Waco Star Party announcement

Here's something my local club is doing:

WACO STAR PARTY

June 5th, 2010
8:40pm to 10:30pm

The Central Texas Astronomical Society (CTAS) will have our Waco Star Party for members and the public on Saturday June 5th starting at 8:40pm, regardless of weather. We will meet as usual at the Waco Wetlands. Bring your telescope (if you just got a telescope and want help with it, this is a great place for that) or just enjoy those of the members as we explore the night sky of June.

We will begin with an indoor program on the life-cycle of stars, even if it's cloudy.

Then, weather-permitting, we hope to see objects both inside our Solar System, elsewhere in and around our Milky Way Galaxy, and outside our galaxy. In our Solar System, we will look at Mars and Saturn. Elsewhere in our galaxy, we would like to look at the Beehive open cluster of stars (M44) which can be seen with the naked eye as a faint glow, the Hercules globular cluster (M13) which is a ball of older stars that orbits our galaxy, and a nebula that is the remains of a burnt-out star (M97). Outside our galaxy, we will look at the Leo Triplet of galaxies, a trio of three galaxies that can be seen in one telescope field of view, and the Whirlpool Galaxy (M51)--a cannibal that is eating up a neighboring galaxy which can also be seen.

Experience it yourself and work with other local amateur astronomers to explore all that the night sky has to offer. This event is free to the public and is sponsored by CTAS.

Directions to observing site:
Lake Waco Wetlands at 1752 Eichelberger Crossing Road.

Directions: From Interstate 35 take the Exit 330 and proceed west (toward Meridian) on Hwy. 6/Loop 340. Continue for approximately ten miles to the intersection of Hwy 6 & FM 185. Turn right onto FM 185 and continue 0.6 miles then turn left on Eichelberger Crossing Road. The Lake Waco Wetlands Research and Education Center will be 1.6 miles on your right at 1752 Eichelberger Crossing Road.

AstroInfo 3.10X

Thanks to hard work by Jochen Hoenecke, AstroInfo has been updated to allow for larger catalogs. No more installing a dozen star catalogs where one will do. The result is that if you want mag 11 catalogs, it's much faster.

AstroInfo is a pretty full featured (except for telescope control) free (GPL) planetarium program for PalmOS. Includes Tycho-2 catalogs up to magnitude 11 (but if you don't have enough memory, you can install smaller versions, like up to 8.5 or up to 10).

Before upgrading, make sure you delete all the old catalogs, as the new version is not compatible with many of the old catalogs.

This should be considered a beta, or maybe even alpha, test version:

https://sourceforge.net/projects/handypalmstuff/files/

Waco area cloud cover predictor

Using NOAA weather maps, some time ago I made a little online Waco area cloud cover predictor, which is now hosted on a better server than before. It shows data for about a week ahead of time (unlike the otherwise superior clear sky clock), every couple of hours, and it shows a mini map of the area. The numbers are percentage cloud covers. My experience is that small numbers are overestimated--about 20% on the map equals to the sky looking clear.

Custom moon map service relocated

I've relocated the custom moon map service to http://pruss.mobi/cgi-bin/moon.pl.  This may only be a temporary fix.

Need hosting for my custom moon map service

It being hot weather, and the air conditioning being in operation, I want to take a long hard look at always-on heat emitters, like our home server. Currently, besides doing some file serving that we can do, and some work-related stuff that I can move to my office server, it serves up custom moon maps--you choose the features you want, and it makes the map. Bandwidth requirements are low as I only have one user about every second day. My current server is a 2ghz P4 with 512mb RAM, so nothing fancy is called for. Just apache+modperl (with Perlmagick). If anybody is interested in volunteering some server CPU time and bandwidth, email me.

Moon and Saturn

Last night, I had a nice time looking at the Moon and Saturn.  The shadow of the ring seemed rather more offset from the ring then I remembered it--must be due to the way things are tilted.  The Moon was lovely, both in my 8" Coulter, and in the 6" F/5 I'm building (where it was super-sharp at 125X, even though I was hand-holding).  I was particularly struck by a crater with a lovely double peak near the terminator.  The deep parts of the crater were dark, and there were two gleaming white peaks there.  Maybe it was Burg?  I didn't check with a map at the time.  Burg looks slightly too far from the terminator in the Virtual Moon Atlas, though.  But maybe.

6" F/5 Dobsonian: Secondary mount and first light!

I glued the secondary mirror to its support the standard way, with silicone sealant and some toothpicks to ensure spacing, which toothpicks I removed after a couple of hours of drying.  It's a nice-looking 1.5" minor axis mirror.

I had a hard time deciding on the secondary mirror mount.  I wanted two-axis collimation done in Coulter-style, by having the support rotate along one axis and the secondary mirror along the other.  But I was having a hard time figuring out what the support should be.  I considered a two-vane support going across the aperture, using maybe a hacksaw blade (I went to the length of grinding teeth off it) or a steel ruler or even a hacksaw blade epoxied to a steel ruler.

But I also had some 1/8" thick 6" long 1" wide steel strips.  I bent one near an end--sandwiched it between two others, and hit it with a mallet, and then did the final fine adjustments by grabbing the end with an adjustable wrench and just bending by hand.  It was hard finding the exact right place for it and the exactly right bend.

In the evening my friend came.  We put in the primary.  And then tried to mount the secondary.  I was very nervous about dropping something on the primary.  My initial solution was to tie a safety line to my secondary support strip, and tie the other end to the focuser so if I dropped it, it wouldn't hit the primary.  I never dropped it, fortunately.  Then I had an idea for a better safety measure--I gently put a scrunched up T-shirt on top of the primary.  Good idea!  I dropped a fender washers two or three times on it in the course of the evening.

With my friend there, we measured off half of the diameter of the tube and cut a piece of wood to help center the strip.  Moreover, we cut a small piece of hardwood to act as a small carpenter's square, for squaring the strip against the focuser tube (which I racked in all the way).  Also, to get the vertical positioning right, I put a laser collimator in the focuser and used Inkscape to draw a little centering target which my friend cut out and we taped over the front of the secondary.  (My laser collimator emits a cross, so I aligned it with one of the crosses on the target.)

Eventually, I gave up trying to get it completely perfect, and mounted it.  Then I drilled a hole for the secondary mount on the support strip after aligning the target on the secondary with the laser (sorry, no offset).  And mounted the secondary to it.  (By the way, that big screw will have to be trimmed slightly.  And I will glue its head down so as to make the collimation entirely tool-free.

The secondary support is mounted to the tube with a carriage bolt.  One end of the carriage bolt is capped with a plastic wingnut, and the other goes into a plywood disk on the outside of the tube.

I collimated with my laser, and it was time for first-light.  The sky was clear.  I plunked my "30mm" Rini (probably 26mm or so) in the eyepiece for 28X with an approximately two degree field.  And, hurrah, stars came into focus, while handholding the tube.  With another friend's help (he saw us over the fence working away, and dropped in to kibbitz), and the scope leaning on the earlier mentioned T-shirt on the trunk of my car in the driveway, we saw a lovely but tiny sharp image of Saturn.  We then looked at Mizar and Alcor, and split Mizar.  Didn't look at any deep sky objects.  At one point it looked like I saw a dark nebula, but it was just leaves on a tree.

The diffraction spike from the single vane support didn't bother me and more importantly didn't bother my friend--it's his scope, after all.

So, the tube is done is done.  Now it will be time for the mount.  We'll make a hexagonal ring, about 7" wide, around the middle of the tube (the center of gravity with my 13mm Hyperion plus a Barlow is in the middle;  it'll be even further front once my friend attaches a Telrad), attach the altitude bearings to that, and make a standard Dobsonian box, probably on a circular base.

6" F/5 Dobsonian: Wooden Crayford focuser

Update: I now prefer the much simpler design of this focuser.

Like I said, I hate making focusers.  If I were making this for myself, I'd probably stick with a push-pull Crayford like on my travel scope.  But I'm making this for a friend, so I made a more normal Crayford.  The draw tube is aluminum with 1.5" outer and 1.25" inner diameter.  Actually, my eyepieces and laser collimator didn't fit when I got it, so I had to sand the inside of the tube.  The method was to take a screwdriver, wrap some sandpaper and foam around the handle, affix it at one end with duct tape, and spin the screwdriver with a drill.  Took a while, but eventually I got the bore large enough.

The main part of the focuser is a particl board plate, with two 5/16" dowels along the sides to fit the curvature of the tube, and three posts.  The two of the posts on the right are, I think, oak, and the one on the left is cut from 1"x1" poplar square rod, and they all have little plywood thingies behind them to keep them from falling over.  They are both glued and screwed to the plate.  The two posts on the right get ball bearings (the cheap ones for skateboards that one can buy on ebay, with wood screws JB Weld'ed inside them), and the one on the left has a hole  cut out in it for a holder for the focusing shaft.  There are two screws on the holder for adjusting tension.

The non-fixed parts consist of a little H-shaped poplar thingy that fits in the slit in the left post.  It has some V-shaped holes cut in it and lined with bondable PTFE.  Between the H-shaped thingy and its post there is a folded rubber thing to add some spring, cut from a bicycle inner tube.  The adjustment screws on the post bear against the rubber.  The shaft is 1/4" stainless steel.  The knobs are cut from pine boards.  They're not as straight as they could be, but they're light.  I cut the knobs by first drilling about 1/3" deep into a pine board with a 1.25" paddle bit.  Then I cut the pieces out with a larger (1.5" or 1.75") hole saw.  Result: cylinders with a recessed hole that lightens it and makes it look better.  I then put a bolt through each, and spun it against sandpaper on a drill.  The shaft then fits in the holes that the hole saw mandrel made.  I put some PTFE rings on the shaft, and I filed the ends of the shaft to make it rougher and less round, and glued the knobs in placed with, of course, JB Weld.  (I use JB Weld for most bonds other than wood-wood.  I use Titebond II for most wood-wood joins.  Except that the dowels at the bottom of the focuser, to make the focuser hug the tube, were attached with Gorilla Glue, because I wanted a glue that would (a) dry quickly and (b) make little gussets.)

Motion is delightfully smooth.  The next major step will be mounting the secondary.

6" F/5 Dobsonian: Drilling a focuser hole

I was really nervous about making the focuser hole--drilling in a cardboard tube can be messy.  On my Coulter 8" when I replaced the focuser, I had to enlarge the focuser hole, and it was a quite big mess.  I thought of trying to use a rotary tool, but I couldn't figure out which bit was appropriate, and had no scrap to try it out.

But I decided that the glue-impregnated cardboard just might take a hole saw, and risked drilling with a hole saw.  Success!  There was just one little bit of tearout on the inside, but I glued that down while impregnating the hole with water-diluted Titebond II.

The focuser is going to be a Crayford.  It's almost finished--it just needs some 5/16" dowel glued on the underside for mounting on a curved tube, and I'll buy that tomorrow after dropping the kids off at school.  I'll post on it when it's finished.  This morning I got to do some trigonometry to try to figure out where to place the dowels so the center of the focuser board would be tangent to the telescope tube, and the dowels would be tangent to the focuser board and the tube.  Somehow the calculation didn't work out.  Then I found a simpler method with Pythagoras' Theorem, which did work out.  Geometry is fun.  I don't know how some people manage to do serious woodworking without using trigonometry.  I guess they might be really good at scale drawings, or just able to eyeball things in ways I can't.

6" F/5 Dobsonian: Mirror cells

I used a router and a hand saw to make a simple secondary cell out of 1" square poplar rod.  It will eventually attach it to a simple two-vane hacksaw blade spider (I used a cheap Harbor Freight rotary tool with a cut-off disk to grind the teeth off the blade), and it will adjust about two axes by direct rotation.

The mirror came with a plastic primary cell.  Unfortunately, that would have required quite a bit shimming to fit in the 8" inner diameter tube, as the cell was rather small in diameter.  So I made one.  As I often do, I laid it out in Inkscape.  (The annotations are for the benefit of the blog--they weren't there in my original file.)  I am very bad at measuring (but getting some cheap digital calipers for $8 from a Hong Kong seller on ebay helped a lot--and then I got $4 back as one of the jaws was chipped and a set screw was crooked, so it was a great deal) so my best way for precision is to print out a cutting template, attach it to the piece and drill and cut right through it, or at least make marks with a pencil or drill bit through it.

The plan was to use scrap material.  The cell itself was to be a triangle with corners snipped off made of two layers of 1/2" Baltic Birch plywood, cut from the circular inner waste generated by routing the tube reinforcement rings.  I cut the cell with a jig saw, not very precisely, and cut a ventilation hole with a hole saw.  I then drilled and countersunk holes for collimation screws in only one of the two triangles.  I JB Weld'ed 2" long machine screws into their countersunk holes, and then I glued the other piece of plywood on top of this one (with Titebond II), covering up the screw heads, and clamping hard.  As a result, the heads of the screws are trapped within what is basically a solid piece of plywood (two pieces of plywood glued together are basically one thicker piece of plywood!)

There would be a rectangular baseplate made from a piece of scrap red oak that I had.   The baseplate would be mounted in the tube, near its bottom (not quite at bottom, as the plywood reinforcement ring on the tube would   I rounded the corners of this scrap piece with the router using approximately the right diameter to fit in the tube, bearing in mind I could always sand it smaller (as I indeed had to) but couldn't make it larger.  (By the way, here is a hint for how to measure things off from the router.  I cut things with a 1/4" up-cut spiral bit.  For measuring, I replace the spiral bit with a small length of 1/4" stainless steel rod, and measure from that with the calipers.)  Notice from the diagram that the rectangle would be somewhat off-center in the tube--this was on purpose, to fit better with the collimation screws.  I drilled holes for the collimation screws (actually, I did that while drilling them in the triangular cell, because they needed to line up exactly).

I also made a bit of a countersink around the holes, so that the collimation springs that would go on the screws (I had some springs that someone once sent me) would be countersunk, which would make the assembly have a lower profile.  I didn't have a paddle bit of the right size for these countersinks, and I didn't think I could control my router for such small work, so I did something wacky.  I chucked my 1/4" spiral cut bit into my cheap Harbor Freight drill guide, locked its height, and used a drill to route out the countersinks.  It wasn't very neat, but it was good enough, and the lower speed was less scary.  May not have been good for the bit, I already somewhat damaged the bit in an earlier episode when it was accidentally cutting against cement.

I also cut three ventilation holes in the baseplate with a hole saw.  The result coincidentally (honest!) looks like a certain rodent from a company that protects its intellectual property with a zeal that one may think violates the Greek maxim meden agan.  In defense of this design, I will say that the placement was entirely functional.  I made the inner hole as large as I could while keeping strength around the collimation screw holes, and the small holes are also located in such a way as to be fairly symmetric, and not too close to any of the alignment holes or the inner hole.  Four wood screws hold the base plate to the tube.

The mirror is glued to the cell with three 3/4" blobs of silicone sealant, with the positions optimized with Plop. I used some removable 1/4" particle board spacers to make sure the blobs wouldn't flatten out.  One wants the mirror to float on the blobs, and not have stresses put into it by the differences between thermal expansion of wood and glass.  By the way, when I removed the mirror from the original cell, I was horrified to see it was attached with two blobs of 1/16" thick rubbery stuff.

6" F/5 Dobsonian: Primary and tube

I've been missing making a telescope, but didn't need another one.  So I persuaded a colleague to make one with me.  The optics were cheap--a 6" F/5 mirror (with a 1.5" secondary) from a Cloudy Nights seller for about $60.  In classic style, this was going to be mounted in a Sonotube, with most of the rest made of 1/2" Baltic Birch plywood.

Before I even got my hands on the mirror, I cut altitude bearings from 3/4" red oak.  They are slightly more than semicircles.  It's traditional for altitude bearings to be circular, but using semicircles (or slightly more), the radius could be made larger for semicircular bearings without wasting money on a wider board, thereby making for greater stability.  Moreover, it's easier to cut less than full circles on my fixed-base router.  And I cut lightening holes with a hole saw.

I measured the focal length of the mirror at around 29".  The time before that I measured the focal length I projected the moon onto a piece of wax paper, and then measured the distance.  That wouldn't work this time, as we didn't have a moon in the evening sky.  So instead I put a red LED light some distance (d₁) away from the mirror surface, focused it on a piece of wax paper, measured the distance of the wax paper from mirror surface (d₂) and used the formula 1/d₁+1/d₂=1/f, where f is the focal length.  I did this twice and averaged. 

The mirror did have a chip on the back side, and I was worried that this may have set up stresses and distorted things, so I tested it as described in this post, and it was fine.  Hurrah.

The first hitch was that the Sonotube that my friend managed to get was only about 0.095" in thickness and very flimsy.  Following Cloudy Nights advice, I did a couple of things:

• Cut four plywood rings with a router for outside reinforcement.  Currently, one is installed on an end, and I'll put another on the other end, and I don't think more is needed.  A pair of plywood rings rigidify a tube by a lot.
• I only needed a 29" tube (that's the focal length; one can't assume the tube length is the same as the focal length, but that's how the calculations worked out for me).  Since the Sonotube was 48" long, I had 19" to spare.  I cut that into three rings, two 7" wide and one 5" wide.  I cut snips out of these so I could roll them into a smaller diamater (snip width: 2(pi)(thickness)) that fits inside the larger tube for reinforcement.  I would eventually glued the 7" wide rings at the ends of the 29" tube, and the 5" ring in the middle, but first...
• I impregnated all the cardboard--cardboard reinforcing rings and tube--on both sides, with a 1:1 mix of Titebond II and water.  Titebond III would have been better as it's waterproof, but II is water resistant, and it's what I had at home.  After impregnating, I inserted the rings inside the tube (the waterly Titebond was good enough for gluing them in place).  When I impregnated the insides, I replaced some of the water with DecoArt black acrylic, to make for an initial coat of dark (smudgy blackish gray!) for the inside, which eventually will have to be made much blacker.

The result is a very solid and strong tube, though right now I only have one plywood ring in place.  (One problem: the inner diameter of the rings is too small by about 1/16", and it took about 1.5 hours of sanding to get the one that I installed the right size.)

My 8" F/4 travel scope: Light shield

The light shield is made out of a coat hanger and some foam board (found by a dumpster when students were moving out last year) tied with wire ties. For transportation, the foam board removes so everything can go flat. The coat hanger hooks into a hole on the strut and focuser board.

And I think that's all I have to say about this project. Feel free to ask questions. I am really grateful to all the nice folks on the ATM forum on Cloudy Nights for their suggestions, and I did a lot of looking around the web to get ideas.

My 8" F/4 travel scope: Strut

The telescope started out as a two-strut design (the picture shows an early stage with the struts not cut to size). The struts are 1" square poplar, and attach inside the mirror box with carriage bolts and knobs (unfortunately, one has to be careful not to bump the carriage bolts against the primary--space is tight). However, I removed one strut and found that it was basically just as stable with only one, so in the end there was only one.


I then cut the strut in half, with a diagonal cut, so it would easily fit in a small suitcase. Four machine screws hold the halves together, and it is just as solid as if it were a single piece. I used JB Weld (yes, again) to capture the nuts for the machine screws, and to reinforce the thin edges of the wedges. In general, I don't like dealing with nuts flopping around, so I like to JB Weld them.

By the way, I finish wood with a mix of Titebond II and water (about 1:1, but I am not very precise) and when I want to paint it with somewhat glossy paint, I replace some or most or all of the water with DecoArt Crafter's Acrylic paint. So, that's the black paint on the strut. It's a cheap and easy finish. It doesn't look great, but I am all for cheap, easy and functional. And, as a bonus, it's a low VOC paint. Inside the mirror box, I then went over with the acrylic paint again to get a flatter layer.

My 8" F/4 travel scope: Focuser

I hate making focusers and am too cheap to buy. This is a push-pull Crayford: the draw-tube moves against PTFE runners. The draw tube is made out of super-cheap PVC conduit (something like two or three dollars for 12 feet). Unfortunately, the conduit's inner diameter is significantly more than 1.25", so I lined it with PTFE strips, which I sanded down to fit eyepieces.


The focuser's tension is adjusted by having a piece of metal glued on its bottom part (with JB Weld), and with a thumbscrew bearing against the top part, and with PTFE on it, on one of the three posts.


Here is a picture of the focuser board at an early stage in the production. The elongated hole is for the secondary stalk.

My 8" F/4 travel scope: Secondary mirror

I get confused by three-screw collimation arrangements, and I couldn't figure out how to make one. So the secondary mirror collimation is done like in my Coulter scopes, by rotating along two axes (and one can adjust the position up-down because the support stalk fits in an elongated hole in the focuser board). Basically, the cell is two pieces of softwood that swivel around a screw. The gray square knob at was made by putting a nut in a square made out of painter's tape, and pouring JB Weld into this cast.


The stalk started as a piece of threaded rod. Unfortunately, the support wasn't solid enough--collimation shifted too much with elevation. So I JB Weld'ed (there is a theme here, isn't there) a small square steel rod in parallel with it to reinforce, which helped.


And here is a picture of the cell before it was painted and the mirror was glued to it (with silicone glue). I later cut and sanded it smaller.
I did have one problem with the scope--when I viewed Jupiter, I would get a long smear in one direction. It turned out that the secondary mirror had a distorted edge on one end. I tested by looking through the telescope at an LED flashlight with aluminum foil and a pinhole, if memory serves me. I blacked out the bad part, and the smear disappeared. It might be a good idea reorient the primary so that the blacked out part of the primary aligns with the blacked out part of the secondary, but currently the blacked out part of the primary aligns with most of the secondary stalk, which is also good.

My 8" F/4 travel scope: Primary mirror cell

Because of the damage to the primary mirror, I didn't want to put much stress on the mirror, so I went for a six-point primary support cell, with the mirror glued with silicone glue. The positions of the points were optimized with Plop.


The cell consists of a piece of scrap hardwood. It has carriage bolts coming in through recessed holes on the top surface, JB Weld'ed in place. The springs are valve springs from an old mower. I went to a mower repair shop, and the man there removed them from a junk mower for me for $5. Super stiff, great stuff. Because the springs are big, I made recessed holes for them (with a 1.25" paddle bit in a drill).
There are, of course, lots of ventilation holes.


The carriage bolts come out of the bottom of the mirror box, where the collimation is adjusted with knobs.

My 8" F/4 travel scope: Rocker box and altitude bearings

The altitude bearings are made from an old rotating CD case we had. The case had a top and bottom particle 3/8" particle board circle. I cleaned these out, sanded one side of each circle, glued them together (Titebond II, clamped with several layers of bricks), and then cut the resulting 3/4" circles in half. Like much of the scope, the bearings are held to the box with 1/4-20 carriage bolts and knobs.


The rocker box is made up out of a circle of 3/4" particle board with an old record lying on it (bought on ebay for about a dollar, shipped). On it, there is a very low profile rocker, made of a piece of particle board and some softwood, with bondable PTFE pads on the underside and where the altitude bearings go. The rocker is too low profile for good balance, however, so I had to add some extension springs.

My 8" F/4 travel scope: Overview and mirror testing

Here is my home-made travel scope, which I made for airline travel. It's about 16.5 pounds in total. The mirror box, after removal of the altitude bearings, fits in a backpack (with a cardboard and plastic cover to hold it in place) while all the other parts can be tossed in a suitcase (ideally mostly in Ziploc-style bags). The secondary mirror cell bolts to the inside of the primary mirror box, in a corner, for transportation. Assembly requires one Philips screwdriver, and the rest is one home-made knob and a bunch of three-lobe knobs going on carriage bolts. Originally, I wanted it all to be no-tool assembly, but using Philips screws saved some weight and space on the focuser board and on the strut joint.

This is a low-cost 8" F/4, made from a mirror that had a crack in it on one side, below the front surface, so I got both the primary and the secondary for about $40. Moreover, a large chunk of the primary was duct-taped over, presumably to cover up the area distorted by the crack. I ended up testing the mirror by using an LED flashlight covered with aluminum foil with a pinhole, holding the flashlight at a little more than twice the focal length, while putting my eye at about twice the focal length. When the two distances are just right, I could see a big blob reflected on the mirror--I think that was the image of my pupil illuminated by the pinhole light. As I moved my head around, the blob moved. Moreover, as the blob got closer to the area with the crack, the blob distorted in weird ways. Monitoring where the blob was distorted and where not showed me where the figure of the mirror was distorted, and I masked off the area--quite a large area--with black felt. And, yes, it works just fine with the area masked off.

The mirror box is made of some hardwood that I had found lying around and used a friend's table saw, but it could have been done with a jigsaw if one had a good blade. Besides some simple hand tools, I used a power drill (with a hole saws and a 1.25" spade bit), a Harbor Freight jig saw that was on sale, and one elongated hole got cut with a friend's small router, though it could have been done with a rattail file, too.

The next couple of posts will highlight various parts of the design. Please feel free to ask questions, e.g., in comments. The design is very simple and I made it with very minimal woodworking skills and tools.

In the interests of full disclosure, I admit that I am including some Amazon Associate links in these posts, but only for products that I actually bought from Amazon (sometimes the link may point to a different quantity--I don't keep that good track).