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AVR Tachometer

AVR Tachometer

2003-12-30 by William Nachefski

Hello All!
I am just getting started into AVR's.  I am seeking help on a 
circuit.  I need to build a tachometer with opitcal pick up.  The max 
RPM to be counted will be around 200,000 RPM.  I was told that pretty 
much all of the tasks could be handled in code with a 
microcontroller.  My pickup is a Phototransistor/LED its set up to 
give one pulse per revolution.  So basically all I need is a 
frequency counter with a 1 sec gate time, and then multiply the value 
by 60,(my guess)Then to display the data on a 6 digit LED display.  
I don't know really anything about M.C's but bought a few 28 pin 
Mega8 chips to experiment with.  What should the circuit look like?
I am thinking the only thing I need on the board would be the display 
+ multiplexing components and the Mega8 with a connector runing from 
a input pin(interupt pin?)Let me know if I am on the right track.  Or 
if someone else has built one of these.  Any help would be greatly 
appreciated!

Thanks
Happy Holidays
William Nachefski

Re: [AVR-Chat] AVR Tachometer

2003-12-30 by Jesper Hansen

> I am just getting started into AVR's.  I am seeking help on a 
> circuit.  I need to build a tachometer with opitcal pick up.  The max 
> RPM to be counted will be around 200,000 RPM.  

Hmmm. Playing with model jet engines ? ;-)


/Jesper
www.yampp.com

RE: [AVR-Chat] AVR Tachometer

2003-12-30 by Al Welch

William,

Perhaps you may want to run your phototransistor output through a schmitt
trigger such as an 74ls14 chip which will make the pulses cleanly toggle
between digital one and zero. Otherwise there could be a slow rise and fall
shape to the output which could confuse your counting.

Seems like you could then use an external interrupt input to interrupt when
the input pulses, add one each time. Then setup a  timer to provide your one
second window. The display could run in the foreground to post answers from
the timer.

Al Welch
Show quoted textHide quoted text
-----Original Message-----
From: William Nachefski [mailto:slaphappysamy@yahoo.com]
Sent: Tuesday, December 30, 2003 12:18 PM
To: AVR-Chat@yahoogroups.com
Subject: [AVR-Chat] AVR Tachometer


Hello All!
I am just getting started into AVR's.  I am seeking help on a
circuit.  I need to build a tachometer with opitcal pick up.  The max
RPM to be counted will be around 200,000 RPM.  I was told that pretty
much all of the tasks could be handled in code with a
microcontroller.  My pickup is a Phototransistor/LED its set up to
give one pulse per revolution.  So basically all I need is a
frequency counter with a 1 sec gate time, and then multiply the value
by 60,(my guess)Then to display the data on a 6 digit LED display.
I don't know really anything about M.C's but bought a few 28 pin
Mega8 chips to experiment with.  What should the circuit look like?
I am thinking the only thing I need on the board would be the display
+ multiplexing components and the Mega8 with a connector runing from
a input pin(interupt pin?)Let me know if I am on the right track.  Or
if someone else has built one of these.  Any help would be greatly
appreciated!

Thanks
Happy Holidays
William Nachefski




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Re: AVR Tachometer

2003-12-30 by William Nachefski

--- 
I guess the 200,000 rpm gave me away.  Yes this is for a jet engine, 
but not a model.  Its a rather large homegrown one.

In AVR-Chat@yahoogroups.com, "Jesper Hansen" <jesperh@t...> wrote:
> > I am just getting started into AVR's.  I am seeking help on a 
> > circuit.  I need to build a tachometer with opitcal pick up.  The 
max 
Show quoted textHide quoted text
> > RPM to be counted will be around 200,000 RPM.  
> 
> Hmmm. Playing with model jet engines ? ;-)
> 
> 
> /Jesper
> www.yampp.com

Re: [AVR-Chat] AVR Tachometer

2003-12-31 by Bernd Felsche

On Tue, Dec 30, 2003 at 08:18:21PM -0000, William Nachefski wrote:

> I am just getting started into AVR's.  I am seeking help on a 
> circuit.  I need to build a tachometer with opitcal pick up.  The max 
> RPM to be counted will be around 200,000 RPM.  I was told that pretty 
> much all of the tasks could be handled in code with a 
> microcontroller.  My pickup is a Phototransistor/LED its set up to 
> give one pulse per revolution.  So basically all I need is a 
> frequency counter with a 1 sec gate time, and then multiply the value 
> by 60,(my guess)Then to display the data on a 6 digit LED display.  

By that do you mean you want 1ppm resolution?

That's a tough task. And you won't get it by multiplying a simple
count by 60. You'd have to count at least 60 pulses per rev.

> I don't know really anything about M.C's but bought a few 28 pin 
> Mega8 chips to experiment with.  What should the circuit look like?

Schmitt trigger to "square-up" the signal, feeding to an interrupt
pin. LED display is probably easiest, given the number of required
digits. You can MUX and drive the digits from the Mega8; unless the
display is huge.

Depending on the accuracy and range of speeds you really need, you
could measure the period between pulses and invert. Display the
result, reset counter and start counting on the next pulse; stop
when the next pulse arrives. etc. Because one pulse per rev results
in timing of much less than a millisecond, you'll probably want to
average over a set of results spanning at least a tenth of a second.
(Moving average.)

If the machine stops spinning faster than that, you have a bigger
problem than speed measurement anyway.

> I am thinking the only thing I need on the board would be the display 
> + multiplexing components and the Mega8 with a connector runing from 
> a input pin(interupt pin?)Let me know if I am on the right track.  Or 
> if someone else has built one of these.  Any help would be greatly 
> appreciated!

-- 
/"\ Bernd Felsche - Innovative Reckoning, Perth, Western Australia
\ /  ASCII ribbon campaign | I'm a .signature virus!
 X   against HTML mail     | Copy me into your ~/.signature
/ \  and postings          | to help me spread!

Re: AVR Tachometer

2003-12-31 by William Nachefski

I Need a pretty broad range, from say 15,000 rpm to 200,000.  
Accuracy doesn't have to be that percise as long as its within a 
couple of thousand actuall rpms.  What I meant was With each complete 
rotation of the turbine rotar shaft I get one pulse from the 
Phototransistor.  So that equates to one pulse to the M.C. per 
revolution.  Thanks for the help guys keep the suggestions comming!
William

--- In AVR-Chat@yahoogroups.com, Bernd Felsche <bernie@i...> wrote:
> On Tue, Dec 30, 2003 at 08:18:21PM -0000, William Nachefski wrote:
> 
> > I am just getting started into AVR's.  I am seeking help on a 
> > circuit.  I need to build a tachometer with opitcal pick up.  The 
max 
> > RPM to be counted will be around 200,000 RPM.  I was told that 
pretty 
> > much all of the tasks could be handled in code with a 
> > microcontroller.  My pickup is a Phototransistor/LED its set up 
to 
> > give one pulse per revolution.  So basically all I need is a 
> > frequency counter with a 1 sec gate time, and then multiply the 
value 
> > by 60,(my guess)Then to display the data on a 6 digit LED 
display.  
> 
> By that do you mean you want 1ppm resolution?
> 
> That's a tough task. And you won't get it by multiplying a simple
> count by 60. You'd have to count at least 60 pulses per rev.
> 
> > I don't know really anything about M.C's but bought a few 28 pin 
> > Mega8 chips to experiment with.  What should the circuit look 
like?
> 
> Schmitt trigger to "square-up" the signal, feeding to an interrupt
> pin. LED display is probably easiest, given the number of required
> digits. You can MUX and drive the digits from the Mega8; unless the
> display is huge.
> 
> Depending on the accuracy and range of speeds you really need, you
> could measure the period between pulses and invert. Display the
> result, reset counter and start counting on the next pulse; stop
> when the next pulse arrives. etc. Because one pulse per rev results
> in timing of much less than a millisecond, you'll probably want to
> average over a set of results spanning at least a tenth of a second.
> (Moving average.)
> 
> If the machine stops spinning faster than that, you have a bigger
> problem than speed measurement anyway.
> 
> > I am thinking the only thing I need on the board would be the 
display 
> > + multiplexing components and the Mega8 with a connector runing 
from 
> > a input pin(interupt pin?)Let me know if I am on the right 
track.  Or 
> > if someone else has built one of these.  Any help would be 
greatly 
Show quoted textHide quoted text
> > appreciated!
> 
> -- 
> /"\ Bernd Felsche - Innovative Reckoning, Perth, Western Australia
> \ /  ASCII ribbon campaign | I'm a .signature virus!
>  X   against HTML mail     | Copy me into your ~/.signature
> / \  and postings          | to help me spread!

Re: AVR Tachometer

2003-12-31 by fnatmed

--- In AVR-Chat@yahoogroups.com, "William Nachefski" 
<slaphappysamy@y...> wrote:
> --- 
> I guess the 200,000 rpm gave me away.  Yes this is for a jet 
engine, 
> but not a model.  Its a rather large homegrown one.
> 
> In AVR-Chat@yahoogroups.com, "Jesper Hansen" <jesperh@t...> wrote:
> > > I am just getting started into AVR's.  I am seeking help on a 
> > > circuit.  I need to build a tachometer with opitcal pick up.  
The 
> max 
> > > RPM to be counted will be around 200,000 RPM.  
> > 
> > Hmmm. Playing with model jet engines ? ;-)

It doesn't *have* to be for jet engines :)  I'm looking to do the 
same thing, but it's for tracking the speed of the compressor wheels 
in a vehicle turbo.

On the track at 32lbs of boost, loading can spike the turbo speeds 
pretty nastily, which leads to rapid failure.  I need a way to 
monitor turbo speeds to modify the fuel delivery system etc etc blah 
blah.

I've seen the results of a #2 turbo grenading and spewing bits of 
chrome-vanadium steel down into the intake.  The pistons, valves, 
etc, were not at all happy about this state of affairs.  Not my car 
thankfully, but ugly nonetheless, and I don't want it happening to 
mine.  I currently stay below 28lbs, but those 32lbs pulls on the 
front straight are incredibly addictive :)  Gives new meaning to the 
word whoosh.

Dean.

Re: AVR Tachometer

2003-12-31 by fnatmed

--- In AVR-Chat@yahoogroups.com, "William Nachefski" 
<slaphappysamy@y...> wrote:
> I Need a pretty broad range, from say 15,000 rpm to 200,000.  
> Accuracy doesn't have to be that percise as long as its within a 
> couple of thousand actuall rpms.  What I meant was With each 
complete 
> rotation of the turbine rotar shaft I get one pulse from the 
> Phototransistor.  So that equates to one pulse to the M.C. per 
> revolution.  Thanks for the help guys keep the suggestions comming!

How is the turbine blade assembly attached to the shaft, and what 
are you using to actually trigger the phototransistor ?

In my case, the compressor wheel is topped with a regular nut.  I've 
painted the flats of the nut in alternating white and black, so 
there are 3 pulses per rev.  I originally tried pointing directly at 
the blades themselves, but that wasn't consistent enough.

I'm using plastic light pipes to send a white LED light to the nut, 
and to read the reflection back.  Problems though ...

The paint doesn't last.  Need a good way to color the nut flats that 
will withstand turbo temps.  The light pipes melt.  Need a source 
for high-temp lexan or something.

Dean.

Re: AVR Tachometer

2003-12-31 by William Nachefski

32LBS!  Wow thats alot of boost.  I run my chevelle on 18 lbs, and 
thats as far as I dare go.


--- In AVR-Chat@yahoogroups.com, "fnatmed" <fnatmed@y...> wrote:
> --- In AVR-Chat@yahoogroups.com, "William Nachefski" 
> <slaphappysamy@y...> wrote:
> > --- 
> > I guess the 200,000 rpm gave me away.  Yes this is for a jet 
> engine, 
> > but not a model.  Its a rather large homegrown one.
> > 
> > In AVR-Chat@yahoogroups.com, "Jesper Hansen" <jesperh@t...> wrote:
> > > > I am just getting started into AVR's.  I am seeking help on a 
> > > > circuit.  I need to build a tachometer with opitcal pick up.  
> The 
> > max 
> > > > RPM to be counted will be around 200,000 RPM.  
> > > 
> > > Hmmm. Playing with model jet engines ? ;-)
> 
> It doesn't *have* to be for jet engines :)  I'm looking to do the 
> same thing, but it's for tracking the speed of the compressor 
wheels 
> in a vehicle turbo.
> 
> On the track at 32lbs of boost, loading can spike the turbo speeds 
> pretty nastily, which leads to rapid failure.  I need a way to 
> monitor turbo speeds to modify the fuel delivery system etc etc 
blah 
> blah.
> 
> I've seen the results of a #2 turbo grenading and spewing bits of 
> chrome-vanadium steel down into the intake.  The pistons, valves, 
> etc, were not at all happy about this state of affairs.  Not my car 
> thankfully, but ugly nonetheless, and I don't want it happening to 
> mine.  I currently stay below 28lbs, but those 32lbs pulls on the 
> front straight are incredibly addictive :)  Gives new meaning to 
the 
Show quoted textHide quoted text
> word whoosh.
> 
> Dean.

RE: [AVR-Chat] AVR Tachometer

2004-01-01 by Larry Barello

You don't need the schmitt trigger: all AVR input pins are schmitt triggers!

200krpm = 3.3k/s  You could use the ICP function on timer1 with 16us (8 mhz
clock/128) resolution and measure from 18 ticks/pulse (~200k) to 65000
ticks/pulse (~60 rpm).  Is that enough range?  Heck, make it really simple
and interrupt on the pulse leading edge and calculate the RPM every
interrupt, stuffing the string-o-digits somewhere for your foreground task
to display.  The time between even the fastest RPM is plenty for lots and
lots of calculations.  you could even do it in floating point and have
cycles to spare.

Calculation is easy: 62500 * 60 /(Current Timer - Previous timer) = RPM.

Make sure you declare current and previous timer as unsigned int.

If you want finer resolution at the top end, use a 1us clock and your range
will be about 1krpm to 3.2mrpm.

Cheers!
Show quoted textHide quoted text
-----Original Message-----
From: Al Welch [mailto:alwelch@axxiomchromatography.com]

William,

Perhaps you may want to run your phototransistor output through a schmitt
trigger such as an 74ls14 chip which will make the pulses cleanly toggle
between digital one and zero. Otherwise there could be a slow rise and fall
shape to the output which could confuse your counting.

Seems like you could then use an external interrupt input to interrupt when
the input pulses, add one each time. Then setup a  timer to provide your one
second window. The display could run in the foreground to post answers from
the timer.

Al Welch

-----Original Message-----
From: William Nachefski [mailto:slaphappysamy@yahoo.com]

Hello All!
I am just getting started into AVR's.  I am seeking help on a
circuit.  I need to build a tachometer with opitcal pick up.  The max
RPM to be counted will be around 200,000 RPM.  I was told that pretty

Re: [AVR-Chat] Re: AVR Tachometer

2004-01-01 by Snowden

I guess it would depend on the temp, but maybe powder coating would work.

Bruce


fnatmed wrote:
Show quoted textHide quoted text
> --- In AVR-Chat@yahoogroups.com, "William Nachefski" 
> <slaphappysamy@y...> wrote:
> 
>>I Need a pretty broad range, from say 15,000 rpm to 200,000.  
>>Accuracy doesn't have to be that percise as long as its within a 
>>couple of thousand actuall rpms.  What I meant was With each 
> 
> complete 
> 
>>rotation of the turbine rotar shaft I get one pulse from the 
>>Phototransistor.  So that equates to one pulse to the M.C. per 
>>revolution.  Thanks for the help guys keep the suggestions comming!
> 
> 
> How is the turbine blade assembly attached to the shaft, and what 
> are you using to actually trigger the phototransistor ?
> 
> In my case, the compressor wheel is topped with a regular nut.  I've 
> painted the flats of the nut in alternating white and black, so 
> there are 3 pulses per rev.  I originally tried pointing directly at 
> the blades themselves, but that wasn't consistent enough.
> 
> I'm using plastic light pipes to send a white LED light to the nut, 
> and to read the reflection back.  Problems though ...
> 
> The paint doesn't last.  Need a good way to color the nut flats that 
> will withstand turbo temps.  The light pipes melt.  Need a source 
> for high-temp lexan or something.
> 
> Dean.
> 
> 
>  
> 
> 
> Yahoo! Groups Links
> 
> To visit your group on the web, go to:
>  http://groups.yahoo.com/group/AVR-Chat/
> 
> To unsubscribe from this group, send an email to:
>  AVR-Chat-unsubscribe@yahoogroups.com
> 
> Your use of Yahoo! Groups is subject to:
>  http://docs.yahoo.com/info/terms/ 
> 
> 
>

Re: [AVR-Chat] Re: AVR Tachometer

2004-01-01 by Bernd Felsche

On Wed, Dec 31, 2003 at 09:59:56PM -0500, Snowden wrote:
> fnatmed wrote:
> > --- In AVR-Chat@yahoogroups.com, "William Nachefski" 
> > <slaphappysamy@y...> wrote:

> >>I Need a pretty broad range, from say 15,000 rpm to 200,000.
> >>Accuracy doesn't have to be that percise as long as its within a
> >>couple of thousand actuall rpms.  What I meant was With each
> >>complete rotation of the turbine rotar shaft I get one pulse
> >>from the Phototransistor.  So that equates to one pulse to the
> >>M.C. per revolution.  Thanks for the help guys keep the
> >>suggestions comming!

> > The paint doesn't last.  Need a good way to color the nut flats that 
> > will withstand turbo temps.  The light pipes melt.  Need a source 
> > for high-temp lexan or something.

> I guess it would depend on the temp, but maybe powder coating would work.

You may be able to slip a collar over the nut, one that's basically
round with shiny, flat surfaces machine into it to reflect.

A Hall sensor may do the trick as well; less sensitive to getting
dirt on the surface. You should be able to pick up the corners of
the nut as they pass closest to the sensor. Just make sure that you
have good ventilation around the magnet and sensor. Magnets don't
stay magnetic for long when they get too hot.

Of course, one could go back to scratch and look at the acoustics of
blade-passing or roller-bearing frequencies, but getting accurate
numbers is difficult.

Taking the speed reading off the cooler, compressor side should be
obvious for any sensing.

-- 
/"\ Bernd Felsche - Innovative Reckoning, Perth, Western Australia
\ /  ASCII ribbon campaign | I'm a .signature virus!
 X   against HTML mail     | Copy me into your ~/.signature
/ \  and postings          | to help me spread!

Re: AVR Tachometer

2004-01-01 by fnatmed

--- In AVR-Chat@yahoogroups.com, "William Nachefski" 
<slaphappysamy@y...> wrote:
> 32LBS!  Wow thats alot of boost.  I run my chevelle on 18 lbs, and 
> thats as far as I dare go.

Heh, yeah.  I run daily at 21-23lbs, and track at up to 28lbs.  
Depends on the track.  The turbos max out thermally at around 23lbs 
anyway - 2lbs gains boost but at a tremendous cost in heat and 
efficiency loss to heat.  Good for twisties, only good for a short 
time on the straights.

32lbs on a warmed up but not track-heated engine is a rush.  
Once :)  Then I get into a buddies 890 RWHP monster, and we can suck 
the headlights out of the Porsche Turbo with our wake-vacuum as we 
go by.  Fun fun :)  Oh, BTW, these are all daily-driven full-
interior street Supras.  Not trailer queens.

To keeps things AVR related, I'm working on the 2nd design spin of a 
vehicle datalogger, learning from the first one.  The original was 
discussed at length on avrfreaks.net, and the design morphed several 
times from that.  Basic features were/are :

AVR Mega128 based
16 (now 16 or 32) analog inputs, 0-14V, 0-5V, 9-14V
6 digital inputs
I2C temp sensors, any number (er, say 16 max)
Serial input for GPS logging
ADXL202 2-axis G-sensor
USB
MMC card for data storage
RTC for time-stamping of data
Simple LCD screen

Things I've learned ...

- Optoisolaters can take way too much current from the signal being 
measured.  Use an opamp buffer instead.

- Power spikes on the +12V line can be murder.

- Solid, quiet power supply section design isn't as easy as it looks.

- Mixing analog and digital on a single board is hard.  Really hard.

- 2 layers may be a lot cheaper, but it forces some bad compromises 
in layout.  See previous point.

- Believe it or not, 3mm of plastic bezel between the  alum endcaps 
and the alum enclosure actually makes a difference in EMI.  Go metal 
to metal instead, even if it's not as pretty.

- DB25 and DB37 leak EMI too.  Dang, means to do it RIGHT, we need 
those expensive AMP connectors.  Hmmm, shielded DB pcb connectors ?

- There is no perfect EDA software.  They ALL have bloody blasted 
quirks.

- Changing EDA software is a pain.  I use Protel 99SE, which has its 
own share of quirks and bugs, and I'm getting tired of them.  Protel 
DXP is a bloated pig, though it's really really pretty.  Altium 
won't release SP3 for DXP now, rolling into Nexar.  More alpha 
software for us to test, oh goodie.  Pulsonix is nice, but lacks 
features.  Zuken CadStar looks nice, has tons of features, and I 
still can't quite figure it out.  Gotta shake that 99SE bias and 
just relearn I guess.

Dean.

Re: [AVR-Chat] Re: AVR Tachometer

2004-01-01 by Alex Gibson

fnatmed wrote:
> --- In AVR-Chat@yahoogroups.com, "William Nachefski" 
> <slaphappysamy@y...> wrote:
> 
>>32LBS!  Wow thats alot of boost.  I run my chevelle on 18 lbs, and 
>>thats as far as I dare go.
> 
> 
> Heh, yeah.  I run daily at 21-23lbs, and track at up to 28lbs.  
> Depends on the track.  The turbos max out thermally at around 23lbs 
> anyway - 2lbs gains boost but at a tremendous cost in heat and 
> efficiency loss to heat.  Good for twisties, only good for a short 
> time on the straights.
> 
> 32lbs on a warmed up but not track-heated engine is a rush.  
> Once :)  Then I get into a buddies 890 RWHP monster, and we can suck 
> the headlights out of the Porsche Turbo with our wake-vacuum as we 
> go by.  Fun fun :)  Oh, BTW, these are all daily-driven full-
> interior street Supras.  Not trailer queens.
> 
> To keeps things AVR related, I'm working on the 2nd design spin of a 
> vehicle datalogger, learning from the first one.  The original was 
> discussed at length on avrfreaks.net, and the design morphed several 
> times from that.  Basic features were/are :
> 
> AVR Mega128 based
> 16 (now 16 or 32) analog inputs, 0-14V, 0-5V, 9-14V
> 6 digital inputs
> I2C temp sensors, any number (er, say 16 max)
> Serial input for GPS logging
> ADXL202 2-axis G-sensor
> USB
> MMC card for data storage
> RTC for time-stamping of data
> Simple LCD screen
> 
> Things I've learned ...
> 
> - Optoisolaters can take way too much current from the signal being 
> measured.  Use an opamp buffer instead.
> 
> - Power spikes on the +12V line can be murder.
> 
> - Solid, quiet power supply section design isn't as easy as it looks.
> 
> - Mixing analog and digital on a single board is hard.  Really hard.
> 
> - 2 layers may be a lot cheaper, but it forces some bad compromises 
> in layout.  See previous point.
> 
> - Believe it or not, 3mm of plastic bezel between the  alum endcaps 
> and the alum enclosure actually makes a difference in EMI.  Go metal 
> to metal instead, even if it's not as pretty.
> 
> - DB25 and DB37 leak EMI too.  Dang, means to do it RIGHT, we need 
> those expensive AMP connectors.  Hmmm, shielded DB pcb connectors ?
> 
> - There is no perfect EDA software.  They ALL have bloody blasted 
> quirks.
> 
> - Changing EDA software is a pain.  I use Protel 99SE, which has its 
> own share of quirks and bugs, and I'm getting tired of them.  Protel 
> DXP is a bloated pig, though it's really really pretty.  Altium 
> won't release SP3 for DXP now, rolling into Nexar.  More alpha 
> software for us to test, oh goodie.  Pulsonix is nice, but lacks 
> features.  Zuken CadStar looks nice, has tons of features, and I 
> still can't quite figure it out.  Gotta shake that 99SE bias and 
> just relearn I guess.
> 
> Dean.

-EDA software, tried eagle yet ?
www.cadsoft.de

Tip for power supply, put it in a seperate metal
case inside main case if you have the space.

For connectors just find out the part
number for the non-mil spec versions.
For most parts only difference is the mil spec version gets tested
a lot more.

Also if you have a local airport / airfield go and see if you
can find an avionics technican or shop that
would be willing to give you the old connectors.
Especially if their is somewhere that does
modifications on jets.

Or find where the miltiary or Boeing or airline surplus gets sold.

I used to work for airline maintenance in Sydney
and we had buckets and drums of old connectors
sitting around.

A lot of places just throw out the old wiring looms and connectors 
removed during mods.
Wiring would range from 000AWG to 32 AWG
depending on aircraft and systems.

Alex

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