On Bicycles, and.... what else is there?

Steve Hill has proposed a preliminary route for stage 3 of the 2010 Tour of California . Check out his map here . However, this prediction is, well, a bit dull. Basically repeating what was done in 2009 with the exception of the crossing of the Golden Gate Bridge from Sausalito, We already know that there will be an extra climb on this year's route. This one actually has one less climb, omitting the climb out of Sausalito. So I propose an alternate. It adds only 8 km to Steve's route, from 194 km to 202 km. But it's more a quality thing than a quantity thing. Here's my map. Steve's route has riders turning right at the top of Tunitas Creek Road, climbing briefly on Skyline Blvd. before descending to Highway 84, then descending 84 and continuing the final 10 km of that road to the coast. Yawn.... Instead I propose they cross Skyline at the top of Tunitas, descend technical Kings Mountain Road, turn right on Highway 84, left on Portola Valley Road, right at ...

In the last post I discussed some data Metrigear presented on their blog showing accelerations measured at the pedal spindle, decomposed into radial and tangential components. I wanted to step back and discuss the derivation of power from pedal speed. Okay, to be honest I'd prepared this blog post and skipped past it to post the one responding to Metrigear's data. So I'm a bit out of sequence: this one was mostly written before the Metrigear post. Mechanical power is the component of force in a particular direction times the speed in that direction at which the power is being applied. We've already worked out the force components, and determined the direction of propulsive power, so all that remains is to determine the speed along that direction. So all that remains is to determine the speed along that direction. We'll assume again the coordinates of the right pedal: Axes for right pedal The propulsive force is applied in the x direction, which is a fixed d...

The last post in my Metrigear series I conjectured how the Metrigear determined which direction was propulsive. Since the spindle spins with the pedal stroke, but since acceleration due to orbital motion is always in the same direction, averaging over time indicates which is the direction to the center of the orbit, and the propulsive direction is orthogonal to this in a well-defined way depending on if a pedal is a right pedal or a left pedal. So all that's left is to determine how fast the pedal is moving. Given a crank length L , each revolution of the pedal the pedal moves a distance 2π L , or using the definition of a radian, each time the pedal moves though an angle of one radian it moves an arc length L . So if we know the angular rate at which the pedal is rotating, and we know the crank arm length, then we know the rate at which the pedal is sweeping out its orbit: its orbital speed which we multiply by the force in the orbital direction to derive propulsive force. I w...

Last post I made an estimate of my power up Soda Springs road on Saturday. It's worth doing an estimate of possible errors with this: body mass : around 1 lb equipment mass : let's say 1 lb rolling resistance coefficient : 20% seems reasonable. This was really seat-of-the-pants. wind drag coefficient : 10% seems about right distance 0.1 miles. Exact starting location, the placement of the finish, and line through the corners are all factors altitude gained : 15 feet sees consistent with individual reports wind speed : Zero was assumed. Given variable winds reported at Redwood Estates , a conservative estimate of error of this estimate is probably 1 mph transmission coefficient : based on differences in chainline, I'll say 1%. This doesn't affect the derived Powertap-equivalend power, but it does affect the significance of comparisons in power from one ride to the next. time : 2 seconds seems good: 1 second with recording the finish time, and 1 second for a delay i...

The Soda Springs Low-Key went rather well in most regards. As a participant,I was pleased with my finishing place. I usually train with a PowerTap , but for most races (especially hillclimbs!) I leave the powertap wheel home and instead use a carbon race-only tubular (either my Reynolds MV-32T or my Mt Washington). On hillclimbs, though, I can generally estimate the power. The key parameters are total weight, rolling resistance coefficient, wind drag coefficient, and air density. For PowerTap-equivalent power I do not need drivetrain efficiency, since drivetrain losses aren't measured by the PowerTap, anyway. Given these, it's simple enough to calculate power from speed. So, some numbers: weight : I was 125 lb in the morning upon wakening. Given input - output, I was probably close to this at the start. Curiously, I'd been almost 3 lb lighter the last time I weighed myself two days before. A lot depends on what I've been eating and how hydrated I am. Additiona...

Saturday was another Low-Key Hillclimb , up Soda Springs Road, and once again I got to see the Vector in action as Clark Foy rode his prototype up Soda Springs Road. I'm sure we'll see data from that test on the MetriGear Blog . For now, I'll move my discussion of how I view this really cool power meter away from force and towards acceleration and velocity. The Vector's motto is "Direct your Forces": power is the product of a velocity (in this case the pedal's velocity around its circle) and the force in that direction. I've already talked about how the Vector might measure a variety of force components. The key is to convert those force measurements into a measure of propulsive power. The first problem to be solved on generating power is to determine in which direction the pedal is driving the bike. As I've already discussed, the relevant velocity is the velocity is the rotational valocity of the pedal rotating in its orbit The translationa...

The previous analysis described how local curviture of the pedal spindle might be used to extract out moments of force applied to the body: the total downward force and the twisting torque. The sensors would measure the distortion of the pedal spindle, which with an appropriate calibration factor, would yield the values of the bending moment, from which the force and torque on the pedal body can be derived. Of course, this is total speculation on my part, as I really do not know how the Vector really works: it is just a plausibility argument that (1) the problem is non-trivial, and (2) the solution may be tractible. Given the coordinate axes defined for the pedals (right pedal shown here): Axes for right pedal it is clear that this analysis applies to the force in the y and z directions, and to torques applied about these axes. For a force in the x direction, the spindle does not bend, but rather stretches. In this direction, it should behave like a linear spring: fractional str...

Back to measuring forces on the pedal: a reminder of the force diagram: Force diagram of pedal Assume the sensors measure the torque (the bending moment) on the pedal spindle at each of the associated points, x 1 and x 1 . Forces F 1 and F 2 are applied at the points x 3 and x 4 . The goal is to determine F 3 and F 4 from the measurements τ 1 and τ 2 . Simply enough: two equations, two unknowns ( F 1 , F 2 ): τ 1 = F 1 ( x 3 ‒ x 1 ) + F 2 ( x 4 ‒ x 1 ), τ 2 = F 1 ( x 3 ‒ x 2 ) + F 2 ( x 4 ‒ x 2 ). Note the second equation is the same as the first with the x 1 's replaced with x 2 's, and the τ 1 replaced with τ 2 . Multiply the top equation by ( x 3 ‒ x 2 ), and the bottom by ( x 3 ‒ x 1 ): ( x 3 ‒ x 2 ) τ 1 = F 1 ( x 3 ‒ x 1 ) ( x 3 ‒ x 2 ) + F 2 ( x 4 ‒ x 1 ) ( x 3 ‒ x 2 ), ( x 3 ‒ x 1 ) τ 2 = F 1 ( x 3 ‒ x 2 ) ( x 3 ‒ x 1 ) + F 2 ( x 4 ‒ x 2 ) ( x 3 ‒ x 1 ), and substract the two and combine terms: ( x 3 ‒ x 2 ) τ 1...

As I remain busy with the Low-Key Hillclimbs , I am trying to squeeze in some time to continue with my thoughts on the MetriGear , which I think will be the most exciting power meter to hit the market yet. As I've emphasized in previous blog posts, Vector's motto of "Direct your Forces" makes it clear the ephasis is on force, not just power. Power is a single scalar quantity for each pedal, but force contains many more components. Indeed, since the pedal rotation varies around the pedal stroke, and since the orientation of the pedal inspindle into which the Vector is installed cannot predicted, the Vector must measure multiple force components and extract the one which contributes to propulsion. Providing users with not just this propulsive force, but non-propulsive forces as well, may be beneficial to pedal stroke optimization or bike fit, as I've discussed. Key to all of this is being able to measure these forces and torques. Recall each pedal has three axe...

Despite fears of the pumpkin-seeking-hoard wrecklessly hurtling their oversized vehicles down narrow Tunitas Creek Road, yesterday's Low-Key Hillclimb was a wonderful success. First, Bike Hut. Bill, who runs Bike Hut and Potrero Nuevo Farms, met us and was super-friendly, extending us wonderful hospitality in allowing us to start our ride there. It made me wish we could start every climb at Bike Hut. I assure you as long as Low-Key and Bike Hut continue to co-exist, we'll be back. It's only too bad the ride options from that location are a bit limited: Tunitas is basically the only option. Lobitas Creek Road is an alternative start to Tunitas Creek Road, but it adds a dangerous, narrow descent on what's a bidirectional road. Then the weather: early morning fog retreated to reveal blue skies and warm temperatures. Perfect! Then the volunteers: what a great group we had! Registration went smoothly, results went smoothly, the course marshals were great, and we had...

It was clearly an act of inspired brilliance, not a brilliance of genius, but a brilliance which transcends genius in its impression: a brilliance of anti-genius. I scheduled the Tunitas Low-Key Hillclimb for the weekend of the Half-Moon Bay Pumpkin Festival . Okay, I try to be open-minded, and I'm sure there's more to it than this... but why are people willing to jam Highway 92 into a quagmire of creeping traffic to look at squash? Okay, the squash might tend to be largish, exciting I'm sure, but I still fail to embrace the thrill. Squash is good for soup. In any case, it's too late to change plans now, so on we go to Tunitas Creek, and hope the squash seekers have better sense than to toss their over-sized vehicles onto the narrow, winding descent of Tunitas Creek Road.

Wow -- Old La Honda road has worried me every since I decided to put in on the schedule. The locals don't, I'm sorry to say, have a reputation of being happy about cyclists riding up their beautiful road. And so many do -- at any given time on a weekend day there's probably around 10 of them on the 3.2 mile climb. It's perfect in almost every way: not too long, but not short; not too steep, but steep enough; decent pavement but not smooth enough to be without character; a steady enough grade to stay in a single gear all the way, but varied enough to shift if you want to; and shaded from the wind and the sun. Combined with the relatively low car traffic (maybe 2-3 cars pass on a given climb up), and it's proximity to the densely crowded peninsula, it's as close to cyclist heaven as you can find in our car-obsessed culture. But despite a few hic-cups, everything went amazingly well. This was due to the excellent work of coordinator Doug Simpkinson and all the...

Now for torques.... There's three torque modes for each pedal, or six for the pair, which I've described by using sums and differences of the corresponding torques for each pedal. I'll focus here on the torques for each pedal. First, there's T x . This is the torque driving the pedal spindle to screw into the crank arm. I say screw into because the handedness of my coordinate system is the opposite of the handedness of the threads: positive torque is counterclock for the right pedal and counter-clockwise for the left pedal, looking from the outward side of the pedal. I hope I got that right ... Since the pedal is spinning relative to the spindle, and this induces a force, this torque should generally be somewhat positive. How positive depends on how effective the pedal bearings are. Work can be calculated as the integral of torque with respect to angle. So < T xl  +  T xr &gt × cadence, where <> denotes an average with respect to rotation angle (not...

Okay, so back to the Metrigear Vector for a bit. What I discussed before was how the MetriGear Vector is trying to move the emphasis from power to force. Get force right, get velocity right, and power is automatically right. I mentioned how one can derive twelve components of force. One of these components, F rz - F lz , drives the chain, and therefore provides propulsive force. It is assumed none of the other force components are propulsive. I need to make a disclaimer here: I don't work for Metrigear, so can't be sure they make the same assumptions I do. I'm just running with the idea and saying what assumptions I might make. Axes for pedals at 3 and 9'oclock So, other than the propulsive mode, I think the next most interesting mode is F rz + F lz . This describes right-left imbalance. Obviously at any point in the pedal stroke, the right will be applying more or less torque to the crank than the left. But averaged over the pedal stroke, the difference should, ...

Well, we had some hiccups with results.... a malfunction on the timer causing times to be deleted, then some mis-shouted numbers at the finish. The combination made for a tough time untangling the results, with heavy reliance on photos. Ron Brunner saved the day by recovering results from the video. I really want to have a back-up position for double-checking numbers of finishers. Someone to check the number with the stem sticker to make sure everything is good. Good numbers are by far the most important thing in good results, especially on popular climbs where other riders are passing by, making photos tough. We've done helmet stickers to help with this before. Maybe time to break out that option again. Or a ribbon tied around the handlebars. Anyway, week 1 results are posted . Still preliminary: two riders still unidentified. Next week may be a challenge. We'll be starting in small groups to mitigate traffic impact. Turn-out might be on the high side, so we'll real...

A single point mass can aquire three independent momentum coordinates, for example along principal axes x , y , and z . The macroscopic rigid body ( i.e. not compressable or deformable) can additionally aquire momentum associated with rotation about these axes. With each momentum component, there are associated force (for translation) or torque (for rotation) components. For modeling purposes, we can consider each pedal a rigid body. There are then two times six equals twelve total degrees of freedom, constituting six force degrees of freedom and six torque degrees of freedom. For one pedal, the forces and torques associated with these degrees of freedom might be listed: F x F y F z T x T y T z where F x is the force through the center-of-mass along the x-axis, T x is the torque about the x-axis passing through the center of mass, and similarly for the axes y and z. For two pedals, one can then define separate forces and torques for the left and right pedals: F lx F ly F lz T lx ...

Okay, a bit of a change in topic.... The Low-Key Hillclimbs begin this Saturday! Very exciting. Week one is Montebello Road, an excellent road for a hillclimb: basically dead-end with a bit of steep (but not too much) and some gentler slopes in the middle to give beginners some recovery but test the pacing strategy of the stronger riders: I won't be able to ride any of them myself until week 3 (I'm working the first two weeks), but it's always great to be out there any enjoying the day, generating data. If you want to join in on the fun, but don't want to climb, please go to the website and volunteer to help! We can always use help at registration on week 1 of the series.