Help Understanding Mathematical Relationship Of This Mechanical Stopwatch's Indices

[Quiet 1]

This is a simple, sixty second, vintage, mechanical stopwatch. One full revolution of the sweep hand is 60 seconds. However, I am totally confused trying to understand the relationship of the 4 different registers indices. The outer register's index is simply sixty seconds. But, the outer "red" register has the numeral 20 (and so on) at the ten second 'tick'. The "black" register below it has the numeral 20 at the 12 second 'tick'. The "white" register has the numeral 20 at the 15 second 'tick'. And, the lower "red" register corresponds to the outer 60 second index..

I understand the basic, straightforward, time, speed & distance calculation of the "60 Second" register. I first though that the other three registers were designed to "read" the time, speed & distance in something other than units per hour. Perhaps kilometers per hour, nautical miles per hour, or whatever??? However, even my almost nonexistent math skills tell me there is no relationship to any of those. Nor, to the speed of sound as in perhaps the stopwatch actually being a telemeter to measure "flash / bang" distances.

Can anyone explain the registers relationships? And, or, why the dial would be configured this way? And, or, how and or, for what specific purpose it may have been designed to time? Any responses will be genuinely appreciated. (I'd even be grateful for any SWAGs but I know that is an anathema to mathematicians.)

 

[Cubist]

I'm not a knowledgeable person in the field of vintage stopwatches. So my comments are from a mathematical/ engineering viewpoint only, and I'm just guessing rather than stating certain facts! It does look like an interesting item. I just looked up what the "7 jewels" means. Apparently it's a number of rubies in the mechanism that increase both accuracy and the lifetime of mechanical watches! Anyway...

The black scale that goes from 0 to 100, during a minute, enables directly reading 1.20 minutes, or 1.2 minutes, rather than converting 1 minute 12 seconds to minutes (the black 20 aligns with the outer 12). Otherwise, to calculate this, would involve calculating 1+12/60 = 1.2. BUT, mathematicians and engineers prefer to work in seconds (which are the SI unit of time) rather than minutes. (We wouldn't usually convert seconds to being a fraction of a minute, we're much more likely to convert minutes to seconds.) Therefore I don't think that the black scale would ever be of much use to the vast majority of people (in modern times anyway). Also consider that there are no fine markings on it, so you can only read off 20,40,60,80, or 100 and you have to guess where 25,30 might be. Not very useful IMHO.

The red scale that goes from 0 to 120 in a minute could be useful to avoid writing 1/2 after the number of seconds. You could record the results in 120ths of a minute instead, or "half seconds". Therefore if you're writing a list of timings, which might look like { 10 1/2, 9, 8 1/2, 12, 12 1/2 } seconds on an old typewriter, it might be more clear if it is written as { 21, 18, 17, 24, 25 } half seconds.

I have absolutely no idea about the white scale that goes up to 80 in a minute! Why on Earth?

Overall, my thoughts are that these extra markings (and colour) seem most likely to be a sales gimmick, a marketing strategy to make it stand out from other models when viewed alongside in the shop. Honestly I can't imagine them being much practical use to most people. Having said that, it does look nice! Does it still work?

 

[JeffM]

You have the idea.

The black scale measures percent of a minute, etc.

 

[Quiet 1]

I'm not a knowledgeable person in the field of vintage stopwatches. So my comments are from a mathematical/ engineering viewpoint only, and I'm just guessing rather than stating certain facts! . . . . . . . . . Large Snip . . . . . . . I have absolutely no idea about the white scale that goes up to 80 in a minute! Why on Earth? . . . . . . . . Snip . . . . . . Honestly I can't imagine them being much practical use to most people. Having said that, it does look nice! Does it still work?

Great thanks for you response, Cubist. I collect vintage, mechanical stopwatches and have several "Decimal" varieties so I understand the desire to record and read "decimal fraction hours" and even "decimal fraction minutes" (down to .001 of a minute. . . That model's sweep hand makes a full revolution every six seconds.). I also have one that records to .005 and it's sweep hand makes a full revolution every 2 seconds. Fun to watch.

Thanks again for your response. And, yes, it does work. Moreover, you're probably correct about the dial simply being a 'marketing gimmick'. And in that regard it worked because that's the only reason I bought it. (I've never seen another one like it.)

 

[JeffM]

80 in a minute means 3/4 of a second.

 

[Cubist]

I also have one that records to .005 and it's sweep hand makes a full revolution every 2 seconds. Fun to watch.

That's really cool. It reminds me, I have a "dial micrometer" from my dad somewhere (not sure of the proper name for it). It has a depth plunger, and pressing it gently makes the hand go around SO FAST with very little force. It's an amazing thing. I've seen him use it for checking that a wheel/ shaft is true. Clamp it somewhere so that the plunger touches the wheel, and then slowly spin the wheel on its bearing. The dial shouldn't move too much during the rotation.

Moreover, you're probably correct about the dial simply being a 'marketing gimmick'. And in that regard it worked because that's the only reason I bought it. (I've never seen another one like it.)

I did a google image search for "vintage stopwatch" and the ones with solid red registers certainly stood out to me. The word gimmick seems a bit harsh now, because aesthetics are very important for a product's success. I also found another make of stopwatch that looks similar while I was searching. Type in "vintage stopwatch Lustro" and click on the image search button!

 

[Cubist]

80 in a minute means 3/4 of a second.

True. Out of interest do you know an application, or industry, that may have used this?

I find it quite annoying that there's no fine scale on the 80 register, and it's not very easy to use the outer seconds scale to help with judging how many eightieths there are between the numbers. I guess that for every 3 seconds, there are 4 eightieths.

 

[Quiet 1]

80 in a minute means 3/4 of a second.

Uh, ok, if you say so. Can you, without making my eyes 'glaze-over', explain how to 'calculate' that?
(As stated in my OP I'm exceedingly math challenged. And, I should add, exceedingly old.)

 

[Deleted member 4993]

Uh, ok, if you say so. Can you, without making my eyes 'glaze-over' explain how to 'calculate' that?
(As stated in my OP I'm exceedingly math challenged. And, I should add, exceedingly old.)

Right now Jeff probably is taking his "beauty-nap" (we are very old too ...)

It takes 60 seconds (the wide white band) to sweep 80 divisions (bottom - narrow white band)

So to cross 1 division (imaginary - no markings) of the (narrow white band) it will take (60/80=) 3/4 seconds.

80 divisions swept in 60 seconds → 1 division swept in 3/4 second.

 

[Quiet 1]

Thank you, Subhotosh Khan. I actually grasped your explanation with clear eyes. i.e. 3/4 second or, as a decimal 0.75. Wow! By jove, I think I've got it. And, thanks again to all who replied.

 

[JeffM]

@Cubist I was taking my nap as the great Khan suspected. (Actually, I was helping to select a candidate for the local school board.)

I suspect that the purpose is to allow calculation (estimation) of times to different fractions of a second using interpolation, something that used to be taught. So if the hand points to 23. It represents APPROXIMATELY 22.5 seconds to 23.5 seconds, but it represents APPROXIMATELY 45.5 half seconds to 46.5 half seconds, which refines the approximation. Moreover, it represents approximately 68.5 quarter seconds to 69.5 quarter seconds. It allows for tighter measurements. I do not think it is a sales gimmick. but rather a way to refine estimates depending on the scale that is relevant.

 

[JeffM]

Upon reflection, I realize that my answer above can be sensible only if the watch itself does not jump discontinuously from second to second. The watch must move to positions between tick marks.