Reflections on the potential of human power for transportation

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

Sunday, January 20, 2013

The Prius Electric Bicycle at the Detroit Auto Show



The Detroit International Auto Show has been going on this week and the unanimous star of the show is the new 2014 Corvette Stingray. With 450 horsepower, 450 ft.lb. of torque, a seven-speed manual transmission (starting to sound like derailleur transmissions here) and a 52K$ price tag, the ‘vette excited a lot of sports-car minded attendees and journalists.

While the Corvette launch is typical fare for large auto shows, what is less typical is the presence of vehicles at the other end of the horsepower spectrum, electric bicycles. Both Toyota with its Prius Parlee and Daimler AG with its Smart E-bike displayed models.
 
http://www.triplepundit.com/2013/01/years-detroit-auto-show-concept-car-bikes/

 The Smart bike is shown below.

This is not the first time that vehicles with pedals have show up at large auto shows. In 2011, Ford displayed an E-bike at the Frankfurt Auto Show, but Europe has always taken the bicycle more seriously that the US as a transportation alternative to the car. I like to think that the appearances of these bikes in Detroit is an acknowledgement that human-powered commuter vehicles are playing a more significant role in the transportation matrix







.
Now, while pedalectric bikes offer one form of hybrid human-powered commuter vehicle, they are ill-suited to commuting in inclement weather. An extensive discussion of the characteristics of an ideal HPCV are discussed in “Rx for a Healthy Commute”, below


Now to get displayed at a large auto show, a HPVC needs to be a product of an auto company, like Toyota or Daimler AG. Even though they are developed by non-auto-company enterprises, there  was one vintage and is one new vehicle that deserved and deserve to be displayed to the general car public at a large US auto show.
One HPVC was the Pedicar from 1973, below.


Production of the Pedicar was only 20 vehicles. It didn’t catch on, even though there was a gas crisis going on during its public release. At $550, the cost may have been a deterrent when compared to a bicycle and, even though similar vehicles were used in Europe after WW2, US consumers were just beginning to think of bicycles as commuter vehicles.  If it had an electric assist, which it was ideally suited for, it might have experienced the sales it deserved.
The auto companies did take notice of the Pedicar, however. An industrial designer from Chrysler drew this lampooning cartoon of it.

A modern vehicle which deserves recognition at a large US auto show is the Drymer trike from the Netherlands. With a bit more weather protection, the Drymer would be an ideal all-weather pedalectric commuter vehicle.


So the future is looking up for human-powered commuter vehicles. If the general public begins to consider pedalectric bicycles as viable transportation alternatives, they may be ready to accept and purchase vehicles like the Pedicar and the Drymer.

Hephaestus

Tuesday, January 15, 2013

The Pedal-powered Porsche and the Ultra-Efficient Car

A lot of bicycle technology was incorporated into early automobiles; ball bearings, pneumatic tires, the differential and the list goes on. The efficiency demonstrated by modern human-powered vehicles should be an example for potential improvements in car design. While the two art-piece cars on view below are seen as jokes by the car community, they serve as a departure point to discuss a possible directions for aerodynamic improvements for that most popular commuter vehicle.
I don’t recall how I stumbled on the pedal-powered Porsche. After discovering it I asked the machinist at work, who is a Porsche devotee, about it and he just laughed. It seems it is a big joke among sports-car buffs. The people at Top Gear knew all about it. Driven by Richard Hammond, it holds the record for the slowest lap on their test track.  And there is a follow-on Enzo-Ferrari-like vehicle which appears to be slightly more aerodynamic due to the fact that the Enzo is based on a formula one (F1) car layout. More about the F1 layout later…
Now clearly, both these vehicles, created by Hanes Langder, should be categorized as art pieces. Weighing 100kg and having a huge aerodynamic footprint compared to any enclosed recumbent tricycle; the vehicles cannot be expected to be even as fast as an upright mountain bike. Nevertheless, the human-powered vehicle builder in me is bothered by the laughter associated with the vehicles. Pedal-powered vehicles can be viable transportation alternatives, especially with a small power assist, but the vehicles need to be ultra efficient for 1/3rd of a horsepower (250W) to be able to move the vehicle at anything greater than a walking speed. 
In contrast to the Ferdinand and the Fahrradi, RJK pedalectric velomobile is intended to be a viable commuter vehicle. I have no idea of the weight, but the cross-section of the vehicle appears to be smaller than Herr Langder’s creations, even if the open cockpit incurs more air drag. Of interest is the RJK has front-wheel drive and rear-wheel steering, which may result in a weight reduction from a shortened drivetrain. However, the vehicle’s speed in the video, with one peddler, does not seem to be very fast.
A minimal weight, minimum cross-section, maximum streamlined recumbent bicycle, such as the Varna Tempest, can probably cruise at about 50mph given a 250W input power.
Unfortunately, low visibility, difficult entrance and egress, limited steering etc. prevent such a vehicle from being a practical for commuting. The posts on this blog have spent probably an excessive amount of verbiage discussing how to optimize a vehicle that would use the bike lanes for commuting. See “Rx for a Healthy Commute”, below. But how could the lessons learned from human-powered vehicles make a more efficient car?



These lessons are minimize air drag, minimize weight and minimize rolling resistance. This discussion will primarily focus on efforts to reduce air drag. Weight reduction is assumed to come through use of lightweight materials, space-frame and/or monocoque construction techniques and optimization of load paths that route the payload weights as directly as possible to the wheels. Narrow profile, high-pressure tires would reduce rolling resistance.
Air drag is proportional to the cross-sectional area of the vehicle, the drag coefficient of the vehicle’s shape and the cube of the vehicle’s velocity. The goal in streamlining the vehicle is to reduce the form drag, the product of the area and the drag coefficient. If the form drag gets very low, then skin drag gets significant, and it is beneficial to reduce the total-wetted surface area of the vehicle.
The conventional-rectangular four-wheel layout for cars does not lend itself to being enclosed by classic streamlined shapes.  The difficulty lies with the wheels. Early cars left the wheels exposed and concentrated on enclosing the passenger and engine compartment, the fuselage. Since the top of the wheel is moving a twice the velocity as the vehicle, a rotating wheel has more drag than a static one. When the aerodynamics of the vehicle became more of a concern, the logical approach was to use a streamlined shape (teardrop) for the fuselage and enclose each wheel in a streamlined wheel pant as well. The structure that attached the wheels to the main fuselage also needed to be streamlined, often with wing-like sections. This approach minimizes the vehicle cross-section but results in added interference drag where the various streamlined elements came in contact with each other. The typical result is similar to the 1938 Hispano Suiza Xenia shown below.

Or the contemporary Enzo Ferrari …


This aerodynamic layout, enclosing with the fuselage and wheels separately originated with early motorized carriages. I like to think of it as the F1 layout, even though F1 cars cannot enclose their wheels.
The alternative approach is what most contemporary cars employ, enclosing the entire vehicle in one or more streamlined shapes. The upside is that interference drag can be reduced while the downside is the cross-sectional area of the vehicle is increased and the aero shapes are less conventional and less efficient. If the vehicle area must expand excessively to allow the use of a shape with a low drag coefficient, the resulting vehicle may not benefit from an overall reduction in form drag. The Schlorwagen, below, has a low drag coefficient of .15 and looks very streamlined from the side view.

 


 But in the front view, the cross-sectional area of the vehicle appears to be rather large.





The track (transverse wheel spacing) for the rectangular-wheel layout is determined by the width of the fuselage and the roll-over resistance of the vehicle when cornering. If the passenger compartment can be kept narrow, for example if the seating is reduced to two people in tandem, and the vehicle is allowed to lean like a motorcycle, that the cross-sectional area can be additionally minimized. See “The Drymer and Varna Lean Forward” below.
Going to a three-wheel layout can bury one of the wheels in the fuselage and thereby improve the drag coefficient, especially if the steered wheel is buried. The downside of this approach is that, for a given rollover resistance, a three-wheel vehicle must be approximately 50% wider track than a four-wheel vehicle. This adversely increases the cross-sectional area.
For simplicity, this discussion will concern itself with the more-conventional four-wheel rectangular layout. 
The design team at Edison2, who won the Progressive Automotive X-Prize for a four-wheel, four seat vehicle that bettered 100mpg, have been refining the F1 layout with the second iteration of their Very Light Car.




Interestingly, the top view of the Very-Light Car Mk2 looks a lot like a modern version of the Hispano Suiza above albeit with a much greater degree of fender seperation and more streamlining. Edison2 is probably at the leading edge for efficient vehicle design, both in aerodynamics and lightweight vehicle construction.



One means of reducing the air drag even more than the Very-Light Car is to narrow the passenger compartment by going to two-passenger tandem seating, similar to the Messerschmitt car from the 1950’s.

 It is of interest that the earlier Messerschmitts were three-wheeled with the single-driven wheel in the back. This is a later version which employed a larger engine. The rear seat of the Messerschmitt could hold a second person or haul cargo. An interesting design feature (shared by my friend Jerry Onifer) was that the center of gravity, c.g., of the vehicle was located in the rear-seat compartment. The idea was that the vehicle’s dynamic performance would remain independent of the load that was being carried in the rear seat.
So the vehicle I envision is similar to the So-Cal Bonneville streamliner in the photo at the beginning of the article. I would use narrower tires enclosed in wheel pants and the structure connecting the wheels to the fuselage would fit within horizontal wing shaped enclosures. Assume a vehicle height of 40” (that of a low sports car). If the c.g.is lower than 20”, for a one-gee rollover resistance the track could be 40”. This is less than ½ the track of a typical car. There could be some additional benefits to having such a narrow vehicle, since it takes up less width on the road.
Once you have a design for a vehicle that is aerodynamically efficient and light weight any source of motive power will benefit from the vehicle’s efficiency. I do not believe that electric propulsion is the magic bullet that solves fossil-fuel consumption problems. If the vehicle design allows for an extended driving range with batteries, the vehicle will get exceptional gas mileage with an internal-combustion engine as well.
The above being said, I envision the tandem ultra-efficient car being propelled by a hybrid power plant. The power source would be a small gas turbine driving an electric generator. The electricity from the generator would, in turn power an electric motor located in each of the four wheels. There would be onboard batteries to provide for increased power for acceleration and regenerative braking. There will be a weight penalty for using four motors instead of using one motor with four times the power. Having a motor in each wheel also violates the suspension principle of minimizing unsprung weight. On the other hand, having motors in each wheel that can be controlled independently eliminates three mechanical differentials as allows for unprecedented traction optimization under microprocessor control. Volvo used a turbo-generator and wheel motors in a concept car during the 1990s and Jaguar used twin turbo-generators more recently.

The X-Prize-winning Very Light Car weighed 830lb., was powered by a 30kW IC engine and had a drag coefficient of .16. Could a tandem two-seat version maintain the same drag coefficient, significantly reduce the cross-sectional area, weigh less than 200lb and be powered by a 7.5kW turbo generator? And would a pair of pedals get you to a gas station if you ran out of fuel?

Hephaestus