# New to Gage Block Calibration Reports

#### dgriffith

##### Quite Involved in Discussions
In a cal report for gage blocks, a company indicated their uncertainties as described below.
Question: What does the L in +1L and +2L mean?

Measurement Uncertainty:
0.01 - 0.95 in. = ?(3 + 1L) uin.
1.00 - 4.00 in. = ?(3 + 2L) uin.

On longer lengths, it is only stated as:
5 inch = 11 uin
6 inch = 18 uin, and so on.

#### Jen Kirley

##### Quality and Auditing Expert
Hello,

As NIST describes in 3.3 of its document Uncertainty and Dimensional Calibrations (from Journal of Research of the National Institute of Standards and Technology), L involves the potential error due to thermal expansion. That is, the block's length as affected by temperature. The length can differ between actual use conditions and the conditions within a calibration laboratory. The amount of difference depends on things like material and how long the block is.

I hope this helps!

#### dgriffith

##### Quite Involved in Discussions
Yep. I've already accounted for environmental factors. Just didn't know what the L was, so now I know its additional length due to temps, etc.

So why the 2L? I guess I'm missing something in the terminology. The additional length is multiplied by two for longer blocks? It seems like the gaging face would grow (or shrink) uin per in/in. Why would it matter just because 1 inch was reached?

Last edited:

#### Jen Kirley

##### Quality and Auditing Expert
NIST describes L as simply Length in 3.3 of its document Measurement Assurance for Gage Blocks; NBS Monograph 163; 1979

ΔL/L = αL ΔT

L is the length, ΔL is the change in length of the object, ΔT is the temperature change and αL is the coefficient of thermal expansion (CTE)

Because temperature-impacted length of gage blocks tends to lessen as they get longer, the figure L in a formula, representing length as a result of temperature's impact, does not change at a straight line. The figures you quoted would have seemed obvious if the thermal expansion coefficient was traceable in terms of 1L for 1 inch, 2L for 2 inch etc. But it's instead traceable on a curve. So the 1L or 2L etc. is meant to help to mathematically calculate temperature's actual "error" introduction to the gage block's length.

All, if I got this wrong please feel free to chime in. Hershal?

#### Hershal

##### Metrologist-Auditor
Trusted Information Resource
I think you did a good job Jennifer. Well done.

Z

#### zancky

from my understanding

0.01 - 0.95 in. = ?(3 + 1L) uin.
1.00 - 4.00 in. = ?(3 + 2L) uin.

means
if You have a gauge block of nominal length 0.05 in. the uncertainty is ?(3 + 1*0.05) uin.

if the length is 1.20 the uncertainty is ?(3 + 2*1.2) uin.

i.e
1) they are fitting formula for range of length
2) the laboratory have more "trouble" in measuring parts over 1 inch

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