Reflections on the potential of human power for transportation

Monday, December 30, 2013

The Technical History of the Bicycle: Part 3, The Safety Bicycle



This final installment of the “Technical History of the Bicycle” will take us from the Michaux velocipede to the modern safety bicycle. The modern bicycle owes it current configuration largely to the use of the chain-and -sprocket drive. The details of the evolution of the chain and sprocket drive and related multi-speed transmissions are covered in Frank Berto’s comprehensive book, “The Dancing Chain” so I refer those interested in the associated details to that source. Here we will discuss the evolution from a higher level and discuss some of the interesting dead ends that were developed along the way.

McMillan’s bicycle, discussed in Part 2, had almost all of the characteristics we associate with the modern bicycle.

To clarify that assertion, let me list five features of the bicycle. Of note, because of several record performances by Fran├žois Faure on a recumbent during the 1930’s, the Union Cycliste Internationale, UCI, came up with some very specific dimensions for a racing bicycle to prevent recumbents from being considered valid vehicles for competition. For the purposes of discussion I will keep things more general.

1       1. Two inline near-equal sized wheels 20 to 30 inches in diameter
2      2. Steering by rotating the front wheel about a semi-vertical axis
3      3. The rider seated between the wheels with the pedals below the rider
4     4. The pedals drive the rear wheel
5     5. The ratio between pedal rotation and wheel rotation can be something other than 1:1

The problems with McMillan’s design are a result of the crank-rocker mechanism he used. The ratio of pedal strokes to wheel revolutions is fixed at 1:1. The pedal cadence must be low due to kinetic energy fluctuations in the limbs (the fixed-gear nature of the drive helps with this). The drive has dead spots at the ends of travel. The direction of pedal motion does not point to the rider’s center of gravity, which would maximize the development of pedal force. This drive, also known as a harmonic treadle, is still found in children’s kiddie cars where performance is not an issue.

It appears that McMillan did increase the diameter of the drive wheel to get more vehicle speed per pedal stroke.

When Pierre Michaux added pedals to the Draisienne, the pedal location being in front of the rider necessitated that they attach to the front/steered wheel. The limitation that one crank revolution resulted in only one wheel revolution caused increasing drive wheel size to get more speed, a trend that was only limited by the necessity that the rider be able to straddle the wheel. These vehicles were known as Ordinaries, Penny Farthings, High Wheelers (I suspect the latter term came into use only after the safety bicycle became common) or just plain Bicycles. To minimize the coupling between pedal thrusts and steering inputs, the steering axis was nearly vertical and the direction of applied pedal force was vertical as well. This placed the rider directly over the front wheel where only the slightest obstruction to wheel motion caused the rider to pitch forward into a “header”.

Despite the header tendency, the ordinary became quite refined. Tangent spoking of the drive wheel, double-butted tubing, ball bearings, ergonomic saddles and handlebars were improvements on the basic design. And I must admit the simplicity of the Ordinary made it a beautiful machine. In fact, I saw a touring exhibit of bicycles from the Smithsonian during 1976 that featured a restored 1888 Columbia Light-Roadster Ordinary with its black frame and nickel plated accents. It was, and remains, the most beautiful bicycle I have ever seen.

Although Frank Berto points out that a front-steering, rear-chain drive safety precursor was built as early as 1869 by Meyer and Guilmet, the majority of attempts to remedy the “header problem” stayed closer to the Ordinary design. 

To reduce or eliminate headers, three approaches were taken in addition to the modern safety design. The rider was moved back from over the large front wheel by an intermediary-drive mechanism. The front wheel was reduced in size and some type of gearing was used to increase the wheel-pedal rotation ratio. The ordinary was turned around with the big wheel in the rear doing the driving and the little wheel up front doing the steering.

Several bicycles employed crank-rocker linkages. The rocker link oscillated back and forth, moving a connecting rod that caused a crank to rotate. Pedals could be attached to the rocker link or the connecting rod.

The Singer Xtraordinary from 1885 used a crank-rocker linkage to move the pedals back from the driving wheel and reposition the rider. The pedals were attached to the connecting rod (similar to point C, above) so the pedal path was egg-shaped but almost elliptical. The long axis of the path was oriented at an approximately 45deg. angle with the larger arc facing away from the rider. Unlike having the pedals attached to the rocker link, which stopped moving at its extremes of travel, the egg-shaped pedal path kept the feet in continuous motion, more like a circular-pedal path then a pseudo-linear pedal path.

The Facile and Geared Facile from 1887 (below) also used a crank-rocker linkage to move the rider rearward, but in this application the pedals were attached to the rocker link (point B, two pictures above).




 

















With the regular Facile, the cranks were connected directly to the front wheel. With the Geared Facile, the cranks were interconnected by an axle that rotated freely in the front wheel hub. There was a gear attached to the connecting rod that drove a second gear attached to the wheel. If the tooth count on the crank gear was Nc and the tooth count on the wheel gear was Nw, then for each pedal revolution the wheel would move 1+Nc/Nw revolutions. This would allow a smaller wheel to be used and maintain the same vehicle-to-crank-speed ratio. I must confess that the Geared Facile is my favorite linkage-driven Ordinary bicycle because of the elegance of the drive mechanism.

The crank-rocker mechanism was used in numerous bicycles in the late 1800’s. As mentioned elsewhere, the problems associated with dead-spots of these linkages were reduced because whenever the wheel moved the linkage moved. The kinetic energy of the system kept the pedals from stalling at the ends of their travel. Many examples can be seen in Archibald Sharp’s xtraordinary book, “Bicycles and Tricycles: An Elementary Treatise on Their Design and Construction”, published in 1896 and republished by MIT Press in 1977. (Thank you D.G.W.!)

The Kangaroo Safety from 1884 employed a split-crank approach.  There were chain-sprockets on either side of the wheel hub and crank sprockets attached to each crank arm. Chains connected the crank sprockets to the wheel sprockets. This allowed the virtual center of the crankshaft to be located below the wheel center and the wheel to be geared-up and therefore made smaller in diameter. One wonders if the backlash between the two pedals through two chain drives was disconcerting to the novice rider.

























The Crypto-Bantam Safety used an internal crank-hub planetary gearbox to increase the front wheel speed and allow a drastic reduction in wheel size.

The model above was an early version of the design from the 1890s. The clean lines and triangulated frame look very modern and the rider’s position could almost be called semi-recumbent. I suppose this should be no surprise since the planetary-hub drive located in the front wheel is a recurring favorite approach for recumbent designers.

One obvious solution to the Ordinary’s header problem would be to turn the design around, which is what was done with the Eagle from 1890. Unfortunately, since the conventional Ordinary’s saddle location was slightly behind the wheel hub, the Eagle may have had the tendency to tip backward. 


The American Star from 1884 took the Eagle concept and added a novel drive system to allow the saddle to be located in front of the wheel hub.


The Star was driven by what I will call a constant-torque treadle. Of the precursors to the modern safety bicycle, I saved the Star for last because of its transmission. After the chain and sprocket drive, the constant-torque treadle is probably the most popular alternative transmission. I tallied at least 16 uses of this approach, the last being a bicycle from the 1990’s.

Unlike the crank-rocker mechanism (or harmonic treadle) the constant-torque treadle has essentially a constant ratio between pedal speed and wheel speed. The average output torque over a pedal cycle is about 1.5 times that of a rotary-crank drive.

 The cable  is wrapped around a pulley that is connected to an output shaft by a one-way clutch or ratchet. Applying force to the pedal lever causes the cable to unwind and stretches the return spring. The rotation of the pulley causes the output shaft to rotate. Removing the force causes the cable to wind back up due to the force of the return spring. As the pulley rotates to wind the cable back up, the output shaft remains stationary.

The tensile member could be a cable, a belt or a chain. The cable mounting location on the crank lever can be varied to produce different gear ratios. The individual pedal levers are often coupled so as one moves forward the other moves back. The cable drums can be made non-circular to cause the gear ratio to increase from beginning to end-of-travel (Of course this makes the drive an increasing-torque treadle instead of a constant-torque treadle!). Prone to dead spots at the ends of travel like the crank-rocker, it nevertheless appears to have demonstrated outstanding performance in climbing very steep hills when low pedal cadences were used. I will go into more detail on the reasons for this performance in an upcoming post on human-power production.

That brings us to the Rover Safety of 1887, what historians consider to be the first true safety bicycle.

Let us agree that all of the bicycles we reviewed were safer that the conventional Ordinary in terms of addressing the header problem. Then way, among a consumer base that was very pro-Ordinary, did this design become the new standard? By moving the propelling function to the rear wheel and having the front wheel only do the steering, the problem of pedal forces causing unwanted steering inputs was eliminated. The gear ratios could be easily changed, originally off the bike but later while riding. However, I do not feel that either of these improvements were enough to supplant the modified-Ordinary approach. The most profound advantage was the modern safety bicycle was significantly more aerodynamic than the Ordinary. And given the lure of the bicycle is that one could travel faster than any other non-motorized vehicle at the time, greater speed was an improvement that could not be ignored. Traditional Ordinary riders initially said the safety bicycles, like tricycles, were for older individuals and people with families who could not risk injury, but when faced with being passed by riders on safety bicycles, they dropped the taunt and changed horses.
The improvement in performance in an article of sporting equipment is difficult to ignore.

The 1930s saw a resurgence in horizontal, recumbent bicycles (the laid-back rider orientation had periodically surfaced previously, but this approach was not singled out for its improved speed potential) and they were beginning to show dominance over the modern safety bicycle in at least short-distance track competitions.

This might have been another step in bicycle evolution but the Union Cycliste Internationale decided to intervene and made the decision that these new designs were offering unfair advantages to their riders.  As mentioned in the beginning of this post, they came up with dimensional requirements for racing bicycles that would exclude recumbents from competition.

One might have been forced to wonder what the next stage in bicycle evolution would have been like, but due to the efforts of Prof. Chester Kyle at the University of California, Long Beach, bicycle evolution was resumed with the formation of the International Human Vehicle Association forty years later.
From a racing perspective, the bicycle may be near its performance limits. The flying 200m speed of 83mph and the hour-long speed of 56mph will no doubt be eclipsed, but not by great amounts. From a bicycle evolution standpoint the frontier is improving commuter vehicle performance to the point where, in first-world countries, the bicycle is more than just a commuter novelty for the enthusiast, it is a viable ecologically friendly alternative for the masses.
 
Hephaestus

Friday, December 6, 2013

The Technical History of the Bicycle Part 2: The Wheel Gets Cranks and Pedals



As was discussed in the first part one of this series, the Draisienne seated scooter, many of the aspects of the modern bicycle were realized with one quantum leap of inventive genius. The obvious shortcoming of the design was that the vehicle could move forward no faster than the rider could move his leg backward. The running-style leg kick propulsion needed to be replaced.

What may not have been realized by the would-be inventors of the time was a mechanism was needed that would reduce the speed of limb motion and allow use of greater limb force. The assumption here is that the arms, the legs of both would be used to propel the vehicle.

In hindsight, a crank attached to a wheel is such an obvious and simple solution, one wonders why it took almost 50 years after the Draisienne to be incorporated. As is the case with many simple solutions to problems, they are derived from more complex predecessors. The crank was a piece of a more complex drive mechanism.

The first recorded attempt to add non-running propulsion to a Draisienne was by Lewis Gompertz in 1821.



Mr. Gompertz added a rocking crank with a gear sector which drove a pinion gear attached to the front wheel by a one-way clutch. Although this approach as a technical dead end, it is interesting for two reasons. It was the first case where the rider had to propel and steer a bicycle with the same mechanism. This would become a recurrent theme for inventors trying to add arm power to the bicycle. The one-way clutch the drive used is also of interest since the stresses associated with ratchet-type devices are very high due to the small size pawls reacting large forces.

The next attempt at adding non-running power to the bicycle was by Kirkpatrick McMillan in 1839. While McMillan’s invention was also a dead end, a similar drive system would be the direct antecedent of the crank drive. The drive would also be resurrected numerous times by would-be bicycle innovators.

Both Gompertz and McMillan’s approaches reflect the thinking that what was needed was a mechanism to convert linear motion to rotary motion. The arms or legs moved in large arcs which approximated linear motion and the bicycle’s wheel rotated. This thinking overlooked the fact that arms and also legs could comfortably move through rotary motions.

The classic approach for converting linear to rotary motion is known as a crank-slider mechanism, which was used in steam engines and later internal-combustion engines.



Since a stable sliding link associated with this mechanism is difficult to build without incurring undesirable frictional losses, a long rocker link is often substituted for the slider when pure linear motion is not required. (The kinematics guru at the U. of Wisconsin, John J. Uicker Jr., often said “Never use a slider if you can use a pivoting link”.)



 McMillan used a crank-rocker mechanism to drive his bicycle. McMillan mounted his pedals on the rocker link. Often, when a crank-rocker mechanism is used for human-powered propulsion, the pedals are attached the connecting rod. Now various pedal paths can be obtained with mounting the pedal on this link. If the pedal is mounted in position A, the pedals go in a circle. If the pedals are mounted in position B, the pedals go in an arc. If pedals are mounted in a location between A and B the pedal path is an asymmetric tear-drop shape, a hybrid of the arc and the circle.

In a typical bicycle-development scenario, the next and final step in bicycle propulsion occurs in 1861. One story relates that Pierre Michaux, a builder of perambulators, invalid carriages and three-wheel velocipedes, added pedal cranks to a broken Draisienne he was repairing.



During the period between McMillan’s bicycle and Michaux’s bicycle there were other wheeled human-powered vehicles being built. Four wheel vehicles called velocipedes (not to be confused with the term applied to the later Michaux-style bicycle) were being produced.

One such velocipede, made by Willard Sawyer, may have provided Michaux with the idea of mounting pedal cranks directly to the front wheel of a Draisienne.



Sawyer used crank-rocker mechanisms to drive his velocipedes. The cranks were double-sided allowing the connecting rods to be mounted between the wheels. In some cases the cranks drove the rear wheels and the rocker links were in front. In these cases the straps to hold the feet were near the rocker links and consequently the feet moved essentially back and forth along with the rocker link. In other cases, like the vehicle in the photo above, the cranks drove the front wheels and the rocker links were located in the rear. The foot straps were located close enough to the cranks that the feet essentially moved in near-circular paths. In fact, with drive mechanisms oriented in this fashion, the connecting rod acted like a pedal, providing a pivot between the foot and the crank.

Since Michaux worked on velocipedes of this type, it is not a stretch to assume he saw this type of mechanism with the double-sided cranks attached to the two drive wheels and extrapolated the idea of a single-sided cranks attached to a single wheel with pedals replacing the connecting rods. 
 
And that, as they say, is history.

Pedal cranks are simpler and more efficient than the crank-rocker mechanism. Nevertheless, the crank-rocker mechanism will reappear in the final stage of bicycle evolution, the development of the safety bicycle.

Before we leave this second part of the technical history of the bicycle, let’s take a parting look at the crank rocker mechanism but with a few substitutions. We will reuse the pedal cranks attached to the wheel. In the role of the rocker link we will use the rider’s upper leg and in the role of the connecting rod we will use the combination of the rider’s lower leg and foot. (Since there is often not much motion between the foot and lower leg, for the purposed of this exercise we will consider the pair a single link.) So the conventional bicycle is still propelled by a crank-rocker mechanism, but with the rider providing two of the links.



I mentioned the efficiency of the pedal-crank-drive approach when compared to other approaches. The efficiency stems from two effects.

First, the thigh, shin and crank mechanism has a relatively constant kinetic energy associated with it. I am referring to the energy stored in the moving thigh and shin. In mid-stroke the thighs are rotating fastest while the shins are rotating slowest. Conversely, at the top and bottom of the stroke where the thighs reached their extremes of travel and have stopped rotating, the shins are rotating their fastest. This near-constant kinetic energy of this system allows for extremely high pedaling cadences. Cadences of 300rpm have been recorded, five revolutions per sec., by Reg Harris, the famous British track cyclist. Harris had an amazingly muscular lower body and, as a result, a lot of kinetic energy stored in this spinning legs.

The second effect is that the pedal-crank mechanism allows for power production to be pulsatile as opposed to continuous. Each leg produces power over approximately 25% of the stroke (this assumes the rider is only pushing down on the pedals and not pulling up, but even so, these two motions utilize different muscle groups.) I have mentioned in previous posts that power production is more efficient with a work-rest cycle instead of a constant work cycle. The is probably due to the fact that the rest period allows for the aerobic energy sources in the muscle to be replaced easier than if the muscle has no rest period. (More on the biomechanics and bioenergetics of human power production in an upcoming post…)

So the crank-pedal method of bicycle propulsion has endured not only because of its simplicity but also because of its efficiency.

Hephaestus

Sunday, September 1, 2013

The Technical History of the Bicycle: Part 1, The Draisienne Seated Scooter



Few would dispute that the bicycle is the most efficient means of converting human power into vehicular motion. It satisfies numerous functions while being extremely simple and light weight, in part, due to the fact that most of its components do multiple roles.  With a bicycle, a runner can double his speed for the same level of effort.

The modern bicycle is a result of multiple contributors to numerous to mention. Most bicycle historians list at least four significant steps in bicycle evolution. Those being:

1.       The Draisienne seated scooter
2.       The velocipede or boneshaker
3.       The ordinary of high-wheel bicycle
4.       The safety bicycle

 Since the ordinary is just a velocipede with un-equal-sized wheels, the above vehicles introduce the three technical innovations I have listed below.
1.       The seated scooter
2.       Leg pedal cranking
3.       Chain and sprocket gearing

It is hard to over emphasize all the factors that fell into place when Karl von Drais invented what he christened the laufmachine (running machine). Von Drais had studied mathematics and mechanics in Heidelberg but worked as the master of forests for the Duke of Baden. It has been speculated that he was looking for a faster alternative to walking the forest paths when he invented his seated scooter, now known universally as the Draisienne.
As one would expect it all begins with the wheel and walking. If, in the early 1800’s, you didn’t have a horse, you walked from place to place, or ran if you were in a hurry.  To explain the popularity of the Draisienne, it is useful to compare it to walking and running using four factors involved in a moving human.

Stride length
Cadence
Efficiency
Postural support

Speed is the product of cadence and stride length. (Stride length is analogous to gearing in machinery).  Now, runners go faster than walkers because their cadence is higher and their stride length is longer. A walker’s stride length is just the maximum spacing between the feet at the end of a step cycle, because, by definition, a walker always has one foot on the ground. A runner, on the other hand can have both feet off the ground simultaneously. As a result, during the period of time that the runner is flying through the air, the effective stride length is increased over the maximum foot spacing.


 The great Cuban middle-distance runner Alberto Juantorena airborne.

With walkers, rearward leg motion is accompanied by the entire body moving forward.  With runners, the period of the leg accelerating the body is shorter and when airborne the motion of the leg is only moving the mass of the leg. So, on the average, the runner’s leg motion is associated with significantly less mass than is the walkers. For a given force, the acceleration can be greater when moving a lesser mass, so a runner’s cadence is higher than a walker’s.

A wheel rolling on a horizontal surface provides vertical support but allows horizontal motion with low resistance. Von Drais realized that if you supported a rider on a wheeled vehicle whose seat height required that the leg be almost completely extended to touch the ground, the airborne phase of running could be extended into a gliding phase where the backward leg stroke resulted in an enormous stride length. Even though the forward speed of his running machine could not exceed the maximum speed the leg could be moved rearward, the time that the vehicle stayed at that speed was longer and therefore running speed could be maintained with less effort.

Von Drais may not have appreciated that, as a result of the short-duration kick and long-duration glide associated with the running machine, the aerobic efficiency of moving the vehicle was improved over walking and running.

For a given level of aerobic power generation, the oxygen consumption is lower if the power is produced in short-high-amplitude pulses with longer rest intervals as compared with longer-lower-amplitude pulses with shorter rest periods.  As a graduate student, I was able to demonstrate this effect using a pedal drive with an adjustable, cyclically-variable-gear-ratio. I measuring instantaneous mechanical power, average mechanical power and oxygen consumption. My speculation as to the cause of this effect is that the longer rest periods between the power pulses are more conducive to replacement of chemical stores in the muscles than during activities with shorter rest periods.

And, since the rider was seated and could additionally support his body with his arms, the running machine reduced the energy necessary for postural support when compared to walking or running.

Now all the gains associated with the Drasienne could be realized as long as the weight of the vehicle was not excessive. This was no mean feat when wagons and carts were constructed mostly of iron and wood. The obvious solution to minimizing weight was to limit the number of wheels the vehicle had, but could one make a controllable vehicle using only two wheels? Despite the biomechanical improvements associated with a kick-and-glide propulsion approach, the real quantum leap von Drais made was creating a two-wheeled vehicle that could be balanced.


The fascinating thing is that there were no precursors to the Draisienne. Earlier bicycle historians postulated that things began with a child’s stick horse. A wheel is added to the bottom of the stick, and then another wheel is added inline with the first. This is then scaled up to adult size and the antecedent of the Draisienne is created. Not only is there no solid historical evidence for this scenario, but more importantly, the two wheel version of the stick horse could not be balanced.

 Here is a key point. The ability to steer is necessary to balance an inline-two-wheeled vehicle.

Why are steering and balancing linked in the function of a dynamically-stable two-wheeled inline vehicle?
Let me propose a simple model of the bicycle-rider system, possibly a bit too simplistic for the academic dynamicists out there and it does leave out things like the precessional effects of the wheels. But it did aid me in understanding what was going on during ten years of experimenting with rear-steering recumbent bicycles.

The two mechanisms that allow a bicycle-type device to balance are castor and lean-steer. Consider the bicycle as a system with two masses and three-degrees-freedom for motion. The front mass consists of the wheel, fork and handlebars. The back mass consists of the rider and the rest of the vehicle. The front mass is attached to the back mass by a pivoting connection. From a disturbance standpoint, we will ignore one motion DOF, that being the bicycle moving forward. The disturbance motions are the fork mass pivoting with respect to the frame mass and the frame mass leaning from side to side. The two disturbance motions are not independent and the nature of their coupling is determined by the steering geometry of the vehicle.
Now for castor to occur, the contact point of the front wheel with the ground must be located behind where the steering axis intersects the ground, where behind is defined as opposite the direction of motion. For any angular disturbance of the fork mass, castor results in a moment being generated that tends to reduce the disturbance until the contact patch is inline with and behind the steering axis.

Lean-steer occurs along castor as long as the steered wheel is at the front of the bicycle. As you lean a bicycle to the side you will observe that the fork mass rotates toward the direction lean. A disturbance that causes the frame mass to lean results in the fork mass steering the vehicle in the direction of the lean. The vehicle is now going in a circle and the radial acceleration associated with the change in direction picks up the frame mass and corrects for the lean disturbance.

So the amazing thing is that von Drais could not evolve his design based on non-steered precursors but has to create it in one quantum-leap of imagination.

Notice for the Draisienne restoration above the steering axis appears to be located near the front of the triangle supporting the front wheel and the axis is near vertical. The contact point “trails” the steering axis by almost half a wheel diameter. Compared to a modern bicycle with several inches of castor, the Draisienne has a many times that. However, the friction associated with the largely wood on wood steering pivot is much greater than that associated with a ball-bearing steering headset. The torque of the castor moment must overcome this friction to return the fork mass to being aligned with the direction of motion.  So a significantly greater amount of trail would make sense.

The weight of the Draisienne was about 44lb. With no cushioning from pneumatic tires or frame compliance, let alone suspension, the ride must have been bumpy on all but the smoothest of roads. Prior to inventing the Draisienne, von Drais was a forester. The mountain biker in me would like to imagine him gliding along smooth single-track trails, but there is no documentation of this. Since horse’s hooves and rain make for very bumpy roads, the opportunities for extended gliding might have been less than frequent.

There we numerous variations on the Draisienne, mostly involving changes made in the materials of construction but probably with little weight saving. Whether referred to as the Draisienne, the hobby horse or the dandy horse, the outlines of the modern bicycle are unmistakable. It would take over 40 years for the next step in bicycle evolution to be invented.
Hephaestus