. That is: initially there are big changes in the measurement, but change slows down as it approaches the true value of the quantity being measured, eventually reaching it.
So how does all this relate to measuring drag factors? We must first talk about another type of syetem behavior. When we first start to pull a drag sled we introduce a change in horizontal force. The spring scale responds to the change by bouncing (oscillating) around the actual horizontal force. Similar oscillations can be seen as a pulled drag tire encounters irregularities in the road. Each time a change in force is introduced the reading changes, oscillations get big, then smaller and smaller until the reading on the spring scale again settles at the value of force applied. It is important to note that while the scale is oscillating it reported some values of force that were actually higher than the stabilized value. Other values were lower than the actual value. This type of system behavior, characterized by these oscillations, is called a second order system.
Now we are ready to introduce the acclelerometer. Just as a yard (meter) stick measures distance, or a
speedometer measures speed, an accelerometer measures acceleration. The g-Analyst is a purpose built
electronic vehicle dynamics recording accelerometer. It conveniently reads acceleration in the units of g.
One g is equal to the acceleration of gravity. As it turns out, when used in skid tests, the g values
reported by the g-Analyst are equivalent to the coefficient of friction.
The picture is not quite complete. There is one more thing to consider. In our example with the freezer we assumed the temperature in the room was always 80 degrees. And, the temperature inside the freezer was always 20 degrees. We modeled the temperature change as an abrupt one (a step input). That's not what really happened. Each time we opened the door some cold air got out. The freezer got warmer and the room got a little cooler. Abrupt changes, like the freezer model, are interesting to think about in examples, but applications are rarely that simple. Skid tests are no exception.
From an acceleration standpoint, a skid is a dynamic event. As the skid pilot slams on the brakes the tires begin producing a slowing force at the tire contact patches. Over a short time this force builds to a maximum, the static friction limit, at which time the tires begin to slip, then skid. With the tires now skidding, the force generated at the contact patches decreases. The car now slows based on the kinetic friction coefficient. As the car approaches a stop the friction increases again and the car finally comes to rest. Acceleration is proportional to the braking forces. So each change in force produces a change in acceleration.
Imagine the damped accelerometer chasing these rapidly changing values. This thought provokes the following question: just what is the accelerometer reporting? The user of any such device should be comfortable with the answer for the instrument he is using.
These complications aren't the entire story. Just like the rifle sight, accelerometers have repeatability and bias errors to contend with. Fortunately, there is good news to go with this bad.
Most commercially available accelerometers have fairly fast sampling rates. The g-Analyst samples acceleration at a rate of 10 samples per second. This high sampling rate can do wonderful things for repeatability. For example 3 seconds of g-Analyst skid information would give 30 data points to assess. Compare this with the two data points generated from two conventional skid tests or 5 data points gathered from 5 drag sled pulls.
Bias can also be easily addressed with the g-Analyst. 1 g, the acceleration read by pointing the accelerometer vertically, is a convenient standard to have 'hanging around'. Similarly, 0 g read with the accelerometer pointed horizontally is an easy calibration point to check. These thoughts have guided my approach to friction testing.
When friction values are important I skid test. Skid tests are always conducted in the questioned area, in the same direction of travel and under similar ambient circumstances. If possible I will use the suspect vehicle. I instrument the test car with a g-Analyst. I have a checklist that I follow to verify the accelerometer's readings at 1g and 0g before the tests. This checks for bias error. I run two skid tests at a speed greater than 40 M/H. For each test I measure the test speed and skid lengths. After the tests I again check for bias error with the gravity checks.
Next comes time for the data interpretation. I choose my friction coefficient as the plateau value (horizontal part) of the g vs. time curve. I look for a value where the g values have stabilized for a second or more (repeatability). Why a plateau? Remember the freezer example. A stabilized value allows us to 'explain away' the transient response characteristics of the accelerometer.
The accelerometer also records the grade in the skid area after the car comes to rest. This is the additional piece of information we need to convert the coefficient of friction to a drag factor.
Finally with my f value from the g-Analyst I also calculate an f-number based on conventional skid testing protocol. These numbers are usually slightly higher than the plateau value. Yes, this more conservative value will result in slightly slower speed estimates when used with a suspects skid distance.
But there is yet one more consideration to be made. A plot of a 100 M/H test on the same surface would have a similar beginning and end. The obvious difference would be the plateau area (Phase 4). This part of the plot would be longer. Stated another way, the car would have spent much more time skidding at that lower rate. This observation has clear implications for using averaged skid values obtained at speeds lower than the suspect's speed.
This method assures that friction values will be conservative, and resulting speed estimates will reflect minimum estimates. From a criminal standpoint, testifying from a conservative minimum is a very comfortable place to be.
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