You are still incorrect. For the familiar bicycles we ride every day, trail is the most important factor governing bicycle self-stability. Sure, you can read the supporting text for the Science paper and find a half dozen or more two-mass-skate bicycles with surprising stability properties, and there may be more to discover, but if they do not reflect the properties of the designs we have found to be useful, or suggest new alternatives, then the analysis is of purely academic interest.

Here's A. L. Schwab, one of the authors of the Science paper, explaining that not only does mass distribution have "a strong influence on bicycle stability, but so do gyros and trail". Now, even though the Cornell-Wisconsin-Delft team avoid ranking the importance of these factors, we know, through experiment and analysis, that trail is a very relevant factor influencing the stability of the familiar bicycles we ride every day. You have been consistently discounting this very important factor.

Sigh...

On the contrary, the Science paper mentions that negative trail can have a dramatic effect on bicycle stability: "When Jones modified his bicycle by placing the front-wheel ground contact in front of the steer axis (negative trail, c < 0) he could not ride no-hands." Have you read the paper?

One of the most surprising results is that it is possible to construct an unusually weighted "bicycle" that remains stable despite having slightly negative trail. However, this has little relevance to the practical sort of bicycles we ride which lack large amounts of mass ahead of the front wheel.

First, try googling "bicycle castor". You will find that the unfortunate clause in the Wikipedia article you cite is the only reference on the internet that equates caster with trail. The word "caster" when used with regard to vehicle suspensions refers to an angle, not a linear measurement. The confusion probably arose due to the fact that castor angle can be inferred from rake, trail, and wheel size, which are all linear measurements.

Trail is a guideline used by bicycle designers. It is neither necessary nor sufficient for stability: The authors of the Science article (sources and preprint here) built a stable negative-trail "bicycle"; and they show that the eigenvalues for conventional bicycles are unstable above a critical speed. However, the suggestion that trail - the largest force affecting steering - is irrelevant to the stability of conventional bicycles is ludicrous. You can do the math and calculate eigenvalues as you alter trail, or simply ride a bike equipped with an adjustable trail for to see this for yourself.

To quote Jim Papadopoulos, "perhaps the main message is that our reasoning about how trail affects bicycle stability has been quite wrong for 120 years". This is not a denial that trail affects stability, but rather a search for a better model. Unfortunately, that better model has not yet yielded any insights of use to the designers of actual ridden bicycles.

Forget about the handlebars for a moment. The fact is that you can't turn to the right unless your center of mass is to the right of the bicycle's wheels. If you try to turn from a stable position, you will soon find yourself fall to the left and will crash unless you correct your course by turning left. That's the crucial point.

OK, so how do you get your center of mass to be positioned to the right? Most riders do so by countersteering - turning slightly left first. Most riders are not conscious of this process. There are other ways. You might hop the bike to the left, or tilt the bike and rely on the curvature of the tires. As a somewhat proficient unicyclist, my eyes have been opened to the variety of subtle influences that can influence the behavior of a wheel, so, sure, pushing handlebars is not the only way to turn.

FWIW, I built myself a nice road bike a little while ago with a subtly more stable frame (combination of wheelbase, angles, trail) than is currently in fashion. It is quicker at turning than my old bike because I can apply a lot of countersteering while keeping better control through the middle and exit of a turn.

Well... Bicycle frame builders don't talk about caster, which refers to an angle related to head tube angle and possibly rake (I'm not sure which angle it actually refers to). We do talk about rake (the distance the fork is offset from the steering axis) and trail (the distance between the point where the steering axis intersects the ground and the vertical projection of the wheel axis onto the ground).

Unfortunately, you are misinterpreting the conclusion of the very interesting article you cited. The fact that a highly unusual, riderless "bicycle" with bizarre mass distribution happens to be stable does not invalidate the fact that trail forces are the most significant contribution to stability in conventional bicycles. If you don't believe me, read the literature (starting with the article I cited earlier) or ride a bike built with zero or negative trail.

By the way, the authors of the study you mentioned are friendly and eager to discuss their results. They joined the framebuilders forum (now a google group) and contributed to the discussion we were having about the article. Unfortunately, they are not able to relate their result to conventional bicycles. The best insight they are able to offer about it is that the eignevalues for their weird machine indicated stability.

Not so - shifting your weight does not alter your center of mass. Weighting the outside foot is good practice for aggressive riders whose inside pedal might otherwise strike the ground in a sharp turn.

I don't see what makes bicycling "nerdy", but if that's what you are looking for try a unicycle.

This paper" states that "contrary to common belief, gyroscopic forces play only a limited role in balancing and steering". The "feel" of a bike (pedal or motor) is said to be dominated by "trail", and aspect of steering geometry; gyroscopic torque is "non-negligible", but "much smaller than trail torques".

Gyroscopic steering is said to assist no hands bicycle riding, but I'm not a motorcycle rider and don't know about wheelie stability.

Nope. Memory is allegedly an issue for Ni-Cd batteries, and then only for very specific usage patterns. Li-ion does not exhibit this type of problem.

On the other hand, Li-ion cells lose capacity with time, whether or not they are being used. The capacity loss is faster at higher temperatures and if the battery is kept at full charge - exactly the environment in a plugged-in laptop that sees a lot of use.

Nah. Li-ion cells are charged at constant current (typically 0-8-1C) until they reach their target voltage (4.2V), then held at constant voltage until the current drops below the minimum charge current. No fancy curves, usually no adaptation for health.

The trick is balancing the charge in multi cell batteries (not necessary for NiMH which tolerate a little overcharging), thermal management, "gas gauge" status, etc.

Apple uses li-poly (soft pouch) cells in their batteries, which do require a battery management system for protection. Most other brands use 18650 (cylindrical) cells, which have built in protection and will not explode due to over/under charging or thermal runaway. As a rule, li-poly has better energy density but doesn't last as long.

See the most recent Antikythera mechanism paper [Nature V468 P496, 25 Nov 2010] for proof that our knowledge of the mechanism is incomplete. For example: "Evans’s hypothesis forces a rethink of other parts of the mechanism, too. Previously, scholars assumed that the positions of the Sun, Moon and planets were all displayed around the same zodiac scale. But if the zodiac scale had been tweaked to accommodate the varying speed of the Sun, it would no longer be accurate for showing the positions of the other bodies."

Note that the gearing for any planet display is missing from the fragments of the mechanism. Even if we had instructions about these presumed dials (which we do not), the actual gearing is still a matter of speculation, not certainty.

It implements some of the same math, but misses some features of the original. For example, I don't see the pin and slot drive used to approximate the varying angular velocity of the moon due to its elliptic orbit. Nor the spherical phase of the moon display on the front dial.

More importantly, we can only speculate about features that have been lost to history. Estimates of the gear count range from 30 to 70. No one today known for sure.

Still, it is an impressive bit of lego work!

I run a Taig tabletop CNC mill and I have to wonder if you would be frustrated with the capabilities of a $400 CNC router like this. Approach it like a mill and you will find problems with rigidity, vibration, backlash, accuracy, speed, etc. I find it hard to imagine anything more aggressive than engraving aluminum on a machine like this - even my Taig with its 2.5" square steel column and real ways has to work hard to get the job done. BTW, you won't need coolant for aluminum if you have proper spindle speeds. A little compressed air spray will keep the end mill downright cool.

Also, I do not suggest HDPE for mold making unless you know what you are doing. The surface tends to form a fuzzy mess when coutouring 3D shapes. Try machinable wax instead - it machines beautifully and has a higher melting point.

The phrase "inherently fallible" is part of the headline of this recent Eureka Alert regarding Biometrics. Original work by the National Research Council.