Wednesday, September 30, 2009

MetriGear Vector Pt 2: Coordinates Defined

As I noted last post, the MetriGear Vector ("Direct your forces") is targeted as much as a force meter as a power meter. Get force right, get velocity right, and you get power right.

Power associated with mechanical work equals the product of a velocity magnitude ("speed") and the component of force applied in the direction of that velocity. This is equal to the vector dot-product of velocity and force. Virtually every power meter deals with this relationship. For example, the iBike estimates the forces acting on the bicycle, then multiplies those forces times the measured speed of the bike. The Polar power meter estimates the tension (force) in the chain, and multiplies it by the speed of the chain. The SRM and Quarq Cinqos measure the torque (an integral of force times distance) in the crank spider and multiples it by a rotational velocity (a speed divided by a radius). The PowerTap does a similar calculation, measuring a torque in the hub and multiplying by a rotational velicity of the hub. So generally all existing "power meters" are force based.

Where the Vector differs from these other units, however, is that it is measuring multiple forces components, not just one in a single direction. These other units are essentially measuring a single force (or torque). The PowerTap, for example, will record and report hub torque, but except for calibration purposes that number isn't of much independent interest from the power number (except at zero speed, where power is automatically zero and thus provides no information).

To consider the force components on a pedal, I'll define coordinate axes:

Axes for right pedal

A few comments on this:
  1. the coordinate axes are relative to the spindle relative to the direction of motion of the pedal as it rotates. The angle of the pedal body is irrelevant. The Vector sits in the spindle, not the body, so the body of the pedal is effectively (from the perspective of the Vector) part of the shoe.
  2. The coordinates shown here for the right pedal are actually a left-handed coordinate system. There's no problem with left-handed coordinate systems (relative to the more conventional right-handed coordinate systems) as long as one is self-consistent.

For the left pedal, taking the mirror image of the schematic for the right pedal, results in a right-handed coordinate system:

Axes for left pedal

it would have been more appropriate for the right pedal to have a right-handed coordinate system, and the left to have a left, but these coordinates (to me) make more sense.

For this analysis I'll assume the right pedal is at 3 o'clock (pointing forward), the left pedal at 9 o'clock (pointing backward). There's no loss of generality here; it just avoids complexity in the math. I'll further assume the bike is on rollers or another form of stationary trainer. Thus the pedals are turning in circles relative to the intertial coordinate systems, but not translating through those coordinates.

This last assumption is worth discussing a bit. If the bike is moving forward, then the motion of the pedal consists of two components: a translational component (moving with the rest of the bike) and a rotational component (spinning about the hub axis). As I mentioned, power equals force in the direction of a velocity times the magnitude of that velocity. Suppose the bike is coasting forward and I'm pushing forward on both pedals but not spinning them. Is this propulsive? Does it contribute to bike motion? Well, probably not. If both feet are pushing forward, then Newton's third law (for every reaction there is an equal and opposite reaction) suggests there needs to be something else pushing backwards. Unless the rider is pushing against the ground with his foot, then this "opposite" force will be against either the saddle or the handlebars. Since I don't have Vectors in my seat post or stem, I won't be measuring these components of power. But I can generally rely on Newton's law that pulling on the handlebars while pushing on the pedals will not move the bike forward. So the only pedal velocity I'm interested in is the rotational velocity: the velocity of the pedals rotating about the hub. This is why I choose to have my coordinate axes in the frame of the bicycle, rather than the frame of the ground. These coincide if the bike is on a trainer, which is the case I'll assume.

Okay, enough of all of that. I'll continue with this next time...

Tuesday, September 29, 2009

MetriGear Vector Pt 1: Introduction

MetriGear is a new company in Silicon Valley California, which has developed a very promising product: a module of acceleratometers and piezeresistive strain gauges which can be inserted in the hollow axle of a bike pedal, provide force, pedal velocity, and power data via ANT+ Sport communication to any sufficiently cooperative ANT+ Sport head units. It is being developed first for Speedplay pedals, although there are other candidates.

Schematic of MetriGear Vector

Velocity Nation, one of the best techie cycling web sites on the web called the MetriGear Vector "by far and away the most exciting thing at (Interbike)". So what's the big fuss?

Well, first of all the Vector looks to be the Weight Weenie leader in power metrology. When coupled with shoes drilled with 4 holes (versus the more common 3) such as Bonts, Speedplay X1's and Zero Ti's, especially when tuned with aftermarket Al bowties, probably have the best combination of functionality and low weight of anything presently on the market. The first version of the Vector will add around 25 grams to the weight of a normal Speedplay pedal (50 grams for the pair). When coupled with, for example, the Specialized SpeedZone ANT+ Sport computer, easily the smallest power-equipped head unit announced so far, power metrology may be available for under 100 grams total. Truly fanatical weight weenies might even get by using the Vector in only one of the two pedals, assuming power from one pedal can be doubled to yield no power (obviously not valid with a L-R pedal imbalance), shaving 25 grams from that total.

Another advantage is the Vector is the most promising solution for tandem bicycles. Tandems drivetrains are more complex than single bikes. Related to the advantage for tandems is that it works well with track bikes. I'll write more about these later.

Still another advantage is Vector's ability to separately report power to the left leg and the right leg. It's generally considered optimal that power be equally partitioned between the two legs. Since the body is relatively biaxially symmetric, an equal division of labor limits the preferential overload of muscles on one leg. Additionally, a left-right imbalance may be an indicator of poor form which has other misaligment implications. So that Vector is sensitive to this is a big deal.

Yet another advantage, and one which got Velocity Nation excited, is Vector's capability for a high sampling rate. This is hardly a unique capability to pedal-based systems; there's no reason hub-based or crank-based systems can't also use a high sampling rate. (On the other hand, the chain-based Polar power meter, and the wind-based iBike, are incapable of high sampling rates). But previously systems have sampled at a fixed rate, for example one per second. If a higher sampling rate were used, for example 10 times per second, it would reduce the riding time which could be stored, for example 1 hour instead of 10 hours. But Vector promises to offer a variable sampling rate. Velocity Nation provides the example of the start of a kilometer time trial on the track as an application for a high sampling rate, where the first pedal stroke could be analyzed in detail.

But there's a lot more than all of this. Vector's catch-phrase is "direct your forces". The idea, they say, is to shift from a paradigm of power to a paradigm of forces. I'll discuss this further next post.

Saturday, September 26, 2009

cool stuff at Interbike

I've never been to Interbike. It's always a question of "if I take a day off from work to attend Interbike, that's one less day I can take off for (SuperTour, riding in Europe, flying out to see World Championships, traveling to any place more interesting than Vegas...). Days off are too precious. But honestly, this year I wish I'd been there.

Favorite stuff I wish I'd seen at Interbike:
  1. MetriGear Vector: Well, actually I was at their open house "dry run" immediately prior to Interbike, so I'm very familiar with what they showed there. But Metrigear are all great guys, I really love their product, and it would have been fun to see how they were received there (by all accounts quite well).

  2. the Guru Photon: Wow! A sub-700 gram custom carbon fiber frame. Incredible. It totally fails my $3.50/gram saved test versus my 860 gram Fuji SL/1 frame. And I think I'd be intimidated ordering a custom bike. After all, when I got my Fuju SL/1, I thought the slack 71 degree head tube yielding a crazy 6.75 cm trail would result in really poor handling. Yet I discovered when I'd actually ridden the thing I liked the increased stability in corners when descending. The thing just holds a line. My Ritchey Breakaway is a more racer-like 5.62 cm head tube angle. Better handling, right? Yet I prefer descending on the Fuji. Anyway, the Guru Photon is really, really cool.

  3. The Reynolds 92.2 clincher rims: see the Velonews article on these. I find this really notable not because it's the first approach to carbon clinchers which makes any sense to me. Typical clincher rims have walls on each side with a hook at the top of each. Beads in the U-shaped tire fit under the hooks, keeping the tire from popping out. These rims have no hook, avoiding the need for the material to support such large bending moments. The tire is held in place because the tire is round, the rim is round, and the rim diameter exceeds the diameter of the tire bead. In other words, the tire would need to expand its radius to come off the rim. I thought this was quite outside-the-box thinking: using three dimensions instead of just two. But then it was pointed out this is how car tires work. I've never owned a car much less reseated a car tire, so it's no surprise I find the concept a new one.

  4. The Quarq Qollector: This is a "sniffer" for ANT+ wireless signals. It pulls data out of the electromagnet spectrum and records it. This is totally cool. It means if I run multiple power meters, speed sensors, whatever, it will record them in synchronized files. Running a tandem with multiple power meters, for example a two pairs of MetriGear Vectors? No problem. These Vectors are prototypes and are sending out data related to force parameters none of the head unit manufacturers have anticipated? No problem. Someone rides past and I'm curious what their heartrate and power are? No problem. If they're in range, it records it. Very very cool.

  5. The Specialized SpeedZone ANT+ Sport Head Unit: the weight-weenie solution for displaying power data from the Metrigear Vector. Basically it gives me displayed power numbers for under 100 grams total. For Old La Honda, not so useful: I don't need power data for pacing there. But it would have been useful on Mount Diablo where there were flat sections preceding the main climb and I suspect I went out a bit too hard. No way to know in hindsight, because I didn't want to lug my beefy PowerTap wheel and Cervo head unit up the side of the mountain. A hit of around 100 grams would have been quite tolerable, however.

  6. The ride demo. I'd have loved to give a spin to some of those bikes there. In particular the Tarmac SL/3, the Gary Fisher Superfly, the LiteSpeed C1, and the Fuji SST-1.0, and any of the latest time trial frames would have been high on my personal list.

Di2 doesn't make my list. For some reason, it just doesn't excite me.

Anyway, enough of that. One of these years I'll go. Life is too short to not go see in person something I end up devoting so much attention to from afar. And among Interbikes I recall following, this is one of the most exciting years.

Sunday, September 20, 2009

Filbert confronted

Out for a Sunday spin, riding north on Broadway.... oh, the tunnel. Right on Columbus... lots of traffic. Okay, left on Filbert. Better. Oh. There it is. Up ahead...

Flashback to 2006. Frank Chan leads his famous Steepest Hills of San Francisco ride.

The crew from the 2006 Steepest Hills of San Francisco Ride, led by Frank Chan.

It's funny; when I did that ride I was feeling like I should do a real training ride instead. But I put aside the racer self, and embraced the explorer self, and decided to have some pure fun instead. A really relaxed ride, for sure, with the exception of many short brief bursts of pain.

And the worst of it all: Filbert. Filbert from Levensworth to Hyde is listed in John Summerson (The Complete Guide to Climbing by Bike) as the 4th steepest 1/10th of a mile in the United States: 31.5%. There's even a Wikipedia page on the road's steepness. Nasty.

Back to that ride: When the group arrived at the base of Filbert, it was decision time. Go, and the only out is to topple over, or stop. I stopped: unclipped, dismounted, and walked up the hill. The memory has haunted me ever since.

Years later I was telling my girlfriend that riding 18th Street from De Haro to Rhode Island, a shorter and easier climb, was "mostly mental". It's a confidence thing, I'd said. If you think you can't do it, you won't. Yet I said it knowing when the money had been on the table on Frank's ride back in '06, I'd folded. I was hardly one to give such advice. I was a fraud.

So here I was this afternoon, facing down this nemesis from the past. I'd known this confrontation would occur, eventually. Really it was the main reason I hadn't yet swapped the well-worn 34 cog on my Ritchey for a 36, which I generally prefer. And here it was: the time was now.

The view from the bottom (Wikipedia).
A couple walked by. One of them asked me if I was going to climb it. I told them it was one of the two steepest streets in San Francisco, one of the five steepest in the U.S. "No, I probably won't," I said, "It's one-way, after all -- that's my excuse."

But it's not much of an excuse. Sure, it's one-way on this block only, uphill forbidden due to safety concerns, but it's wide enough to support bidirectional traffic. The perpendicularly parked vehicles are a bit pesky. But on this Sunday afternoon, I could easily see nobody was getting into their parked car.

They moved on, and I decided to go. Without thinking too hard about what awaited me, I pushed off, clipped in, and turned into the hill.

There's not much advantage to a fast start. Momentum won't get you far on this beast. I hit it as a slow pace, then confronted the grade. One stroke. Two. Three. Too much! I unclipped, got off and walked back down the hill. Defeated, again. I'd survive the failure. Probably. Eventually.

Then I paused at the side of the road. I thought back to the advice I'd given on 18th Street. I thought back to my friend Janet's advice on climbing steep hills on a mountain bike: keep the body low & forward, chest towards the bars. This keeps the center of mass as far forward as possible, avoiding deweighting the front wheel. And bending the arms avoids pulling on the bars, which would also lift the front wheel. Standard bike geometry is not optimized for 31.5%.

So I banished the negative thoughts from my head, pushed off, clipped in, and confronted Filbert one more time.

One stroke, two, three..... four, five. I was moving. I was steady state. There was no turning back now.

The top was approaching. Two concerns drifted into my mind. One: many steep hills steepen as they approach the end of the block, a consequence of the flattening of the hillside to accomodate the cross-street. Webster approaching Broadway. 22nd approaching Kansas. I had very little margin for this to get steeper.

The other concern was the wind. It was typically gusty today, moderate by San Francisco standards, but still significant. A gust of a headwind as I crested the top would be game over.

I could feel the road steepening ominously under my wheels as the top approached. But I was fully committed. I focused on Janet's advice, and on keeping my legs moving. There it was... so close.... I was there! I'd done it! I'd used every bit of my 34/26 low gear, but I'd achieved my goal.

The guilt of the years lifted from my shoulders. I felt refreshed, free. The ride home from there was fairly effortless. Steiner, normally steep, passed without the slightest insult. Compared to Filbert, trivial.

The first thing I did was to grab my loaded Ritchey Breakaway and stepped on the scale: 69.5 kg. Then I downloaded my PowerTap data.

PowerTap data from Filbert Street

Robert Chung promoted the idea of calculating road grades from power data. It's the opposite of what has typically been done: to estimate power from the route profile. With the Chung method, if you know power, you know speed, you can estimate the wind resistance and rolling resistance, then all that remains is power going into climbing. If you know weight then you can calculate road grade.

So for rolling resistance coefficient I estimated 0.7%. This is on the high side for tires pumped to 115 psi, as I'd done with mine just prior to the ride. But Filbert is rather rough, as roads this steep must be, and cement instead of asphalt. So I viewed 0.7% as a reasonable estimate. There's also the issue of normal force versus total weight on a steep climb. Yadda yadda. Let me simply address that by saying I don't believe rolling resistance drops on steep roads. I used total weight. Feel free to debate this point with me.

For wind resistance, I used the CdA value I'd extracted from repeated climbs of Old La Honda: 0.36 meters squared. I was rather hunched over on the climb, so I viewed this value as probably reasonable. In the absence of a strong wind wind resistance really isn't a big factor on a climb this steep, and I feel the hill mostly sheltered me from the prevailing wind.

The resulting profile is as follows:

Derived profile for Filbert Street

So I get quite close to the published value of 31.5%, although clearly the block falls far short of the promised 1/10th a mile (160 meters). The data confirm what I felt: the climb steepens slightly as it goes on, with a substantial section at 32%. Wow -- 32%. That's steep.

Saturday, September 19, 2009

bike geometry comparison

Here's a comparison of some geometry numbers from 2009-2010 bike frames. I plot head tube length versus reach.

Now it's a standing question in the age of sloping top tubes what's the single best number to describe the size of the frame. The only parameters which can't be adjusted are front-center and rear-center and bottom bracket drop, so these are likely candidates. Considering the body fixed with relation to the bottom bracket by an appropriate choice of seat post length and offset, stem length and angle, the front center and chainstay length, in combination with the bottom bracket drop, determine how weight is distributed between the front and rear wheels. But it doesn't feel right to use these parameters to describe bike size. After all, a touring bike designed for a short person might have longer dimensions than the longest Cervelo road racing machine, the Cervelos known for their tight wheelbases.

The next candidate is Cervelo's favorite number: reach. This describes the lateral distance from saddle to handlebars with seatpost chosen to yield a fixed saddle setback with respect to the bottom bracket. Of course a fixed stem assumption is unrealistic, but generally one want to keep stem length within a certain range (8 cm for a short rider up to 13 cm for a tall rider) to keep a certain range of handlebar motion with steering. So for these plots I'll use reach.

The other parameter is head tube length. This is the other geometry parameter describing where the handlebars end up. I figure you generally want a head tube which requires neither a tall stack of spacers nor one which requires slamming a -17 degree stem against the end of range. You want something which puts a stem reasonably close to the head tube while allowing for some range.

I'm sticking with carbon frames in this analysis, since they tend to have internal headsets, while there's still a lot of metal frames out there with external headsets. External headsets add to the effective head tube length.

Okay, the data... click on images to view larger versions:

It's clear there's a wide range of geometries available, despite the seeming homogeneity associated with the dominance of OEM Taiwanese manufacturing (Trek and Time being exceptions). Despite this, on the WeightWeenies forum you get people all the time asking questions like "Should I get bike X or bike Y?" without providing any information about their body size or geometry preferences. It's almost like asking which shoe should I get, Nike or New Balance? Well, which one fits better?

True, pro cyclists tend to make do with the geometry of their sponsoring bike company. But there's no reason for you or me to live with that restriction.

What about me? I think I like the Madone Pro Fit geometry the best: ideally I'd like an 11.5 cm head tube @ 72 degrees, a 75 degree seat tube, and a 39 cm reach. None of the bike nail this head-on, but a bunch of them are in the neighborhood. But not all, obviously.

Monday, September 14, 2009

Old La Honda: iBike analysis

A friend of mine sent me data from his iBike, taken on a climb of Old La Honda on May 10 2009 at 8:47 am. Conditions on Skyline Blvd, the top of the climb, were cool and calm: pretty much ideal climbing weather.

The iBike records altitude, road grade, acceleration, and relative wind speed. It uses a coast-down test wherein, since applied power is zero, it calibrates wind resistance and rolling resistance to the rate the bike decelerates, wind resistance dominating initially, then rolling resistance taking over as the speed drops sufficiently. Given this calibration, it can then derive how much power is being applied to the pedals based on how the bike decelerates (or accelerates) relative to how it did so in the coast-down test, adjusting for the measured road grade. Fun stuff.


The iBike measures the altitude and road grade separately, but of course the road grade is derived from the derivative of the altitude with respect to distance. A direct measure of road grade is more accurate, but can be off slightly if the gradiometer is tilted. So the iBike calibrates a tilt offset to the altimeter over long time scales. I applied a small correction factor to the measured grades, such that the net altitude gain derived by integrating the grade over distance equaled the net altitude gain measured by the altimeter. Here's the result:

Old La Honda grade derived from iBike data

I integrated these data to generate a hill profile. Recall I'd calibrated the grade to match the total climbing with what was reported by the altimeter:

Old La Honda profile derived from iBike data

No surprises: although grade fluctuates about the mean of 7.3%, it fails to do so over any substantial length scale, so the profile is pretty much minor deviations from a straight line.

The primary point of this blog post, however, is the effect of wind speed. Plotted next is the measured bike and wind speeds. The wind speed sensor is the real novelty of the iBike (well, plus the offset-correcting gradiometer). Absolute wind speed is the difference of the two. Note the absolute wind speed is quite modest: only ±1 meter/second typical. That's ±2.2 miles/hr for the metrically challenged.

Wind speed and bike speed recorded by iBike on Old La Honda Road

Well, from the coast down data we know the relationship between relative wind speed, bike speed, and power due to air resistance. We further know total power as derived from the iBike. As was derived in this blog earlier, given these we can determine the effect of a fractional change in power on bike speed. The following plot shows two fractions:
  • the fraction of power due to air resistance
  • the fraction of speed change due to the absolute wind speed

Effect of wind on power and speed on Old La Honda, derived from iBike data

We normally think of climbing as being all due to overcoming the effect of gravity, not air. It's true the majority of power, in this case around 92% (if you believe the iBike's derivation of CdA and Crr), is divided between climbing power and rolling resistance power. Yet the effect of air resistance is still significant. The wind is fluctuating between a tailwind and headwind. This may be all real, or may be due to noise in the detector. But assuming the noise part averages out to zero, the effect of these fluctuations on speed should be quite small. For the purpose of this analysis, let's treat the wind signal as real.

It's simple enough to convert the a speed difference to a time difference. The final plot shows the deviation in climbing time due to the effect of the absolute wind speed:

Effect of wind on climbing time on Old La Honda Road, measured with an iBike

So over the whole climb, despite "calm conditions", the prevailing wind seemed to be responsible for around a 9 second reduction in the climbing time. Assuming this is typical, it goes to show that one shouldn't take differences in climbing time of on order 10 seconds too seriously. It could simply be a minor shift in the winds. Similar time differences may occur due to drafting behind other riders for a part of the climb. And if you have a good wheel to follow for the full distance, someone riding just a bit faster than you can sustain on your own, even bigger time advantages may be possible.

Sunday, September 6, 2009

another firefox memory hog post

Okay, I couldn't resist on this one.... after clicking a link to a photo-intensive page, my laptop with its measly (????) 1.5 GB RAM came to a grinding, swap-induced crawl. First, I killed the tab for that page. Okay: time to start killing the few aps which were running.... leaving only firefox, with a few innocuous tabs still open, including my training diary which I wanted to finish updating. Then I dropped firefox.

Okay, so I screwed up that screen grab big-time. But if you could actually read it, you'd see 940 MB freed up by the death of the bloated firefox beast. Wow.

Okay, vent done. Back to cycling....