Tube Miter Software

Giles Puckett wrote a nice little windows app some years ago called tubemiter that will plot out a curve on a piece of paper that you then wrap around a tube to act as a cutting guide. This is a great idea, only his application is limited because A) it doesn't allow for tubes that meet with an offset (i.e. the center axis of the two cylinders don't intersect). And B) it only prints the end miter, it's up to you to figure out how to align it.

I'd like to extend his application by adding more reference lines, an offset parameter, and possibly even the ability to put multiple miters on a single printout to minimize compounding errors from measurement. If I could plot out both my headtube and BB intersections, and print it on an 11x17 piece of paper, that would be awesome.

Instead of using a standalone windows application, I decided that the best bang for the buck would come by writing a script for my favored CAD program, DeltaCad. By using a CAD program rather than a standalone app, I can dimension and draw in other references as needed. I can also plot multiple intersections and cut and paste them onto my final drawing. The only drawback to this approach is that the macro runner is a bit flaky when run out of wine under linux, such is life I suppose.

I should point out that modifying the script to work with elliptical tubing would be pretty trivial. If anyone is interested I'd be happy to make the changes.

You can download a demo copy of DeltaCad from the website, and a copy of my script here. To run it, go to the macro tab. Click "Edit macro list" and add the tubemiter file to the list. Then select it from the pulldown and select run macro.

Stuff I need to Order

This is a list of stuff I need to order to actually continue to make any progress on the bike. Hard to make things when you don't have the materials...

From Nova:

• Head Tube
• BB shell
• 10x cable stops
• breezer dropouts (with boss)
• MTB fork blades (29er)
• 4 Pinch bolts
• canti bosses (max offset)

From Atom:

• Seat

From Online Metals:

• 20ga flat sheet
  
• Square tube (for idler mount)
• 6" 5/8" x .065" tubing
  
• 2' 1.125" x .065" Aluminum 6061 -T6
  

From McMaster-Carr:

• Weld nuts (90563A640)
• silver brazing alloy (??) (76955A72)
• silver flux (black, white?)
• 6mm SS bolt (for fixturing) (92000A450)
• 6mm SS socket head bolt (91292A141)
• 8mm SS socket head bolt (for idler axle) (92290A461)
• 8x10mm bushing for idler bearing holder (6679K13) (might need 10mm version)
  

To-Do List

I find it helpful to write down all the things I need to accomplish from time to time just to wrap my head around what's coming and to sort out the places I need to understand better. This includes what needs done, as well as any points on how to do it that I've thought of.

Things I need to do in order to get the maintube, HT, and BB brazed up. (I'll do rear fork and finishing steps, seat mounting, sprint stays, etc. later)

• Level jig on saw horses
• Decide if I am brazing FD mount along with everything else or later separately, and what size tubing I'm using for it.
  
• machine appropriate spacer blocks
• figure out how to miter the thing.
  
• Prepare jig
  
• Draw out maintube, head tube and BB locations on jig (FD mount?)
  
• mount spacer blocks
  
• machine wooden square blocks for angle alignment brackets and mount
• Drill and prepare for BB fixing bolt
  
• Mark out maintube
• Mark 90 deg longitudinal lines on maintube
• Mark intersections for headtube, BB, and seat mounting penetrations
• Print out tube miters for HT and BB penetrations, align with longitudinal lines, transfer to tube with centerpunch and marker.
  
• Prepare HT
• Use cutoff tool on lathe to cut partway through tube to mark accurate square cutoff for cutting to length later with hacksaw/file (post brazing)
• drill breather holes
• mark intersection with maintube for positioning purposes
• Cut maintube
• Cut out headtube penetration.
  
• start with dremel
• clean up to marked line with 1" drum in die grinder
• Test fit in jig, wash rinse repeat
• Cut out BB penetration
• hacksaw lower bevel & rough out
  
• finish with 10" half round file and 1" drum
• Test fit
  
• Cut and fit plate for lower bevel under BB
• Cut and fit FD mount
• Drill holes for seat mount
• This is important to do before any brazing since I am doing it on the mill and any brazing material could throw it off depending on exactly how I mount it
• Mount HT, BB, lower bevel plate in jig.
• spot braze LH side of headtube, and Top and Bottom of BB (braze both LBP and BB )
• Take frame out of jig and flip over
• remount (if this is hard, something warped)
  
• braze RH side of ht
• take frame out of jig, mount in frame stand and finish braze all joints.
  
• aligning and brazing seat mounts: (assuming working on LH side)
  
• start by running a SS bolt all the way through from the RH side of the frame so that the nuts are tight but it only contacts the first couple threads on the LH nut
• mount a piece of AL flat stock to the LH nut using a short bolt
• sight along the maintube and ensure that the flat stock is parallel with HT, also measure with square.
  
• adjust as needed
• carefully remove flat stock without shifting nut
• braze in nut
  
• repeat for other side

Steering Geometry

In spite of the fact that the modern bicycle has been around for considerably over a century and even the recumbent bicycle for over 80 years, understanding bicycle steering is a persistently difficult problem in dynamics.

Contrary to popular belief, gyroscopic forces play only a minimal role in determining 2 wheel vehicle stability. Check out this site for a whole bunch of interesting experiments with counter spinning wheels and interesting steering geometries.

Another bit of required reading is David Jones' classic treatise on bicycle stability in which he attempts to build unridable bikes.

For this subject and just about everything else related to bicycle technology, check out Bicycling Science.

Finally for a good, relatively concise writeup on the dynamics of 2 wheel vehicles , check out this wikipedia article.

Boiling down the above, there are really 3 variables that we can vary with our design.

• Fork Rake
• Head Tube Angle
• Wheel Diameter

The combination of the above give us:

• Trail
• Mechanical Trail

The difference between mechanical trail and trail seems subtle, and in fact it is, but Jim Papadopoulos makes the case in bicycling science that MT is a more relevant measurement of how the bike actually handles. It represents the lever arm through which the perpendicular component of the vertical support force acts. In other words it is the lever length that forces the wheel to turn in the direction of a turn when you lean the bike. It's also interesting to note that two bicycles which have the same T may have a very different MT due to differences in head tube angle.

Having said all that, increasing T and MT all other things being equal will cause the bike to be more stable. Stability is a bit of a loaded term since it is usually used in the above mentioned documentations to discuss the ridabilty of a bicycle hands-free. For my purposes however I'm considering a more subjective view. A "stable" bike is one that feels like it is "on rails" and wants to hold it's line. An unstable bike is one that is lively feeling and handles quickly. The best handling bikes are compromises between the two. It would be easy to make a bike so stable that it was practically impossible to knock over once at speed. Unfortunately it would also be so stable that swerving to avoid that car or pothole would be equally impossible.

For my particular design I'm starting with an existing fork. It's a kinesis 650C Aluminum Tri fork. It's light, good quality, and fits the 559 wheel size adequately with either long reach brakes or some creativity. I measured the rake on this fork to be 34.54mm, and it's axle to crown length is 340.36mm. I'm also decided on using 559 rims with 25mm tires for the purposes of this design. If I ever want to use wider tires (for touring for example) I'll need to make a new fork anyway since this one won't clear wide tires. At that point I'll simply optimize it's rake for the new wheel size.

Since I have 2 of my variables fixed already by deciding on a fork and a wheel size, I need only to decide on head tube angle. The first thing I did on my drawing was to draw in the fork rake by drawing a circle with radius 34.54 centered on the front axle. Then for the heck of it I drew in case where the headtube was simply perpendicular to the maintube. This is the maroon line. This gives me a headtube angle of about 71.3, T of 68.61 and MT of 65. These T and MT numbers are very high. The highest MT listed in a table of common values in Bicycling Science (Table 8.1, p274 of Third ed) is 58.5, and the highest T's are 76.2 and 69.8, but both are found on track bikes. This does however put it close to the Bacchetta Aero, which is obviously a successful design.

I am still uncomfortable with the very high MT and T numbers so I decided to see what I would get if I fixed the trail at 60mm. This is a good common number for a stable touring (or similar) bike. This is the blue line. I get a HTA of 72.8 and a MT of 57.32. These are still on the stable end of normal, but they are much more inline with what is out there in the upright world. This also puts my trail nicely between the 70's of the Aero and the 50mm of the Volae Team.

Drawing the Frame in CAD

We now have all the info we need to draw up the frame in CAD. To recap we are going to use the following values: (SR = seat reference mark)

SR above ground = 609.6mm (24")
C of G behind SR = 39.7mm
BB center above SR = 228.6mm (9")
BB center in front of SR = 783mm
Heel Clearance = 75mm

FYI the CAD program I'm using is a nice shareware program called DeltaCAD. It's pretty easy to use and I've gotten used to it's quirks. There are more featured apps out there, but familiarity is worth more than features in this case. It's a windows app but runs well under wine on linux.

Step 1:
Draw a horizontal line that is 2000mm long. Then in the center draw a vertical line that is 1000mm tall. The horizontal line is the groundline and the vertical line is the center of gravity.

Step 2:
Draw a vertical line that is 609.6mm tall, 39.7mm in front of the C of G. This represents the SR. Then draw a second vertical line that is 609.60 + 228.6 = 838.20 mm tall, 783mm in front of the SR. This is the BB center.

Step 3:

Now we need to know the wheel dimensions. We are going to use conventional 26" mtb wheels, but with narrow, 25mm tires. To get the outer diameter of the finished wheel, you take the bead seat diameter of the wheel, 559mm for us. Add 13mm for the bead height, then divide by 2 to get the radius and add the tire dimension (25mm). So we get (559+13)/2 + 25 = 311mm.



Draw a horizontal line 311 mm above the ground line.

We now need to find the front axle location. To do this we will need the heel clearance dimension which is 75mm. I've defined this as the distance between the arc defined by a 175mm crank and the top of the tire. But in this case we really want to find the distance that is 175mm + heel clearance + wheel radius = 175 + 75+ 311 = 561mm away from the BB center. Draw a circle with this radius and mark on the axle line where it intersects. This is the front axle location.

Step 4:

Draw in the wheel and measure the distance from the c of g line. In this case it is 630.92mm. We will use this in the next step.

Step 5:

Now that we have the front axle distance from the c of g, we can find the location of the rear axle. But first we need to decide on the weight distribution. I said previously I want between 45 and 50% on the front wheel. So I'm arbitrarily deciding on 48%. Now we need to solve for the wheelbase. 630.92 = (100%-48%)*wheelbase. Wheelbase = 1213.31. Mark out the rear axle location 1213.31mm from the front axle and draw in the wheel.

Step 6:

We are going to braze in the BB for this bike off center so that the top edge of the BB shell is a the same level as the top of the maintube. This give us better front derailleur clearance. So I took a look at Nova cycles and found this BB shell. It has an OD of 31.8mm so we draw a circle of that diameter centered on the BB center.

We then need to ensure that the maintube clears the seat. Conveniently we used the low point of the seat for the SR, so we just need to account for the thickness of the seat and a little extra. The seat I am considering is wood, and is ~3/8" thick. So I gave 15mm of clearance. I draw a circle with r=15 centered on the SR.

Then draw a line that is tangent to both circles and ends at the rear tire (we'll shorten it later). This is the top edge of the maintube.

Step 7:

Finally draw a parallel line that is 50.8mm below the top line of the maintube, then draw a longer parallel line that is halfway between them that extends to the rear axle. Mark the offset from the axle.

So far so good! The wheelbase looks good as does the rear axle offset. Next time I'll talk about steering geometry.

BB to Seat Distance Measurement

This is pretty simple. I again took my mockup seat and this time just placed it facing the wall. I put a mark on the wall with masking tape that is the right height above the seat base to represent the pedal when the crank arm is horizontal. In my case, as discussed previously, this would be 9" above the seat reference.


I then put on my cycling shoes, sat in the seat, put my heels on the mark and pushed myself backwards. Then fine tuned it a hair to get the leg bend that seemed right when my cleats were on the mark. For me the distance from the wall to my seat reference was 96.3cm. I use Time ATAC pedals which have a stack height of about 1cm (not including the cleat here). And I'll probably be using 170mm cranks. So my actual BB center is 96.3 - 17 - 1 = 78.3cm in front of my seat reference.

Interestingly when I get my new, real, seat I can use this same method to figure out where the seat reference is. I'll prop the seat up at 28 deg from horizontal and push away from the wall the right distance, measure 96.3cm, draw my mark, and there we go.

Weight Distribution

As I discussed in the last post, I am trying to optimize weight distribution for this bike. To that end I need to know where my center of gravity is when in riding position, or at least where a vertical line that passes through my C of G is. I'm not going to worry about the weight distribution of the bike itself since that would add a huge amount of complexity to the process (without actually having the bike yet) and really it would only change the result by a pound or 2 in either direction which isn't enough to matter.

To do this I basically took a mockup bent seat I built previously that is set at 28deg from horizontal when sitting on a flat surface. I put it on a pair of 2x4's that were supported at the ends by a bathroom scale on one end and some scrap on the other to make it level. I put it roughly in the middle but just marked it so it's position is known. I then took 3 sets of readings 1 each with me on the contraption and with me off of it. I then swapped the scale to the other end and did another set of readings. Here is a link to my raw data.


As you can see I had some help with this. Also the living room is not really as much of a disaster as it looks in the pics. I swear!



Looking at the data. We take the average of the loaded measurements and subtract off the average of the unloaded measurements for both front and back respectively. This gives us 102.33 lbs on the front and 81.66 lbs on the back. So 55.62% of the weight was on the front. The 2x4's were 206cm between the measurement points. So to calculate the c of g, we take (100%-55.62%) * 206cm = 91.42cm which is the distance the c of g is from the front of the 2x4. We also know that the seat reference mark was 87.45cm from the front. So my C of G is 91.42-87.45 = 3.97cm behind the seat reference mark. Good to know!

Factors in Frame Design

The type of frame I am building is pretty simple, but there are still a number of factors to consider. Many of these techniques would be applicable to building any recumbent. Some of the factors will be inputs into the design and some will be outputs. Because I am building my first frame, I am considering the existing work that is out there, particularly from Volae and Bacchetta, with the expectation that if I am near them in terms of geometry, I'll have something that works. Having said that I am designing this frame from scratch and thinking about all the trade offs.

Lets look at the factors in detail:

• Weight Distribution: I'd like to design this bike so that between 45 and 50% of the total weight is carried on the front wheel. Equal weight distribution is rumored to be nearly optimal in terms of handling. I don't know this from experience but it sure sounds good on paper so I'll go with it as a design criteria. In order to figure this out we need to find our center of gravity, which is dependent on several other things.

• Seat Angle: I need to consider seat angle in order to calculate my center of gravity. I've fixed this for the purposes of this process at 28 deg from horizontal. I built a mockup seat that I could change the angle of and found that to be a comfortable angle for me. Using the same seat that will ultimately be used on the bike would be better, but I don't have it yet.
  

• Seat Reference: The next thing to consider is where we are measuring the seat from. I decided to use the lowest point of the seat as my reference. I will be able to transfer this to the final seat I use later.
  

• Bottom Bracket Height: This is calculated relative to seat height and it's something I don't have a good way to calculate. I could let it be an output of the process and optimize some other variables... but I decided it's easier to just pick a number and design around it. In this case I just copied the bacchetta aero dimension of ~9"

• Wheelbase: This will be an output of the process in my case. I'm not going in with any preconceived notions of what it should be other than to say it should be in the same ballpark as the common highracers on the market. For reference the Aero is in the range of 1240mm and the Volae Team is around 1195mm.

• Seat Height: I wish I could say that I arrived at this through some clever method, but really I just looked at what is out there and picked 24". That's in between the Bacchetta Aero which is around 23" and the Volae Expedition which is around 25".

• Distance from BB to Seat Reference: AKA leg length. This was determined experimentally using a method I'll describe in a later post. It's a very important measure if I want to optimize weight distribution since I'm going with a sliding seat type of build. Using an adjustable boom would make this less important but would be more complex in other areas.
  

• Steering Geometry: This really deserves a whole post of it's own so I'll pretty much say that what I'm going for is something between the Aero and the Volae bikes in terms of geometry. The trail is the most meaningful number when describing different geometries (all other things being similar). For reference the Aero has a trail of 71.5mm and the Volae Team has a trail of 50mm. Taken in a vacuum this would suggest that the Aero is more stable almost to the point of being dead while the Volae is a bit quicker steering. Overall I'd favor stability but I'll probably bring the trail in a little in my design. I'm going to let this mostly be an output however as long as it's within "normal" ranges.
  

• Heel Clearance: I've defined this as the distance between the arc defined by the pedal spindle on a 175mm crank and the top of the front tire. This is not a standard definition AFAIK but it's easy to measure from pictures and works well for designing in CAD. For reference the Aero has a HC of 60mm and the Team of 86mm. I split the difference and rounded up a little and decided to go with 75mm. Again, this is something that only experience will tell me what works well, and I don't have experience so I'll just guess but keep it within established ranges.
  

Frame jig construction

This is pretty simple. It's a piece of 2cm MDF with stiffeners screwed and glued to the underside.

The whole thing is about 6.5' long x 16" wide. It's within about .005" of flat (according to my level) Good enough. I used one of the factory edges of the MDF as a routing guide with a pattern bit to straighten the long stiffener pieces. I cut out the cross pieces on the mill, but the same router technique could have been used there.

Brazing Experiments

Last weekend I finally got the oxygen bottle to go with the torch I picked up on ebay some weeks ago. I am using propane driven with an acetlyene regulator after some reading on the framebuilders list that this is a safe and reasonable option. The whole kit cost me only about $180 including shipping but not including the propane since I already had the bottle on my grill.


I had also ordered some 1" x .035" wall tubing from Aircraft Spruce to practice on. Overall I'm very happy with the results. Even my first braze had reasonable penetration and draw through the joint. I brazed up my second and third joints in a sort of drunken H and tried to break them and was unable to. I twisted and mashed the tubing all to hell and even bent the heavy wall 3/4" steel pipe I was using to try to bend it with, but the joints didn't budge.

I also cut apart my 1st and 4th attempts to look at the penetration and overall fillet quality. I'm not saying I'm anything like a pro yet, but what I did on my first few attempts would have easily held a bike together and even looked reasonably good with a bit of cleanup. That's good enough for me for this project.

Recumbent project

For several years now I've been wanting to build a recumbent bike. Perhaps it's my inner geek showing through, but they just strike me as an inherently better platform for long distance, on-road touring and endurance riding. Recently I've been having upper back problems which have further encouraged the idea.

The style I'm interested in is a high-racer in the Volae or Bacchetta model. To my inexperienced eyes this type of bike has several advantages overall and several specific to the home builder.

Highracers use common sizes of wheels and thus gearing which makes finding parts easier, particularly out in the middle of nowhere. I can pick up MTB wheels at nearly any bike shop in the world. Other sizes may be more hit or miss. They have an aerodynamic position which is superior to most unfaired bikes of any stripe with the exception of low racers. However they put your head height near that of most cars which is better for riding in heavy traffic. They are also more "normal" looking somehow. Due to the higher rider height, they play nicer with riders on conventional diamond frame bikes than most recumbents.

Specific to the homebuilder, the main frame is nothing more than a straight piece of .035" wall 2" diameter cromoly tubing. The rear fork is comprised of common MTB fork blades. The rest of the frame is all common frame builder parts. There is no tube bending required or other complex techniques. The jigging for the frame can be quite simple. The fork presents a slight problem in that you are restricted to either tight clearance 650C tri forks which limit tire choice, or MTB forks which are way overkill on clearances. There are other choices, but the two I listed are the most common and cheapest.

Material is something I pondered for a long time. Carbon fiber is a reasonable option and a number of homebuilders have used it to make beautiful bikes. Jim Scozzafava has made some bikes that are the equal of many production bikes costing many thousands of dollars. I also tossed around the idea of an Aluminum carbon hybrid with AL tubes and wrapped carbon lugs. But in the end I settled on fillet brazed steel. I thought about using my mig welder, but I wasn't able to get good enough welds on the thin tubing to satisfy my inner perfectionist.

Steel has a few advantages. First it's relatively cheap and commonly available. It's also reasonably forgiving of mistakes. The biggest factor to me is that I am reasonably sure I can make a durable and long lasting bike from steel. I am not as sure with any of the other materials. There are also a lot of frame parts readily available for steel frames. The same cannot be said for carbon. This isn't a huge issue, but each little thing I need to make myself adds time and effort.

Seats, mounting, stay construction, idlers, steering mast and handlebars, etc are all things I've thought about a lot, but those will have to wait for later posts.

First Post

My goal for this blog is to be a repository for all the bikish stuff I do. Building, riding, whatever. Not much of a mission statement I guess, but it's all I got.