Any measurement taken with a mechanical device is subject to errors that may be caused by the condition of the device or by the procedure used in taking the measurement.

Some of the most common sources of errors are the

- standards to which the chain is manufactured,
- any damage to the chain, slack in the chain,
- variation in the tension on the chain, and
- changes in chain temperature.

With proper chain care and reasonable effort with each use, the effects of these errors can be kept within acceptable tolerances for all but the most accurate measurements.

If necessary, each of these conditions can be mathematically offset if they are checked and compared to a known standard.

Table of Contents

## 1. Proportional Errors

When a chain is manufactured, it is intended to have a certain length, plus or minus some tolerance. It may or may not actually meet those specs. When a field measurement is made, the acceptable error may be more or less than the chain is designed for.

For precision work, we need to measure several known distances and determine if this chain is the right length. If not, we next need to determine whether the error is in one or more specific locations in the chain or if the error is proportional along its length.

If a known distance of 50 feet is measured as 49.995 feet and a known distance of 100 feet as 99.99 feet, then all measurements taken with that chain should be multiplied by a factor of 100/99.99 (known distance over measured distance).

## 2. Constant Errors

If a chain is kinked or broken and split back together, there is a good chance that there will be consistent error for all distances measured with that part of the chain.

This error must be added or subtracted each time.

## 3. Sagging Correction

When a chain is hung at each end and not supported along its length, the weight of the chain causes it to flex and pull the two ends together. It is impossible to apply enough external force to completely overcome the sag.

Sufficient tension must be applied for all measurements to minimize the effective shortening of the chain. For accurate measurements, a correction must be made using the formula below.

true:

*C *_{s }= Sagging correction between supports, (Ft.)

*with whom *= Weight of Tape, (Lbs/Ft.)

*W *= Total weight of tape between supports, (Lb.s)

*l *= Distance Between Supports (Ft.)

*p *= Applied voltage, (Lb.s)

## 4. Voltage correction

While a certain amount of tension is desirable to compensate for the sag effect, it will also stretch the chain. It is generally believed that steel cannot be stretched very easily and indeed it is not. That is one of the reasons it is used for making necklaces. But steel will still stretch to some degree if stress is applied to it.

When comparing a chain to a known distance, the applied tension should be checked. Subsequent accurate measurements should be made with the same voltage, or if not, a correction should be made. The formula for this is also listed below.

true:

*C*_{p} = Correction per distance L

*p *= Applied voltage (Lb.s)

*p _{0} *= Tension for which the tire was standardized.

*l *= Length, (Ft.)

*a *= Cross section of the chain.

*E *= Elasticity modulus of steel. (30*10^{6}^{ }pounds/in^{2})

## 5. Temperature Correction:

Whatever material is used to make a necklace, that material will expand and contract with every change in temperature. Some materials are affected more than others, but each chain will change its length slightly when heated or cooled.

If accurate readings are required, an adjustment should be made for the change in temperature between the current temperature and the temperature at the time the chain was checked against a known distance. This formula is also shown below.

true:

α = coefficient of thermal expansion (0.0000645 / 1^{O }f)

*l *= Measured length

*t *= temperature of chain

*t *= Standard temperature (68^{O }F )

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