B Looking for quality data from ticker time experiments (for quadratic regression analysis)

[neilparker62]

TL;DR Summary

Trying out quadratic sequencing and quadratic regression analysis

Hi

I'm looking for pictures of quality data from ticker timer experiments. Especially if you have samples of tapes showing free fall. I want to experiment with quadratic sequencing and quadratic regression analysis of ticker timer data. If you are so kind as to post a pic of your ticker timer tape, could you please include on it some kind of scale reference which enables me to measure distances on the tape. Otherwise just a pic of the tape is fine - I don't need the tabulated data since I will be drawing up my own tables. Thanks .

(Am asking here because the data sets and/or pictures of tapes I have found so far online are not very convincing).

 

[Tom.G]

Can't help but...
What is "ticker timer tape"?
Stock market ticker tape is the only one I've heard of.

 

[sophiecentaur]

What is "ticker timer tape"?

It's a rather outdated school demonstration / experiment in which a paper tape is pulled by a falling (or otherwise accelerating) object. Regular marks are made on the tape by a vibrating arm with a pin. I liked the class exercise because it's a very tangible demo of the relationship between s,a and t and kids tend not to manage to mess it up and they get results they can stick in their books.

 

[neilparker62]

It's a rather outdated school demonstration / experiment in which a paper tape is pulled by a falling (or otherwise accelerating) object. Regular marks are made on the tape by a vibrating arm with a pin. I liked the class exercise because it's a very tangible demo of the relationship between s,a and t and kids tend not to manage to mess it up and they get results they can stick in their books.

I wonder if you could create a precision ticker timer device using a laser to burn small holes (or just marks) on the ticker tape ? Don't know how accurate 'traditional' 50Hz or 60Hz ticker timer devices are in terms of their frequency ?

 

[neilparker62]

Here is a "traditional" ticker timer data set graphed and analysed on desmos.

https://www.desmos.com/calculator/nb7pnzzu47

 

[sophiecentaur]

Don't know how accurate 'traditional' 50Hz or 60Hz ticker timer devices are in terms of their frequency ?

The 'ticker' is mains driven. The accuracy is 'appropriate' if the tape lengths are measured with a ruler. As an exercise in graphing and analysis it's fine with plenty of system noise. I have no idea how much the tape will drag or stretch.
I wouldn't have thought that additional frills (laser marking etc) would be worth while as the rest of the equipment components (trolley and ramp) suit each other.
If you want better results then start from scratch with more modern tech but the thread title suggests that the errors are part of the exercise.

 

[neilparker62]

Re Mains (UK and other 50 Hz countries)

±1%

National Grid is obliged by its licence commitments to control the frequency within ±1% of 50Hz so it can fluctuate between 49.5Hz to 50.5Hz.

I think a pulsed laser could improve on this anyway. Re trrack and trolley, I'm not thinking along those lines I'm thinking only about a relatively heavy object in free fall. Heavy so that it's motion is minimally impeded by the 'paper trail' behind.

Above data set is from a "free fall" experiment and it's clear there are some problems with drag and/or frequency because the value of g (from regression) is quite a bit less than expected. But at least the data set showed reasonably constant "second differences" which is more than can be said for various other data sets I've looked at.

 

[sophiecentaur]

Re trrack and trolley, I'm not thinking along those lines I'm thinking only about a relatively heavy object in free fall.

If you want to get a 'good' value for g then I( wouldn't think that a moving tape would be a good idea. Tinkering with an already aged design won't produce worth while results. Search around for methods for measuring g and take your pick.

 

[neilparker62]

For the reasons you mention above, the ticker time experiment is a very good one for the classroom. So it might be worth putting some effort into modernizing it - perhaps along the lines I suggest with a laser. Or other electronic means. Accuracy can be improved without necessarily wanting to rival the CODATA value (9.806 65 m s-2)

Looking at various videos, it also seems that analysis techniques haven't advanced much. Students should definitely be putting their results on a spreadsheet and should be taught the basics of regression analysis. Ticker tape data should also be checked for constant second differences - something that is notably absent from anything I've seen. Video demonstrations show a calculation of acceleration based on v(t) at the end of the tape minus v(t) at the start of the tape. Then you look in between and the second differences are showing very obvious non constant acceleration.

Am thinking of writing an Insights article along these lines.

 

[Tom.G]

If you are going to use a LASER to mark the tape, that better be photo-sensitive tape! The power needed to mark plain paper will need much shielding to avoid skin and eyes.

Just sayin'.

 

[neilparker62]

Ok thanks - will google for that. Could be an interesting raspberry pi programming poject!

 

[neilparker62]

Sat through 25 minutes of this mostly in a total daze but I think it's more or less what we need. Just thinking for the ticker timer one could adapt the light gate to count perforations in ticker tape - presuming we can get perforated ticker tape!

A very eloquent young techie team!

 

[DaveE]

Kind of interesting from a nostalgic perspective. But why not use video analysis now that everyone has a smart phone?

https://www.fizziq.org/en/post/video-analysis-for-teaching-physics

 

[neilparker62]

Kind of interesting from a nostalgic perspective. But why not use video analysis now that everyone has a smart phone?

https://www.fizziq.org/en/post/video-analysis-for-teaching-physics

Well I did that using a couple of slow motion free fall videos I found. I can't say the results were very convincing. For example I used a pixel ruler to measure displacement data from the following strobed free fall:

https://techtv.mit.edu/videos/831-strobe-of-a-falling-ball

The value of g obtained was really low but perhaps I've got problems with the starting point or maybe the strobe frequency - which they don't mention. I guess MIT expects you to calculate it which I did (or attempted to do anyway).

https://www.desmos.com/calculator/c6ag71iso0

Also:



In both of these I measured at constant time intervals and expected to see constant second differences in the data sets. But this was not the case in either. Possibly this problem will go away if we use very high fps for the videos.

https://www.desmos.com/calculator/c6ag71iso0

 

[neilparker62]

I have concluded there is some problem with the above slow motion video - the lack of constant second differences in position readings is an artefact of the slow motion. It looks as if the video is taken with a 12000 fps camera since 8 frames x 15 = 120 corresponds to 10ms on the timer. This means frame interval should be about 83 micro seconds and if I do frame stepping I don't always get that.

Would be good if someone could somewhere post a similar free fall video against an accurate background scale. Using a high speed (high fps) camera. And including a timer.

 

[DaveE]

Would be good if someone could somewhere post a similar free fall video against an accurate background scale. Using a high speed (high fps) camera. And including a timer.

Literally my first google search hit:


I'm sure you'll want to look for a better one.

 

[neilparker62]

I'm sure you'll want to look for a better one.

Thanks - the one I posted above is actually what I wanted but I'm not sure whether there's a problem with its displayed timer or if there is some other experimental 'snag'. I will try to put together a post which explains the problem in more detail.

 

[jtbell]

What is "ticker timer tape"?

It's a rather outdated school demonstration / experiment in which a paper tape is pulled by a falling (or otherwise accelerating) object. Regular marks are made on the tape by a vibrating arm with a pin.

That method must be reeeallly old.

In all the introductory labs that I did as student and instructor/professor from the 1970s through 2000s, the standard equipment for this sort of thing was the "spark timer." The tape remains stationary, and the falling object produces electrical sparks that burn holes / leave marks on the tape.

Here's a version for free fall:

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/ffallex.html

They're also used with air-tracks to measure acceleration along an inclined track, or the effect of friction on a level track.

 

[tech99]

We just count how many dots every 10cm (or suchlike). It works very well and timer accuracy is more than adequate. The ordinary optical classroom timer gates do not do the required task. It is very good for children to set up and manipulate the little ticker printer rather than spending yet more time looking at a screen and a mobile phone.

 

[neilparker62]

That method must be reeeallly old.

In all the introductory labs that I did as student and instructor/professor from the 1970s through 2000s, the standard equipment for this sort of thing was the "spark timer." The tape remains stationary, and the falling object produces electrical sparks that burn holes / leave marks on the tape.

Here's a version for free fall:

http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/ffallex.html

They're also used with air-tracks to measure acceleration along an inclined track, or the effect of friction on a level track.

Thanks for the link - very informative. My data (measured from the slow motion free fall video in post #14) has the same problem with first differences being "wobbly" and second differences even more so. Gets worse at higher sampling frequencies: The regression fit below gives g=9.67 m/s/s which is not too bad I suppose Quadratic fit (a * x^2) on the underlying position data gives g=9.85 m/s/s.

I think there's scope to give some careful thought as to how to reduce 'wobble' and generate data sets which are more linear at first difference and more constant at second!

 

[Tom.G]

My data (measured from the slow motion free fall video in post #14) has the same problem with first differences being "wobbly" and second differences even more so. Gets worse at higher sampling frequencies:

This post is sort of like throwing stuff against the wall to see what sticks.

Hmm... that sounds more like an instrumentation problem, as in the camera or its optics, or maybe vibration from not being solidly mounted... or even in the setup of the tape versus the dropped object.

For instance there are five occurences of "groups of 3" in the graphed data.

Tracking it down could be a major research project in itself though!

Any chance you can beg, borrow, rent, or steal, a high frame rate camera ("slow motion" camera)? And maybe put a metronome or a high resolution fast mechanical timer in the frame. (Even a recently calibrated oscilloscope syncronized to the power line.)

Cheers,
Tom

 

[Swamp Thing]

The discussion on ticket tape experiments gave me a feeling of nostalgia. As a child, I read the series from the Physical Sciences Study Committee (PSSC) that our local library had. We did not have access to the kind of equipment they described in their lab manuals, but I still loved reading about that kind of stuff.

Regarding a modern version, maybe thermal paper is available in narrow strips? And maybe it will record pulses from an eye safe laser? And I think most thermal paper can be marked with a fingernail, so an electromechanical tapper might also work.

 

[neilparker62]

This post is sort of like throwing stuff against the wall to see what sticks.

Hmm... that sounds more like an instrumentation problem, as in the camera or its optics, or maybe vibration from not being solidly mounted... or even in the setup of the tape versus the dropped object.

For instance there are five occurences of "groups of 3" in the graphed data.

Tracking it down could be a major research project in itself though!

Any chance you can beg, borrow, rent, or steal, a high frame rate camera ("slow motion" camera)? And maybe put a metronome or a high resolution fast mechanical timer in the frame. (Even a recently calibrated oscilloscope syncronized to the power line.)

Cheers,
Tom

Thanks for the suggestions on possible causes of error in the data set. Apologies if my posts are a bit erratic. I think the main request is exactly what you've asked for - namely a data set from a high frame rate camera video of free fall motion set against an accurate scale and including an equally high rate timer device. Unfortunately I don't have such kit available to me unless I invest lots of time in doing a Arduino or raspberry pi project perhaps.

Have written to Dr Rod at his very excellent Hyperphysics website requesting such. I said for me the "experimental jury" is still out on constant g since I have yet to see convincing evidence of constant second differences in a free fall data set.

Edit: Graphed the first 14 points of the Hyperphysics dataset. I would say after that the bob hit some kind of "speed wobble" since thereafter the data is inconsistent. Probably this is about as good as it gets for (reasonably) constant second differences. Values of g calculated on regression fits of original data and first differences and mean of second differences are (again reasonably) consistent.

https://www.desmos.com/calculator/u153wz7jkh

 

[neilparker62]

 

[sophiecentaur]

I would say after that the bob hit some kind of "speed wobble" since thereafter the data is inconsistent.

Good idea. Could you video the tape as it's pulled through, to see if a wave forms?

Edit: The bob is fairky massive but the tape could have a transverse vibration and catch on the slot it runs through. Of course, the tape method and mechanical marker has always been aimed at potentially clumsy kids. I have always found that it's aimed at moderate experimental skills and they nearly all get results that they 'understand'. Most exercise books tended to have a convincing graph, made with sections of their tapes. Sometimes, a value of g (actually g cos(θ)) on a sloping runway would turn up.
'Improvements' to this basic method would still fall short of methods with no contact on the falling object - nearer to free-fall.

 

[neilparker62]

Good idea. Could you video the tape as it's pulled through, to see if a wave forms?

I'm doing a 'virtual experiment' using the Hyperphysics data set so I don't have access to the physical equipment. But if you look carefully at the section of tape photographed (don't know if it's representative of the data set shown ?) , you'll see the dots are not quite in line which indicates a small transverse oscillation the amplitude of which could increase with time.

 

[sophiecentaur]

I'm doing a 'virtual experiment'

Sorry. I keep forgetting the rules of your game and want to get 'practical'.

 

[neilparker62]

I've written an "Insights" article on the use of Quadratic sequences to analyse free-fall data sets.



Would like to request contributors to this discussion to review the above (if you have time!). Please let me know if you find any obvious mistakes or have some suggestions for improvement.

Edit 24/3/2025: Updated the pdf doc after correcting some mistakes I found in it.