Build a Wheel

Building a bicycle wheel is one of those endeavors which seems complicated to the uninitiated. It looks difficult, and seems like it would be dangerous if you screw up. It’s actually pretty easy to build a wheel, if you can follow step-by-step instructions. There are hundreds of machines in Taiwan doing that very thing, as you read this.

Building a good wheel may be slightly more difficult. I’m a Jack, not a Master, so it may be the case that I’ve never actually built a good wheel. But it’s easy to tell when you have an unridable wheel, and any wheel which is ridable probably passes quality control for a machine-built wheel. So if you’re satisfied riding on machine built wheels, then no worries: build a wheel! It’s fun!

Sheldon Brown has very good instructions on how to build a wheel, so I won’t try to bore you with the step-by-step. Instead, I’ll provide the background thought-track I used while I was building a wheel tonight.

The reason I’m building this wheel is because I bought a Sturmey-Archer 3-speed hub: just like the ones on the bikes of our parents’ generation (or: your generation, mom and dad) when they were young, a decade or so before the big bike boom of the early 1970’s. In fact, this hub was built in 1966: not the best year, but it should have a lot of life left.

The hub came with spokes and nipples, so I only had to supply the rim. I chose a Sun CR-18, which is a nice, strong, inexpensive rim which supports wide tires and looks nice on “retrogrouch” bikes. I also have Sun CR-18’s on a few of my other bikes, so I can swap wheels without mismatching anything. (I’m sure it’s not worth pointing out that I didn’t describe the rim as “light” or “aerodynamic.” At least it isn’t chromed steel.)

Lacing the wheel comes first. This seems like it should be the hard part, but it’s not!

Oops. I’m sure it’s impossible to tell, but all of the spokes in this picture are off by 2 spoke holes on the rim. If you put them in the wrong place, the valve stem will be obstructed by spokes and it’ll be hard to pump up your tire. The fewer spokes you have in your wheel, the more wrong places you have left to put them. Just like when weaving baskets, the key is to find your mistakes and fix them as soon as possible, to avoid taking apart anything you don’t absolutely need to.

I vaguely remember the first time I built a wheel. When I was a kid, I built a set of wheels for my BMX bike, with Dad’s help. I’m guessing I was around 13 years old? I’d guess we bought all the parts at Bike Nashbar, back in the days when it was an interesting enough store to sell things like frame building lugs, instead of just being a discount/clearance outlet. If I remember correctly I bought some kind of plastic rims? What the heck was I thinking?

I don’t know why I remember this, but I’m pretty sure we laced the wheel incorrectly. I think I interlaced the spokes over each other too many times. It was pretty tight, working on a small 20″ wheel. In any case: it didn’t matter. I wasn’t the hardest BMX/freestyle rider around, but I did certainly beat up those wheels; but I never had any broken spokes (though it may have gone out of true, I really don’t remember).

Eventually, I traded the wheels with a friend who had some solid-spoke “mag” wheels (they were plastic, not magnesium, but that’s what we called them all) which I put on my freestyle bike. (No more BMX for me!) It was a 1984 Haro Freestyler frame and fork, which I got cheap because it was a year or so out of date.

I rode that bike basically everywhere, at least until I got a driver’s license. When I was on an internship in Richland Washington after college, I had my parents mail it out there so I could ride with the other 13 year olds, because there was literally nothing better for a 23 year old to do in that gods-forsaken desert (so say we all). I left the bike there when I left; hopefully the neighborhood kids appreciated it, or at least made some money on ebay. (The family I stayed with lived in a type A converted to single-family use.)

When the wheel looks done, the fun has just begun!

Putting the spokes in properly is necessary, but not sufficient, to build a proper wheel. The next phase, which can be a lot trickier, is making sure the wheel is “true” and that the spokes have enough tension. The rim can’t wobble back and forth, and must be round without any any “bumps” in it. It also must be centered left-to-right with respect to the hub.

At this point, you’re basically debugging: identify the place where the wheel is the most out of spec, and correct it (preferrably without affecting any other adjustment in the process). Repeat
until you’re finished. (How close to perfect is “finished,” anyway? Sheldon doesn’t say.)

Wheel building machines are really good at making wheels perfectly straight and true when they come off the machine. The problem is, the wheels are often undertensioned: without enough tension in the spokes, wheels go out of true, and spokes fail prematurely.

Bicycle wheels work in a counterintuitive way. To most people, it seems that when riding a bike, the hub must “hang” from the spokes between the hub and the upper part of the rim. If that were the case, then when weight was added to the bicycle, those spokes would increase in tension. In fact, that’s not what happens at all for properly built wheels. Instead, the spokes between the hub and the ground decrease in tension: a bicycle wheel works as if it had thick spokes under compression, and the weight is borne by the lower spokes. This is why high tension is so important in bicycle spokes- weight on the bike reduces the tension in the spokes, it doesn’t increase the tension.

Improperly built wheels with tension that is too low do work as if the hub was hanging from the rim. In those wheels, the spokes fatigue and break much more quickly than in a properly tensioned wheel.

Machine built wheels also generally don’t stay true for very long, because machines can’t tell the difference between twisting a spoke, and turning the nipple on the end of the spoke. If a spoke is twisted without the nipple turning, eventually that stress will relieve itself, and the wheel will go out of true. You can reduce that effect by lowering spoke tension, but then you’ll have an undertensioned wheel: choose your poison.

I haven’t built many wheels from scratch, but I have rebuilt, repaired, and retrued many more machine built wheels. Machine built wheels are really inexepensive: cheaper than buying the parts reqiured to build the identical wheel, and far less expensive than a hand-built wheel. So, why not just buy a machine-built wheel, and finish it by hand? In fact, this is what a good bike shop should do for every new bike they send out the front door. Not many shops actually do this, unfortunately.

I think it’s a great deal to buy a machine-built wheel, then retension it myself. I’ve had much better luck with wheels I’ve finished this way, than with wheels I’ve ridden straight out of the box.

“Department store bikes” are ridden, on average, less than 20 miles over their entire lifetime. Yes, I ride more in 2 days than the average Wal-mart bike is ridden ever! The bikes are built with this in mind: most of them can’t ever be adjusted properly, or won’t stay in adjustment. Mike had a Wal-mart road bike. I built him a replacement, a 25 year old Schwinn with a handful of parts I had lying around the basement, and it worked better and he enjoyed it more than his brand new Wal-mart bike.

(Mike, are you still riding that World Sport? Do you still like it? Daniel has another World Sport from the same year, and he seems to be enjoying it as well. I think they must have been on sale that year.)

This is my truing stand and dish stick. I don’t have a multi-hundred-dollar Park Tools professional truing stand. I have a fork stuck into a hole in an ugly coffee table. It works just fine, and it was free. The truing stand is used to identify high and low spots on the rim, and locations where it is untrue from side to side. I used a few scraps of masonite and a nut and bolt attached to the fork’s cantilever post, as a feeler gauge. Although this is a completely adequate substitute for a proper truing stand, it requires understanding how a truing stand should be used, before you can build and use it effectively.

I also built my own “dish stick” out of plywood and masonite instead of paying for the real thing. A dish stick, or “wheel alignment gauge,” is used to make sure that the lock nuts on the hub axle and the sides of the rim are centered in relation to each other. If they aren’t centered, you’ll need to misalign your brakes to compensate for the crooked wheel.

At this point, my new wheel is “almost done” and only requires a bit of fine tuning before I put it on a bike and try it out. It took me about an hour and a half to get to that point on the wheel, and slightly longer to write about it (or, to write about what I was thinking while I was building it).

A Project Built for Two… or Three?

How does an adult carry two kids with one bike? I have several bikes, a rear kid seat, a trailer, and a trial-a-bike pedal trailer. The only combinations of kid carriers which will work together with one bike are the trail-a-bike with the trailer behind it, or the rear seat and the trailer.

With Martine on the trail-a-bike, I already use my lowest gear up some of the hills around here. I’m not sure I could handle dragging another 40+ pounds on two more wheels behind her. And I know she has no interest going back to riding in the trailer; she never enjoyed that even when it was her only choice.

The only other options I know of require a two-seater bike of some sort. With a tandem, any of the we have could hold a third passenger easily. Or, Marla and I could carry both the trail-a-bike and trailer behind us as a group of 4.

I’ve been researching this lately, since I don’t think I’ll enjoy staying home all summer whenever Marla takes the cat car. We found several solutions aimed specifically at the kid-adult tandem market.

  • The Love Bike is a compact kid-adult tandem, with the child riding in front. This gives a better view for the child, and takes up less space, but it looks like it’d have horrible handling.
  • The Kidz Tandem is another child-adult tandem with the child in front, but it uses a steering linkage instead of a compact wheelbase and shared steering.

The problem with these child-specific solutions is, not only are they expensive, but they’re only useful for children of an appropriate size. I expect they’d hold their resale value well if taken care of, but it would be better to get longer use out of them.

So I considered a full tandem, suitable for use by adults as well as children. One good option which doesn’t take up a lot of space, and adjusts easily for use both by children and adults is the Bike Friday Family Tandem. This is a small-wheeled folding bike, and the rear seat can adjust for use by very short and very tall riders.

The Bike Friday was my preferred solution, but then I came across another option on craigslist: a used Burley Duet tandem, with a kidback stoker kit. On a tandem, the front rider is the Captain, and the rear rider is the Stoker. A Child Stoker kid or “kidback” converts an adult-sized tandem for use by children otherwise too small to ride it. It adds another set of pedals which are within reach of the seat, but the child can’t put their feet on the ground.

I bought the tandem. It’s a pain to get into the basement, and I haven’t tried getting it back out again yet; we’ll see how that goes. The main problem with it is the space it takes up, and moving it around when we aren’t riding it. It weighs about as much as Marla’s recumbent weighed, but it’s much more unweildy. It uses the same roof rack that we already had, for use with the recumbent.

The tandem doesn’t need a lot of work, but it does need some; and it wants some more. So I get to learn about tandems.

Most aspects of bike hacking and maintenance apply equally to tandems, with a few exceptions. First of all, there are a lot more chains and chainrings to take care of, and some of the chains are longer than a normal bike chain. Cables for rear brake and derailers must also be extra long in order to reach.

I want to reduce the stem length slightly, and increase the height. It turns out this tandem has a 1 1/8″ threaded headset, which is an uncommon enough size that I don’t have anything suitable sitting around. Both seat binder clamps were broken due to misuse; luckily they’re cheap and easy to replace. The front seat post was stuck in the tube, but again very luckily, I was able to loosen it with oil and brute force instead of having to resort to cutting tools.

At this point I basically need to wait for some pars in the mail before I can make much more progress.

An initial short ride tells me this handles very differently than an ordinary bike, or even a bike with a trail-a-bike: it’s going to take getting used to. Martine rode on it a bit, and I think she’s going to really enjoy it. But it’ll be a while before I try two kids at once.

Beer Batch #25: Crippled Kriek

I wanted to brew a cherry beer, but I didn’t find a specific recipe I liked the look of. Crippled Kriek is a first attempt at getting what I want.

I called it “crippled” because I expected a cherry beer that didn’t taste like a proper Kriekbier, but instead, I got a beer that didn’t taste much like cherry. The rest of the flavor came out as I intended, and it’s a good beer; it just doesn’t taste like cherry.

Crippled Kriek

Brew date: March 29, 2009

Ingredients for a 5 gallon batch:

  • 1/2 lb Crystal Malt
  • 1/2 lb Chocolate Malt
  • 1/4 lb Roasted Barley
  • 6 lb LD Carlson Light Golden DME
  • 1oz Hallertau hops, 8.6AA for 60 min
  • 1oz Hallertau hops, 8.6AA for 10 min
  • 1tsp Irish Moss
  • 49oz Cherry Puree (3.3lb canned)
  • 1/4 gallon yeast starter, using WLP500 abbey ale yeast and WLP810 SF Lager

Same process as usual: Steep the grains, add the DME, and then boil for an hour. I added the cherry puree directly into the primary fermenter, after measuring the original gravity.

For the yeast starter, I used some 2nd generation Abbey Ale yeast, in hopes of getting some of its taste profile, and some 2nd generation San Francisco Lager yeast, because I knew it would ferment in my chilly house temperatures. In the end, I think the ale yeast failed and the lager yeast succeeded.

Original Gravity: 1.062

Notes:

  • Started yeast on March 26 using 1c DME in 4c water, and boiling for 30 min
  • Pitched yeast at 70F
  • April 8, 2009: Gravity = 1.014
  • April 9, 2009: Gravity = 1.014; rack to secondary
  • April 21, 2009: Gravity = 1.014; rack to the keg

The taste is a lot more clean than I had hoped for. I’d prefer the more interesting flavor which the Abbey Ale yeast would impart, but instead I think this is just the lager yeast.

For the recipe, I started with my gruit recipe (but without the herbs) and added the Roasted Barley to give it a bit more of a chocolatey/smoky flavor and a darker head. This part of the flavor turned out just as I had hoped.

In retrospect, I should have paid attention to the recipes which called for 10lbs of cherries. Another possibility would be to add the cherries in the secondary fermenter, instead of the primary.

As usual, it’s a good, drinkable beer. It just didn’t come out how I wanted it to.

Rodback: Finished

I finished the rodback chair. I used mustard Real Milk Paint with the anti-foaming agent, and I’m still very happy with the results. I didn’t use an under coat of the Butternut Squash, as I did on the perch, but this chair surprisingly turned out a bit more orange than the perch.

This is a really comfortable chair. I really like the feel of the deeply carved seat. Overall I’m very happy with the way it turned out, despite the mishaps.

I used epoxy to fill the crack in the seat as well as I could. Unfortunately it didn’t fill completely, but I’m confident it’ll be strong enough. The sawdust-filled epoxy seems to hold paint well enough, but it expands and contracts differently than the surrounding wood, so it does stand out a bit.

There was another unforseeable circumstance that set things back slightly. I used two different woods when making spindles, and one of the spindles I chose for this seat was made from the yellow/green wood I haven’t identified. When the first coat of paint dried, that spindle stuck out like a sore thumb: it turned dark brown, almost black!

So that spindle has several more coats of paint than the others, just to turn it yellow. It’s not a perfect match for the rest, but it’s close enough. I have a bunch more of this wood, and it seems to be turning brown on the outer surface as it ages. Probably something in the milk paint just accelerated that process. Now I’m not sure what I want to do: I’d like to use the spindles, but I’d rather not have to add 5 coats of paint to all of them. Maybe I should use a darker color, but then I wouldn’t have matching chairs.

On all of the pine seats I’ve painted recently, there are tiny surface cracks in the paint. I think this may be related to tiny pockets of pine pitch in the wood. I think it looks basically fine, the paint hasn’t chipped on any of them. Peter Galbert heats his seats and washes them with naptha to avoid problems with pitch.

This one is marked “Alan Ferrency 2009 4” on the bottom of the seat. I must say, I didn’t expect to make 4 chairs, even stools, in the same year! And there may be more to come.

That Looks Just About Right…

This is a sketch of the rodback chair. I made it before I started working on the chair using tracing paper over a photograph of the chair I was inspired by. I changed things where necessary to show the chair I planned to build.

Rod Back chairs are a later (1800-1820) “degenerate” style windsor. They typically have much straighter legs and less deeply carved seats than earlier styles and most of them used a square stretcher pattern instead of the “H” stretchers here.

I like the more comfortable deeply carved seats of earlier chairs, but I prefer the turnings used on later chairs. So, I paired the seat shape and leg angles of an earlier Comb Back chair with the turnings and square back of the rodback. Compared to the photograph I traced, this seat is carved more deeply, the swell in the spindles is higher, the posts are different, and the leg angles are different.

I took a photo of my chair-in-progress, from approximately the same angle as the photo I traced. It looks pretty close!

I like the much slimmer look of my chair, compared to the sketch. I think the angles are a bit exaggerated in my chair because I was very close to it when I took the picture.

Since the chair isn’t finished yet, I’ll take this opportunity to be critical. The front legs of the chair are splayed a bit more than the plan called for; I’ll have to see whether I built it incorrectly or planned it incorrectly. It may be only because the front of the seat is higher than the chair I planned from. That’s the main thing that looks a bit odd with it, when I look at one portion of the chair critically, instead of standing back and admiring it.

It’s quite comfortable, but I haven’t spent a lot of time sitting in it yet since I haven’t epoxied the seat back together yet.

Today I trimmed the spindles. If it weren’t for the unfortunate crack, it would be basically ready for a quick sanding and a few coats of paint.

There are a few other things that didn’t work as well as I would have preferred, but worked out in the end. I didn’t orient the seat blanks properly. When carving the wood along the join, in some places I needed to carve in one direction on one side of the line and the opposite direction on the other side, which made things tricky. It’s easier to glue up seat blanks when both halves come from the same board.

I used wedged through tenons on the post-rod joint. This worked well enough, and it’ll be strong, but I had problems with drilling a through hole without breaking the grain out on the other side of the post. I think I need to replace my crappy 1/2″ bit, as I did with my 5/8″ bit. Although these bits from Highland Hardware got good reviews in Fine Woodworking, they’ve been horrible in my experience.

I’m also not completely happy with the wedged joints between the spindles and rod. They’re a bit loose. I may dab a bit of epoxy in, while I’m patching the cracked seat. In general, I need more practice carving spindles. That’s understandable, since I’ve been working on stools lately, and I’ve been using suboptimal spindle wood.

I’m in the home stretch now. I’ve been wondering whether I have enough stamina for another chair, but Marla tells me I can’t stop making chairs (or at least parts) until I’m done clearing the wood off the porch. I guess I’ll have to at least rough out a bunch of spindles, rods, and legs.

Nearly a Chair

My rodback chair is almost fully assembled. One more night to glue things up, and then it’s down to trimming and finishing.

In fact, pretty soon I’ll probably have two chairs! Well, two halves of one chair, anyway.

When inserting one of the spindles, the seat cracked. A few of the spindle ends might have been a bit too fat, but in this case the main problem was that this hole ended up directly over a crack on the bottom of the seat. Here, the crack goes all the way through the seat. I should’ve made this spindle loose rather than risk splitting the seat, if I had realized it might be a problem.

I expect I can salvage it, though I’m not sure which glue would be best to use here. Super glue might keep the crack from spreading, but it won’t fill the space to hold the cracked parts together. Maybe urethane (gorilla) glue would work better for that, but I’m not sure how to get it in the crack and keep it there; and I wouldn’t want it to push the seat apart even more.

Maybe I’ll use both. Start by applying super glue to the edges, and letting it dry. Then, clamp the seat lightly so it can’t expand any further, push some urethane glue into the crack, and apply tape on top to keep it in place while it dries.

The worst part will be finishing it. The crack will definitely be noticeable, and milk paint doesn’t stick to super glue. I’m not sure about the urethane glue, though.

I think the rest of my seat plank is not checked on the surface the way this one is. Both of my pine seated stools have check-cracks on the bottom, which are not a problem. The difference in this case is the spindles. With 9 holes across the back, I would have had to plan a lot farther ahead to avoid putting this crack in the middle of one of them.

Chairlike

I’m making progress on the Rodback chair.

The turnings other than the stretchers are done. This maple is wonderful to turn, and it seems very stable when it’s drying. Now that I have the legs tapered, I can measure the stretcher lengths and turn them as well.

The spindles and rod are roughed out, but they’re still oversize. The drying rack worked very well, after I put a rack on it to keep the pieces from falling down whenever I bumped it.

I’ve also drilled and cut the seat. After tapering the leg and post holes, I set this picture up so I could see what the chair will look like when it’s done. I think the shape of the post turnings will be fine.

I’ve started carving the seat, but I need to sharpen one of my spokeshaves and it’s giving me trouble. Once that’s taken care of, I’ll finish the seat and “leg up:” finish the stool half of the chair.

After that, I’ll finish the rod and assemble the two posts and the rod to each other. Then I’ll finish the spindles, drill the rod, and put the rest of the back together.

Drying Parts

Dad suggested I could use my forced-air heat (as limited as it is these days) to dry my chair parts faster. I did this a bit already with some stool legs, but I had figured these parts would be sitting around long enough to be dry by the time I’m done with the stool portion of the chair.

Tonight I turned a preliminary set of back posts (I’ll see if I like the shape or not). Now I have all the turnings and spindles done for one chair, but the spindles are still much wetter than I expected. When I brought the parts upstairs to put them by a heating vent, I remembered another reason I didn’t do this yet: there’s no place upstairs the parts would be safe from kids using them as play swords, and probably hurting each other.

So, I set up a hanging support in front of the vent in the basement (and opened it, for the first time in years). It isn’t enclosed, so it probably won’t overheat things, but it’ll be a lot more dry there. I also found a use for a few of those old botched leg turnings I had lying around…

Bending Sticks

I had some free time today, so I decided to bend the rods for the rodback chair.

I built the steam box a week or so ago. The bottom board is a 11″ wide pine board, and the upper portions are made from dimensional 2″x6″ lumber. It’s heavy, but it works. There are 3 dowels set into the box, to raise the parts to be bent above the bottom of the box.

I closed the box as Brian Cunfer did: using open-celled foam (like chair seat foam). Where the box sits over the pot, there’s a 4-5″ hole. I used 3/4″ or 1″ foam at the seam with the pot to make sure it’s sealed fairly well. In each end of the box I used a chunk of 1 1/2″ thick foam to seal the ends, while still letting steam pressure out. The wood joints are sealed either with gorilla glue or silicone.

I made two bending forms from 2″x6″ lumber screwed onto plywood. One side has the shape of the rod, and there are blocks to wedge the rod against and hold it into place. The parts should dry on the form, so in order to have a spare “just in case,” I made two forms so I could bend two parts at once.

The rodback sticks are about 20″ long. I shaved one from ash a week or so ago. The other I made today, out of the odd greenish/yellowish open grained wood I haven’t managed to identify well yet.

I steamed them for 45 minutes in the steam box. The pan started about half full of water, and didn’t come close to running out. After that, you have to work quickly: bring the stick to the bending form, bend it into place, and pound wedges in to hold it onto the form.

The ash felt quite stiff when I bent it; basically what you’d expect a green stick from a tree to feel like when you bend it. It didn’t crack, so the initial bend was a success. But, I wouldn’t be surprised if it sprung back at least a bit after it has dried.

When I bent the other stick, it felt the way I remember from the previous times I bent parts. The stick resists bending pressure, but then releases. I want to describe it as a “chalky” feeling, though I’m not sure why. I’m more confident this stick will stay bent.

Neither of the bends were immediate failures, but we’ll see if they stay bent in a week when I take them out. I think it’s likely they will both work.

While I’m waiting for the spindles and rods for the chair to dry, I’ll build the lower half of the chair: basically, everything I’ve already done for stools, but with a place to install the top. I’ll drill the holes for the top before I carve it, but the upper portion isn’t assembled until after the entire stool is complete.

A Slight Change of Plans

In the last few days, I figured out how my angle calculation tool was incorrect, and fixed it. Now it’s correct, just not very convenient to use. The reference axes are a bit “here and there” so you really need a sense of what makes sense, in order to extract the right answer.

I then went over all of my previous calculations, and made corrections to the seat plan.

Luckily, the amount of error in an angle calculation was directly related to how far away from perpendicular the hole is. Because of this, the errors on my spindle angles were so small that they almost all rounded off in the same direction as before. The exception was with the outside posts, which had to shift their sight angle by half a degree.

Today, I used my new plan to drill test holes for the back spindles in a scrap of dimensional lumber, to see if the back matched my expectations. It was basically a complete success: I have nothing to change with these angles. The tops of the spindles form a good curve (when viewed from above), and they’re evenly spaced. As shown here, I built up the test back with some spindles I’ve already shaved, along with some sections of 1/2″ pipe. The pipe is a lot straighter, and allows better measurements. (I picked this tip up on Peter Galbert’s blog as well, unsurprisingly.)

This gave me better information than I had about the shape of the seat back. The top of the end posts here are close to where the horizontal rod will end up. It’s wider in relation to its height than I expected. Obviously, my spindles are too long; I’ll need to trim them down on both ends and/or make some new ones. I think it’ll look fine when it’s finished, but it will be a significantly smaller chair than the bow back I made previously. This is good, since that’s what I was aiming for.

Back to the plans: My original leg lines were a complete mess. I couldn’t even figure out the values I used to I calculate them, let alone the error introduced by the tool. Always show your work! They were reasonable angles, and would have made an adequate chair, but they wouldn’t have matched my original intent. From a design perspective, I don’t know whether my plans or the old angles would result in a better chair, but I’m going to try my original plans and work from there.

I’ve already shaved some spindles, and they need to dry a lot before I can use them. I’m not using a kiln right now, so I really need let them sit around for a while: hurry up and wait. Next I need to make the top rod, bend it, and let it dry as well.

This requires a steam box, so I started building one. It is small, 30″ long, becuase I plan to use it in the kitchen. We’ll see how well it ends up working in the next week or so. I also need to accurately measure the location for the rod, so I can figure out how long to make it and build a bending form.