Geo....I think the time observed will depend on the type of ZERO GRAVITY CHAIR your sitting in...there are some nice ones for sale on EBAY...I was thinking of getting one......and.....checking .......the......time.........difference.........between ........Earth.........and......(grins)......Pluto???...beam me up Scotty.....ther's no intellegent life down here.

Steve,

One final question before I vote. On the watch you mention, without doing any alterations on it, only adjusting the slow/fast, how much time difference can you get in one (Earth) 24 hour period? Say for example it is keeping correct time set as fast as it will go, if you slow it down all the way, how much time will it loose in 24 actual hours? Not that it will help me with my answer, just wondering.

I think I have an anniversary clock that keeps martian time.



Andy

Member of Chapters 168 and 185.

Andy -- From what I recall, the total range of adjustment on an average 992-B (or 4992-B, etc.) is about 6 minutes per day. With the watch adjusted so it keeps good time with the regulator in the center of the scale, it would be possible to make it run faster or slower by about 3 minutes per day. With the watch adjusted so that it keeps good time with the regulator all the way toward "fast," moving it all the way toward "slow" should make it lose something close to 6 minutes per day.


George -- Studies with humans indicate that without exposure to any means by which to judge the passage of time, most people tend to fall into schedules of 25-hour days. Also, for what it's worth, a number of episodes of "Star Trek" involved watches, including an episode of "The Next Generation," which involved Mark Twain losing his pocket watch.

====================

SM

For those who are ready for the solution to the "Mars Time" problem, click on Page 2 of this topic. It contains a copy of an e-mail from a writer (Tim) to me, as well as my reply, which I believe explains the solution fairly well.

At the moment, 9 votes have been cast. Three for 17505.2, three for 17518.4, one for 18508.7, and two for "None of the above."

==========

SM

Oops!

I thought sure the reply above would post to the bottom of page 1, but it didn't. Sorry about that!

===COPIES BEGIN===

Hi Steve,

I'm finally getting around to doing the research for the article about living on Martian time for Astronomy magazine. Thanks for agreeing to talk to me about the watch you designed and made for the team.

Here are some questions I have to get us started:

1) [The scientist] mentioned that you specified a particular model of watch for the modification. What model was it, and why did you choose it?

2) What makes this a challenging project? Apparently, [the scientist] received a lot of replies from watchmakers that "it can't be done" prior to your agreement to take it on. Why would others say it can't be done? Why were you so sure it could be done?

3) What were the major modifications you made? Was this a matter of manufacturing different gears with an unusual number of teeth?

4) What kinds of experiments did you do to come up with the design, or was it merely a matter of mathematical calculations?

5) How long did the design/ experimentation phase take before you produced a viable Mars watch?

6) What was the biggest problem you had to overcome?

If you could recommend any basic book on watchmaking that would help me to understand the technical difficulties the project, please let me know. I would be happy to read it so I could understand things better........

==========

Hi again Tim!

Your questions are very good, and I'll try to provide the most detailed answers I can so as to afford you the greatest possible amount of information from which to draw.

1) [The scientist] mentioned that you specified a particular model of watch for the modification. What model was it, and why did you choose it?

[The scientist] seemed more interested in a pocket watch than a wristwatch, and with that in mind, I suggested any "late-model" American made "railroad approved" pocket watch. Although production of the last of those ended around 1970, spare parts for many models are still available, and that's an important consideration for any watch that's going to be carried in actual use. Another bonus for American railroad pocket watches is that they're highly accurate (for mechanical watches), and extremely well made. With proper care and adjustment, they're capable of rates within 30 seconds per month, and can last a person for an entire lifetime.

An excellent "late-model" railroad watch was the "992-B," which was produced by the Hamilton Watch Company of Lancaster Pennsylvania, from about 1940 until about 1970. A "variation" of this model, used primarily as a navigators' watch for Army and Air Force aviators, was produced for the US Government during W.W.II and again during the Korean Conflict. Those watches were designated as the "4992-B" model, and differ from the standard railroad models in three basic ways: First, they have 24-hour motion work, instead of the usual 12-hour type (in other words, the hour hand makes only one revolution in 24 hours, rather than the usual two). Second, they have center sweep seconds hands, rather than the small subsidiary seconds hands (at the 6 o'clock position on the dials), and finally, they have a "hack" feature, which stops the watch when stem is pulled out for setting. That allows the watch to be conveniently coordinated to the exact second with other time standards, and it isn't a feature commonly found on most railroad models.

After a bit of discussion and explanation, [the scientist] decided the 24 hour dial would be best for the Mars watch (since AM and PM would be more readily apparent), and he also thought the "hack" feature might be useful as well. With those being important factors, it essentially narrowed the range of possibilities to the Hamilton 4992-B, and its counterpart, a model produced by the Elgin National Watch Company of Elgin Illinois. Since the Hamiltons are a bit better (and more common), that's what he decided to get, and after consulting with me, he finally bought one on eBay, which is the watch I modified to become the "Mars watch."

2) What makes this a challenging project? Apparently, [the scientist] received a lot of replies from watchmakers that "it can't be done" prior to your agreement to take it on. Why would others say it can't be done? Why were you so sure it could be done?

Until I asked and was informed that the difference between Earth time and Mars time wasn't a huge amount, I wasn't sure it could be done either, but when [the scientist] told me that the difference was only about 40 minutes per day, I knew that I could accomplish that in a way that perhaps other watchmakers hadn't considered (as explained below).

3) What were the major modifications you made? Was this a matter of manufacturing different gears with an unusual number of teeth?

No. There would have been no way to accomplish it with gearing alone (as the ratios would have been much too complex), and a modification to the "time base" would have still been necessary. Of course, that being the case, it made more sense to simply modify the time base exclusively, and leave all the gearing alone.

In short, any mechanical clock or watch contains an "escapement," which is the internal "time base." For all practical purposes, the escapement is merely a mechanism which precisely regulates the rate at which a stored kinetic force is expended. In watches, the stored force is contained in a "mainspring," and the escapement regulates the rate at which that spring unwinds. The escapement is powered by a series of gears (wheels and pinions), and the hands are simply attached to the axles of certain gears, to display the positions of those gears relative to a fixed scale (the dial of the watch).

In mechanical watches, the rate at which the escapement operates is determined by the moment of inertia of the "balance wheel," and the strength of the "balance spring" (sometimes called the "hairspring"). Essentially, the balance wheel and spring serve the same purpose in a mechanical watch that a pendulum does in a mechanical clock. The pendulum, however, relies upon the force of gravity for it's "return power," while in watches, the balance spring serves as an "artificial gravity," which "returns" the balance wheel toward a constant center during its period of oscillation, exactly the way gravity returns a pendulum toward center in a clock.

The gearing of most pocket watches (including the one I used for the Mars project), is designed to keep correct "Earth time" with an escapement operating at 18,000 beats per hour. The "beats" are the "ticks" (and "tocks") of the watch, and are caused by the operation of the escapement. For each oscillation of the balance wheel, a "tick" is produced as the "escape wheel" advances one tooth. Of course, divided by 60 (the number of minutes in an hour), a standard watch with an 18,000 bph train (gear train), should tick exactly 300 times per minute.

As noted above, the rate is determined by the relationship of the "moment of inertia" of the balance wheel, and the strength of the balance spring. If the moment of inertia is increased, the wheel will rotate more slowly, and the rate of the escapement will slow accordingly. Conversely, if the moment of inertia is reduced, the wheel will rotate more rapidly, and the rate will be increased. Think of it like whirling a piece of chain in the air; if the length is short, it's possible to make the section whirl quite rapidly. On the other hand, as the length is increased, it's rate of rotation will slow accordingly. Essentially, this is the same principle that applies to pendulums, and to the balance wheels in watches.

Of course, with pendulums, their rate is determined by their length, and the force of gravity on Earth, which is essentially constant. If a pendulum was subjected to a change in gravity, however, it's rate would change accordingly; if the force of gravity was increased, the rate of a pendulum would increase, and if the force of gravity was reduced, so would be the rate of the pendulum. Since in watches, the balance spring provides an "artificial gravity," increasing its strength will increase the rate of oscillation of the balance wheel, and reducing its strength will reduce the rate.

In any event, the balance wheels in virtually all American pocket watches have between 14 and 20 "balance screws" around their perimeter, which are to provide a means of correctly matching the moment of inertia of the wheel to the strength of the hairspring, in order to provide the desired rate. The rims of balance wheels usually have more (threaded and tapped) holes (usually at least 24) than there are screws, in order to allow for equalized distribution of the weight screws around the perimeter of the wheel. Of course, if a particular balance spring and wheel are "matched" so that oscillations of the wheel will occur at exactly 18,000 beats per "Earth hour," removing screws will increase that rate, and adding screws will slow it down.

4) What kinds of experiments did you do to come up with the design, or was it merely a matter of mathematical calculations?

My several years experience as a watchmaker have taught me that in an average pocket watch, a pair of balance screws will change the rate of a balance wheel by about 500 beats per hour, which when calculated mathematically, is very close to the difference in daily rate between "Earth time" and "Mars time." Of course, by simply changing the rate of the escapement, the rate of the watch can be changed without the need for changing any of the gearing, and that's exactly the approach I took. I calculated the exact number of "beats per hour" necessary to make a watch designed to advance the hands one hour in 18,000 beats, in order to extend that period of time to correspond with the extended length of the Martian day.

5) How long did the design/ experimentation phase take before you produced a viable Mars watch?

and

6) What was the biggest problem you had to overcome?

The design was implemented exactly as calculated, and the actual modification work didn't take but a couple of hours. The biggest problem was "confusing myself" with the units, which turned out to be more of a problem than I'd originally imagined. Jeff provided me only with the information that a "mean solar day" on Mars is equivalent to 88,775.2 mean solar Earth seconds, which when reduced to ordinary units, means that when exactly 1 mean solar day has elapsed on Mars, 24 hours, 39 minutes, and 35.2 mean solar Earth seconds will have elapsed on Earth.

Knowing that the Martian day is 39:35.2 minutes longer than the Earth day, it seems logical to assume that the rate of a watch needs to be slowed by that amount in order to keep proper Martian time, and in order to accomplish that, the calculations would be as follows:

First, one would divide the number of seconds in a Martian day by the number of seconds in an Earth day:

88,775.2 / 86,400 = 1.02749074074074074074074074074074
(That's how much longer a mean Martian second is than a mean Earth second)

Next, we would multiply that number by the beats per hour of our watch:
1.02749074074074074074074074074074 x 18,000
= 18,494.83333333333333333333333332

For a difference of: 494.83333333333333333333333332 beats per hour.

Therefore, in order to make a watch LOSE 39:35.2 minutes in one Earth day, the rate of a watch would need to be reduced by that number of beats subtracted from 18,000 bph, which is: 18,000 - 494.83333333333333333333333332
= 17505.1666666666666666666666666667 bph

Unfortunately, while that SEEMS perfectly logical, it is NOT correct! A watch so adjusted would lose 39:35.2 minutes in exactly 24:00:00 mean solar Earth hours, and at that rate, it would be slow by an additional minute or so by the time the entire day had passed on Mars (a period of an additional 39:35.2 minutes, during which interval the rate differential would continue to accumulate).

Although it might not be initially obvious, the relationship between different time standards is NOT reciprocal. Just to use a nice round figure, let's assume that a "mean solar day" on Mars is exactly 24 hours and 40 minutes, as measured by mean solar Earth time. A Martian day is therefore 40 minutes longer than an Earth day, but as strange as it seems, the reverse is not true; an Earth day is NOT 40 minutes shorter than a Martian day!

The reason for the apparent anomaly is the actual difference in units of time that are each described as a "day." For Earth, a day is composed of one period of actual time, but for Mars, it's composed of an entirely different period.

For the purposes of analogy, consider the following: If "A" has $1 more than "B," then "B" has $1 less than "A," and the situation is reciprocal so long as the monetary units remain constant. If, however, "A" is Canadian, and has $1 Canadian more than "B," it doesn't necessarily follow that "B" has $1 US dollar less than "A." The reason is that the "standard" of comparison isn't constant; even though both units are called "dollars," $1 US dollar is not equivalent to $1 Canadian, and in like manner, 1 Earth "day" is not equivalent to 1 Martian "day."

Now, consider the following: A pair of clocks set to exactly 12:00:00. Let's assume that both clocks are started at exactly the same instant, but by the time one clock reaches 1:00:00, the other has advanced only to 12:59:00. In short, the fast clock is ahead of the slow clock by exactly 1 minute. Now, by the time the slow clock reaches 1:00:00, the fast clock will not read 1:01:00, it will read 1:01:01. The reason is that as time continues to elapse, the rate error continues to accumulate, and since the fast clock is gaining on the slow one at a rate of 1/60 per unit, if it gains 1 minute per hour, it will gain 1 second per minute as well.

So....... While in reality, 1 mean solar day on Mars is 39 minutes and 35.2 seconds longer than 1 mean solar day on Earth, 1 mean solar day on Earth is actually only 38 minutes and 31.7 seconds shorter than 1 mean solar day on Mars. What was actually necessary was to make the watch lose 39:35.2 minutes in 24 hours 39:35.2 mean solar Earth minutes (for an actual loss of only 38:31.7 minutes in exactly 24:00:00 mean solar Earth hours), and in order to accomplish that, the calculations are as follows:

First, one would divide the number of seconds in a mean solar Earth day by the number of seconds in a mean solar Martian day:

86,400 / 88775.2 = 0.973244780073714280564842433472411
(That's the conversion factor, which can be applied to an 18,000 bph watch, or anything else.)

Now, when one multiplies that by the number of beats per hour in the standard 18,000 bph watch, the result is:

0.973244780073714280564842433472411 x 18,000
= 17518.4060413268570501671638025034 bph

That IS the CORRECT number of beats per hour to which a watch with a standard 18,000 beat per hour escapement must be adjusted, in order for it to lose exactly 39:35.2 mean solar Earth minutes in exactly 24 hours and 39:35.2 mean solar Earth minutes, and therefore keep perfect mean solar Martian time.

Using a watchmakers' timing machine (essentially a microphone and a microprocessor with a precision internal time base that instantly converts the ticking of a mechanical watch into a digital number of beats per hour), with only a few trial and error attempts, I was able to make the escapement accomplish the necessary beat count with sufficient accuracy to make it keep Martian time within a second or two per day, which is within the mechanical limitations of the watch.

Basically, it's as simple as that! .........

As for books about how watches work, I'd recommend any by Henry B. Fried, or Donald DeCarle. I'd also recommend a visit to Wayne Schlitt's "Elgin Watch Collectors' Web Site," which can be accessed at the following address:

http://www.midwestcs.com/elgin/

You might also consider surfing the Internet and seeing what sort of information you can turn up about "how a watch works." For the purposes of the Mars watch project, you and I will be discussing analog mechanical watches with "lever escapements," which is only one of a multitude of different types.

An additional resource you might check out is the web site of the Internet Horology Chapter of the NAWCC (National Association of Watch and Clock Collectors). I'm a former VP, although I resigned some time ago because I lack the sufficient time to devote to the job that it really deserves. The web address is:

http://nawcc-ihc.com

or:

https://ihc185.infopop.cc/

Either should take you to the open public message boards, and I'm sure you'll find as many helpful people there as you could possibly want to help answer any ordinary horological questions you might have..........

So-long for now, and as always, please don't hesitate to contact me any time if you have additional questions or comments!

Steve Maddox
North Little Rock, Arkansas

==================================
END COPIES

Sad thing is, I DID vote, and can't remember what I voted, or my reasons for the time I chose. To much going on right now here at work. After reading all this, I'm not sure of anything anymore. (grins) But I'm sure mine was the right answer. Regards. Mark

NAWCC Member 157508
NAWCC-IHC Member 163

I remember what I voted!






Andy

The International 400 Day Clock Chapter 168.
The Internet Horology Chapter 185 nawcc-ihc.org

I made a this calculation:
if 18,000 beats per hour is the rate requiered for two revolutions of the hour hand in 24 hours then for the same two revolutions in 24 hour, 39 minutes and 35.2 seconds (24.6598 hours)the beat rate is sligthly slower at:

Beat rate = (24 H/24.6598) x 18,000 = 17,518.4

Now, about Steve´s last post, it was cool answer for the writer, almost an article by itself..

Nice work Steve...Congrats and applause are in order...BTW...did those NASA guys ever get back to you concerning how the Mars PW kept time with their computer model?

The calculations Carlos performed are exactly the same as mine, except that I used decimal seconds (the original units provided to me), where he used decimal hours, which were derived by an additional calculation. Were it not for that, his arithmetic is far more "elegant" than mine!




Tony -- I haven't heard from the NASA guys about the accuracy of the watch, and like you, I'm curious to know. I've been reluctant to bug them about it, but if I don't hear from them in the not too distant future, I'll write and see what they say.

On a somewhat related note, I did receive an inquiry from a lady at NASA, who wanted to know if I could make a pair of clocks with 18-inch dials, one to keep mean solar Earth-time, and the other to keep mean solar Martian-time. After a bit of thought, I decided the best way to do that would be using AC "synchronous motor" clocks, but I don't think I'm actually going to do the project (I'm a watchmaker, not a clockmaker, and I already have WAY too much to do!).

Synchronous AC clocks aren't actually "clocks," in the true sense of the word, because they have no internal time base. Strictly speaking, they're "meters," which simply run at whatever rate is supplied by their AC power source. Within a considerable range, the voltage they're supplied doesn't make any difference in their rate, but if the AC power falls to 59 Hz., a synchronous AC clock will lose 1 second per minute, and one minute per hour, etc. Therefore, in order to modify one to keep Martian time, it would only be necessary to provide it with a highly stable power supply of exactly the right frequency.

With the frequency adjusted as per the calculations above, ANY ordinary AC synchronous clock plugged into such a power supply would keep Martian time, without any modifications to the clock whatsoever. It's an interesting concept, but I rather doubt that I'm going to proceed with it (and if I do, I'm definitely getting paid this time!).

==================

SM

Steve,

Did you vote in this poll?


Andy

The International 400 Day Clock Chapter 168.
The Internet Horology Chapter 185 nawcc-ihc.org

Andy,

I didn't vote because with so few people participating, I knew it would skew the results.

I was just curious to see if the situation seemed as "unnatural" to everyone else as it did to me.

My first inclination was to assume that the watch needed to lose 39:35.2 per day, but as explained above, that is NOT correct. My initial calculations resulted with 17,505.2, and when I "checked" that by calculating it into a 24 hour day, it seemed correct.

Of course, once I realized that if the watch lost the entire 39:35.2 in 24 Earth hours, it would be slow by an additional amount by the time the Martian day had elapsed, I knew that answer HAD to be wrong. I then calculated the correct answer, but it still took me a while to understand why the 17,518.4 answer was right, and the previous 17,505.2 answer was wrong.

An additional problem came when I actually implemented the calculations in the watch. My timing machine (a Vibrograf B-300) will calculate the number of beats per (Earth) hour, but only in whole number increments. Since the nearest whole number to 17,518.4 was 17,518, a watch set to exactly that rate would lose 9.6 beats per day, which is 1.92 seconds. In order to compensate for the rounding error, I had to set the machine to use 17,518 as the "standard," and then adjust the rate of the watch so that at that measured frequency, it ran 2 seconds per day fast.

In a final test of the watch, it did in fact lose 38 minutes and 32 seconds in 24 (Earth) hours, which is exactly what it was supposed to do, and by the time 24 hours, 39 minutes, and 35 (Earth) seconds had elapsed, the time on the watch showed that 24:00:00 hours had passed, which again, was the desired result (an actual loss of 39 minutes and 35 seconds during that interval).

I therefore presume that the watch is performing nicely, although I haven't yet been informed of the actual results.

===================

SM

It would appear that within the course of the next few hours, we'll get a chance to see how smart those guys at JPL really are.

"Spirit" is supposed to land on Mars today at about 11:35 PM EST.

http://marsrovers.jpl.nasa.gov/home/index.html


I expect the mission will probably go as planned, but I can't help wondering what the London odds makers are giving........

==================

SM

Steve,
You realize that if the rover lands successfully on Mars and "Spirit" isn't working within specs, JPL will expect you to go up there and fix it.

Ed Ueberall
NAWCC 49688
IHC Member 34
The Escapement

http://aolsvc.news.aol.com/news/article.adp?id=20040102162709990001

By the way, the recipient of the "Mars watch" is Steve Squyres, from Cornell University, who's mentioned and quoted in the article above. He was also featured in a PBS "Nova" special about the project, which aired on Sunday evening, and I presume he will be featured again in a subesquent special that's scheduled to air Tuesday evening.

From the looks of things, we'll be hearing a lot about Mr. Squyres in the near future....

I hope his watch keeps working!

=================

SM

Steve,

I watched part of the Nova special last night. I don't know how much of it was recorded in June when it took off, but they predicted that it would land on Mars at a certain time. I am not sure, but I think it landed within a few minutes of the predicted time. How can they possibly have it timed that close to say within a few minutes when it will land? It looks to me like there are so many variables involved. I can't even time it that accurate when I drive a mile down the road! (Then again, I'm not spending quite as much on my trip.)

Andy

The International 400 Day Clock Chapter 168.
The Internet Horology Chapter 185 nawcc-ihc.org

It's easy, Andy -- those guys really are rocket scientists!



Seriously, though, all I can say is that they have a really good idea of how fast Mars is moving, how fast the Earth is moving, and how fast their rockets will move, and they just do the math. Since there's nothing in space to change any of the "variables," things just work out that way.

Of course, the final outcome is determined by the accuracy of the calculations, and in a very basic way, all those calculations depend upon highly accurate time measurements. It therefore is not an understatement to say that in a most fundamental manner, every horologist who ever contributed to the development of precision timekeeping, contributed to the success of missions such as those of the Mars Exploration Rovers.

=============

SM

From the New Yorker, Jan. 5, 2004, pp 27-28:

Bill Nye, a Cornell alumnus, realized that a sundial surrounded by gray rings would not only make photometric calibration possible on Mars, but would also mark the time. He pointed out that because the Rover would be roving between Mars’ tropics, where the sun is more or less overhead, the sundial wouldn’t need a bulky triangular gnomon (shadow-caster) – a stick would do. His sundial, made of aluminum and no larger than a human palm, was built into the Mars Exploration Rover.

Stu