Theoretical Framebuiling Part 2: I Like Big Butts, Tubes and Ride Feel
In my days working in science I had a supervisor that always said – do the experiment on paper FIRST and that means putting down the 5 minutes it takes you to walk to the spectrometer with the samples as well as anything else. He was right. If it didn’t work ‘on paper,’ it was NEVER going to work as you intended in practice aka it would fail miserably. This is the second of three part series on why and what makes a custom fit bicycle frame, different (and better) than ‘off the peg’ one. The posts are intended to shed light behing ‘hand picked, custom butted, special shaped tubing mix’ and all the terms you see and hear mentio’ned about custom bikes. This article is meant to educate and represents a successful experiment ‘on paper’ by an aspiring framebuilder (me). The science, metallurgy, physics and engineering are all researched, the opionions (as harsh as they may be) are all personal. The articles are ranked by order of importance. Part 1 discusses probably the most important aspect – geometry. Part 2 talks about tube forming and butting and its effect on “ride feel.” Part 3 delves in metallurgy and what heat does to metals so for terms like heat treatment, aging, alloying, material stiffness and strength.
A custom bicycle frame is more than just geometry. Riders grow and so does the bicycle to suit them, however, is it a question of just increasing/decreasing tube length? It all starts with something more basic and…
All materials, metals included have mechanical properties that can be represented by a graph like this.
What should you get out of it?
Stiffness or Young Modulus (YM)
This is the ability of a material to resist DEFLECTION (the slope of the line on the left of the graph), or colloquially labeled as STIFFNESS. The YM for a metal IS THE SAME, regardless of the alloy/treatment/shiny sticker/that guy on the internet told me. All aluminum is equally stiff, same goes for steel, titanium, etc.
Typical values are as follows (higher number = stiffer):
- Steel: 200 Gpa (29 Mpsi)
- Titanium: 110.3 Gpa (16 Mpsi)
- Aluminum: 69 Gpa (10 Mpsi)
Steel is the stiffest by a HUGE margin, followed by titanium, both tailed by aluminun.
So given the above how is that steel frames are flexy, titanium ones springy and aluminum ones super stiff??
Design is not just Young’s modulus…
What can be made different for the same metal (by alloying, heat treatment, etc) are the following two properties.
Yield Strength (YS)
This is the amount of force it takes to permanently deform a metal, ie bending and not coming back to original shape.
Ultimate Tensile Strength (UTS)
Ultimate tensile strength (UTS) is the amount of force a material can withstand before it splits apart/breaks. It determines how little/thin material you can leave behind without it being dangerous (higher number = stronger)
- Steel: 400-2050 N/mm2
- Titanium: 810-960 N/mm2
- Aluminum: 310-560 N/mm2
*UTS is usually presented as Mpa which is a 1:1 conversion to N/mm2
Not on the graph above though it is quite an important feature and it is another thing that remains THE SAME for all base metals regarding of alloying (within a couple of %) – density; how light a metal is for the same part dimensions (higher number = denser/heavier)
- Steel: 7.8 g/m3
- Titanium: 4.5 g/m3
- Aluminum: 2.7 g/m3
In short steel is stiff, however, it can be made ridiculously strong so that you don’t need much of it, negating the high density.
Titanium is a nice middle ground since it is almost half the weight of steel and can be made as strong as some of the lesser strength steels.
Aluminum is ridiculously light, though not as strong and quite flexible.
Therefore by a first glance, in a bicycle frame you cannot have all three, notably: Lightweight, Strong, Stiff
Fortunately things get much more interesting and you can have all three and them be a bicycle frame.
How can that happen?
Forces on a Bicycle Frame
The diamond bicycle frame experiences variety of forces that change according to rider position (in and out of the saddle), terrain (rough or smooth), etc. Different parts of the frame, experience different amount and different direction of said stress. It’s complex and trying to figure it all out is an exercise in frustration and in my opinion a lot of cyclists waste time pondering insignificant details.
In general they say everything new is the well forgotten old and I am quoting a finite element analysis (FEA) done quite some time ago by Leisha Peterson and Kelly Londry from the Pegasus Research Company. That research was used to design the TREK 2000 (aluminum) frame. While the data is indeed outdated the principles outlined are universally valid.
Valid how? Let me explain.
Predominantly the distinct situations a bicycle frame is loaded are:
- standing start/climbing out of the saddle,
- steady state pedaling when seated,
- frontal impact/braking
- vertical impact/rough roads.
Overall it is a complex equation. However, the authors found a neat way – calculate strain energy or the energy the frame absorbs when it deflects. This is universal and can be translated from one frame to another. In short a stiff frame absorbs less strain energy than a flexible/noodly one – a stiff spring is what you are looking for. I have plotted the values of the original FEA analysis so they appear nicer.
What you see is that standing starts and climbing out of the saddle against gravity results by far in the greatest amount of strain energy (80 in lb) or 4% of the total energy exerted by a 150lb (68 kg rider). It might not seem a lot, it is noticeable and a larger more powerful rider on the SAME frame would flex it even more, hence why a made to measure bicycle is indeed more than just geometry…..
Even a direct frontal impact (hitting a pothole/curb) is about one third of the standing start/out of saddle climbing with everything else being minute in comparison. The downtube (DT) and the seatube (ST) bear the most of the strain, with the toptube (TT) coming third with the chain (CS) and seatstays (SS) barely registering.
The most important point here is that a round shape is the BEST since it handles all types of forces (bending, torsion/twisting) equally well in all directions. Special tube shapes are the cherry on top that accomplish 3 functions.
- Optimise resisting under load: Ovals for example resist force better when loaded directly in the direction of their large diameter. However when loaded with the same force in the direction of the small diameter the oval would bend/deflect more. An oval tube can be made to have less material than a round one so that results in weight savings. Since different parts of the bicycle experience force predominantly (emphasis on predominantly) in more or less the same direction (ie bottom bracket deflects left and right under pedalling forces, etc), with some experimentation and/or serious computational power you can optimise shapes so that the penalty in stiffness is manageable in the grand scheme of things.
- Aerodynamics: Teardrop and aerofoils and such are said to save you time in time trials. In my opinion this effect is blown out of proportion since even extremely generous tests (with unpublished testing protocols) say an aerodynamic frame saves in the range of 15s over a 40km (25mi) time trial. That is less than a second per kilometer. As mentioned in point 1 above, a teardrop would yield quite a flexy ride under a lot of power (ie out of the saddle efforts) since in the sideways direction (out of plane bending) the aerofoil behaves like a very small diameter tube. In addition the ride would be harsher, since the aerofoil is ovalised in the vertical direction. I am not saying aerodyamics are unimportant, however, unless we are talking timed events on an extremely controlled environment such as a closed velodrome/track, for even the fastest/strongest riders riders, the compromises in ride characteristics (short chainstays, low trail figures, etc) are in my opinion too significant to ignore for 95% of the riding most cyclists do.
- Ease of Fabrication: Simply put, you cannot join a large diameter round tube to a smaller one ie a 44/48 mm round downtube cannot be joined to a regular 1 1/8 in (36/38mm outside diameter) headtube (try putting a marker cap against the side of a small ballpoint pen); the larger tube will have to literally wrap around, which as you can imagine is not a strong structure, or a structure at all…. So as (main) tube diameter increases (oversize, double oversize, especially with less strong materials like aluminium and titanium to a degree etc.) and things like seat posts and fork diameters remain constant, you have to ‘squish’ the large tube or put special shapes/ovalise it (why that can be bad – look at point 2 above). Of course you can increase the size of everything (seattube/headtube diameter) though it adds weight, creates compatibility problems with parts like forks and headsets and let’s not forget it can influence aesthetics….
What type of load you ask?
Bending and Twisting
Of all the strain energy again the DT again takes roughly 40% of the total (mostly torsion and out of plane bending/left and right form the rider’s point of view), the ST (quite remarkably and unexpectedly to me) absorbs 25% of the total energy (mostly out of plane bending and some torsion), with the rest of the tubes contributing a small amount. A note here is that the CS take quite some IN-PLANE bending (left to right) as such the oval shapes with the oval pointing towards the saddle are not ideal. The SS are the perfect place to shed weight since they are not extremely loaded and have to mostly resist an axial load ie buckling on themselves.
Therefore the next logical question is so what does that have to do with custom framebuilding?
Well pretty much everything
Tubes, Shapes and Butts
Tubes come in different diameters, shapes and wall thicknesses. As I mentioned special shapes are the cherry on top so I will discuss round tubes and butting.
A tube with uniform wall thickness is called a straight gauge tube
A tube with varying wall thicknesses is called a butted tube – ie it has one or two butts (on either or both ends). Thicknesses are designate like so: 0.9/0.6/0.9 -0.9mm at the butted ends and 0.6mm in the middle.
- A butted tube will be LIGHTER than a straight gauge one all other things being equal
- A butted tube will be EASIER to deflect than a straight gauge one; call it more compliant.
- A more aggressively butted tube (wider/thinner middle section) will be even LIGHTER and LESS stiff, etc., etc.
Butting accomplishes several things, all of which are interrelated and ranked according to their importance.
- Make welding/brazing possible since too thin material will be easily burnt through/deformed due to the high heat
- Structural Strength– the greatest stresses (in a bicycle frame) occur close to the welded/connected joints so you want more material to deal with that.
- Reduce Weight – not to be ignored when performance is important
- Influences Ride Feel – slightly (emphasis on slightly) deflecting under bumps and taking the sting out of road buzz.
Cycling sidenote: Butting is said to accomplish many things ranging from world peace to making the bike ride by itself with no effort from the rider. Ok, jokes aside, me and you are not the first people who wondered if different tubesets influence ride feel. This article (with thanks to Habanero Cycles for the archive print) tested seven IDENTICAL bikes down to the paint and a blind test could not distinguish the fanciest (read super expensive and lightest) tubing from the entry level one. I have to add that the frames were most likely in the small/medium size and the riders were of average power (more on that below) further watering down any differences. In my opinion with a dense material like steel, making thin tubing sheds significant amount of weight, which is not to be ignored, however, the so called ‘ride feel’ of ‘that tubing vs another one’ is most likely largely due to a placebo effect. Tube size is a whole another matter, as described below.
Beams and Bending
From the calculations by Peterson and Londry most of the forces are bending therefore the tubes when in a bicycle frame act more or less as a suspended beam
The deflection can be summarized by the equations below. Tubes are basically suspended beams.
Deflection at one end is:
- L is length in (mm)
- F is the Force applied/Load in Newtons (N)
- I is moment of inertia (mm^4)
- E is is modulus of elasticity/Young’s Modulus in (N/mm^2)
Moment of inertia for a hollow tube is shown below
Moment of Inertia of a hollow tube:
- D is outside diameter in (mm)
- d is inside diameter (mm)
Young’s modulus and tube diameter/thickness make the game.
In order of importance:
- A longer tube will be (quite) MORE FLEXIBLE than a shorter one, all other things being equal
- A smaller diameter tube will be MORE FLEXIBLE than a larger diameter one, all other things being equal.
- Thinner walled (butted) tube will be EASIER to deflect/MORE FLEXIBLE than a straight gauge one.
UTS sets the limit how thin tube walls can become before we are left with an easily collapsible coke can. The lowest values are as follows: 0.3 mm for steel (though 0.4mm is typical), 0.8 mm for aluminum and 0.7 mm for titanium.
Some examples of various tubes of equal length (600 mm) loaded by the same force (10).
25.4 mm steel (Straight gauge, Butted, Thin butted, Ultra butted)
A diameter that exists in steel, aluminum and titanium with the respective thicknesses
34.9mm (Steel 0.4 mm, Alu 1.1 mm, Titanium 0.7mm)
Cycling Sidenote#2: ‘Conventional wisdom’ continues to advise to go with the smallest frame possible in order to maximize stiffness; this is physics so the argument is valid, however, you compromise a lot of other stuff ie you get toe overlap and suboptimal weight distribution. In addition tracing back such statement to times when bicycle gears were 10 and certainly not electronic and I wasn’t even born, the choice of materials was similar to that of a communist supermarket. It was Reynolds 531, 2 alloys from Columbus and some from Nishiki and Tange, more or less the same thing – CrMo or Manganese steel. Tube sizes and shapes (round only) were standard across the ranges and limited as comparison to what is available at the time of this article. No aluminium, no titanium, let alone carbon. That was it!!! Any color as long as it’s black kind of deal. Steel (for bicycle frames) has gone a long way and the variety and advances in metallurgy in other metals have never been greater. Therefore like all ‘conventional wisdom’ – “Choose the smallest frame is irrelevant and wrong.” This is yet another reason why you are going with a made to measure frame.
Frame Stiffness Comparison: An Experiment in Numbers
A formula looks all nice, so how do we get it to tell us something meaningful. In the case of the frame it is best to create three theoretical riders.
- Big and Strong – a taller/bigger than average person riding a large frame so tube lengths 600mm and putting out a force of 10
- Average – Your average Joe riding a medium sized frame so tube length 550mm, putting out a force of 7.
- Small and Light – Small and light rider, climber type, or a lot of female cyclists riding a small frame with tube lengths 500mm putting a force of 5.
As you saw, it is the front triangle that sees almost all of the stress as such it is safe to omit the CS and SS from the calculations. In addition torsion is also related to tube diameter and thickness, however, pretty much all bicycle tubing is more than adequate when it comes to resisting torsion. I am not saying the rear triangle does not make a difference in ride feel, the biggest gains can be made with the large tubes.
So we put three tubes together in the front triangle, ‘load them up’ under our theoretical riders and let’s see what happens….(For simplicity I assumed it is an equilateral triangle, to avoid cluttering the calculations more. It is a linear relationship anyway so it wouldn’t influence the final results). You average the deflections of the three tubes and you get a frame stiffness value.
I used the formula above and tubing information on what is currently available from the likes of Reynolds, Columbus, Dedacciai, True Temper. All my calculations are in the Excel file at the end of this post.
So how did my experiment turn out.
Steel tubes for frame building come in the following sizes: 25.4 mm (1 in), 28.6 mm (1 1/8in), 31.75 mm (1 1/4 in), 35 mm (1 3/8 in), 38.1mm (1 1/2 in) and 44 mm (1 7/8 in) for some really heavy duty applications. Tube sets are usually labeled as Standard, Oversize (OS), Double OS and my designation BIG (see the chart below). Millions of standard gauge bikes were built using the Reynolds 531 and the like and this is what most (myself for quite some time as well) associated with a steel bike, and why a lot of the negatives about steel have remained.
|Standard Steel||O/S Steel||Double O/S Steel||BIG Steel|
|TT||25.4 mm||28.6 mm||31.7 mm||34.9 mm|
|DT||28.6 mm||31.7 mm||34.9 mm||38.1 mm|
|ST||28.6 mm||28.6/ 31.7 mm||31.7 mm||34.9 mm|
How do these bikes behave under our three theoretical riders?
Without jumping to rapid conclusions, you can see how the advances in metallurgy allowing the introduction of thin walled and hence not heavy OS and Double OS tubing made a really and I mean REALLY significant difference for riders above average stature/power/weight.
Unlike steel where stuff was in a way ‘standard,’ aluminum tubing makers have a bit more freedom in order to maximize Aluminum’s greatest asset – lightness. While it is 1/3 of the stiffness of steel, an aluminum frame can be built to be of extremely high performance. In my opinion aluminum is the PERFECT material for a made-to-measure high performance frame. The material is easy to work with, and a bike can be at the UCI weight limit of 6.8kg and below. Also unlike with carbon, any little creak/bump/fall would not send you freaking out there is ‘hidden damage in the composite matrix.’ Bikes are tools to be ridden.
Again here is chart of tubesets that I gathered from what was available from Dedacciai at the time of this article. There are others, I just picked a manufacturer I highly respect.
|Small Alu||Average Alu||BIG O/S Alu|
|TT||34.9 mm||38 mm||44 mm|
|DT||42.6 mm||44 mm||48 mm|
|ST||31.7 mm||35 mm||35 mm|
How do these bikes behave under our three theoretical riders?
Cycling sidenote#3: Aluminum is often labeled as harsh and a reason why a lot of riders shun away from it. First as you saw above to make up for aluminium’s low strength you have to increase the diameter of the tubing and in order to weld it all together, sometimes that requires ovalisation where you don’t always want it (vertical direction)/larger diameter seatposts, etc., which can contribute to a less than plush ride. In addition, aluminum butted tubing is a recent development, with a lot of work done by Gary Klein (of Klein bikes) in the 1990s and early 2000s as well as Easton sports. I own a touring/expedition frame in what appears to be BIG and THICK, straight gauge tubing that weighs 2350g for the frame only in a compact size 58, this is around the same weight of a heavy duty custom steel frame in size 63 I own (2600g + 350g S and S couplers). Aluminum’s main advantage has always been lightweight. If an equivalent aluminum frame tips the scales like its steel brother, this is poor design/choice of tubing, NOT the fault of the material. When not heavily loaded with panniers front and rear even with 50mm tyres at low pressure, it is every bit a bone jarring harsh riding bike. However, it was designed to take the rider around the world carrying massive loads. When used like this it is a (slightly) different beast, still leaves something to be desired, though what I am trying to say is: Horses for courses and why a made-to-measure frame is not just geometry…. OR in very simple terms, if you are a big and powerful rider, I will not build you a frame with the same tubing as for a small statured one and vice versa – material choice is irrelevant.
I saved it for last since it is a relatively new bike frame material and my current bike – a Seven Axiom SL (review coming soon) is a frame that had surpassed ALL of my expectations and reservations about ‘metal bikes’ and bikes in general. I specified the geometry, Seven did the rest splendidly.
The thing with titanium is that since it is expensive to produce with the aerospace industry being the main consumer, the framebuilders are left with what is not used from big mill runs, therefore, choice of sizes is not overwhelming and it comes only in round shapes. The latter has allowed some framebuilders to butt/shape the tubes to squeeze out (pun intended) a bit more performance from it – not a bad thing, just requires some big and heavy machinery.
|Small Ti||Average Ti||Average+ Ti||BIG O/S Ti||Seven Axiom SL|
|TT||31.7 mm||34.9 mm||34.9 mm||37.3 mm||38.1 mm|
|DT||31.7 mm||37.3 mm||41.5 mm||48 mm||38.1 mm|
|ST||31.7 mm||31.7 mm||35/31.7 mm||35 mm||35 mm|
How did titanium behave under our three theoretical riders?
Three Metals in a Bike
All of the data put together. Interestingly even the small aluminium frame came quite stiff as compared to the ‘equivalent’ steel and titanium ones. I didn’t go with the lightest/thinnest tubing on any of the frames so there is room for improvement, however, I can see, at least in theory, why some oversized aluminium might, with a huge emphasis on might have gotten a bad reputation.
So after going through all the graphs the most logical question is:
Why bother with different materials if you can make more or less equally performing frames?
Here we come to the holy grail of cycling (light)weight.
If we take a stiff frame for our Big & Strong fellow and compare:
Steel to titanium: A titanium frame would have about 20-25% larger tubes (41 mm vs 35/38mm that are about 40 % thicker (0.9/0.7/0.9 vs. 0.6-0.8/0.4-0.6/0.6-0.8) than the steel ones. Therefore you have about 60-75% MORE material. However titanium is ~57% the weight of steel so if we take a 1800-2000g steel frame (normal and a bit on the lighter/performance side for size 60-62) the equivalently stiff titanium one would be in the range of 1550-1700g, roughly identical and what you see in the real world agrees, however, you are left with an EXTREMELY durable corrosion resistant frame. Obviously there are super thin steel tubes such as Columbus Spirit/Life, Reynolds 953 (hence the range) that would bring the difference even closer.
Steel to aluminum: An aluminum frame has even larger tubes, roughly 25-30% more (48/44mm vs 35/38mm) that are almost twice as thick (170-200%), than steel (1.2/0.8/1.5 vs 0.6-0.8/0.4-0.6/0.6-0.8) – 215-260% more material. Therefore the 1800g steel frame would have its aluminum brother come up at 1330-1530g, now the difference is quite significant. A Rock Lobster road frame I saw in size 61 (BIG O/S) using the same Dedacciai tubing as I used for my calculations above, weighed 1380g. The numbers agree again. A difference starting at half a kg (500g) pushing 30+% less for the frame only! With the ultralight tubesets/Scandium differences do get impressive.
Titanium to aluminum: It is a closer match, though the equivalent aluminum frame would still hold an edge by a couple hundred grams and as a raw material it is significantly (5-7 times) cheaper and many more times easier to work with and doesn’t wear out tools to the same degree.
The hair splitters would argue that 500g is a glass of water/large piss and most people carry much more in extra fat. I would wholeheartedly agree. When I see people, even professionals riding positions based on ‘knee-over-pedal’ spindle type of wisdom, with poor mechanics due to unaddressed muscle imbalances caused by sitting behind a desk for 40+h/week, and who also eat a diet based on refined carbohydrates (pasta) and fizzy soft drinks and gels are taken for recovery, the 500g and the bike are NOT your problem. There are bigger fish to fry, you need to get healthy and fit first and while doing that there are people like myself who will be able to make you a bike to help you in the process.=)
Mind you these are calculations for a large and hefty frame (size 60-62); ie not the thinnest/lightest tubing. Most numbers that manufacturers advertise are for a size 54 (medium). Also when things start to overlap ie a steel frame that weighs as much as an aluminum one, durability and crash resistance takes a lower priority than lightweight and race day performance – horses for courses.
In addition, I am aware there are 500g carbon frames out there. Without being condescending, how many times do you dare lean such a bike on the wall, pack in the back of a car or how many heart attacks do you get if you drop it or let alone crash it? Bikes must be ridden, maintained and not babied.
I am repeating myself that the results don’t mean a frame with deflection of 0.40 would ride like a wet noodle as compared a one with 0.30. This aims to show how different tube diameter/gauge choices influence the ability of a frame to resist strain energy and how a lot of the stock options are grossly inadequate for most riders, especially someone tall like me, I can only imagine how much worse stuff is for the more heavily built riders. Stiffness is NOT just how (in)efficiently your power gets transferred. It’s about the front and rear of the frame not going all over the place when turning/cornering, climbing or at speed and scaring you silly in the process.
1. My Seven Axiom SL came to about 0.44 deflection and it is the stiffest bike I have ridden to this day and this is how I requested it so that was used as the control for this experiment and confirmed the results. Therefore just by going ‘by the numbers’ it is entirely possible to make a frame that is just as stiff in steel and aluminum. My first road frame that I rode a LOT was somewhere in the lines of small&light/average aluminum in the charts above and it was quite flexy in every direction (ie each wheel would do its own thing during fast cornering). Therefore the numbers agree on what this above average cyclist has experienced.
2. Back in the day when choices were limited and oversize tubesets did not exist, the large and/or powerful riders were really left behind. Granted with increasing wall thickness you could gain some stiffness back, it added significant weight. I suspect that this is one of the reasons steel gets labeled as old-fashioned, heavy (even flexy) and ‘picking the smallest frame possible’ is quoted as gospel.
Going to double oversize is yet another step in the right direction for powerful and/or larger riders. Manufacturers wouldn’t be making large diameters tubes if there was no market. With advances in steel metallurgy the weight penalty if any is negligible. For the small & light and average rider even standard gauge steel tubes are within what I would call an adequate stiffness range.
3. A masher and a spinner would each flex the frame differently as shown by the FEA analysis as such choosing tubes that would deflect less (for a masher) and thinner and lighter ones for the spinner, you the frame builder can directly influence ride feel.
The above is a theoretical exercise that I did for fun, and the results actually nicely surprised me. I have provided the excel file with my calculations if people want to download it, however, I WARN you that we tend to get focused on the numbers. Experience and rider feedback are ultimately more important, however, it goes to say that like a jigsaw puzzle you can mix and match to achieve a perfectly behaving frame that feels like an extension of the rider, rather than something that you try to coax into doing what you want it to.
The fact that all tube manufacturers sell tubesets does not mean you are bound to use them in that configuration – you most certainly can and results would be satisfactory. It is the final part of the puzzle that is in my opinion what distinguishes a good frame from great one. Each and every manufacture has their ideas on how they see the custom frame and that vision can be combined to make the ultimate dream riding bike.
MS Excel file: tube-butting-and-deflections_thetallcyclist_ver2(Please note I normally use OpenOffice so this is a converted file, some weird behavior is to be expected=) )
Theoretical Framebuilding Series.
- Part 1: My Frame is Bigger than Yours: Geometry
- Part 2: I Like Big Butts: Tube Sizes, Butting and Ride Feel
- Part 3: Metallurgy and Materials
For further information check the ever-increasing Reading List
I welcome comments, however, before asking a question please visit the Frequently Asked Question (FAQ) page.
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