Reflections on the potential of human power for transportation

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
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.

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