Sunday, August 31, 2014

new Cervelo S5: reduced stack

Since the retirement of the RS road bike with more "relaxed" geometry, Cervelo has unified its stack-reach schedule, creating a single geometry shared between the R and S series. This geometry is fairly close to the Trek H2 geometry, the more relaxed of the two geometries Trek supports. The logic used by Cervelo is that the vast majority of riders can be fit with a stem ranging from +6 degrees to -17 degrees using this more relaxed geometry.

And it's true, but many riders object to a bike like the S5 being touted as an "aero" frame had the longest head tubes. This was especially problematic when using the bike with full time trial bars. Indeed the S5 is sufficiently aero that with time trial bars, it's a competitive time trial/triathlon frame. So a lower stack provides more adjustability and allows more reach for the same stack and a shorter stem for most male riders (small women often benefit from a small reach). Riders claim to prefer the feel of stems in the 9-10 cm range over 12-14 cm (although I'm skeptical the difference can be perceived at the hoods or drops).

Here's the geometry data:


I plot it here, comparing to Trek:


So the new S5 is basically middle-of-the-road compared to Trek. A lot of bikes are in this range. So nothing extreme about the new S5.

One interpretation of the results is a 2 cm increase in spacers. But there's others. If you're running a -6 deg stem, which is typical, you can now up to the next frame size and shorten your stem by around 2 cm. If you're running a -17 deg stem you can probably swap to a -6 deg stem. So no hideous spacer stacks required here unless you want an fairly upright position or your arms are exceptionally short. But then you may want to stick with the S2-3, which is still an excellent bike.

Friday, August 29, 2014

Tour magazine sub-800 gram frame test: comparing measured frame mass to claimed

Previously I reported on the Tour Magazine test of "frames under 800 grams" published in the December 2013 edition of the magazine, and summarized on-line.

In the article, they weighed the frame, fork, and bearings from a series of light & expensive bikes. They also bent them, measuring the stiffness characteristics. They then calculate a rating based on these and some other minor factors (warranty, quality of finish).

But it's interesting to compare these weights to what is claimed by the manufacturer. Those aren't listed in the article. The focus of Tour isn't to investigate the dishonesty of bike companies. Rather it's to determine the truth.

Claimed weight is a tricky business. Only Cervelo is totally clear in the matter, publishing a lot minimum, average, and maximum for each size of the RCa frame in their White Paper on the bike. Obviously bigger frames tend to weigh more. If I'm buying a 56-cm frame, I don't care about the mass of a 48-cm frame. If one company sells a 52 cm frame as their small bike, and another a 48, do I take the latter because they can claim a lower number for their smallest bike?

Then there's painted versus unpainted. Some people like to sand the paint off their bikes. But for most, the unpainted mass is irrelevant. Sure, if I'm getting a white bike, which might be relatively heavier, I don't care how good Trek's "vapor coat" is. I want to compare, for example, Cannondale's white to Trek's white. But in general it's more honest to publish the lightest painted bike sold. Key question: would stripping the paint void the warranty? If yes, don't tell me the weight of the unpainted frame.

Then there's the issue of hardware. I'm okay with leaving off the bottle cage bolts, since I can easily ride the bike without those. But the derailleur hanger? Err... no. That stays. And it's not as if I can just go and swap a heavy hanger for a light one, something I can do with bottle bolts.

Let's go through the bikes...

  1. Cannondale SuperSix Evo Black: Google had a cached page from Cannondale claiming "under 700 grams", although the 2015 page has no claim. So I used 695.
  2. Cervélo RCA: I took their reported average for 56 cm frames (see table above). The high for this size was 696.
  3. Corratec Mauro Sannino Prima: "starting at 680 grams." This is a custom bike, which adds a lot of potential variability.
  4. Focus Izalco Max 0.0: I got 750 grams from a dealer.
  5. Neil Pryde Bura SL: There's a big fat "710 grams" on their web page.
  6. Pasculli Altissimo: This is another custom bike. But unlike Corratec, these guys just say "680".
  7. Simplon Pavo 3 Ultra: I got 740 grams off their web page.
  8. Trek Madone 7.9 H1: I got 725 grams from a Jan 2013 VeloNews article (down from 750 grams in 2012).

Only Cervelo was a size-specific mass. The others were all just a single quoted number.

Here's the result:


Amazingly Simplon came in well under the claimed weight. All others were over. I was surprised Cervelo was over. Trek, Focus, and Cannondale are each around 50-60 grams over claimed. The two custom frames were 100 grams over claimed, but I'll cut the custom builders some slack, since they tune stiffness. The Bora came in 90 grams over claimed.

The result is you can't put much faith in claimed mass, comparing different manufacturers. Trek, Cannondale, and Focus each seem to be mutually consistent in how low they are. This is likely because they are referencing a small frame, and Tour measures relatively large 56-58 cm frames. For the customs, you need to say what you want: if you want light, and don't care about stiff, you need to say that. Neil Pryde is the one which is most clearly off target.

Thursday, August 28, 2014

Cervelo S5 and the aero road bars

At EuroBike, Cervelo made two huge product announcements, a new S5 aero-road bike, and a revised on the super-premium "would be fun to ride but I can't comprehend paying $10k for a frame and fork" "Project California" RCa.


The S5 is an interesting case. Cervelo has a range of aero road bikes: the S2, S3, and S5. The S2 and S3 are the same frame but with different part specs. These were designed for the more average rider/racer, with an aero front end combined with the rear triangle which is basically the same as the R-series road frames. The S5, on the other hand, was designed with the racer philosophy that, as Specialized tweets, #aeroiseverything. The idea is that racers, looking for all marginal advantages, would ride the S5, and give up a bit of rear-triangle comfort.

Surprise, surprise. On the Garmin pro team, the S3 got much more use. Racing is a complex dynamic, much different than riding solo in the wind. The riders felt better on the S3 with a bit more compliance than the S5.

And so it was inevitable a revision of the S5 was coming, and soon. So this year at EuroBike, they revealed a new version.

Many were expecting an up-rated version of the S3, an aero-road hybrid. But instead, Cervelo led with the aerodynamics, improving the aerodynamics further of the previous S5 while claimin to have improved the stiffness and comfort at the same time yet without resorting to the less aerodynamic rear-triangle features of the S2-3.

Here's the sources of wind resistance on the bike, according to a BikeRadar report. Initially I thought this represented the sources of improvement, but it was pointed out to me on SlowTwitch Triathlon forum it's more likely total resistance. Defining how each component contributes to total resistance is tricky, since parts interact. In a tandem does the front rider contribute more than the rear rider since the rear rider drafts behind the first? Suppose the rear rider is tucked right behind the captain, in virtually perfect draft. Do I conclude the rear rider has no effect on wind resistance? No -- that would be an error. If I were to completely eliminate the front rider, rendering his wind resistance to zero, the total wind resistance of the bike would barely change: the wind which had been hitting the captain would now hit the stoker instead. So the system is nonlinear: the total is not the sum of its parts.

1% – seatpost 
2% – rear brake 
3% – front break 
5% – rear wheel 
9% – drivetrain 
9% – bottle 
9% – fork 
16% – frame 
16% – front wheel 
30% – handlebar

I was initially shocked the handlebar was listed as responsible for more drag than the frame, but the original S5 has a total CdA of around 0.058 m2 according to Bicycling Magazine data, or 580 cm2. A simple calculation of drag on a handlebar (see later), treating it as a cylinder with air at normal incidence, is 100 cm2 just for the top. If I I assume the drops + the brake levers add an extra 75 cm2 then I'm up to 30% (Damon Rinard of Cervelo clarified that this number includes the brake levers). Of course where the rider grabs the bars there will be no contribution to wind resistance from the bars, however: there's a lot of bar-rider interaction.

Starting with the bottle (9%): they didn't introduce any sort of new aero-shaped bottle. They understand road racers need to use whatever bottles they get handed. Instead they followed the model Litespeed used on its carbon road frames and optimized aerodynamics under the assumption there's a bottle on the downtube. This is an interesting question because at the finish of a race, or in most criteriums, there's often no bottles on the bike. But if you're optimizing the bike for long breakaway then you've got to consider bottles. A quantitative assessment would look at "match burning" episodes from real-race power data. But I think optimizing with a bottle is the way to go.

For the frame, then tweaked transitions from the head tube to the down tube and increased head tube taper.

On the front wheel (and rear), they switched to Hed. Of course you can get Hed wheels with the old S5, as well, if you want to buy them.


The biggest contributor is listed as the handlebar, and for that there was a new $400 aero carbon handlebar. Of course you can buy any handlebar you want and put it on the old S5, but this one comes with the new one. It's slick and aerodynamic, with a claimed savings of 4.4 W, which is apparently at 40 kph based on this BikeRadar article (this was confirmed by Cervelo's Damon Rinard), This corresponds to 7.7 W at 30 mph.

4.4 watts at 40 kph/25 mph corresponds, assuming an air density of 1.214 kg/m3, to a CdA reduction of 52.8 cm2. This makes sense: a standard handlebar has a flat top around 36 cm wide, more or less, neglecting the clamped portion and the transition to the drops, with a diameter of near 26 mm beyond the clamp. The Cd of a cylinder is around 0.95 for broadside impact (Mallack and Kumar, 2014), resulting in a net CdA of 89 cm2 for the top part. If the portion of the rider behind the cylinder can draft the cylinder with 30% efficiency, then that reduces the effective CdA of the bar to around 62 cm2 (if the bar wasn't there, the wind that would have hit the cylinder will hit the body instead: doomed either way). So if I can reduce the wind drag of the top portion of the bar by 80%, I get a reduction of 50 cm2. That's really close for a super-back-of-the-envelope estimate.

Super-simplistic kinetic model: consider a stationary air approximation, with no pressure waves. The handlebar displaces a volume vA or air per unit time, speed v multipled by cross-sectional area A. The air develops a kinetic energy density of 1/2 ρ v2, where ρ is the mass-density. That's total rate of kinetic energy transfer 1/2 ρ A v3. This would correspond to a CdA of 1.

But the air slows. Displaced, it falls behind the handlebar. Eventually the body slams into it. By this time, suppose its velocity had dropped 45%. It now has 30% the kinetic energy it did before. The body now increases the kinetic energy of these molecules back to 1/2 ρ A v3. The total kinetic energy transfer rate has been now (1/2) (1.7) ρ A v3. This is a 70% increase versus if the bar wasn't there. So the bar's effective contribution to wind resistance corresponds to 70% of what it would be without a rider behind the bar.

So basically with 20:20 hindsight it's easy to convince yourself this amount of reduction is "obvious".


Then there's the Zipp bar, formerly the Vuma Sprint, now the $350 SL-70. That claims a force reduction of 6.4 watts at 30 mph. This corresponds to a CdA decrease of 44 cm2, in contrast to 30 cm2 for the Cervelo claim for their bar. We know both used a rider on the bike (Cervelo and Zipp both state this), but there's too many sources of variability to directly compare these numbers, for example the position of the rider and how close his body is behind the bar. Both are in the range of my super-simplistic estimate.

So aero road bars appear to be the real deal: essentially free speed for a modest (on order 100 gram) increase in mass. The Cervelo bar claims 270 grams while Zipp claims 240 grams for their bar, Zipp's bar 70 grams more than the claim for their "SL" round bar.

One slight digression:  the Zipp bars sweep forward on the tops.  I like this.  Ritchey Evolutions, for example, sweep back.  Backward sweep pits you'd wrists in a contorted bend.  Forward sweep yields a more neutral position.  So these bars look comfortable too me.

But which one to choose?

The Zipp claims a bit less aero drag reduction, but that doesn't mean much since it wasn't a 1:1 comparison. It claims lighter mass, but mass claims are notoriously unreliable. And it is selling for $50 less than Cervelo has indicated they'll list their bar for. Overall it seems a win for the Zipp bar but that's not a very reliable win.

Note, though, that while 4.4 watts sounds great, that's out of an aerodynamic drag power of around 266 watts assuming CdA of 0.32 to start with, which saves at most 20 seconds per hour.  This is even smaller than the leg shaving advantage Specialized reported from their wind tunnel on YouTube.  So don't expect any dramatic change from these things.

Wednesday, August 27, 2014

Tour magazine test of "under 800 gram" frames

Tour Magazine did a web feature from an article in the Dec 2013 printed magazine "Lieichte Rahmen unter 800 Gramm." This featured 8 bikes, all exceptionally priced, which presumably get under the challenging 800 gram mark for a bike frame.

Now 800 grams is hardly new. For example, Ruegamer showed a custom frame under 700 grams at the National Handbuilt Bike Show 6 years ago, and that frame is still ridden a ton by weight weenie legend Don Becker of Berkeley. Spin, a company in Germany, was also around the same mass at that time.

But production bikes tend to be overbuilt due to the need for mass production margins and since sometimes the fattest riders buy the lightest bikes, irrationally. It's not a good thing if a 100 kg rider snaps his 51 cm frame after hitting a pothole on his 3 mile bike commute. Additionally, 1500 watt sprinters may perceive an extra few mm of flex in a super-light frame, causing irrational fear that precious watts are being squandered. So the game has more often then not been to claim lower weight by changing the protocol (for example, without paint, without derailleur hangers, even in the case of Pinarello without bottom bracket shells.... I'm still waiting for a company to leave out the epoxy and just weigh the carbon fibers). Cannondale, for example with the Evo, used an "equivalent" mass attained by adjusting for various design features on the frame, on the basis they could have made it that light had they designed the frame differently.

Despite this, big US media almost always report the claimed mass of the frame. After all the claims are from advertisers, and it doesn't do well for advertising revenue to indicate any lack of trust in their claims. It's been said "the customers of magazines are the advertisers, the product is the reader; they deliver the product to the customer."

The German magazine Tour, however, ruthlessly weighs every frame they review, and that includes the frames of complete bikes, which obviously requires disassembling it. They weigh not just the frame, but also the fork and bearings, reporting each separately and rating the bike on the combined total. This is important, because usually everything else on a bike is replaceable, and in any case there's almost always various component options for each frame, so a "fair" comparison comparing like-to-like with different companies becomes impossible.

I say "ruthless" because while it's common to report the lower mass associated with smaller-sized frames (the most infamous case of this might have been the Guru Photon first shown at Interbike, a tiny custom), they target a "medium" frame, medium by German standards, which is typically what is called a 56 cm to 58 cm. The other difference is they are willing to use a white version of a bike, and since white paint needs to be applied generously to fully occlude the black background, white frames tend to be heavier, especially relative to a clear coat option. So the numbers are often on the high side. The result is if you come out light in the Tour magazine tests, that says a lot.

So back to the "800 g" article. They measured the following:

  1. Cannondale SuperSix Evo Black, a personal favorite of mine. I test rode a Cannondale Evo back soon after they first appeared in a local SportsBasement and it was very nice.
  2. Cervélo RCA: the famous $10k frame described in Cervélo's white paper. This is a wonderful combination of light, aero, and optimized stiffness but with an anomalously tall head tube which calls for a relatively long, -17 degree stem to get a racing bar position.
  3. Corratec Mauro Sannino Prima: I've heard of Corratec, but don't really know anything about them.
  4. Focus Izalco Max 0.0: Focus has always been a practioner of the "fatty down tube" style of frame design, which I don't like. But they do claim low masses.
  5. Neil Pryde Bura SL: Neil Pryde made big claims about this frame, but in the end, it wasn't particularly light compared to competition. I suspected this wouldn't do as well as some of the others like Cannondale, obviously Cervélo, Simplon, or maybe even Trek (with its expensive vapor coat paint).
  6. Pasculli Altissimo: I don't think I've ever heard of Pasculli.
  7. Simplon Pavo 3 Ultra: Simplon is one of the frames that perennially competes for the top spot in Tour's ratings. The frames are very light, but like the focus, designed with the fatty downtube philosophy which results in poor aerodynamics.
  8. Trek Madone 7.9 H1: Trek historically didn't brag much about weight, at least until the latest Emonda "fatty downtube" design, but the top-tier Madone with vapor coat does very well. Trek always comes through with a really light, super-priced top-end frame, then they beef out frames lower in the range which are sold at a consideraly lower price.

Here's the results, ranking the bikes by total mass:

Cervelo RCa1082704323555763871.48837
Simplon Pavo 3 Ultra1113717324725593941.41878
Cannondale Evo Black1123760303605593961.41162
Focus Izalco Max1164802293695654021.40547
Pasculli Altissimo1203789336785593941.41878
Trek Madone H11204786379395454041.34901
Corratec Mauro Sannino Prima1209783336905474041.35396
Neil Pryde Bora SL1241802374655623901.44103

Tour goes beyond mass, also measuring stiffness (good and bad) to come up with an overall score. I'll leave the stiffness scoring to them: check out the German article.

One thing which pops out here is that despite the title of the article, two of the frames are over 800 grams: the Focus and the Neil Pryde. The Focus makes up for it to a large extent with its exceptionally light fork: the only fork under 300 grams, something which used to be fairly common back in the mid naughts but which is rare now due to increased safety standards. Note the Cervelo fork is 323 grams, well above 300, despite its expensive micro-think nickel coating for strength. The Neil Pryde, on the other hand, complements its 802 grams with the 2nd heaviest fork in the group, only the Trek Madone heavier and just barely. The Trek Madone, however, has the lightest headset bearings by a decent margin.

On average, these bikes have the following masses:

avg bearingsσ bearingsavg forkσ forkavg frameσ frame

Interesting here is that the difference (as reported by the standard deviation σ) in bearing mass is around 40% the difference in frame mass, and the difference in forks is around 80% the difference in frames. So just looking at frame mass, fairly common, doesn't tell nearly the whole story. And there's only a weak correlation among these frames between frame and fork mass. So you really need to consider both, unless you're planning on replacing a heavy fork.

The total mass has an average of 1167 and a σ of 52.4 grams. This σ is larger than you'd expect if the three mass componts were uncorrelated: the uncorrelated result would be 43.4. So there's a positive correlation among components.

On the specific results: the Cervélo wins on total mass (it's also the most aerodynamic, I'm fairly confident). The Simplon and the Cannondale are close behind, trailing by 31 and 41 grams. The Simplon frame is impressively light at 717 grams, only 13 grams more than the Cervelo and 43 grams lighter than the Cannondale. The Cannondale scores strongly with the light bearings and the light fork.

By the way, even though the Cervelo RCa "won" on total weight, the frame weight is higher than Cervelo claimed for even the heaviest of the size 56's. Did Tour include something with the frame that Cervelo does not? The Cervelo number includes "hardware":

Here's rankings by sub-class: frame, fork, and bearings.

Cervelo RCa1082704323555763871.48837
Simplon Pavo 3 Ultra1113717324725593941.41878
Cannondale Evo Black1123760303605593961.41162
Corratec Mauro Sannino Prima1209783336905474041.35396
Trek Madone H11204786379395454041.34901
Pasculli Altissimo1203789336785593941.41878
Focus Izalco Max1164802293695654021.40547
Neil Pryde Bora SL1241802374655623901.44103

Focus Izalco Max1164802293695654021.40547
Cannondale Evo Black1123760303605593961.41162
Cervelo RCa1082704323555763871.48837
Simplon Pavo 3 Ultra1113717324725593941.41878
Pasculli Altissimo1203789336785593941.41878
Corratec Mauro Sannino Prima1209783336905474041.35396
Neil Pryde Bora SL1241802374655623901.44103
Trek Madone H11204786379395454041.34901

Trek Madone H11204786379395454041.34901
Cervelo RCa1082704323555763871.48837
Cannondale Evo Black1123760303605593961.41162
Neil Pryde Bora SL1241802374655623901.44103
Focus Izalco Max1164802293695654021.40547
Simplon Pavo 3 Ultra1113717324725593941.41878
Pasculli Altissimo1203789336785593941.41878
Corratec Mauro Sannino Prima1209783336905474041.35396

Geometry in this review is primarily parameterized by stack-to-reach ratio. A bigger number is a more upright bike, a lower number is a more aggressive, lower or longer geometry. Here's that ranking:

Trek Madone H11204786379395454041.34901
Corratec Mauro Sannino Prima1209783336905474041.35396
Focus Izalco Max1164802293695654021.40547
Cannondale Evo Black1123760303605593961.41162
Pasculli Altissimo1203789336785593941.41878
Simplon Pavo 3 Ultra1113717324725593941.41878
Neil Pryde Bora SL1241802374655623901.44103
Cervelo RCa1082704323555763871.48837

The Trek and the Corratec are the most aggressive, each at 1.35. Then there's a pack at 1.42: Focus, Cannondale, and Pasculli, and Simplon. This seems like a good numberto me. Then there's the Neil Pryde at 1.44, and in a class by itself, the Cervelo is 1.49.

Geometry is plotted here, where each bike's point is at the center of its label:


Adding spacers (assuming a 73 deg HTA) moves you up the near vetical blue dotted lines. Adding a longer stem (0 degrees) moves you along the near horizontal lines to the right. A +6 deg would move you at an upward slope relative to these lines, a -6 deg would move at a less steep slope. The spacing between lines is 1 cm.

The result is that it would take around 3.5 cm of spacers, and a stem 1 cm longer, to match the position of the Madone or Corratec on the Cervelo.

Which of these do I take? I'll eat the SRratio and go with the Cervelo. It wins on mass, it wins on aerodynamics.

Sunday, August 24, 2014

fitting a Cervelo demo R5?

On a recent ride, I found a shop local to the day job, Cupertino Cycles, had a Cervelo Demo R5. Cool! Since reading the RCa White Paper, I've always wanted to try one. Indeed, I've never ridden any of the Cervelo R-series.

Recall, perhaps, the Peloton magazine review of the RCa, the prototype which led to the present R5:

There is a fury to the way the bike reacts to power -- it leaps from under you, but the feeling continues beyond the initial acceleration. Each pedal stroke delivers a new surge forward.

Who wouldn't want to ride this?

Deal is the Cervelo geometry is, as I've described, a bit tall. So it isn't obvious what frame to try. But is low-stack over-rates?

So what I did is I started with the geometry for the Fuji SL/1, which is my race bike (since I've done little racing recently, the poor thing is getting neglected).

I started with the geometry of the size small, which I ride. I use a +6 degree 11 cm stem at present (I used to use a lower position but found that the lower bars didn't actually result in a flatter back, especially since I don't use shallow bars, but instead just caused my shoulders to roll forward, which causes back strain, so I flipped the stem). In conjunction with the 71 degree head tube, this results in an upward 25 degree slope for 11 cm on the stem, which results in the adjusted reach-stack coordinates shown in the plot below. I have 1.0 cm of spacers on top of a low-stack headset cap as well, not shown in the plot:


The original Fuji stack-reach is shown with the "x" on the open black circle toward the lower left, then the result of the stem is shown with a "*" toward the right.

Note this is not a relaxed position: I still have 9 cm of drop, which is plenty. Really the frame is by most standards "too small" for me. I was lured to the smaller frame by the lower mass and by the possibility for lower bar position. But I overestimated how much drop I really wanted. I'd have been better off with the next size frame as it would have bought me a steeper head tube, even if it had been slightly heavier.

From this point, I want to "undo" the effect of various stems to find the frame stack-reach coordinates which would give me the same position with various stem options. I picked stems from 9 cm to 13 cm long, with angles of either +6 deg, -6 deg, or -17 deg. Note the spacing of stem angles is 12 deg and 11 deg, so they are relatively equally spaced. The target for these stem angles were the Cervelo 48 cm, 51 cm, and 54 cm R5. They have head tube angles of 70.5 degrees (this is how they manage to get such short reach on the small frame -- super-slack head tube, then compensate trail with a long-rake fork), 72.2 degrees, and 73.1 degrees. In general, I consider a 73 degree head tube to be superior to a 71 degree head tube, since it results in less wheel flop: the wheel is less prone to flopping over when the bike is tilted, resulting in better cross-wind control. But I've never done controlled experiments to verify this.

Note if the trajectory from the Fuji-with-stem position passes over a frame size, spacers can be added to the frame to bring it up to that trajectory. Additionally if the trajectory falls under a frame size I could remove up to 1 cm of spacers to bring the fit down. There's blue dotted lines on the plot showing what points are accessible by adding spacers, with roughly orthogonal dotted blue lines marking 1 cm intervals. These lines are drawn for a 73 deg head tube, so would apply best to the 54 cm Cervelo, but would also be a good approximation for the head tubes of the other frames, which differ by at most 2.5 degrees.

Fit coordinates I don't consider to be an exact science, and all I need to do is get close. With this in mind, the 48 cm frame could fit with a 13 cm stem at +6 degrees. That's obviously excessive. The 51 cm stem would fit with an 11.5 cm stem at -6 degrees. That's acceptable, not too far from the Fuji except with the stem flipped. And the 54 cm Cervelo would fit with a -17 degree 10 cm stem. That might actually be the best option since it would give the steepest head tube angle and also a shorter stem which would stiffen the front end.

In any case, the shop doesn't have a 51 cm demo, so I'd need to pick the 48 or 54. Given the choices, a 54 would be the obvious pick. However, I doubt they'll have a -17 degree stem available for a test ride. I can check, however.

Also on the plot I show Cannondale and Trek Madone H1, although the stem adjustments aren't drawn for the head tube angles on these frames. I could fit each of these as well, with shorter stems.

Consider, for example, the Evo geometries:

The 52 cm size with a zero degree stem looks like it would work, or a -6 degree stem with some spacers. The 54 cm size could also work fine: I could remove 5 mm of my 10 mm spacer stack, perhaps removing all of them with a headset cap 5 mm taller, and get the same bar position, using a -6 deg stem. There's a small error in these projections due to the head tube angle difference.

This plot shows an alternate route to the same result. Here instead of starting with the target position, I start with each of the three Cervelos. I then extend the various stems away from these positions.


The 13 cm +6 deg stem from the 48 cm Cervelo scores a virtual direct hit on the position I presently have with the Fuji. The 11.5 cm -6 deg stem from the 51 and the 10 cm stem -17 deg stem from the 54 come in within 1 cm of that position, low. This is easily rectified with an extra 1 cm of spacer: no problem.

So again, the big stack Cervelos work. However if I could choose a Cervelo with the Trek H1 geometry I'd probably take that instead. It would shave several cm from these stem lengths. The 54 cm frame (3rd in the series) would provide plenty of options, using either a -6 deg stem with spacers, or a 0-deg stem with fewer spacers.

Saturday, August 23, 2014

Cervelo geometry: R5Ca versus R5 and RCa

The old R5Ca, Cervelo's first version of a super-high-end stock bike ($10k for the frameset alone, and people, to my amazement, actually paid it...), used a relatively novel geometry whereby the downtube was offset forward of the bottom bracket. With the nominal 72 degree seat tube angle, this in effect gave a seat tube angle which was steeper for shorter bikes, more laid back for taller bikes. In this case by "shorter" and "taller" I mean bottom bracket to saddle.

With most manufacturers the same thing is accomplished by changing the actual seat tube angle from steeper in the smallest size (for example, 74.5 degrees) to more laid back (for example, 72.5 degrees) in the largest. But of course the effective STA doesn't then change with the amount of seat post showing.

Here's a plot I did:


But this was an experiment they didn't pursue. Maybe it caused too much confusion to dealers. I don't know...

In the present version of the R5, and the RCa prototype bike which preceded it, the seat tube appears to conventionally intersect the bottom bracket at its axis:


They've gone back to 73 degrees for all frame sizes.

Friday, August 22, 2014

stack vs reach: Calfee Dragonfly, Guru Photon, Lightweight, AX Lightness, Cervelo RCa, Trek Emonda

So far I've been sticking mostly with main-stream bike brands with the exception of Swift. This time I'm focusing on premium frames, including the stock geometries from custom framebuilders.

For reference, I include the Trek Emonda, which is obviously both light and expensive in the SLR with vapor coat model. Then I include the Cervelo RCa, the same geometry as the Cervelo R5, which is the most expensive frame here, at over $10k with the crankset, but it's also (except for geometry) perhaps the best all-around bike ever designed (the white paper is fantastic). Then I include two exotics: the AX-Lightness Vial Evo, extremely rare so far, and the Lightweight frame, which needs to be included by virtue of its name but which actually isn't that light when compared to the Cervelo and Trek. Then there's the Guru Photon, which made a bit splash when it was announced at Interbike around 5 years ago, but for which the low weight shown there was a very small frame built to the spec of a very light rider. Then I include a bike which is not at all particularly light, the Calfee Dragonfly Pro Geometry. The Dragonfly is usually custom built but Craig Calfee offers a standard geometry option.

Here's the stack versus reach:


The Cervelo R5/RCa is the tallest in the smallest frames, with only the Trek Emonda H2 in the larger frames. Note, however, Trek offers the H1 as well, so Cervelo wins on the tallest shortest.

Then there's AX Lightness in the small geometries, coming closest to the Cervelo 51 in the smallest of four sizes, but then following a relatively gradual slope to the largest. The philosophy here is one that going vertical at the head tube is fine: you can invert the longer stems typically used with larger frames, or use spacers. I like this philosophy as I was never a fan of the "SlamThatStem" aesthetic. I like having some breathing room under my bar position for adjustability.

Lightweight is fairly similar to the AX Lightness, following a more zig-zag trajectory through its range. It provides a more reasonable 6 sizes.

The Calfee pro geometry is middle of the road between the Trek H1 and H2, zigging and zagging, with reach actually decreasing between the 2nd and 3rd smallest. But it provides an impressive 10 sizes, the same as Colnago which I showed previously. And since Craig is a custom builder, this range shouldn't be taken as limiting. The zig-zag actually provides more options int he small sizes.

Guru Photon is another bike with a custom option. The stock range is the 2nd most aggressive on this group, with only the Trek H1 clearly lower/longer.

And finally, while Trek Emonda retreated a bit from the very aggressive Trek Madone H1 geometry, it's still the most aggressive in this group.

My preference? The Cervelo RCa white paper is a nerd's dream: I love the description of their design process. And the RCa provides the shortest reach of any of the models I've looked at here (even women's frames, which I don't consider here, tend to hit a lower bound on reach and simply reduce stack in the extra small sizes). The tall stacks, especially in the low reach range, aren't to my taste.

But could it work? My Fuji SL1 has a 51.5 cm stack, 37.9 cm reach, and a 71 deg head tube angle. It has an 11 cm, +6 deg stem, which is thus sloped upward at 25 degrees: 10.0 cm lateral, 4.6 cm up. So this is a net position of 56.1 cm vertical, 47.9 cm lateral.

The 54 cm Cervelo R5 has a reach of 37.8 cm, stack of 55.5 cm. So with 10 cm stem at -17 degrees, which preserves stack and extends reach, that puts me at essentially the same coordinates. So perhaps there is sanity in the Cervelo madness after all. At least for me a reasonable stem: -17 deg and 10 cm, seems to put me right on the 54 cm Cervelo RCa.

Given that the engineering on that bike is just amazing, balancing aerodynamics with light weight, that's the bike I'd take. Of course, that's the bike a lot of people would take, given it's $10k a pop for frame, fork, and crankset.

The Emonda is attractive except for downtubes which look like parachutes. I've not seen wind tunnel data but until I do and I'm proven wrong, not for me.

Thursday, August 21, 2014

Trek Emonda: geometry comparison and other comments

I'd left the Trek Emonda out of my previous comparisons for two reasons. One is it's technically a 2015 bike. Note, however, I'd included the Specialized Tarmac 2015, but that was an iteration on an existing bike. But more importantly I left it out because I don't like it.

You'd think I would, as it's marketed as a weight weenie special. But, unlike another weight weenie special, the Cervelo R-Ca, the Emonda is designed with down tubes which show an utter contempt for wind resistance. And for what weight savings? 30 grams. Yes -- 30 freakin' frams: the claimed weight for the Madone Vapor Coat H1 is 720, the claimed weight for the vapor coat Emonda H1 is 690 grams. There's a lot of ways to save 30 grams. 30 grams will save around 0.35 seconds up Old La Honda.... which I'm pretty sure will be squandered to wind resistance by the Emonda's bulbous down tubes. If the CdA of a rider on a Madone is 0.35, and if the Emonda is 100 grams equivalent of force more wind resistance at 30 mph (according to the Cervelo RCa white paper, the RCa is 102 grams more and the Madone 76 grame more than the Cannondale Evo, and the Emonda is almost surely more than the Cannondale Evo judging by the bulbously eccentric down tubes), then that's a CdA difference of 0.009. If you're going up Old La Honda in 16.5 minutes, that's 12.2 mph. That speed reduces the force difference to 16.5 gram-equivalents. That's 869 joules of work up Old La Honda. If you're riding at 300 watts, that's 2.9 seconds.

So weight savings is great, but paying 100 grams-equivalents of added drag at 30 mph for 30 grams of mass reduction saves you 0.4 seconds but costs you 2.9 seconds for a net time which is 2.5 seconds slower, assuming 300 watt power.

Note I assumed the wind resistance difference is 100 gram-equivalents at 30 mph. This is my best guess. But even if I'm off by a factor of two, and it's only 50, then it's still a full 1 second slower despite the mass advantagr.

So, you say, 30 grams? But what about the 4.6 kg weight? Madones are least 1 kg more.

This is really a matter of marketing by Trek. The reason the bike is so light starts with the mutant-light wheels which stock on the $14k Emonda. They are over 100 grams lighter than my Mount Washington wheels, which are already crazy light. There's a bunch of other similarly weenie-special parts on that top end Emonda. If you were to put those parts on the Madone, you'd have a bike which was very close in mass to the Emonda, with the possible exception of the semi-ISP on the Madone. The frame itself plays relatively little role in this impressively low mass. And indeed, Trek have priced the top-end Emonda so high, I'm fairly sure you could set up a Madone with that part list for less.

And if you look beyond the SLR, the top-priced Emonda frameset, the bikes aren't even remotely light. It's 1050 grams for the SL version, and 1200 grams for the S version, according to Trek. For comparison, 1050 grams is the same weight as this late 1990's Trek 5500, repainted. That's progress. My 2008 Fuji SL/1 is 860 grams for a size small.

Anyway, back to geometry. The top end Emonda comes only in the H1 geometry, according to the web site, but you can still get the SLR frame built to a more conservative part spec with the H2. The H2 Emonda is basically the same as the H2 Madone, but on the H1 Emonda Trek went a bit taller. Since a number of pro riders have adapted the Emonda over the Madone, this doesn't seem to be too much of an issue.


Note the H1 is slacker now, but it's still more aggressive than the Specialized Tarmac and Venge. If you slam the stem on your Tarmac, your fit on the Emonda H1 would have around 1 cm of spacers with the same stem, and your fit on the Madone H1 would have around 2 cm of spacers for mid-range sizes. In the smallest geometry only the Tarmac is close to the Madone and longer than the Emonda. Curiously the largest Emonda goes super-long, an apparent attempt to capture more of the statistical tail of tall riders, which makes sense.

Other aspects of geometry are similar to the Madone, which is a good thing. Bottom bracket drop is size-dependent, which makes sense since smaller bikes have shorter cranks and so can have a lower bottom bracket without cornering clearance penalty. Trail is relatively low, around 5.6 mm except for the smallest size which is only up to 6.1 cm in the Emonda (5.8 cm in the Madone). The moderate trail is due to the heat tube angle dropping to only 72.1\v{0.3}\-\-o\N on the Emonda (72.8\v{0.3}\-\-o\N on the Madone). Cervelo uses long-rake forks (> 5 cm) on the smallest R5's, but Trek uses a 4.5 cm fork on the smallest Madone and Emonda. Overall I think every aspect of the Trek geometry makes sense. Indeed the Emonda H1 would fit me better than the Madone H1.

So it's not really lighter, and it's obviously a lot less aerodynamic: why would any of the pro riders choose the Emonda over the Madone? One possibility is they didn't choose: the choice was made for them based on marketing. Another possibility is they fail to appreciate the importance of aerodynamics, which has strong historical precedent. Pro cyclists aren't necessarily more sophisticated than weekend warriors. But a third possibility is they've considered the aerodynamic cost, and balanced it against a benefit in ride quality. Indeed, Peloton Magazine in its latest issue reviewed the bike and said it was the "liveliest" Trek yet. Does this translate into better race results, despite the parachute-like aerodynamics? I can't say. Racing is an extremely complex dynamic. But I'd guess not.

Wednesday, August 20, 2014

Canyon versus Storck: Stapel-erreichen Smackdown

I previously showed the Canyon Aeroroad. But Canyon's perhaps more popular bike is the Ultimate, a perennial competitor for Tour Magazine's lab-dominated bike of the year ratings. A prime competitor is Storck, a more niche German company known for its engineering-based approach to bike design. Included in that approach is a relatively unique approach to geometry.

Here's a comparison of Trek, Specialized, Canyon, and Storck road bikes, where I've left off the endurance bikes this time:


Canyon is clearly sticking to the stack-reach design philosophy with both of its models. And for once a bike company does the obvious which is to make the aero bike lower. And the longest Ultimate is incredibly long. It must be those tall Norwegian customers.

But the Storck 0.6 is a bit bizarre. The smallest size differs only in stem length, essentially (actually with the head tube angle being slacker than 73 deg, slammed stem will result in the smallest being slightly higher). Then after that "constant bar height" move, it goes constant reach (straight up). The Aernario is basically the same with the addition of a larger size with longer reach & stack.

Tuesday, August 19, 2014

Stack-Reach smackdown: Trek vs Specialized

Last time I compared Trek to Cervelo for stack-reach. The Madone H1 and the even more aggressive Domane Race were much longer/lower than the Cervelo H1, and even lower than the more race-geometry Cervelo R-series from 2008. The Madone H2 and Cervelo R5 were comparable. The Trek Domane 6 was substantially more relaxed than the Madone H2. It's really designed more as a century bike than a race bike, although it may provide a good fit for some racers.

Here I compare the Specialized line to the Trek line. I already looked at the 2015 Tarmac. In the following plot, I add in the Roubaix endurance bike as well as the Venge aero road bike:


The Venge is basically identical to the Tarmac. The Roubaix is fairly close to the Trek Madone H2, not nearly as relaxed as the Roubaix: around 2.5 cm spacer difference. The Madone H1 is more aggressive than the Tarmac, however: with two lines of Madone they can afford to be more aggressive on the longer/lower version. This suggests for racing the Roubaix may well be the better choice than the Domane, unless you want to spring for the super-low, super expensive Domane Race.

Monday, August 18, 2014

Stack and Reach of Trek Madone, Domane

Previously I plotted the Trek Madone stack-reach. Consistent with using "race bikes" from other manufacturers, I used the more aggressive of the two geometries, the H1. The H1 used to be called the "pro" geometry, in contrast to the more relaxed "performance" geometry, but Trek decided, apparently, that this implied the more relaxed geometry was a lower standard, compelling weekend warriors to buy bikes which didn't fit them well. So the "pro" became H1, and the "Performance" became H2.

In addition to the Madone, the Domane is also a legitimate race bike, sold for comfort at some cost in mass. The standard Domane, as is the standard with "endurance" bikes, has relatively relaxed stack. To compel professional riders, most notably Fabian Cancellara, to ride the frame a lower-stack model needed to be developed. Since the UCI requires bikes given to professional riders be made available to the public, Trek made available a "Domane Race" version, with low stack. I must say this looks to be a very attractive bike.

Here's how the stack-reach numbers compare on these frames:


I show for comparison Cervelo geometry, 2008 and 2014.

The Madone H2 is very similar to the H1 with 4 cm of spacers. They also have an additional size in the H2: 8 versus 7 for the H1. This is very impressive. A lot of bike models are sold in only 6 sizes. Cannondale sells 8. The Trek Madone has 15. But even if it's relatively relaxed versus the H1, the H2 is within 1 cm of spacers within the Cervelo R5. So it's hardly endurance category.

The Domane Race is even more aggressive than the Madone H1, which should make Fabian happy. Obviously with Trek selling only one model, at over $10k each for the full bike, the intent isn't widespread distribution on this one.

The Domane is more relaxed still. A Domane with slammed stem is like an H2 with between 2 and 3.5 cm of spacers on the stem, depending on size.

All of the bikes are clearly designed to a stack-reach standard, since the parameters sweep out nice smooth curves in stack-reach space. They're not straight lines, like Cervelo pioneered, but then perhaps straight lines aren't optimal.

Sunday, August 17, 2014

stack-reach comparison: Specialized, Colnago, Felt, Parlee, Cervelo

More stack-reach comparisons, retaining the tall (Cervelo R5) and long (Trek Madone H1) winners from last time:


First, there's a new obvious "tall" winner, and that's the Parlee Z5 tall model. Of course this isn't a fair comparison, as it would make more sense to compare the Parlee tall geometry to the endurance geometries of other bikes, but I put this here for comparison since I recently test-rode a Parlee ESX. The regular Parlee Z5 geometry corresponds to around 2.5 cm less spacer height, and has more traditional road racing geometry (clearly not designed to a stack-reach spec, however, since the curve zig-zags).

Specialized is interesting, as the smallest 3 models are essentially constant reach, changing only in stack. This is because top tube length is directly canceled by seat tube angle. This keeps the reach the same as the top tube is lengthened. The bikes still fit bigger riders, however: adding spacers to the smaller frames would bring them to a shorter reach for the same stack as the larger frames (see dotted blue lines). The smallest Specialized is a good fit to riders who want a relatively low stack with what is still a moderate reach. Note for the same stack, it's 2.5 cm more reach than the small Cervelo R5.

The Canyon AeroRoad is another bike, like Cervelo and Swift, which is apparently designed to a stack-reach curve. The largest Canyon wins the "long and low" award for this comparison, beating out the Trek Madone.

Overall, though, the Felt F1 is lower than the Canyon. It covers a significantly longer reach range than Madone for essentially the same stack range, going from shorter in the small sizes to longer in the longer sizes.

Colnago has two models, a sloped top tube and a parallel "traditional" top tube, for its C60. The geometries are very similar, although the traditional model has fewer sizes. Colnago, like Specialized, is also constant-reach for part of the size range, with four having essentially the same reach. With the limited reach range, Colnago goes from Canyon-like in the small sizes to Cervelo-like in the large. Colnago's sloped model has the most sizes of any model here: a remarkable 9. Colnago's are pricey, but they want to make sure you get a good fit. They actually used to run even more sizes. Cannonondale is another range with a closely spaced size range: I showed them last time. But even Cannondale only has 8.

Saturday, August 16, 2014

Trek Madone, Scott Addict, Cervelo R5, BMC SLR01, Swift Carbon geometry comparison

More bikes added to the stack-reach plot I showed last time. It's tempting to add more and more but I run out of colors, and humans have only 3 color receptors so there's contrast only between so many...


Again the mostly vertical blue lines indicate points which can be matched to fit with the same stem but with more spacers on the lower stack, longer reach frame. Spacers reduce reach and increase stack. I additionally added mostly horizontal blue lines, which are spaced by 1 cm spacer height apart, again assuming a 73 degree head tube. These lines would correspond to points which you could reach with the same spacer height, but different length of 0 degree stem. Of course stems aren't typically 0 degrees 6 degrees, 10 degrees, and 17 degrees are popular, and these can be flipped positive or negative. But the spacing between these lines is the key point.

For small riders, Cervelo and Swift rule, Swift providing less stack, the Cervelo geometry at this size only relatively unchanged from the 2008 Cervelo. For big riders there's several contenders: Cervelo, Trek, BMC, with Trek providing the lowest stack. It would take around 2.7 cm of spacers to bring the Trek up to the bar height of the Cervelo.

In the mid-range, Trek is the low-stack king of this group, with Cervelo the big-stack leader by far. Note the difference between the Trek and the Cervelo here is around 5 cm of spacer. This is why among the pro riders you see so many slammed Cervelo stems with riders on small frames.

Cannondale clearly is not designing to stack-reach. Personally I don't care: I only need to fit one bike, so for a given point on this chart which would be my best fit, all I care about is which bike is closest. The shape of that bike's curve doesn't matter. If I were fitting a team or running a bike shop I'd feel differently. In contrast both Swift and Cervelo are clearly designed to stack-reach: their ranges form essentially perfect lines on the plot.

Wednesday, August 13, 2014

Swift Carbon, BMC SLR, Cervelo old and new: geometry comparison

Last time I noted that Adam Blythe when he switched from the BMC Pro Tour team to the NFTO continental team his stem went to something truly disturbing: a giant horizontal protrusion from the front of his otherwise very nice looking Swift Carbon frame. The obvious explanation is frame grometry: the BMC allowed a lower, longer position than the Swift. So I decided to check this.

Here's a plot of reach (x-axis) versus stack (y-axis) as reported by various frame brands (I need to be careful not to say "manufacturers"). I compare the BMC SL01 with the Swift Ultravox Ti, along with two favorite references, Cervelo old (2008) and new (2014).


Slight digression: Cervelo decided to take a fresh look at geometry back in those days by setting a seat tube angle of 73 degrees for all frames. They reasoned that the human body when it's shorter or taller is still optimized by the same seat tube angle: the desire for steeper seat tubes in smaller geometries is more driven by the desire to avoid foot-to-toe overlap. But skilled riders don't worry about foot-to-toe overlap, they decided: if there was contact, then it was at such slow speed that it wasn't a problem anyway (turning at such a radius at higher speed would result in a crash, overlap or no). Their point was it was reach which mattered, and while a steep seat tube would allow for a short top tube without overlap, the fit advantage of a shorter top tube was squandered when the seat needed to be jammed back on the rails. So they advocated for stack and reach being the two dimensions by which geometry should be primarily judged.

I like Cervelo: I don't always agree with them, but they are dogmatically engineering-driven: everything on their bike designs except for paint job is justified by sound functional reasoning. It's no coincidence it's on paint and graphics that they tend to go terribly, terribly wrong. But I digress.

Anyway, they complemented their R-series frame, which tended to follow a low trajectory in reach-stack, with an RS series, which allowed for a more "relaxed" position. But they subsequently determined that shorter riders benefitted most from the R-series geometry, while taller riders more from the RS-series, and so they redesigned their geometry to follow a straight line in reach-stack. At shorter reach, the stack was close to the original R-series. At longer reach, it became similar to the RS.

An additional big change they made was to go to longer rake forks and slacker head tubes on the smallest sizes. The combination of a slacker fork and more fork rake increases the front-center while allowing for the same trail. Thus the toe overlap problem is minimized while retaining responsive handling.

Another change: they increased the chainstay length from 399 mm to 405 mm, the minimum recommended by drivetrain manufacturers. With 10 or 11 speeds in the rear, the chain deflection angle becomes large the shorter the chainstay length. With 399 mm, there could potentially be chain rub against the big ring on the small-small cross-gear. The change was just 6 mm, but at some point the next mm makes a difference.

Anyway, digression over. The point of this post was Swift versus BMC.

Of the four bikes on the plot, the Cervelos offer the widest range of reach. It appears from the plot that the 2014 R5 has less than the 2008 geometry, but this is misleading: the angle between the coordinates of the top of the head tubes, which determines stack and reach, is 82.6 degrees between the two frames. That means if you added spacers on the old bike to bring the bars up to the same level on the new bike, with the same stem, the bar on the old bike would actually be further back.

For supporting long-and-low, however, both the BMC and the Swift are well ahead of the Cervelo 2014. Compared to each other, the Swift is lower at short reach, while the BMC is lower at around 40 cm reach, the longest the Swift offers. BMC's largest frame is a full cm longer than Swift's, but this isn't relevant to Adam, since he doesn't ride a large frame.

One thing is clear, however, which is that Swift Carbon followed Cervelo's "new" model of designing to stack and reach. However, they did so using a "lower and longer" trajectory. Those who find the Cervelos too upright might find a better fit with these bikes.

How to reconsile this with the photo of Adam's bike remains a mystery.

Tuesday, August 12, 2014

NTFO win in London

Adam Blythe, 2013 BMC, 2014 Continental team NFTO, won the London-Surrey Classic this past Sunday in a remarkable upset, beating the World Tour riders otherwise dominating his winning breakaway. I watched the final 10 km on youtube, although that video seems to have since been pulled. Too bad -- it was an impressive final.

Adam was there with 5 pro tour riders including Sky's Ben Swift and BMC's former world champion, Philippe Gilbert. Although Blythe was on BMC last year, obviously his preparation for this race was handicapped by the lack of top caliber race opportunities available to his team, NTFO. Despite this, he took his share of the pulls, longer pulls than some of the others. Surprisingly there were no attacks in the final kilometers, the group instead working together until the end game began well within the final kilometer. Adam went from relatively long, not wanting to get jumped by Swift, and it worked. He held his gap to the finish, winning his home "classic".

Good stuff.

The NFTO bikes and kits look really good. The jersey and shorts are well-fitting and make good use of color, mostly black and red, a distinctive combination. The bikes are Swift, a small company which also sponsors the Drapac team in Australia. Their frames aren't particular light and are certainly not aero, but they look good and delivered Adam to the win in the race.

In addition to Shimano Di2, which is hard to argue against from a functionality perspective, the team has wheels and bits from Enve Composites. Enve stuff looks really good, is well made, but is heavy for carbon. In this case, however, with the UCI 6.8 kg rule, this wasn't much of a handicap.

The bike looks really good. Here's a photo from the team blog:


And here's NFTO rider's Russell Downing's bike (BikeRadar article). Note the Enve stem. Russell runs only 49 mm saddle-to-bar drop, not much for a pro (I have 80 mm on my Ritchey Breakaway):


One notable thing about Adam's bike is the stem: a truly impressive demonstration of :


Whoa! Is that a stem on your bike or are you just happy to see me?

One thing of note is the stem isn't Enve: it looks like an FSA to me. This is because the NFTO philosophy is fit first, sponsorship second. Pro Tour teams could learn something. Enve doesn't make a stem like that: it may be FSA, but I'm not sure.

His BMC last year wasn't quite so extreme. Here's a photo of his 2012 BMC from Cycling Weekly:


And here he is racing in Qatar last year. Unlike Andy Schleck, for example, Adam can reach his drops. He seems reasonably comfortable, although the mutant bend in his back allows his rather exceptional saddle-to-bar drop.


You'd think the Swift Carbon must be some sort of endurance bike geometry, but it doesn't seem so. The geometry is described here. The head tube lengths seem quite reasonable. The trails are slightly long in the middle frame sizes, but otherwise I see nothing exceptional. In contrast, BMC seems longer. Did Adam's position change?

As nice looking as the NFTO set-up is, there's nothing to replace doing the big races with a Pro Tour team, and hopefully Adam makes it back to the top level next year.

Friday, August 8, 2014

Specialized puts a 1980's Allez in the "Win Tunnel": the Venge beat it, but what about the Tarmac?

For a long time I've been alarmed by the trend in carbon bikes to go to fatter and fatter tubes in a never-ending quest for higher stiffness-to-weight ratio. Indeed the trend predates carbon fiber: it goes back far further, to Cannondale, and before that, Klein with their fat-tube aluminum bikes. To save a relatively small amount of mass, giving up a large amount of wind resistance.

But then as the quest for lighter carbon frames started approaching a limit, there was an effort to gain performance elsewhere. So wind resistance got renewed interest. Starting perhaps with the Kestrel Talon, there were a series of "aero road" frames which, at the cost of around 200 grams more or less, performed much better in the wind tunnel.

These frames had a hard time catching on with professional riders, however. Road cycling is performed mostly in packs, with fatigue and avoiding crashing both major factors, so optimizing the bike is a lot more than optimizing speed at a given power: it's about positioning yourself within a pack, of reacting to attacks, of confidence at speed. For whatever reason the aero frames didn't provide these things, and the majority of riders remained with the fatter-tube bikes designed for stiffness and handling.

This led to a compromise: bikes like the Scott Foil, Cervelo R5 (and RCa), and the Trek Madone incorporated aerodynamic features like truncated foils into their frame designs in order to split the difference aerodynamically between the "aero" bikes and the bikes designed without any consideration to aerodynamics. These, I thought, had hit the sweet spot.

But they were basically working to undo the damage which had been done going to fat tubes in the first place. What of the lowly steel bikes with their relatively narrow one-inch tubes? How would these do in the win tunnel? Tony Rominger set an impressive hour record in the 1990's on a steel tube frame, going more than 53 kph. This is fast by any standard. Of course, Rominger used EPO, which helped, but nevertheless it was clear his steel round tubes didn't handicap him too badly. Nobody has much of a financial interest in showing whether standard steel tubes do compared to, for example, a Specialized Tarmac or Trek Emonda.

Finally Specialized, ironically, delivered. Specialized built their own wind tunnel in Morgan Hill, California, which allows them to investigate a lot of questions which become harder to justify if you're using a commercial facility with a high cost/hour. But for some reason they compared an old steel-tube Specialized Allez bike with a state-of-the-art Specialized Venge, an "aero road" bike designed to be on the leading edge of UCI-mass-start-legal frames.

Here's the video:

So the result is the Venge was 50 seconds faster per 40 km. What do I do with this number? First, I need to make some comparisons.

The test rider in the video has a relatively relaxed position compared to most pro racers. Tour magazine did a wind tunnel test with a dummy rider and got a CdA of 0.32 m2. Analysis of rider speed-power data has shown a good match for climbs of a CdA = 0.35 m2. I'll assume this rider is more like the pro racer climbing position than the more aggressive Tour magazine dummy.

I'll then assume that the 40 km time is at an assumed speed of 40 kph. This is an excellent time on a road bike with drop bars.

Then I'll assume that the time comparison is under the assumption power is proportional to speed cubed. This is a standard approximation which neglects the effect of rolling resistance, but it's commonly used.

I start with the fractional time savings: 50 seconds out of 1 hour is 1.39% time saved.

I assume power saved is three times speed saved, so the power difference, and therefore the difference in CdA, is 4.17%.

Given the baseline CdA value of 0.35 m2, I then get an absolute difference in CdA of 0.0146 m2.

There's a common standard, especially in the US, that tests on wind tunnels are done at 30 mph (Specialized echews imperial units and uses 50 kph = 31.1 mph, but plots with 30 mph are common). Assuming 30 mph and an air density of 1.2 kg/m3, this difference in CdA corresponds to a difference of 21.1 watts, or a difference in force of 1.57 Newtons, which is 160.4 gram-equivalents of force, or 0.353 pounds less retarding force on the Venge versus the steel bike.

This isn't at all surprising, as was described in the video. Round tubes aren't close to optimal for wind flow, while the shaped tubes on the Venge, along with the hidden cables, are. Additionally the downtube shifters on the steel frame add some wind resistance. The other components are probably a wash.

But my interest isn't so much in the pure aero road frames, but rather in the middle-ground frames like the Madone and the Cervelo R5, and even more so in the bikes like the Emonda and the Tarmac. Is is possible my humble steel Ritchey Breakaway is actually faster on the flats than these super-expensive carbon bikes?

For comparison of results, it's best to compare with other tests which included a rider on the bike, since some parts like the seat post or handlebars may affect wind resistance more on a naked bike than with a rider. Both Cervelo and Tour magazine use dummies: Cervelo uses its dummy of Dave Zabriskie in his CSC days, while Tour used a clothing mannequin. I don't have good data from Cervelo, but I'll show some 2012 data from Tour.


Recall I concluded the CdA difference between the steel bike was 0.0146 m2. The horizontal lines on the Tour magazine plot are 0.0100 m2. A difference of 0.014 is thus comparable to the spread in values from the Tour test for moderate yaw values from 0 to 10 degrees. Curiously the Cervelo and the Venge both have issues at zero yaw, but move to the front of the field at 5 degree yaw. This was also seen by Tour in their 2011 test of the Cervelo S3. In any case, the Venge is 0.011 m2 better than the "reference bike" with the same wheels at 5 deg, and 0.029 m2 better at 10 deg, 0.027 m2 at 15 deg. Whatever the reference bike, the Specialized test of the steel bike seems to be doing a bit better, depending on what sort of yaw angle averaging Specialized used in the 50 sec/40 km number quoted in the video.

The next plot is from Bicycling magazine showing bike-only data, no rider.


The bikes here are the Cervelo S5, the Specialized Venge, the Felt AR1, the Blue AC1, the Scott Foil, and the Specialized Tarmac, all with the same wheels. The difference between the Venge and the Tarmac is approximately 250 grams equivalent force at 30 mph. Recall I calculated 160 grams equivalent foce between the Venge and the steel frame. This suggests, the steel frame is around 90 gram equivalent force less than the Tarmac.

This isn't a fair comparison: different tests and one with and the other without a rider. But it makes sense: narrower tubes = less wind resistance. But I'd love to see a straight-up head-to-head time trial comparison.

Thursday, August 7, 2014

fun with LaGrange Multipliers

I was watching a tutorial for some modeling software when I saw a reference to Lagrange multipliers. Lagrange multipliers... it range a bell from my distant past but I didn't recall what it was. Fortunately Google is my friend and I pulled up a video from MIT on a "recitation" -- what MIT calls sessions with teaching assistants which occur between lectures taught by professors designed to provide practice, review, and supplemental material.

The problem posted on the video was the following: suppose I want to optimize (maximize or minimize) a function

f(x, y, z) = x2 + x + 2 y2 + 3 z2,

where the solution is constrained on the unit sphere:

g(x, y, z) = x2 + y2 + z2 - 1 = 0

Lagrange multipliers are based on the assumption that for points g(x, y, z) = 0 if the function f(x, y, z) is optimal along contours in g(x, y, z), then the gradient of f(x, y, z) and the gradient of g(x, y, z) must differ only by a scale factor λ, assuming the derivatives of both functions are continuous. This means there exists a λ for which the function f'(x, y, z) = f(x, y, z) - λ g(x, y, z) has zero gradient: the gradients of f and g, both pointing in the same direction, cancel when the gradient of g is multiplied by the Lagrange multiplier λ.

This is very clever, as is pretty much everything in math named after someone. To test myself, I applied it to the test problem. And, after I fixed an extremely embarrassing algebra error, it worked. I got 6 local extrema for f'(x, y, z), for which the global maximum was a tie between the two points in x, y, z space (1/4, 0, ±sqrt(15)/4) with a value 25/8, and the global minimum was (-1, 0, 0) with a value of zero.

But Lagrange multipliers were overkill, I thought. This problem is easily solved without them. All I need to do is apply the constraint to substitute for either x, y, or z, then find extrema in the 2-dimensional plane.

So that's easy: I picked z2 = x2 + y2 and that changed my function f to the following:

f(x, y) = x2 + x + 2 y2 + 3 ( 1 - x2 - y2 ),

which is trivially simplified:

f(x, y) = -2 x2 + x - y2,

which yields the derivatives:

fx = -4 x + 1,

fy = -2 y .

Some care needs to be applied here since I need to make sure the resulting points actually lay on the unit sphere: x2 + y2 must be no greater than 1.

No problem so far. But here's where things went bad. There's only solution for fx = fy = 0, and that's x = 1/4, y = 0, z = sqrt(15)/4. Note I found this same solution with the Lagrange multiplier method, but here I'm missing the point (-1, 0, 0). What's wrong?

The problem is a boundary, a singularity. Although the gradient with respect to x is non-zero at (-1, 0, 0), and for that matter at (1, 0, 0), moving along the surface of the unit sphere results in no change (to first order) of x: dx= 0. So the points can still be constrained extrema even though the 2-dimensionsal equation, with z2 replaced with the constraint for x and y, is not extreme at that point.

What I should have done was recognized I had a boundary at x2 + y2 = 1 and tested the points along this boundary for local extrema in f(x, y). Along this boundary z = 0, so f(x, y) = x2 + x + 2 y2.

For these points I can simply x2 = 1 - y2, yielding:

f(y) = 1 + y2 + sqrt[ 1 - y2 ].

This has only a single derivative:

fy = 2 y - y / sqrt[ 1 - y2 ].

This has a singularity at |y| = 1, but it is clearly zero at |y| = 0, which reveals the local extrema at the point:

( ±1, 0, 0 )

These points were made obvious from the Lagrange multiplier method. I would have missed them otherwise.

Anyway, I don't get to do as much calculus as I'd like during the day job. It's fun to return to this basic stuff to keep from losing it completely. It's tempting to solve all extremum problems numerically, which tends to work well for a single variable, but get up to 3 and it's not so easy. Constraint problems are quite common: this is a useful tool to have at hand. However, the classic problem with exemplary problems like this is they are hand-picked to be solvable. Trying to apply this method to arbitrary analytic functions is considerably more challenging.

For example, to test myself on a Caltrain commute I tried to find the extrema of the following simple equation:

f = (sin(x) + cos(2y)) exp(-x2 + y2),

subject to the constraint:

g = (x - 1)2 + y2 = 0

Unfortunately this got fairly ugly fairly quickly:

f' = (sin(x) + cos(2y)) exp(-x2 + y2) - λ [ (x - 1)2 + y2 ]

f'x = [ cos(x) - 2x (sin(x) + cos(2y)) ] exp(-x2 + y2) - 2 λ (x - 1) = 0

f'y = [ -2 sin(y) - 2y (sin(x) + cos(2y)) ] exp(-x2 + y2) - 2 λ y = 0

f'λ = (x - 1)2 + y2 ] = 0

I don't know what to do with this.

What does this all have to do with cycling? Optimization problems relative to constraints are a common application in cycling as well as in other areas. For example, suppose I have to ride a course consisting of ten one-kilometer segments and I want to ride the course as quickly as possible for a given normalized power. I might assume power is constant over each of the one-kilometer segments, as is the road grade and wind speed. I'm not sure if Lagrange multipliers would help here, but it's a problem I've solved before numerically.

Monday, August 4, 2014

Caltrain 2030 ridership projections 11 years pessimistic

In 2009, Caltrain projected 72 thousand boardings by 2030, a rate of annual increase of 2.3%. These projections are obviously extremely important, since capacity increases need to be planned well in advance.

Indeed, as was predicted by essentially all rational observers at the time, the ridership has exploded far in excess of that "extremely conservative" schedule, Ridership survey reports are available here. Here's the annual ridership:


At the rate ridership has been increasing it would hit 72 thousand not in 2030, but rather in 2019:


A key thing, though, is that ridership will not increase at this rate. There simply is not the capacity. At some point trains get so full that the experience of riding on the train is worse for a sufficient number of passengers than the experience of driving, or the experience of working from home, or the experience of moving closer to work, or the experience of changing jobs closer to home, or the experience of moving to Portland. There's a breaking point.
Here's a photo I took on a recent commute on one of the 60-something days when the San Francisco had a weekday evening home game. It was like this all the way from Mountain View to 22nd Street, where I somehow managed to fetch my bike and get off the train:


But this argument applies also to past data. The rate of increase would have been even greater had Caltrain had the capacity to support it. Even I, with an exceptionally strong anti-car bias, have been pushed to close to the limit by commutes like this. My alternative isn't driving, but changing life circumstances in other ways to avoid the problem. If Caltrain doubled its capacity today, it wouldn't need to wait for 2030 or even 2019 to hit that 73 thousand number: it would be there by next year.

Instead, it responds to record ridership numbers by slowing the trains. With "deferred maintenance", with too many riders boarding trains purchased with too few entry points into too few cars, the allocated 2 minutes per stop isn't enough.


To a large degree, Caltrain rules its own future. More service = more riders. Status quo = poor service = limited ridership and reduced quality of life in the Bay area.

Sunday, August 3, 2014

error in bike rack force calculation?

I was looking at an excellent web page in how to make your own wall-mounted bike rack (link here). But one aspect of it was bugging me... the calculation of the force acting on the hook in the wall.

I encourage you to look at that site -- it's a bit annoying in that it requires you to click through 5-separate ad-laden pages to see it all, but I suppose that pays the bills.

Here's my diagram of how the rack would look on my wall... either in the recommended arrangement of hanging the bikes wheel up, or in a way a bike shop friend of mine recommended, wheel down. Either or a mix would be compatible with the 2-tier arrangement of hooks. With only a single tier, you'd need to alternate up-down.



Here's a separate example of such a rack with bikes hanging from the front wheel:


Going back to the original web page where the bikes are also hung from the front wheel, the part I'm most interested in here is on page 3, which described the physics. Here's the diagram from the web page, although the physics are essentially the same if the bike is hung from the rear wheel:


The argument is the net torque on the wheel about the point of contact with the wall must be zero. The wheel is free to rotate about the front hub. The frame is pulling down on the front hub with force (M - Mfw)g, where M is the mass of the bike, Mfw is the mass of the front wheel, and g is the acceleration of gravity. Additionally, gravity is working on the front wheel with force Mfw g, operating through the center of mass. Therefore the total torque operating about the point of contact with the wall, in the absence of the hook, is M g Rw, where Rw is the rolling radius of the wheel (L1 in the diagram). To prevent the system from accelerating about that point of contact, a counterbalancing torque must be applied at the hook. The argument is since torque must be force times distance, the magnitude of this force equals the weight of the bike multiplied by the ratio of the wheel radius to the distance from the wall contact point to the hook contact point. So if the distances are equal, the hook is pulling on the rim with the bike weight.

There's an obvious problem with this analysis. The full weight of the bike needs to be supported in the vertical dimension, all at the point of contact from the hook.

So where did the argument go wrong? The problem is that the hook and the hub are not the only components of torque operating on the front wheel. The bottom wheel is also in contact with the wall (or the bike would rotate). This point of contact also exerts a torque about the point of contact between the front wheel and the wall.

Going back to the point that the full weight of the bicycle must be supported by the front wheel, I analyze the torque on the front wheel about the hub, rather than about the point of contact with the wall. The combination of the frame and gravity are pulling on the hub with force M g, vertically. This exerts zero torque about the hub. This force must must be balanced by forces applied at the other two points of contact to the front wheel: the wall contact point and the hook contact point.

Assume there's negligible friction, and therefore the contact point between the front tire and the wall supports essentially zero vertical force: the point of contact between the wheel and the wall supports purely horizontal force. This point thus contributes nothing to supporting the bike vertically. If the hook came loose, the bike would fall. I think this is a fair assumption.

Then the vertical force supported by the hook-rim contact is M g, the full weight of the bike.

We now need to balance the rotational torque on the front wheel. The forces acting on the hub (the bike weight) exert no torque: the forces are acting at zero distance from the wheel's spin axis. The forces acting on the wall contact point also exert zero torque: the assumption is these are perpendicular to the tangent of the wheel, or in other words that they operate along the radius of the wheel, and radial forces exert zero torque. So all torque must be exerted by the hook, and since total torque must be zero, the hook must exert a purely radial force.

Since we know the perpendicular component of the hook's force is M g, and we know the net force must be radial, then it's easy to calculate that the horizontal component of the hook force must be M g / sine θ, where θ is the angle of the contact point relative to the horizontal.

This result can be checked trivially in two limits. In one case the bike is hanging from a hook in the ceiling. Then the hook supports the bike weight, no more. The sine of a right angle is 1, so the formula works. In the other limit, the hook is nailed into the wall with infinite force, forcing the rim to be contacted at the same point the tire contacts the wall, which is an angle of zero. In this case the supporting force is infinite. Obviously something would fail (the hook would pull out of the wall, or the wheel would deform to move the contact point).

The net magnitude of the force operating on the hook is the quadrature sum of the horizontal and vertical components:

F = M g sqrt[ 1 + 1 / sin2 θ ],

where θ is the angle of the hook relative to horizontal, and M g is the weight of the bike.

So, for the case in the web page, where the support is an equilateral triangle, sin θ = sqrt[3] / 2, and therefore instead of a net force M g, which the web page predicts, the actual net force would be M g sqrt [ 2/3 + 1 ] = M g [ 5 / 3 ] ≈ 1.29 M g. So the rim needs to support 29% more than the bike weight instead of just the bike weight.

But what about the original argument about torque operating about the point of contact between the front wheel and the wall? The answer is that is balanced by the point of contact between the bottom wheel and the wall. The excess is supported there as a force operating over the length of the wheelbase.