Masses and Weights
Influences to consider when refining measurements
by Philip Stein
Weighing is one of the oldest branches of metrology. It's also one of the most interesting. Weighing and measurement of mass are outstanding examples of how a complex scientific process can be engineered so it is simple enough to be practiced by the general public and widely used in commerce.
Mass measurement is also interesting because, with care, it can be carried out to very fine levels. The best mass measurements have uncertainties of the order of a few parts per billion! Time and frequency are the only other parameters that come to mind that can be measured with this level of precision.
Mass measurements are an excellent example of some principles I have previously explained in this column. The basic concepts, tools and methods are easy to understand. The hard part comes in the refinement of the measurements by consideration of a wide range of important and not so important influences.
Mass and weight
Mass is an inherent property of matter. Most of the time, we experience mass as weight--the attraction of objects to the earth as a result of the local acceleration of gravity. Expressed in its most simple form, weight = M x g where M equals mass and g equals the local value for gravity.
To measure mass, we almost always measure weight. The worldwide standard of mass is an object, an artifact known as the International Platinum Kilogram (IPK). This cylinder of polished metal is in the care of the International Bureau of Weights and Measures in Sevres, France, and is the single reference against which all other masses are defined.
There are two weighing principles in common use. These same principles are frequently used for other measurements as well. The simplest and less precise method of weighing is through the use of a scale. A spring mechanism is compressed or expanded under the force of M x g, and the change in dimension under this force is proportional to the applied weight within the appropriate range of the spring. Scales for weighing fish, grocery store scales and postage meter scales, for example, all work this way.
For more precise measurements, a balance is used. The unknown weight is compared with a known weight (calibrated by reference to the IPK). The easiest balance to imagine is a two-pan equal arm balance such as the one being held by the typical image of justice. When the weight in the two pans is the same and the arms are in fact equal, the balance beam reaches equilibrium at a level position. Otherwise, it tips one way or the other, and weight is added or subtracted to the pans until it does balance.
The balance has an obvious advantage because we don't need to know the value of gravity. Since gravity affects both weights and both pans equally, we can compare our known and unknown without reference to g. This advantage is so powerful that spring scale systems are also arranged to follow it. If we calibrate a spring scale with a known weight in the location where it will be used, the effects of variation of local gravity are also cancelled. Over the continental United States, local gravity varies by as much as about 0.2% or 2,000 ppm. This a potentially large error, and scales should not be moved without recalibration in the place where they will be used.
A precision balance is a delicate instrument that requires considerable care and frequent maintenance. Newer instruments make use of the balance principle and are more rugged and practical. The most common device is the force restoration balance. The single weighing pan is suspended on a flexible member such as a mechanical flexure. A sensor detects the position of the pan as deflected by the applied weight.
An electromagnet (solenoid) is used to provide an equal and opposing force to the weight on the pan and restores the pan position to a neutral or centered value as determined by the sensor. The current through the magnet is thus proportional to the applied weight when the pan position is restored. Precision electronics drive the magnet and measure the current, converting the display to a direct readout of mass.
Of course, this restoring force is proportional to local gravity, so the system must be calibrated with a known mass before the reading will be correct. The sensor needs to find only the neutral point precisely. Other displacements are used only to tell whether the electromagnet needs more current or less. Because of this, the sensor does not need to be very linear, only very repeatable at the balance point.
Calibration and operation of any precision balance are done according to a statistical design usually known as a weighing design. Imagine a two-pan balance in which the arms are of nominally equal length (of course, exact equality is never achieved). The simplest weighing design is one in which the imbalance is recorded with the unknown on the right pan and the standard on the left, after which the unknown and standard are exchanged and the imbalance again observed. The average (mean) value of the two imbalances is an indication of the actual difference between the two weights and is independent of arm length.
All that remains is to calibrate the mass required to cause the observed imbalance. This is done by adding a small known mass, called a sensitivity weight, to one pan and observing the change in imbalance. This is a single substitution design.
More complex designs are used to cancel the effects of temperature changes during the process, to reduce sources of uncertainty, such as bearing friction in the balance, and to compare combinations of several weights in a set with larger single weights, such as 1 kg vs. 500 g + 200 g + 200 g + 100 g. Weighing designs can also be used on single pan and force restoration balances by weighing combinations one at a time instead of in pairs.
For higher precision work, other precautions must be taken. Air currents from room drafts or from convection due to temperature gradients can exert up or down forces on a pan and weights. Magnetic force restoration balances can be affected when you are weighing ferromagnetic materials, and electromagnetic interference can upset the balance electronics. Off-center loads on the weighing pan can introduce errors, as can leveling of the instrument.
The most significant influence on weighing is air buoyancy. This is so important I will devote an entire column to the subject. Look for it in the November 2002 issue.
PHILIP STEIN is a metrology and quality consultant in private practice in Pennington, NJ. He holds a master's degree in measurement science from the George Washington University in Washington, DC, and is an ASQ Fellow.