# Accuracy of a meter stick

Gold Member

## Main Question or Discussion Point

I was grading my labs and in this lab, we used a meter stick and a wooden protractor. A group finally wrote in their write up that they believed the error was due to the inaccurate nature of the equipment. This begs the question, what sort of tolerances do you see in the manufacture a typical wooden meterstick and protractor that you'd find in a university physics department?

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russ_watters
Mentor
Did they really mean the inaccuracy of the meter stick or the imprecision of humans being able to use it? I'd be surprised if most meter sticks had worse than a 1mm accuracy over their full length.

How far off were their results? Have they compared their meter stick to any others to check the accuracy?

Gold Member
They had decent results, they were simply finding the result of adding two vectors, A + B = C on the sidewalk and they were off about 5%. I'm more concerned with how they view equipment. It always stuck in my head when I was in the first or second year of my undergrad and I was in a lab and our professor asked what we could do to make more accurate measurements. Of course, what do we say? "Electronic equipment" (we were using ol fashion measuring stuff, i forget which though :). The professor then replied "How do you know electrical equipment is more accurate".

They did mean the inaccuracy of the meter stick. I think they even mentioned twice about needing more accurate equipment for smaller errors. They also mentioned human error so I don't feel they're mixing up the two. I was hoping to find online some manufacturers tolerances but finding them isnt as easy as I thought. I wanted to mention it on this students report but I suppose demonstrating in the lab will be good enough to prove the point.

nvn
Homework Helper
Pengwuino: Commercial measuring devices tend to be very poor quality. So I would say the meter stick and protractor could easily have an accuracy error of +/-0.3 %. Or, for very poor quality, maybe up to +/-0.5 %.

D H
Staff Emeritus
To add to what Russ said: There is also a human error in interpretation. Suppose you made draw two solid circles on a sheet of paper separated by some known distance. You make copies of this, hand these out to your class, have them measure the distance between the circles, and compare the results. You will probably see a bimodal distribution because some students will assume you meant center to center while others will assume you mean the edge to edge. Some will round, some won't. There are lots of places that human error and human (mis)interpretation can slip in, even in a simple assessment such as this.

FredGarvin
I remember from my undergrad physics labs that the rule of thumb we used was usually the uncertainty/inaccuracy was 50% of the smallest increment. That didn't include parallax error.

Gold Member
Pengwuino: Commercial measuring devices tend to be very poor quality. So I would say the meter stick and protractor could easily have an accuracy error of +/-0.3 %. Or, for very poor quality, maybe up to +/-0.5 %.
Worse case scenario, that's 0.5% of the 5% error they recorded. Definitely not something that can be attributed to equipment error.

D H said:
To add to what Russ said: There is also a human error in interpretation. Suppose you made draw two solid circles on a sheet of paper separated by some known distance. You make copies of this, hand these out to your class, have them measure the distance between the circles, and compare the results. You will probably see a bimodal distribution because some students will assume you meant center to center while others will assume you mean the edge to edge. Some will round, some won't. There are lots of places that human error and human (mis)interpretation can slip in, even in a simple assessment such as this.
None of this woudl be the case since there was no copying or possible way of misinterpreting the instructions (that wouldn't result in outrageous errors).

Gold Member
I remember from my undergrad physics labs that the rule of thumb we used was usually the uncertainty/inaccuracy was 50% of the smallest increment. That didn't include parallax error.
This is where I always have to think abit about what's in question. 0.5mm is the precision in the measurement. However, the accuracy... how would we figure out the accuracy?

D H
Staff Emeritus
What were they measuring? Not just vectors, how were the things they were measuring drawn? You mentioned vectors on a sidewalk. How does that differ from measuring circles on a paper, conceptually? What they did measure versus what you wanted them to measure might well have been two different things.

Gold Member
Using a piece of chalk and a meter stick, they went outside and drew a 1.413m vector North. Then, from that tip, they measured a vector due east at 0.468m or something. They used a metal L thingy, forget the name, that allowed them to draw the second vector perpendicular to it. They then used the meter stick to draw and measure the resultant vector. A 5% error meant a ~8cm error which is well above equipment error in my mind.

nvn
Homework Helper
Pengwuino: If I understand your reply in post 7, you are saying there is still a 4.5 % error unaccounted for. I think a significant amount of the remaining 4.5 % could be attributed to [strike]protractor[/strike] metal L square misalignment, and to the chalk equipment error. [strike][...] Protractor[/strike] L square misalignment, extrapolated over a large distance, would seem to be a major culprit, creating a significant percentage of the error in a linear distance measurement, I would think. This could be calculated.

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Gold Member
The protractor wasn't used to measure the length of the new vector. It's strictly an issue with the meter stick.

Bystander
Homework Helper
Gold Member
Using a piece of chalk and a meter stick, they went outside and drew a 1.413m vector North. Then, from that tip, they measured a vector due east at 0.468m or something. They used a metal L thingy, forget the name, (It's called a "square.") that allowed them to draw the second vector perpendicular to it. They then used the meter stick to draw and measure the resultant vector. A 5% error meant a ~8cm error which is well above equipment error in my mind.
Kids & chalk? That's arctan(1-2cm over the lengths of the legs of the square) error in the angle.

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D H
Staff Emeritus
The metal L thingy,

is an L square.

I see several measurement and construction errors that are easily made. Add in some boneheaded student errors and an error of 5% looks quite possible.

Some of the sources:
1. Drawing a 1.413 meter long straight line using a stick that is only one meter long. They might well have mis-measured or put a bend in this line.
2. Drawing a line normal to the first line. Get the angle wrong and you have a good sized error. Watch a do-it-yourself construction project on TV and you will get the idea of how big an error people can make in this regard.
3. Drawing a 0.468 meter long line along that normal, starting from the first line. What if they started from the edge of the first line rather than the centerline? They used chalk after all.
4. Measuring the resultant diagonal. Here is where the errors can really stack up.

An 8 cm error does seem a bit out-of-whack however.

I dont like the phrase human error, as it basically means 'I didnt follow the instructions' which is a blunder rather then an error.

In this case, I dont think the blunder was their fault as it is pretty hard to draw a straight line 1.4m long with a 1 m ruler on the ground.

Peng if you want to know why they got answers so far off the mark get htem to answer it. Ask them to justify why they put their answers with regards to error. This will let you know if they have the concept of magnitude of error, and where its coming from.

Also dont let them use human error, make then brake it down, becuase its a cop out answer.

i think you looking at it wrong, your thinking of the error in absolute terms. because you think 8cm is alot, dont forget that its all relative. think in relative terms as in the 5%. is that alot? in my opinion no. not considering that those kids are on their hands and knees taking measurements greater than the measuring device, not once but twice. the first being the first leg and the second being the resultant vector which is as you know is about 1.5m.
what were the error percentages of the other labs?

on a side note, why do they call it an L square. isnt more appropriate to call it a squared L? eh...

D H
Staff Emeritus
think in relative terms as in the 5%. is that alot? in my opinion no. not considering that those kids are on their hands and knees taking measurements greater than the measuring device, not once but twice. ...
... with a fat piece of chalk, to boot.

Integral
Staff Emeritus
Gold Member
Definition of government work:

Measure it with a micrometer, mark it with chalk, cut it with an axe.

As already mentioned measuring a chalk line on concrete will have to be done carefully and errors will add up. Did you do a formal error analysis of the complete computation?

nvn
Homework Helper
Pengwuino: Assuming each side of your metal L square is 200 mm in length, and assuming the chalk line width is tc = 5 mm, I got a maximum possible equipment accuracy error, in the resultant vector length, of +/-2.9 %. Of this value, 0.5 % is meter stick equipment accuracy error; the remaining 2.4 % is chalk equipment error. If we instead assume tc = 6 mm, it increases the maximum possible equipment accuracy error to +/-3.4 %, in the resultant vector length.

If either side of your metal L square is longer than assumed above, it would decrease the chalk equipment error.

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D H
Staff Emeritus
nvn, did you account for the fact that two of the length measurements involved lengths longer than the measuring device? This creates multiple sources of error.

Have any of you done home repairs? Use the wrong equipment, and you are bound to get right angles that aren't right, straight lines that bend, measurements that are off. A meter stick, a piece of chalk, a L square are what I would classify as the wrong equipment.

Yep. getting bob on 90 degrees and then mesuring a length with the wrong equipment is nigh on impossible. My shelves are testament to that, I blame the crap spirit level tbh, going to get myself a nice sexy laser one.

For this i'd use my ultra low tech multi purpose string. Cut to length, put into tension for a perfectly straight line, cover in chalk + twang agaisnt the ground(optional). Bobs your Monkhouse.

I love string it's just so damn useful.

D H
Staff Emeritus
I love string it's just so damn useful.
Plus its about as low tech as you can get. Failures? Who cares? Compare the cost of a string failure against a failure of string's high tech equivalent, the laser level.

mgb_phys
Homework Helper
Definition of government work:
Measure it with a micrometer, mark it with chalk, cut it with an axe.
Remember hubble?

Super accurate meter stick $$, end cover to protect end of meter stick$$ - forgetting to remove end cover - priceless.

nvn
Homework Helper
nvn, did you account for the fact that two of the length measurements involved lengths longer than the measuring device?
D H: Yes, I accounted for the two long length measurements exceeding the measuring device length, and I updated the numbers in post 19.

alright, time for an uncertainty analysis
do we use RSS os simple sum?
does anyone have a NVLAP tape measure?
dang it, cal stricker is out of date!!

opps, i let my metrology leak out

dr

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