Reflections on the potential of human power for transportation

Monday, January 2, 2012

The New Balance: Life after Leonardo da Vinci's Bicycle

It was too much to expect.  That the world’s most creative mind would have conceived of the world’s most efficient means of transportation. That Leonardo da Vinci would conceive of a machine with the three essential sub-systems of the modern bicycle almost 300 years before Karl von Drais. Those sub-systems being a pivoting-fork front-wheel steering layout, rotary pedal propulsion and a chain and sprocket transmission.
I don’t know who was more disappointed, those of us that are Leonardophiles of the Italians. It was just too good to be true.

Now all of the hoopla over the Leonardo’s Bicycle Hoax should not be allowed to detract from the quantum leap Karl von Drais took when he invented his laufmaschine (running machine) or what history calls the Draisienne.  
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 with 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 of 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 the forward vehicle speed equaling the rearward speed of the foot, any speed advantage was gained by gliding, similar to a classic-style Nordic skier or a person using a scooter. 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 Draisine, 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.
And Leonardo? His notebooks show sketches for chain-sprocket drives, ratchets and ball bearings. But the invention of a dynamically-stable two-wheeled-inline vehicle was 300 years in his future.


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