Compensating for mechanical play

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I'm currently looking into the feasibility of a hobby project to
construct a telescope mount with computerised goto capability (that
is, you tell it where to point via computer rather than try to find
objects manually which is always a problem when the object is too
faint to see with the naked eye).

There are two aspects to this problem: one is the initial locating
of objects which needs a moderately high level of precision, pointing
to within maybe 15 arcminutes or less on two axes, and the subsequent
tracking of that object as it move across the sky.  This is a
constant movement of 15 arcseconds per second on one axis and needs
to be as accurate as possible.

The reason I am posting here is that obviously that level of
precision is going to be impossible to attain mechanically.  A
precision engineering shop may get somewhere in the ballpark but
certainly not an amatuer construction.  Therefore I'm looking into
methods of compensating for any mechanical inaccuracies electronically
and I'm interested to hear from anyone who has similar experiences.

The way I see it there are two possible approaches.  I can measure
the position of each axis directly.  I doubt a resistor-based
servomechanism would be accurate enough, but I do see high resoution
shaft encoders in the 8000 - 10000 counts per turn range that would
be in the right neighbourhood for the job if that resolution actually
translates into the accuracy it implies.  Anyone have any experience?
Mounting them directly to the axis for precision may be difficult
(the telescope will weigh somewhere in the region of 150kg) but I
think bearing that can take that and still accommodate encoders on
the ends are just about doable.  I want to avoid putting them onto
a seperate axis attached via gears because obviously that will
introdice play of its own, although I could see friction wheels
rather conventional gears possibly working.

The other approach is simply to use steppers and attempt to compensate
for play, either with a fixed offset when changing directions or
monitoring current consumption to get an idea of the load (we can
assume the telescope is almost perfectly balanced on its axes).
Speed isn't really an issue so high gearing ratios are possible.
Anyone have any comments?

-- 
Andrew Smallshaw
andrews@sdf.lonestar.org
0
Reply andrews (352) 9/6/2007 5:25:56 PM

Andrew Smallshaw wrote:

> I'm currently looking into the feasibility of a hobby project to
> construct a telescope mount with computerised goto capability (that
> is, you tell it where to point via computer rather than try to find
> objects manually which is always a problem when the object is too
> faint to see with the naked eye).
> 
> There are two aspects to this problem: one is the initial locating
> of objects which needs a moderately high level of precision, pointing
> to within maybe 15 arcminutes or less on two axes, and the subsequent
> tracking of that object as it move across the sky.  This is a
> constant movement of 15 arcseconds per second on one axis and needs
> to be as accurate as possible.
> 

A few questions:

1. what will the thermal environment be for the entire system and will
    it be controllable?  Perhaps in a very controlled environment, one
    could calibrate the entire system over its dynamic range, avoiding
    backlash by slewing only certain motions, with the understanding
    that this may not be stable over the long term.

2. can you optically track (which would obviate need for extreme tolerances
    and precision)? Even if the target is not always visible for tracking,
    certainly the background should be useful for that and using an ephemeris
    for reference one should certainly be able to precisely move the mount.

I have a similar stalled project (which includes a homebrew peltier-cooled
imager in development) so I too am interested in this discussion.

Regards,

Michael
0
Reply msg 9/6/2007 5:50:31 PM


You probably look at alt.astronomy or subscribe to
QCUIAG@yahoogroups.com or ccd@mailman.rahul.net

All off these groups are dealing with the problem you are
describing. Once you have solved all of the problems that
you have identified you will start to face a secondary set
of problems starting with mechanical bending of the
telescope tube itself depending on the pointing angle. Image
rotation over time. Cyclic errors from gears compounded
by high gear ratios. Structure temperature changes over
the course of an evenings viewing induces positioning
errors. High resolution shaft encoders are only
useful if comparable system accuracy.

A lot depends on what you ultimately want to do with
the mount. Simple goto systems work quite well for going
out and viewing through the eyepiece. Astrophotography
is a lot bigger problem for control systems.  Current systems
are diverting light from the main tube or using a separate imager
in a secondary scope tube mounted to servo the telescope
to the sky as a way to compensate for system errors. Imaging
now is often done with lots of short images rotated and
"stacked" together with some very good software written
for just this purpose.

Start simple, get sky movement compensation working first
and add more accuracy and control later. This project can
be a lot of work. A trip to a starfest will be time well spent
talking to those that have done it and looking at some of
the solutions they have implemented.

Dark Skies

Walter Banks



Andrew Smallshaw wrote:

> I'm currently looking into the feasibility of a hobby project to
> construct a telescope mount with computerised goto capability (that
> is, you tell it where to point via computer rather than try to find
> objects manually which is always a problem when the object is too
> faint to see with the naked eye).
>
> There are two aspects to this problem: one is the initial locating
> of objects which needs a moderately high level of precision, pointing
> to within maybe 15 arcminutes or less on two axes, and the subsequent
> tracking of that object as it move across the sky.  This is a
> constant movement of 15 arcseconds per second on one axis and needs
> to be as accurate as possible.
>
> The reason I am posting here is that obviously that level of
> precision is going to be impossible to attain mechanically.  A
> precision engineering shop may get somewhere in the ballpark but
> certainly not an amatuer construction.  Therefore I'm looking into
> methods of compensating for any mechanical inaccuracies electronically
> and I'm interested to hear from anyone who has similar experiences.
>
> The way I see it there are two possible approaches.  I can measure
> the position of each axis directly.  I doubt a resistor-based
> servomechanism would be accurate enough, but I do see high resoution
> shaft encoders in the 8000 - 10000 counts per turn range that would
> be in the right neighbourhood for the job if that resolution actually
> translates into the accuracy it implies.  Anyone have any experience?
> Mounting them directly to the axis for precision may be difficult
> (the telescope will weigh somewhere in the region of 150kg) but I
> think bearing that can take that and still accommodate encoders on
> the ends are just about doable.  I want to avoid putting them onto
> a seperate axis attached via gears because obviously that will
> introdice play of its own, although I could see friction wheels
> rather conventional gears possibly working.
>
> The other approach is simply to use steppers and attempt to compensate
> for play, either with a fixed offset when changing directions or
> monitoring current consumption to get an idea of the load (we can
> assume the telescope is almost perfectly balanced on its axes).
> Speed isn't really an issue so high gearing ratios are possible.
> Anyone have any comments?
>
> --
> Andrew Smallshaw
> andrews@sdf.lonestar.org

0
Reply walter20 (872) 9/6/2007 6:02:20 PM

In article <slrnfe0e0r.7o0.andrews@sdf.lonestar.org>, Andrew Smallshaw
<andrews@sdf.lonestar.org> writes
>I'm currently looking into the feasibility of a hobby project to
>construct a telescope mount with computerised goto capability (that

[big snip]

You may already know about this but a very well known name for
software/hardware in driving amateur scopes (and also for interesting
telescope mounts) is Mel Bartels. The home page (link to the
software/hardware is at the top) is...

  http://www.bbastrodesigns.com/

There is a yahoo group at...

  http://groups.yahoo.com/group/scope-drive

I recommend it as a starting point...

HTH

-- 
Steve Goodwin...  www.p2cl.co.uk (includes contact details)
0
Reply x5194 (2) 9/6/2007 6:41:18 PM

On 2007-09-06, msg <msg@_cybertheque.org_> wrote:
> Andrew Smallshaw wrote:
>
>> I'm currently looking into the feasibility of a hobby project to
>> construct a telescope mount with computerised goto capability (that
>> is, you tell it where to point via computer rather than try to find
>> objects manually which is always a problem when the object is too
>> faint to see with the naked eye).
>> 
>> There are two aspects to this problem: one is the initial locating
>> of objects which needs a moderately high level of precision, pointing
>> to within maybe 15 arcminutes or less on two axes, and the subsequent
>> tracking of that object as it move across the sky.  This is a
>> constant movement of 15 arcseconds per second on one axis and needs
>> to be as accurate as possible.
>> 
>
> A few questions:
>
> 1. what will the thermal environment be for the entire system and will
>     it be controllable?  Perhaps in a very controlled environment, one
>     could calibrate the entire system over its dynamic range, avoiding
>     backlash by slewing only certain motions, with the understanding
>     that this may not be stable over the long term.

The temperature range is whatever the weather throws at it: here
in the UK that means between 0-20C 90% of the time.  99% of nights
would be in a range that extends another 5C either side.  Controlling
the temperature isn't an option - heating introduces all kinds of
optical effects due to turbulent air.  It has to work at ambient
temperature.  Equally humidity can't be controlled although that's
probably less of a concern, everything must be able to tolerate a
coating of dew.

> 2. can you optically track (which would obviate need for extreme tolerances
>     and precision)? Even if the target is not always visible for tracking,
>     certainly the background should be useful for that and using an ephemeris
>     for reference one should certainly be able to precisely move the mount.

Optical tracking is certainly an option, but something I'd like to
keep in reserve if at all possible.  In general you cannot use the
same imaging device for both tracking and imaging, so two images
are needed.  There are two main ways of doing it: one is a seperate
guide scope that piggy backs on top of the main which could affect
the balance (unless we were clever) and generally make everything
both bigger and heavier, potentially making accuracy even more
difficult.  The other is to split the image using e.g. a half-silvered
mirror.  This is a much smaller option but wastes light, meaning
that in practice a given setup can only see brighter objects.  One
of these approaches may turn out to be necessary in practice, but
I'm trying to design them out of the equation at this stage.

-- 
Andrew Smallshaw
andrews@sdf.lonestar.org
0
Reply andrews (352) 9/6/2007 7:09:58 PM

On 2007-09-06, Walter Banks <walter@bytecraft.com> wrote:

> All off these groups are dealing with the problem you are
> describing. Once you have solved all of the problems that
> you have identified you will start to face a secondary set
> of problems starting with mechanical bending of the
> telescope tube itself depending on the pointing angle. Image
> rotation over time. Cyclic errors from gears compounded
> by high gear ratios. Structure temperature changes over
> the course of an evenings viewing induces positioning
> errors. High resolution shaft encoders are only
> useful if comparable system accuracy.

I believe I've already worked around some of the problems you've
described, albeit only in theory.  Your point about the gears is
noted, and in part forms the basis for my original question.  Why
do you say my shaft encoders will only be as good as the rest of
the drive system?  I'm proposing to put them at the very end of
the drive train so that any errors can be compensated for, possibly
attached to the load bearing axes themselves.  Do you see anything
wrong with that approach?

Hmm, thermal effects on the structure itself... hadn't thought of
that one.  Something new to address...

<useful but uncontroversial background snipped>

> Start simple, get sky movement compensation working first
> and add more accuracy and control later. This project can
> be a lot of work. A trip to a starfest will be time well spent
> talking to those that have done it and looking at some of
> the solutions they have implemented.

Compensating for sky movement should hopefully be straightforward
as this is an equatorial mount so it's single axis, constant rate
stuff - I've devised a method of getting fairly good polar alignment
for a fixed installation so anything more advanced shouldn't be
necessary.  Having regular progress indication in the RA drive
would be useful though so that any errors can be detected in short
order, say on the order of every few arcminutes rotation.  Of
course, this will all be in one direction only at that point so no
play to worry about there.  At the end of the day, you get reasonable
results from small scopes and clockwork drive, so I'm not overly
concerned by it.  Allowing for the initial positioning is the thing,
even if I don't go for full goto at the outset.

-- 
Andrew Smallshaw
andrews@sdf.lonestar.org
0
Reply andrews (352) 9/6/2007 7:30:24 PM

Op Thu, 6 Sep 2007 17:25:56 +0000 (UTC) schreef Andrew Smallshaw:

> I'm currently looking into the feasibility of a hobby project to
> construct a telescope mount with computerised goto capability (that
> is, you tell it where to point via computer rather than try to find
> objects manually which is always a problem when the object is too
> faint to see with the naked eye).
> 
> There are two aspects to this problem: one is the initial locating
> of objects which needs a moderately high level of precision, pointing
> to within maybe 15 arcminutes or less on two axes, and the subsequent
> tracking of that object as it move across the sky.  This is a
> constant movement of 15 arcseconds per second on one axis and needs
> to be as accurate as possible.
> 
> The reason I am posting here is that obviously that level of
> precision is going to be impossible to attain mechanically.  A
> precision engineering shop may get somewhere in the ballpark but
> certainly not an amatuer construction.  Therefore I'm looking into
> methods of compensating for any mechanical inaccuracies electronically
> and I'm interested to hear from anyone who has similar experiences.
> 
> The way I see it there are two possible approaches.  I can measure
> the position of each axis directly.  I doubt a resistor-based
> servomechanism would be accurate enough, but I do see high resoution
> shaft encoders in the 8000 - 10000 counts per turn range that would
> be in the right neighbourhood for the job if that resolution actually
> translates into the accuracy it implies.  Anyone have any experience?
> Mounting them directly to the axis for precision may be difficult
> (the telescope will weigh somewhere in the region of 150kg) but I
> think bearing that can take that and still accommodate encoders on
> the ends are just about doable.  I want to avoid putting them onto
> a seperate axis attached via gears because obviously that will
> introdice play of its own, although I could see friction wheels
> rather conventional gears possibly working.
> 
> The other approach is simply to use steppers and attempt to compensate
> for play, either with a fixed offset when changing directions or
> monitoring current consumption to get an idea of the load (we can
> assume the telescope is almost perfectly balanced on its axes).
> Speed isn't really an issue so high gearing ratios are possible.
> Anyone have any comments?

Some books have been written about this:
Michael A. Covington, How to Use a Computerized Telescope.
M. Trueblood and R. Genet, Telescope Control.
-- 
Coos
0
Reply chforth (1144) 9/6/2007 8:39:18 PM

Andrew Smallshaw wrote:
> On 2007-09-06, Walter Banks <walter@bytecraft.com> wrote:
> 
> 
>>All off these groups are dealing with the problem you are
>>describing. Once you have solved all of the problems that
>>you have identified you will start to face a secondary set
>>of problems starting with mechanical bending of the
>>telescope tube itself depending on the pointing angle. Image
>>rotation over time. Cyclic errors from gears compounded
>>by high gear ratios. Structure temperature changes over
>>the course of an evenings viewing induces positioning
>>errors. High resolution shaft encoders are only
>>useful if comparable system accuracy.
> 
> 
> I believe I've already worked around some of the problems you've
> described, albeit only in theory.  Your point about the gears is
> noted, and in part forms the basis for my original question.  Why
> do you say my shaft encoders will only be as good as the rest of
> the drive system?  I'm proposing to put them at the very end of
> the drive train so that any errors can be compensated for, possibly
> attached to the load bearing axes themselves.  Do you see anything
> wrong with that approach?

Some of the higher resolution encoders use an analog interpolation
method, so you would need to watch the LSB noise. If you used a 
seek-then-lock scheme, rather than a servo method, you would tolerate
much lower spec encoders.
A really smart system would track the LSB's as it moved, and be
able to interpolate to the final setting.

Stepper motors (esp with microstepping) would seem the best for the
subsequent slow rotation tracking, and they work nicely with any
encoder - interpolation.

You can get ICs with Microstep built in:

http://www.allegromicro.com/en/Products/Categories/ICs/motor.asp

-jg

0
Reply no.spam2900 (819) 9/6/2007 10:06:11 PM

On 2007-09-06, Jim Granville <no.spam@designtools.maps.co.nz> wrote:
> Andrew Smallshaw wrote:
>
> Some of the higher resolution encoders use an analog interpolation
> method, so you would need to watch the LSB noise. If you used a 
> seek-then-lock scheme, rather than a servo method, you would tolerate
> much lower spec encoders.
> A really smart system would track the LSB's as it moved, and be
> able to interpolate to the final setting.
>
> Stepper motors (esp with microstepping) would seem the best for the
> subsequent slow rotation tracking, and they work nicely with any
> encoder - interpolation.

Thanks for your comments.  I think at least this part of the problem
looks feasible enough.  Incidentally, for the low speed tracking
I'm thinking of simply tracking the time between encoder increments.
It appears that the steppers are going to have considerably higher
resolution than the encoders so it is a question of getting them
ticking at the right rate.  Using a 4096-count encoder, the lowest
precision I could get way with, I'd expect an increment just under
every 21 seconds.  If it gets up to 22 or whatever, I know to
increase the step speed a little.  In this way I hope to ensure
that the tracking is much more accurate than the resolution of the
encoders.

As a side note, someone asked yesterday about whether I could
control the temperature in any way.  I had vision of a space heater
or something like that warming the entire building which I dismissed
out of hand.  I've since realised I can of course pop the encoders
in their own enclosures and heat them to a relatively constant 30
or 35C which should aid accuracy.

-- 
Andrew Smallshaw
andrews@sdf.lonestar.org
0
Reply andrews (352) 9/7/2007 6:12:14 PM

Andrew Smallshaw wrote:

> It appears that the steppers are going to have considerably higher
> resolution than the encoders so it is a question of getting them
> ticking at the right rate.  

I'm a little puzzled you're planning on using steppers at all. 
Constant-speed, enormously slow rotation is just about the last thing 
I'd consider steppers for.

The canonical approach has always been to have four or five axes of 
rotation in a telescope mount: one or two fixed ones only needed during 
installation, which point the third exactly at the celestial pole 
(parallel to earth's axis of rotation), and two more to point the scope 
to a direction relative to that axis.  Then you equip that third axis 
with a special motor and gears that does one turn in 24 hours.

The main advantage of this approach is that moving and fixed axes are 
separate, so their treatment can be optimized independently: a linear 
motor for celestial rotation, and a pair of servos (steppers or other) 
for pointing at a star.  A minor advantage is that the servos can be fed 
declination and right-ascension almost unchanged.
0
Reply HBBroeker (609) 9/8/2007 10:50:36 AM

Hans-Bernhard Br�ker wrote:

> Andrew Smallshaw wrote:
> 
>> It appears that the steppers are going to have considerably higher
>> resolution than the encoders so it is a question of getting them
>> ticking at the right rate.  
> 
> 
> I'm a little puzzled you're planning on using steppers at all. 
> Constant-speed, enormously slow rotation is just about the last thing 
> I'd consider steppers for.
> 
> The canonical approach has always been to have four or five axes of 
> rotation in a telescope mount: one or two fixed ones only needed during 
> installation, which point the third exactly at the celestial pole 
> (parallel to earth's axis of rotation), and two more to point the scope 
> to a direction relative to that axis.  Then you equip that third axis 
> with a special motor and gears that does one turn in 24 hours.
> 

<snip>

I had assumed that the O.P. (from the language in his posting) had an
unusual application in mind such as moving target tracking (asteroids,
UFOs, etc.) rather than just backyard astronomy.

Regards,

Michael
0
Reply msg 9/8/2007 12:30:42 PM

On 2007-09-08, Hans-Bernhard Br�ker <HBBroeker@t-online.de> wrote:
> Andrew Smallshaw wrote:
>
>> It appears that the steppers are going to have considerably higher
>> resolution than the encoders so it is a question of getting them
>> ticking at the right rate.  
>
> I'm a little puzzled you're planning on using steppers at all. 
> Constant-speed, enormously slow rotation is just about the last thing 
> I'd consider steppers for.

I'm inclined towards steppers simply for resolution and predictable
handling at low speed.  There isn't just the tracking to worry
about where the steppers are merely ticking over, there is also
the panning from one point in the sky to another at maybe 100 times
that rate.  I wouldn't trust conventional motors to run accurately
at 1% of their maximum speed whatever method is used to control
them.

Later in your post you hint at separate motors for tracking and
panning on RA.  I briefly considered that but dismissed it as
needlessly complex.  The only real avantage to that that I could
see is that one setting would be fed RA directly.  Converting
between various forms, ie, RA to RA offset by sidereal time, is
one thing computers are good at.

> The canonical approach has always been to have four or five axes of 
> rotation in a telescope mount: one or two fixed ones only needed during 
> installation, which point the third exactly at the celestial pole 
> (parallel to earth's axis of rotation), and two more to point the scope 
> to a direction relative to that axis.  Then you equip that third axis 
> with a special motor and gears that does one turn in 24 hours.

You're correct that there are more axes involved than I have declared
here, but I didn't consider them relevant to this discussion since
any adjustment would involve a spanner rather than a computer or
anything electrical for that matter.  I'm planning on a few degrees
of manual adjustment in azimuth for fine tuning precise polar
alignment.   The altitude element will be designed into the mount
(largely non-adjustable and specifically designed for my latitude),
fine tuning being done by re-levelling the mount at its base.

-- 
Andrew Smallshaw
andrews@sdf.lonestar.org
0
Reply andrews (352) 9/8/2007 1:24:08 PM

Andrew Smallshaw wrote:
> On 2007-09-08, Hans-Bernhard Br�ker <HBBroeker@t-online.de> wrote:

>> I'm a little puzzled you're planning on using steppers at all. 
>> Constant-speed, enormously slow rotation is just about the last thing 
>> I'd consider steppers for.

> I'm inclined towards steppers simply for resolution and predictable
> handling at low speed.  

But doing that you're setting aside the important fact that your stepper 
doesn't move remotely like your target does.  A stepper jumps, a star 
moves perfectly smoothly.  Not to mention that all that jumping makes 
the subject problem of mechanical play worse.  It'll shake loose each 
and every thing that can be shaken.  You don't want shaking.

Ultimately the problem is that a stepper doesn't do low speed at all. 
It stops or it moves fast (over a small distance).

> There isn't just the tracking to worry about where the steppers are
> merely ticking over, there is also the panning from one point in the
> sky to another at maybe 100 times that rate.

Which is why it's better to leave these two jobs to two different types 
of drive.  Steppers for fast-or-stop pointing, linear for 
slow-and-steady tracking.

> Later in your post you hint at separate motors for tracking and
> panning on RA.  I briefly considered that but dismissed it as
> needlessly complex.  

You'll probably end up investing more complexity into controlling your 
setup than you saved by a supposedly simpler setup.
0
Reply HBBroeker (609) 9/8/2007 2:02:48 PM

Andrew Smallshaw wrote:

> On 2007-09-08, Hans-Bernhard Br�ker <HBBroeker@t-online.de> wrote:
> 
>>Andrew Smallshaw wrote:
>>
>>
>>>It appears that the steppers are going to have considerably higher
>>>resolution than the encoders so it is a question of getting them
>>>ticking at the right rate.  
>>
>>I'm a little puzzled you're planning on using steppers at all. 
>>Constant-speed, enormously slow rotation is just about the last thing 
>>I'd consider steppers for.
> 
> 
> I'm inclined towards steppers simply for resolution and predictable
> handling at low speed.  There isn't just the tracking to worry
> about where the steppers are merely ticking over, there is also
> the panning from one point in the sky to another at maybe 100 times
> that rate.  I wouldn't trust conventional motors to run accurately
> at 1% of their maximum speed whatever method is used to control
> them.

That was why I suggested Micro-stepping controllers.
That gives the best of both worlds, you get the nice
step-prediction and much lower sensor cost of a ateper, but
the microstep pushes the step-shock effects into the angular noise.

-jg

0
Reply no.spam2900 (819) 9/8/2007 9:39:27 PM

Andrew Smallshaw wrote:

> On 2007-09-06, Jim Granville <no.spam@designtools.maps.co.nz> wrote:
> 
>>Andrew Smallshaw wrote:
>>
>>Some of the higher resolution encoders use an analog interpolation
>>method, so you would need to watch the LSB noise. If you used a 
>>seek-then-lock scheme, rather than a servo method, you would tolerate
>>much lower spec encoders.
>>A really smart system would track the LSB's as it moved, and be
>>able to interpolate to the final setting.
>>
>>Stepper motors (esp with microstepping) would seem the best for the
>>subsequent slow rotation tracking, and they work nicely with any
>>encoder - interpolation.
> 
> 
> Thanks for your comments.  I think at least this part of the problem
> looks feasible enough.  Incidentally, for the low speed tracking
> I'm thinking of simply tracking the time between encoder increments.
> It appears that the steppers are going to have considerably higher
> resolution than the encoders so it is a question of getting them
> ticking at the right rate.  Using a 4096-count encoder, the lowest
> precision I could get way with, I'd expect an increment just under
> every 21 seconds.  If it gets up to 22 or whatever, I know to
> increase the step speed a little.  In this way I hope to ensure
> that the tracking is much more accurate than the resolution of the
> encoders.

I'm not sure I follow the logic. You know the gearing, and the 
step-sizes, so you should already know more precisely than the sensor,
the angular effects.
In fact, you could work backwards, and use the precision
of the stepper, to calibrate the Sensor edges to fractions of a LSB.
The sensor is really just a way to re-sync the stepper after power off,
and get reasonable first seek handling.


> 
> As a side note, someone asked yesterday about whether I could
> control the temperature in any way.  I had vision of a space heater
> or something like that warming the entire building which I dismissed
> out of hand.  I've since realised I can of course pop the encoders
> in their own enclosures and heat them to a relatively constant 30
> or 35C which should aid accuracy.

yes, but the sensor temperature is not really the weakpoint.

-jg


0
Reply no.spam2900 (819) 9/8/2007 9:44:45 PM

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