Physical Consistency an Introduction : Cliff Stamp


The causes of physical inconsistency in measurement

In Measurement Consistency 1 the point was made that there had to be a measurement of the consistency of the work when evaluating knives. If the difference in performance between knives was larger than how much their performance changed from one measurement to another then it could be said that the performance of the knives was indeed significantly different. But what is the general cause which makes performance measurements have a spread and not simply be an exact number?

Random inconsistency

If a 2x4 is chosen from a pile of wood it can be randomally harder, softer or about equal in to another one similarily selected. Such variations in materials cut with knives will introduce corrosponding changes in how the work effects the blades. To reduce these inconsistencies simply repeat the work and average the results. There is a forumla to predict how much the variation will be reduced. If there are N measurements then the inconsistency in the average will be reduced by 1/SQRT(N).

Consider two knives compared for edge retention while chopping 2x4's. Assume the 2x4 inconsistency is so large that one piece of wood can be four times as hard as another. If the knives were used to chop until they would not shave it would require about a thousand or so chops. The inconsistency in the final result due to the wood being inconsistent would then only be 300%/sqrt(1000) or a megar 10% . A more sensible estimate for the variation in wood hardness will obviously mean that the effect this has on the edge retention measurement will be insignificant.

Systematic inconsistency

However continuing the same comparison, what about if one knife uses all 2x4's taken from the top of the pile and the other knife uses 2x4 from the bottom of the pile. All the wood chopped by the second knife is softer than the wood chopped by the first knife due to wood on top seasoning from the sun faster. This means that there is a systematic difference in the material cut. These systematic inconsistencies are critical because they can not be reduced by taking more measurements and they move the results directly away from the true value.

Adding inconsistencies

If cutting is done by hand there are the variations in force, speed and angle of the cut. These are all examples of random changes and they add by taking the square root of the sum of the squares of each change. For example, a 15% variation in force, a 10% variation in speed and a 25% variation in angle add by (15^2+10^2+25^2)^0.5 to give 31%. The result is quite close to the maximum individual variation of 25%. This is a general property when summing squares and in general means only the the maximum random deviation matters.

Systematic deviations just add like regular numbers. If a knife is weighed in the sheath for example there is a systematic error in the weight due to the sheath. If the sheath has a small tool in the pouch then the weight of that tool just adds directly to the systematic error. This obviously leads to the solution to remove the knife from the sheath and weigh it diretly, which anyone would do. In all experiments if the amount of the systematic inconsistency can be likewise determined then it as well can be subtracted, but often this is not easy to determine.

Precision and accuracy

Precision is how different one measurement of a quantity is from the next measurement of the same. For knife performance, the precision it is mainly controlled by the random inconsistencies in the materials cut and the manner in which they are cut. Accuracy is a measure of how different the measurements are from the actual true value, it is mainly influenced by the systematic inconsistencies.

Consider two knives compared for edge retention on cardboard. A special run of carbord is use which is manufacturerd to a high tolerance on composition, a jig is made to keep the angle of the knife to the carboard constant and the knife is moved by an armature which keeps the force constant. All of this would mean that the random deviations would be very small and thus the precision very high.

However what if one of the knives had a different blade to handle angle which meant when it was put in the jig that it resulted in a different cutting angle to the cardboard. This would mean that systematically it was being used in a different manner every cut and even though the measurements were very consistent to each other they did not represent the true performance of the knife and thus the accuracy was low.

Recap

When determing knife performance, it is important to realize that there will be inconsistencies in all measurements from one to the next because of random and systematic variations. The random variations control precision and they will be reduced by averaging and in general only the largest will matter. However systematic deviations will not be so reduced and in general they limit accuracy. Thus when comparing two knives it is most important to carefully consider is there something different each time about how one knife is being used than the other.

References

Measurement Consistency : Cliff Stamp, cutleryscience.com, 2007.

Comments

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Written: August, 2007 Copyright (c) 2007 : Cliff Stamp
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