Saturday, July 4, 2015

Cannondale 2016 Evo: Damon Rinard leads switch to Stack-Reach design

Previously I blew it by posting that Cannondale had retained the old geometry for the new 2016 Evo. This had shocked me since I knew they'd hired Damon Rinard, formerly of Cervélo, the pioneer in stack-reach design, something the old Cannondale clearly did not follow with weird kinks and jogs in its stack-reach progression due to odd jumps in seat tube angle as sizes increased. I'd gotten the geometry chart by clicking links on the Cannondale website, but somehow I'd clicked a link for the 2015 geometry starting from the 2016 Evo page. So I'd been too hasty.

Well, I was finally pointed to the correct geometry chart. Here's a comparison of old Evo and new Evo:

2015 Evo:


And, finally, the 2016 Evo:


Here's the stack-reach progression:


Plotting stack versus reach shows the design has switched to a stack-reach focus, with continuous small increments in seat tube angle rather than descrete jumps, with a design transitioning from closer to the Trek H2 in small sizes to closer to the Trek H1 in larget sizes, but always between the two.

Bottom brackets are 2 mm lower in every size except the 52. Previously there was a jump from 52 to 54, and now there's a jump from 50 to 52. The jump at 58 remains. This is consistent with the trend to fatter tires.

Trails are slighly increased relative to the older Evo, and are significantly larger than on the CAAD-10 curiously, in the small sizes, mostly because the CAAD-10 uses a 5 cm (as opposed to 4.5 cm) rake fork in the smaller sizes. Here's CAAD10 geometry, which other than the trail is similar to the older Evo:


Sunday, June 28, 2015

2016 Cannondale Evo

[b]Comment:[/b] The following post is in error. The geometry chart on the Cannondale site is still the 2015 bikes. Bikerumor had an article where they described geometry changes for 2016, including adjustments to stack-reach in small and large sizes, and a general drop in bottom brackets consistent with the trend to wider, deeper tires. I'll post a follow-up post when I get the geometry chart for 2016.

Cannondale just announced it's 2016 Evo.

There's been a flurry of really attractive new bikes announced this year, including the new Madone 9 from Trek, the incredible Venge ViAS from Specialized, and the new Scott F02 update to the Foil. A common feature of all of these is increased focus on aerodynamics and comfort. Aerodynamics isn't new, with bikes going back to the Kestrel Talon and Cervelo Soloist Carbon examples of carbon frames designed for aerodynamic efficiency. However, the bikes have never been as popular as was predicted because in the end riders like feeing good on the bike, and a combination of drivetrain efficiency and vertical compliance provides a palpable advantage while the advantage of aerodynamic improvements needs to be carefully measured and is thus less obvious. But perhaps starting with the latest Felt AR a few years ago, aero bikes have received an increasing comfort focus, and it's hard to see them not finally becoming the main design used in the pro peloton.

BikeRadar photo

Cannondale's new Evo isn't an "aero" bike, but is more in the style of the Cervélo R5 which is a lightweight bike designed to be aerodynamic. The previous Evo made a nod to aerodynamics, but in a more subdued way by reducing tube diameters. This is important, but tube shape remained unchanged. That's been fixed here, with the new Evo adapting the now common "Kamm tail" approach of a truncated airfoil shape.

For "comfort", they've taken lessons learned in the Synapse. It's nothing as overt as Trek's adoption of the Isospeed linkage used in the "endurance" class (and tall-stack) Domane to the Madone 9. For example, one change Cannondale made was to reduce the seat tube diameter from the common 27.2 mm to the less common but more traditional 25.4 mm. There was a trend for a few years to make seat tubes ever fatter (my Fuji SL1 uses a mountain-bike-style 31.8 mm) but that makes little sense: propulsive torque isn't applied to the seat tube so a bendy seat tube, within reason, makes for a more comfortable ride. But additionally they've flattened the chain stays, like the Synapse, to provide more vertical compliance.

The fork as gotten an overhaul with a very light fork providing a large portion of the claimed 65 gram system mass reduction (the rest, I think, is from the seatpost). Tour magazine in Germany has been rating bikes on comfort using a combination of deflection at the seat tube and deflection at the head tube, the latter being a "fork comfort" rating which is averaged with the seat tube number. Many bikes have been engineered to score well at the seat tube deflection test but on the fork deflection test it's been common that bikes lose a lot of potential points. Jan Heine likes to emphasize the importance of fork deflection, advocating for the traditional high-rake flared out design which was common on steel bikes through the middle of the 20th century. Apparently Tour magazine agrees it's an important issue and the light, more compliant fork is a welcome modification.

One thing they did not change was geometry. I had thought with the addition of Damon Rinard, formerly of Cervélo, to the Cannondale design team that the stack-reach design philosophy would be adopted, but perhaps Rinard joined too recently for such a drastic change. Here's the Cannondale stack-reach chart compared to Trek's stack-reach-based design. Trek uses two curves, the "H1" and the "H2", for its Emonda and Madone. The special race-geometry Domane now uses the Emonda H1 curve. The Madone had a more aggresssive H1 curve but perhaps that will change with the Madone 9.

Cannondale and Trek geometry comparison

The two Evo curves are fully coincident and thus you can't see the 2015 curve, which is occluded. So the old and new Evo are the same.

Cannondale's approach includes some weirdness. For example, going from 52 to 54, the two points which are of similar reach but different stack 3rd and 4th from the left, they increase the top tube length but decrease the seat tube angle and the result is the reach stays virtually the same, the change in geometry almost all coming in the stack. Additionally the bottom bracket increases. Trail between the two is the same. I'd rather have the 3 mm lower bottom bracket so even though I could use a 14 cm head tube to avoid spacers I'd go with the smaller frame to get the same position with a lower bottom bracket and live with some spacers up front. It's just as well since the smaller frame will be lighter.

The importance of a clean stack-reach schedule can easily be overstated: either a bike fits or it doesn't and if a particular size in the Cannondale fits that's all that matters; I don't care what how the other sizes are designed. Still, I suspect this will be changed next iteration.

So this is a really cool bike. I really think 2016 is bringing a tangible advance in bike design from the big companies and my 2008 Fuji SL/1 seems more than another year older. It's more than good enough for me, however.... alas.

Wednesday, June 24, 2015

Garmin Edge 25: simpler, lighter, smaller equals better

SCRainmaker has a "hands-on" (as opposed to an "in-depth" review; still way more in-depth than any other reviews on the web) of the new Garmin Edge 20 and 25. These are, finally, Garmin addressing the simpler/lighter-is-better market for GPS.

On bikes, a huge amount of attention and money is directed towards minimizing weight. The best way to minimize weight of a GPS unit is to ride without a GPS unit. But the prominence of social networking website Strava has increased the value of GPS data. So for many, GPS has become a virtual requirement. What's the point of riding if you can't get kudos?

Yet despite big push for lighter bikes, and with real estate on the handlebars and stem so limited, Garmin has seemingly ignored the value of lighter-and-simpler-and-smaller by producing a series of increasingly complex, heavy, and bulky GPS units. The Edge 500 came out more than a half-decade ago, and yet it has remained the lightest and most compact unit provided by the company until these new units. And the Edge 500, while still a "current" product, has been abandoned for firmware upgrades, the firmware remaining buggy and now not supporting the Vector pedal dynamics metrics which were made available on larger/heavier Edge 510, a unit with a poor reputation for reliability. Indeed, it's remarkably the company ever produced the 500 in the first place: it's simply too elegant, compact, and functional. It must have been an anomaly.

So I was surprised when I saw these new units, which come it at half the weight of the already light (57 gram) Edge 500. There had to be a catch....

And there is. First, the Edge 25: that has ANT+ Sport support and also low-energy Bluetooth. But these are supported only for heartrate straps and for communications with phones. Obviously if you can trade data packets with a heartrate strap you can do the same with a power meter. But the unit refuses to communicate with power meters. Was this an engineering decision or a marketing one? On the engineering side, you might argue that communicating with a power meter would be too large a drain on the battery, which is rated at only 8 hours. After a hundred or so charge-discharge cycles surely that will come down, making the unit barely able to survive a fast century ride. Road races are shorter, so for racers the battery might be sufficient, but add in the extra drain of power meter support and that's pushed a bit further. But they are willing to communicate with a heartrate strap.

So I think this is likely marketing. If they put too much power in the 25, they believe, that will take away sales of more expensive, complex units. But this is monopolistic thinking. In a competitive market, suppliers are compelled to make all of their products as good as possible, otherwise competitors will do so and outsell them. In a monopoly, you're competing mostly against your self or against "none-of-the-above", in which case you can afford to play games like this. I think the GPS market is competitive, so these market-slicing games are a mistake which will in the end cost Garmin marketshare. After all, power meter support will differentiate the units from what might be the #1 competitor to low-end GPS units, which are smart phones and, increasingly, watches.

Another missing feature is a barometric altimeter. Barometric altimetry, as opposed to GPS altimetry, is much more reliable especially in situations where the GPS signal is compromised, for example wooded hillsides or canyons. Barometric altimetry is susceptible to errors from weather fronts, but in conjunction with GPS, those errors can be minimized. The two together are better than either by itself. And good altitude data is really useful for estimating power on climbs when power meter data is unavailable.

A subtle feature of the new units is they are listed by DCRainmaker as being "smart recording" only. Smart recording can result in gaps between data of up to 8 seconds, which is terrible for Strava segment timing and possibly even segment matching. This seems silly because it's a software-only issue. The motivation for having provided 1-second recording on the Edge 500 was analysis of power data. Initially 1-second data recording was available only when power meter data was being recorded. But they eventually allowed 1-second recording as a general option, most likely because of Strava. But this unit has taken a step backwards by being smart recording only. For Strava fans, this alone should be a deal-breaker.

So give me a compact unit with a barometric altimeter and at least minimal power meter support with one-second recording and I'm all over it. I don't need fancy displays. I don't need access to a huge number of data fields at once. I want to see distance and power and I want to record everything else. These are the key things.

On the plus side they did include the same level of navigation support provided by the Edge 500. And while that's flawed and error-prone, it is nevertheless extremely useful when the GPS signal is strong. I used it extensively when riding out of Switzerland last year. So perhaps real-time navigation isn't part of my claimed support for "simpler" but I'll use it if it's there. It can always be ignored.

It's perhaps ironic that the low battery life, good enough for road races but not good enough for century riding, combined with the exceptionally light weight could well have made this an excellent "race day" GPS unit. But then they crippled it with a lack of power meter support and lack of 1-second recording, neither of which would require additional hardware. So instead you have a unit which isn't particularly good at anything. It's unfortunate.

So while this is a good start, but Garmin needs to go further. The smaller-lighter-simpler = better philosophy has been long neglected at Garmin, and it would be great to see it get attention again.

Wednesday, June 10, 2015

Golden State Warriors down 2-1

The Golden State Warriors lost to the Cleveland Cavaliers in basketball last night. They're now down 2-1 in the series. The first team to win 4 is the champion.

I don't care about basketball but there's one thing I like about the game and that's that scores generally increase relatively at random (I hope -- I hope the near miraculous comeback yesterday from a 17-point deficit after three quarters wasn't programmed), and that games are won to some degree seemingly at random. I like random.

As an aside, I do find it remarkable in basketball how often a team with a big deficit claws its way back only to lose in the end by a small margin. I'd like to see a statistical analysis of this. A huge amount of money is at stake for games not being a total blow-out. I do wonder at this. Basketball has long seemed to me to be more about the show and less about a fair contest. And that makes it very difficult for me to care about the result. But this is an aside.

Assuming games are fair, what's the chance of Golden State winning the series?

Assume each team has an equal chance to win games. You can weight results under different assumptions but this is simplest.

Then the key to solving this problem is to recognize that while the series is terminated when the first team reaches 4 wins, this is irrelevant to the odds of who wins. It's easier to calculate the odds of winning if you assume the series always goes 7 games. If you assume that, it becomes a simpler probability problem.

Then all sequences of win-loss are equally probably. Each has a chance 2-n, where n is the number of remaining aims. And since 3 games have been played, 4 remain (I'm assuming we always play the full 7). So I need to count how many of those possible 4-game sequences result in the Warriors winning.

There's one sequence where the warriors win all 4. They win the series then, 5-2.

There's four sequences where the warriors win 3. Then Cleveland wins 1. That win can occur in either game 4, 5, 6, or 7.

The rest of the possible sequences the Warriors fail to win at least three games. So they win the series in 5 of the 16 options. Since each is equally likely to occur, they win in 31.25% of the possible results. That's their chance to win the overall, assuming games are completely random.

To calculate it assumingt he series ends as soon as one team gets to 4 is more complicated. You'd need to start with the odds the warriors win the next 3 games. Then consider the odds they win exactly 2 of the next 3 but then win the 4th. Then add these together.

I can do this: the odds of winning 3 in a row is 1/8 = 2/16. The odds of winning exactly 2/3 is 3/8 (there's 3 ways to lose one game of 3, and there's 8 ways total the 3 games could end up, so that's 3/8). Then I need to divide by 2 because they then need to win the 7th game, which has 50% chances. So that's net 3/16. So the total chances of winning are 2/16 + 3/16 = 5/16. This is the same answer as I got before but is more convoluted.

The principle that cutting the series short can have no effect on the winner, assuming results are random with a fixed chance for each team to win, has more implications than just simplicity in calculating the odds. It also means the sequence of home versus away games doesn't matter. There's been a lot of debate in various sports whether a 2-3-2 sequence of teams A and B being home, which generally has an advantage, is more balanced than a sequence 2-2-2-1. After all, 2-3-2 could result in team B having 3 home games to team A's 2 home games if the series ends after 5. However, if I view it as the series always goes 7 games then it seems the sequence should not matter. And since going to a full 7 never changes the result I therefore conclude the sequence doesn't matter. You can just as well go 3-4. The home field advantage for the series is alwsys with the team with 4.

Friday, June 5, 2015

2016 Trek Madone 9

First I saw it on the UCI list of approved frames for June, then I saw a teaser video posted to the Trek website, and then this uncredited photo was posted to the Weight Weenies forum:

My that looks fast. Maybe it's the color, but it reminds me of the Canyon Aerooad. The Canyon has done rather well in the tunnel, not in the class of the Cervélo S5, but fairly good. See for example Tour magazine data here. So I expect the Trek will be at least this good.

But then there's weight. The Madone 7 was quite light with the vapor coat -- under 800 grams. But then the Emonda came out, pushing that lower, but there's only so far you can go below that. So the Madone was a bike of compromise. Now they want you to buy two bikes: the lightweight Emonda and the "aero" Madone. So the pressure's off on weight. But I wonder how they did. Nothing on this one looks particularly heavy.

From what I see I really like it. The days of bad-riding aero frames are over: bike design has gotten good enough that even the aero mass start frames have what are considered excellent ride feel. I certainly enjoyed my test ride of the Parlee ESX last year.

Anyway, I won't be buying one as I'm happy with the bikes I have, but if I were looking for a bike to road race on, this looks like a winner. In contrast I've never been a fan of the Emonda because it looks so terribly unaerodynamic. That simply makes no sense to me for racing.

Also on that UCI approved frame list is the Scott F02. I look forward to seeing that. The F02 is presumably the successor to the F01 which was the pre-release name of the Foil. It was a clever number-letter conversion play, there, so I wonder what they'll call this one when it's released.

Also on that list is the Specialized Venge "RIM". I'd initially overlooked this, thinking it was a wheel, but the wheels are listed on a separate list, so this is in fact a new version of the Specialized Venge aero-road bike, the rim-brake version as opposed to the disc-brake version. The Specialized Venge design wasn't as aero as many of the current aero road bikes, or any of the Cervélo aero road designs, and so it's due for an upgrade. I'm not particularly happy about the move to disc brakes, however. But that's another matter.

Wednesday, May 27, 2015

Effect of variability in rolling resistance coefficient on cycling power

I looked at how grade variability affected average power when climbing a hill. Honestly I thought the result was going to be larger, but the reality was it was a relatively minor effect. When the hill is very gradual, for example 1%, variations in grade of a certain fraction have little effect on speed. When the hill is very steep variations in grade are more significant, but since they increase power only via wind resistance, and wind resistance is relatively unimportant (assuming still air), again variations in grade have little effect. It's only important in the middle ground where speeds are high enough that wind resistance is relatively important but where grade variations have a relatively large influence on speed.

A virtually equivalent logic applies to rolling resistance variation. A variation in rolling resistance about an average value (averaged over distance) will have the same effect as a variation in grade by the same absolute amount.

So the effect of variability in the coefficient of rolling resistance, by a given fractional amount, can be written almost by inspection by swapping rolling resistance and grade in the previous formula:

ΔP/P = 3 (σCRR / CRR)2 × αwCRR (1 - αw) / (1 + 2 αw) ]2

This will generally be less than the effect of fractional variations in grade, assuming grade is generally larger than CRR.

The definitions are the same as last time:

fmacceleration(grade + CRR)×gravitymass (and speed)-proportional power
fwmass/distance1/2 ρCDA2speed-cubed-proportional power
CRR1coefficient of rolling resistance (for example 0.4%)
CD1coefficient of wind resistance (for example 80%)
ρmass/volumemass-density of air (for example 1.1 kg/m3)
Aareaeffective cross-sectional area of bike + rider (for example 0.4 meters2)
αRR1CRR/(CRR + grade)fraction of mass-proportional power due to rolling resistance
αw11 / (1 + fmm / fws2)fraction of power due to wind resistance
αm11 / (1 + fws2 / fmm)fraction of power due to mass-proportional power

Monday, May 25, 2015

Grade variability and climbing power

I've looked at this matter before, but one factor which I've seen continually neglected in all of the climbing power analysis estimates is the effect of grade variability. Road grade on climbs is almost never constant: it varies about a mean in some fashion. Yet the estimates are almost always done assuming constant speed, constant power.

Now these estimates end up remarkably accurate anyway. Why? Because the grade variability effect is negligible? Well, no. It's because you're canceling one mistake with another. For example, you neglect grade variability, which always increases power, but you also neglect drafting, which always decreases power.

How does grade variability increase power? It's because grade variability typically results in speed variability and speed variability yields variability results in variability in wind resistance and wind resistance, by virtue of being superlinear, is increased more by increases in speed than it is decreased by decreases in speed. So if instead of maintaining a constant speed v, if instead I am v + Δv for half the climbing time, then v - Δv for the 2nd half of the climbing time, the average wind resistance power is increased, assuming still air and no drafting:

[ (v + Δv)3 + (v - Δv)3 ] / 2 - v3 =
[ v3 + 3 v2Δv + 3 v (Δv)2 + (Δv)3 - 3 v2Δv + 3 v (Δv)2 - Δv3 ] / 2 - v3 =
3 v (Δv)2

So the fractional increase in wind resistance power from grade variability, for a given average speed, is:

ΔPw/Pw = 3 (Δv)2 / v2

Note this is just the aerodynamic portion of the power.

This is very simple, but it's in terms of speed, not grade. You can ride a variable grade at a constant speed, and in this case the average power will be calculated using the average grade as is typically done. However, this would result in a variable power, and according to Coggan's normalized power approach this would result in a lower power than could be attained by riding at a constant power, going faster on the flatter portions and slower on the steeper portions. Indeed, I think it's clear that this is almost always done. Essentially nobody rides climbs at constant speed.

So I need a relationship between grade and speed. The key here is that I neglect inertia, which tends to make speed more constant than otherwise. But inertia is only sustained over short distances, so I'm assuming grade variations to a resolution of no better than 10 meters distance or so.

Speed versus grade is a nonlinear problem: a cubic equation. So to estimate this effect you use linear analysis: linearize the nonlinear function.

Back in 2009 I analyzed the effect of grade on VAM, and a part of that calculation was the effect of grade on speed. This calculation begins with the following approximation for power, which is fairly standard in still air:

P = fm m s + fw s3

where fw is the coefficient of power on speed-cubed, fm is the coefficient of power on mass (gravity times rolling resistance coefficient plus grade), m is mass, and s is speed. It's not hard to go from this equation to the following using the chain rule:

∂s / ∂grade = ‒ m s g / (fm m + 3 fw s²)

where fm = ( grade + CRR ) × g, where grade is the road grade, CRR is the coefficient of rolling resistance, and g is the acceleration of gravity (not to be confused with road grade).

The result of this is if there is a variation in grade σ2grade, there will be a corresponding variation in speed σ2s:

σ2s = σ2grade × [m s g / (fm m + 3 fw s²) ]2

So the result is, recognizing that the average value of (Δv)2 ≡ σ2s:

ΔPw/Pw = 3 σ2grade × [m g / (fm m + 3 fw s2) ]2

This equation has too many constants and it's hard to get a grasp for what it means. However, if I define mass-proportional and wind-resistance unitless fractions of retarding force (and of power) αm (mass-proportional) and αw (wind resistance proportional), then I can write this as follows:

ΔPw/Pw = 3 σ2grade × [m g s / (αm + 3 αw) P ]2

But αm + αw = 1, so this can be slightly simplified:

ΔPw/Pw = 3 σ2grade × [m g s / (1 + 2 αw) P ]2

given that ΔP = ΔPw, since climbing power depends only on the average VAM (and is insensitive to speed fluctuations while rolling resistance power depends only on the average speed.

Then if I define αCRR is the fraction of the mass (or weight)-proportional power which is due to rolling resistance, I can multiply and divide by grade, then observe the numerator is a power due to grade, and I can simplify it further:

ΔPw/Pw = 3 (σgrade / grade)2 × [ (1 - αCRR) (1 - αw) / (1 + 2 αw) ]2

This is all in unitless quantities and so is easier to grasp. It works for everything except zero or small average grade (for which you should use one of the previous forms).

The nice thing about unitless quantities is they tend to be more universal without requiring specific estimates for a given rider. For example, suppose we're dealing with a grade which varies 20% about the mean (for example, σgrade is 1.4% with a mean grade of 7%), and 15% of the power goes into wind resistance, and rolling resistance coefficient is around 0.4% (so responsible for around 0.4% / (7.0% + 0.4%) ≈ 5% of the mass-proportional power), then I get a 1.5% increase of aerodynamic power relative to the assumption of constant speed.

If I want to convert this to fraction increase in total power, I need to multiply by the fraction of total power which is aerodynamic power:

ΔP/P = ( ΔPw/Pw ) ( Pw / P ) = ( ΔPw/Pw ) αw

I then get:

ΔP/P = 3 (σgrade / grade)2 × αw [ (1 - αCRR) (1 - αw) / (1 + 2 αw) ]2

So going from that 1.5% I need to multiply by my assumed 15% total power from wind resistance and that brings me to 0.23%, so a small fraction of the total.

I think this is a typical example which implies a persistent underestimation of climbing power in time trial like efforts of 0.7% just considering the effect of grade variability. Of course there's other sources of variability which will have similar effect, for example variations in speed due to non-uniform efforts, such as in mass-start races where tactics come into play (going more conservatively at the base of a climb, attacking toward the finish, etc). But the result ends up being fairly minor assuming I didn't make any errors.

An interesting aspect of this formula is that variations in a grade of a given fraction have zero influence in limits both where grade is zero (because fractional variations of near-zero are near-zero) and also in the limit of no wind resistance (because for climbing power variations in speed average out). It's only in the middle range: climbing hills fast enough that wind resistance is still a factor, that the grade variations are significant.

In summary, here's a description of the parameters I used in this analysis:

fmacceleration(grade + CRR)×gravitymass (and speed)-proportional power
fwmass/distance1/2 ρCDA2speed-cubed-proportional power
CRR1coefficient of rolling resistance (for example 0.4%)
CD1coefficient of wind resistance (for example 80%)
ρmass/volumemass-density of air (for example 1.1 kg/m3)
Aareaeffective cross-sectional area of bike + rider (for example 0.4 meters2)
αRR1CRR/(CRR + grade)fraction of mass-proportional power due to rolling resistance
αw11 / (1 + fmm / fws2)fraction of power due to wind resistance
αm11 / (1 + fws2 / fmm)fraction of power due to mass-proportional power