The Left-handed Cyclist

Raptors Revisited

2012-02-21T19:24:00.000-08:00

Now for those of you who are growing bored with my ongoing discussion of the Human Powered Commuter Vehicle, something completely different, dinosaur biomechanics.

It was like being a kid again, opening Adrian Desmond’s book “Hot Blooded Dinosaurs” and seeing the picture of a sprinting dinosaur, gracefully leaning forward with tail stretched out behind. In an eye blink, the dinosaur love of my childhood (and many others as well), Tyrannosaurus Rex was replaced by this new creature, Deinonychus Antirrhopus.

Deinonychus was discovered and named by Prof. John Ostrom of the Yale-Peabody Museum in 1969. The name for this dinosaur was descriptive of the animal’s anatomy, meaning terrible claw & counter balance. Terrible claw of course referred to the sickle-shaped claw on the second digit of each foot and counter balance referred to a tail made rigid by bony extensions on the vertebrae.

Deinonychus could possibly be the most significant dinosaur discovery of the 20^th Century. The reason for this was the realization that if the sickle claw was used for attacking prey, the animal needed to be very athletic and one that was more than likely warm blooded. To emphasize the point Robert T. Bakker, then a student of Prof. Ostrom drew a convincingly active restoration of Deinonychus, the image that graced Desmond’s book.

Prof. Ostrom also went on to observe strong similarities between the limb structure of Deinonychus and Archaeopteryx the famous proto-bird discovered in the 19^th century. Based on Archaeopteryx, Thomas Huxley advocated that birds descended from dinosaurs and because of the similarities he observed, Ostrom resurrected the idea. Of course, because of numerous fossils indicating the presence of feathers on clearly flightless dinosaurs, the bird from dinosaur decent is now accepted as fact.

21 years would pass since its discovery and Michael Crichton through his book, “Jurassic Park” and the subsequent movie would introduce the world at large to Deinonychus. Well not exactly…

Ironically, the dinosaur mentioned in the book and movie was a misnamed species, Velociraptor Antirrhopus. An amateur paleontologist, Greg Paul, had decided, incorrectly that two raptors were of the same genus. They were Velociraptor Mongoliensis and Deinonychus Antirrhopus. Velociraptor was about 18” tall, weighed about 33lb. and had a long flat skull. Deinonychus was about 40” tall, weighed about 150lb. and had a rather deep skull. Crichton may have known the name was incorrect and used Velociraptor anyway because it conveniently shortened to “raptor”, while I don’t know how to shorten Deinonychus except to shorten it to DA. The movie took additional liberties by significantly enlarging their raptor to make it seem more fearsome, even though DA was fearsome anyway, hunting in packs like wolves. As life imitates art, a raptor was subsequently discovered about the size of the movie raptor, Utahraptor Ostrommaysorum, that weighed about 1100lb. After “Jurassic Park” the term raptor no longer referred to birds of prey like eagles, owls and vultures but instead to medium sized carnivorous dinosaurs with sickle-shaped claws on their feet.

Skip ahead another 15 years and the image of a raptor balancing on one foot and slashing its prey with the other is under attack. The issue of contention is the function of the sickle-shaped claw. One fact is that the horny talon that covered the toe ungual of the living raptor is not preserved in the fossil. As a result the actual shape of the claw can only be guessed at.

The other fact is that only one living animal, a bird, the seriema, has severely curved claws used in a flesh-slicing role, but that is after the prey has been killed by smashing the body on a hard surface

Arial raptors and cats have hooked claws and they use them as grapples to hook on to prey or for climbing, not to cut flesh with the inside edge. Cassowaries and ostriches can inflict severe injuries with the claws on their feet, but in both cases the claws are straight and the offensive motion is a forward kick. So there is a new theory that the claw was only used to scramble up the sides of prey and hold on, while the jaws did the dispatching.

Under the direction of Prof. Phil Manning at the University of Manchester, researchers built a mechanical raptor leg and evaluated the damage the sickle claw did to pig and crocodile cadavers. The machine was designed to duplicate the leg and sickle-claw action of a 90lb. raptor. The results would definitely not be life threatening to the large sauropods that the raptors might prey upon. The wounds to the pig cadaver were between 1.2 and 1.6” deep and the bunching skin made it difficult to extract the claw after penetration. The claw bounced off the crocodile hide. The intent of the testing was to validate the grapple and grasp theory but the results were not at all conclusive.

Before leaving the grapple & grasp theory, allow me a few observations about stress, strain and claw penetration. Strain or the stretching of the tissue is what causes damage to the animal. Strain is related to stress, and stress in its most basic form is force divided by area. The force component in the claw-induced tissue stress is the raptor’s weight since the full weight of the animal can be applied to the claw-tissue interface. The area term in the tissue stress is related to the size and shape of the claw. I find it interesting that 90lb. was chosen as that of the raptor simulated by the machine. Recall that a Velociraptor weighed about 30lb and a Deinonychus weighed 150lb. One must question what claw size was used in the machine since a Velociraptor claw would be too small and a DA claw would be too large.

Then there is the matter of shape. A claw with a circular cross-section would produce the lowest stress in the tissue during a puncture because the tensile or hoop stress at the edge of the wound would be uniform. An oval cross-section claw would produce higher stresses since more stretching would take place along the long sides of the ellipse. Finally a teardrop shape would produce the highest stresses with the peak stresses occurring at the point of the teardrop. For example, if a knife blade had been mounted to the roboraptor’s foot, the penetration would be substantial, since the cross-sectional area is small and the stresses are very high at the edge, something referred to as a stress concentration. In reality, however, bone and horn do not have the strength of steel so a claw as sharp and narrow as a knife blade is not possible.

The claw used in the machine appeared to have an oval cross-section with the short axis orientated through the thickness of the claw. The core of the claw was aluminum and it was covered with Kevlar and carbon fiber.

As an exercise to determine if the horny talon covering the toe bone could have had a sharp edge on the inner curve, I sculpted a DA claw out of .45”-thick glass-filled polycarbonate. I started with the outline of the horny talon Prof. Ostrom sketched around the second ungual with a finely-dashed line in his 1969 monograph on DA.

What resulted was a claw whose cross-section begins at the tip as an oval with the long axis through the thickness of the claw. This transitions to a flat-sided teardrop about 1.4” along the inner edge of the claw. Since the inner edge of the claw is about 3.5” long, 2.1” of the inner edge could be considered sharp. It would be interesting to see the depth of penetration with this claw used on the roboraptor.

The grapple & gasp theory has a lot of dissension. Reasons given for this range from the fact that Velociraptor’s jaws did not have enough bite force to dispatch live prey, to the fact that raptors that were probably too large to scramble up the sides of prey (Utahraptor) still possessed sickle claws. And then how does one interpret the famous Velociraptor vs. Protoceratops fossil?

When a raptor was attacking prey that was significantly larger that it and that could injure it if given the opportunity, it would be advantageous for the raptor to get in, inflict a wound or wounds and get out quickly. The raptor could uses it sickle claws as grapples to run over the back of the prey and get off before the prey could respond. The difference between this dash & slash approach and the grapple & grasp approach is in the extent to which each claw penetration injures the prey. This is probably a more probable scenario for how the sickle claw was used.

The other interesting feature of raptors (the actual family name is dromaeosaurs, named for a dinosaur discovered in 1922 and thereby predating Velociraptor from 1924) is the structure of the tail, which was stiffened for most of its length by bony rods that held it rigid while only allowing bending near the pelvis. Again the above picture is from Prof. Ostrom’s 1969 monograph.

He suggested that lateral motion of the rigid tail could enhance “jinking” or rapid changes in direction.

A recent Velociraptor fossil discovery exhibited a tail with a moderate S-bend from side to side, so for the purposed of the subsequent discussion it will be assumed that the rigidity contributed by the caudal rods was mainly in the vertical plane.

Many bipedal dinosaurs appear to use their tails to shift their centers of gravity (c.g.) over their back legs so they can stand with their torsos horizontal, but they don’t require caudal rods to do so. Since this type of counter balance is basically a static condition, it is logical to assume that the caudal rods were required for dynamic activities, where the forces would be significantly larger.

Of particular interest is how vertical tail motion could be used to enhance the techniques employed to injure prey.

The dash & slash approach assumes that the raptor is moving continuously over its prey. The dynamics of the raptors motion is rather complex and difficult to visualize. However one can observe some of the effects of tail motion on a raptor clinging vertically to the side of its prey. The sketch above is a simple free-body diagram of a raptor in that state. The condition here assumes that the raptor has leapt through the air and landed on the prey and is stationary vertically. Point a is where the sickle claw attaches to the prey, point b is where the hands attach to the prey, point c is the c.g. of the raptor without its tail, point d is where the tail attaches to the body and point e is the c.g. of the tail. (I have made the simplifying assumption that the polar inertia of the tail about point d can be reduced to Mt*L4^2). With the arms grasping the prey, the raptor is in static equilibrium. This means that all the static forces sum to zero. The vertical reaction at the sickle claw, Rv, is equal to the sum of the body weight Fb and the tail weight Ft. The moment about point a =Fb*L2+Ft*(L3+L4) is reacted by the moment Rh1*L1. So statically the maximum force causing the sickle claw to penetrate the hide of the prey is the raptors weight. Now I doubt that a raptor spent much time statically hanging off the side of his prey but it is a starting point to examine the forces involved in its support.

For the above case, if the raptor were to rotate his tail upward with an acceleration At, the force on the sickle claw would be increased over the body weight by Mt*At. Snapping the tail up would drive the claw deeper into the prey.

Due to conservation of angular momentum, rotation of the tail while the raptor is airborne would result in an opposite rotation of the torso. The would allow the raptor to adjust its body posture with respect to the prey the same way long jumpers use their arms to adjust their body position before landing.

As the raptor lands on the prey but before its arms can grasp, there will be a tendency for it to rotate backward because of the unreacted moment of its weight acting about the claws contact point, a. Under these circumstances, if the tail is snapped downward hard enough, the torso could be made to rotate forward, allowing the hand claws to gain purchase. Mt*At*L3 must be larger than Fb*L2 for this to happen. Note that statically Fb=Mb (the body mass)*g, the acceleration of gravity. As the animal lands Fb would be greater =Mb*(g + dg) where dg is the added deceleration to bring the raptor to a vertical stop.

Most carnivorous dinosaurs (Therapods) have the pubic bones of their pelvis facing forward. The fact that the pubic bones of raptors face rearward could be related to increasing the muscle leverage for rotating the tail in the vertical plane.

The sickle claws and the stiffened tail are very specialized adaptations in raptors. It is logical to assume that their function significantly enhances their effectiveness as predators.

Hephaestus

The Drymer and Varna Lean Forward

2012-02-07T19:09:00.000-08:00

In my previous post (“Rx for a Healthy Commute” below), I proposed ten criteria I felt were necessary in the design of a human-powered commuter vehicle, or HPCV. In rough order of importance they are listed below.

1. Weather Protection

2. Statically Stable

3. Reasonable Cruise Speed

4. Cargo Carrying Capacity

5. No Wider than a Bicycle

6. Same Height as an Auto

7. Comfortable posture and ease of entry

8. Two-wheel drive

9. Car-type Wheels

10. Electric Assist for Hills

Now in the pervious post we examined the fact that criteria 5 and 6 seem to be mutually exclusive if you don’t want your tricycle to overturn while cornering. The concept of a leanable trike was proposed as a suggestion to address both criteria. The trike would lean at moderate to high speeds but the leaning mechanism could be locked out at low speeds and when the road conditions were slippery.

The concept of a leanable trike is not a new one and many auto, motorcycle and bicycle enthusiasts have experimented with the idea and at least one motorized vehicle is commercially produced.

There are basically four approaches to designing a leanable trike, two for one-wheel forward, OWF, and two for two-wheels forward, TWF layouts. Again I am only addressing wheel layouts that are symmetric about the front-to-back axis of the vehicle and layouts where the front wheel(s) do the steering.

For the OWF layout, the most common means of providing leanability is to allow the front wheel and the majority of the vehicle mass to rotate about a near horizontal pivot with respect to the rear-wheel pair. The rear wheels don’t lean and maintain their relative position to each other and to the ground. Let us call this configuration the fixed-rear wheel or FRW for short. This FRW is popular for motorized vehicles because it allows both rear wheels to be driven the same as a non-leaning trike. In most cases the motor is part of the un-leaning mass. Since the motor mass does not tilt, the effectiveness of leaning on rollover resistance can be significantly reduced if the motor is heavy.

The Lean Machine is a prototype FRW vehicle from GM produced during the 1980s. The rear-motor pod remains stationary while the body and front wheel lean.

The Carver is a contemporary FRW leaning trike similar to the Lean Machine. The Carver is in production.

The other approach to allow an OFW vehicle to lean uses articulated-rear wheels or ARW for short. Usually a parallelogram linkage is used that moves one wheel down while moving the other wheel up. This approach is not as common as the FRW approach and is more common for human-powered trikes than motorized versions. The reason for this is it is more complicated to power the wheels for an ARW vehicle as opposed to a FRW vehicle. When used in human-powered trikes one has the additional option of driving a single rear wheel, both rear wheels or the front wheel.

The vehicle above is the EcoVia, a prototype pedaled trike that uses the ARW approach to lean. The drive chain connects the cranks to a drive shaft located under the seat. A gear cluster is rigidly attached to the drive shaft and two single-speed freewheels are attached at the outer ends of the drive shaft. The rear wheels are mounted on beams that rotate about the drive shaft. Each wheel has a fixed gear cog that is connected to the drive shaft freewheel by a second and third chain. A parallelogram linkage connects the beams, so as one moves down the other moves up. The dual freewheels on the ends of the drive shaft act as a positraction-style differential between the wheels. More on the EcoVia in a future post.

For TWF layouts, the most common means of leaning the vehicle it to use articulated-front wheels, AFW. Similarly to the ARW approach the wheels are interconnected, again usually by a parallelogram linkage, so as one moves down the other moves up. Of course, the TWF AFW layout has the additional complexity that the wheels must also turn. In almost all cases each wheel rotates on its own pivot and is interconnected by some form of tie rod. In many cases, the linkages for independent front suspension can be modified to couple those linkages and result in an AFW approach.

The Mercedes Life Jet is an example of the AFW approach. The rear wheel is driven in motorcycle fashion. The Life Jet uses coupled parallelogram linkages that allow suspension to be incorporated as well.

The last means of leaning a TWR trike is the fixed-front wheel approach, of FFW. I could not find a photo for an example of a FFW approach but I do recall a three-wheeled scooter that had two front wheels mounted very close together on a common axle.

There are three methods of controlling the amount a vehicle leans to result in a turn where the resultant of the weight forces and the radial acceleration forces are aligned with the midplane of the vehicle; the balanced turn condition. The radial acceleration force is the squared linear velocity of the vehicle divided by the radius of the turn. Therefore, the amount of banking for a balanced turn is determined by the speed of the vehicle and the tightness of the turn.

The most complex method of lean control is used in motorized vehicles that have electrical systems. A microprocessor can combine the inputs from a velocity sensor and a steering-angle sensor to arrive at the appropriate amount of lean. This signal is sent to some form of actuator that leans the vehicle.

The next method is to manually control the amount of lean. The Lean Machine had foot pedals to lean the vehicle and a hand control to do the steering. This method of two-input control doesn’t work as well when the rider’s feet are required to turn the pedals. Several vehicles have combined the steering and leaning controls into one motion. These vehicles used coaster-type steering where the steered wheels were located at the ends of a common axle and the axle pivoted at its middle, like a child’s coaster. The pivot axis was inclined from vertical so the steering motion resulted in a tilting motion as well. These vehicles are correctly leaned for only one speed per steering angle. Since the vehicle requires less steering and more lean as the speed increases, the control is moving in the wrong direction. The control provides more lean with more steering angle. So, this approach works acceptably only for slower vehicles or where the speed range is narrow. Several children’s riding toys used this single input approach.

If the leaning system is well designed, consisting of a mechanism that leans the vehicle about an axis at ground level (mimicking the tilting of a single tire at the ground plane), than the vehicle can be ridden like a bicycle with no leaning control required. The approach, which we can call free leaning, is probably the most popular with light-weight human-powered vehicles and clearly it is the simplest. The addition of a manual lean-lock mechanism for very low speeds and slippery conditions makes this approach work for all conditions.

There is an ever increasing amount of interest in leaning trikes in the human-powered vehicle community. One is in production from Canada and another is nearing production from the Netherlands.

http://www.varnahandcycles.com/video.htm#hc16

The Varna cargo trike is the brainchild of George Georgiev, designer and builder of the Varna Tempest, the world’s fastest HPV (refer to “Back to the Future” below). With his ability to come up with simple but elegant solutions, Georgiev has come up with a very simple design for an OWF tilting trike. The trike is made up of two portions. The front section incorporates the front wheel, steering, pedals and seat. The rear section incorporates the two rear wheels, the freewheel and space for a rather-copious-cargo rack. The two sections are connected by a horizontal pivot behind the seat support which allows the front section to tilt with respect to the rear section. The leaning is therefore accomplished by the FRW approach. Within the horizontal tubes making up the pivot is a torsion spring that resists leaning too far. So the system is basically a limiting form of free leaning. The chain is long enough that the misalignment between the tilted crank and non-tilted freewheel can be ignored. Only one of the two rear wheels is driven, the other just spins freely. The rear-wheel track is 16”. There is also an hub-motor option for electric power assist. The cost is $3590 with electric assist and $2650 without.

The other leaning trike is the Drymer from the Netherlands. The intent is that it will be in production soon.

http://www.youtube.com/watch?v=KtHyF8DQ9ls&feature=related

I must admit when I saw the Drymer video I thought I was watching a contemporary version of the Pedicar. The Drymer is a TWF trike that uses a AFW approach to leaning. The weight distribution of the wheels is a bit odd. Most of the weight is on the rear wheel for reasons of increased traction. As a result, each front wheel is lightly loaded and more prone to lateral slippage than is desirable. As you can see it is semi-enclosed, has a moderate cargo capacity behind the seat, 20 Liters, and has the option of a hub motor in the rear wheel for electric assist that will allow for a speed of 25kph. Cost is to be 6000 Euros for the full-up model with the body and electric assist and 3000 Euros for the base model.

So how do these vehicles measure up against the 10 HPCV criteria? I will add some speculation as to what can be done to meet the criteria if they are not already met.

1. Weather Protection: The Varna has no weather protection. Its long wheelbase and high rider position would make a faring rather bulky but something approximating the Lean Machines body could be made to work.

The Drymer has a body that provides some weather protection but the sides need to be enclosed to make it practical for very wet conditions

2. Statically Stable: Since each vehicle is a trike, they can be made statically stable by locking up the lean. It is not clear that the Drymer has any lean-lock mechanism. The torsion spring on the Varna acts as a lean-limiter.

3. Reasonable Cruise Speed: Without a body the Varna is limited to bicycle like speeds when pedaled. A bit more streamlining on the Drymer might bump up it cruise speed to closer to 25mph.

4. Cargo Carrying Capacity: The Varna has a very large cargo capacity. It should be noted though that the cargo does not lean. The more weight that is carried the less effective the leaning is in preventing overturning when cornering. The cargo capacity of the Drymer seems adequate.

5. No Wider than a Bicycle: I think a target number here should be about 24” or less. The Varna is no wider than the rider’s shoulders so it is definitely narrow enough. The Drymer’s track is about 28” but there appears to be room to narrow that somewhat.

6. Same Height as an Auto: Both vehicles have a safe rider height.

7. Comfortable posture and ease of entry: Both vehicles have good ease of entry and a comfortable rider posture.

8. Two-wheel drive: There is no simple way to give the Drymer two-wheel drive. The Varna, on the other hand could have the freewheel fixed to a continuous axle and put ratchets in each wheel to provide two-wheel-drive with a positraction-type differential effect.

9. Car-type Wheels: Both vehicles could be converted to car-style wheels. In fact the front wheels on the Drymer are supported on only one side. So if the Drymer’s rear wheels were cantilevered and the Varna’s front wheel was cantilevered, they could employ car-style wheels where each wheel was the same.

10. Electric Assist for Hills. Both vehicles already employ electric assist options. However, I question if hub motors are appropriate for the high-torque low-speed requirements hill climbing.

In conclusion, then, the lack of a body on the Varna trike keeps it from having any real potential as a HPCV. The Drymer, on the other hand, has a great deal of potential with more of an enclosing body and some additional aerodynamic improvements.

Hephaestus

Rx for a Healthy Commute

2012-01-28T18:11:00.000-08:00

Before the bike boom in the US, during the early 1970s, the bicycle was considered by many to be a child’s plaything. After the bike boom, its popularity caused it to be considered an acceptable form of recreation for adults. But the idea of using it as a commuter vehicle has never been widely accepted. Nevertheless, there where occasional flashes of insight into the potential of human power for commuting.

Bob Bundschuh’s marvelous Pedicar from 1973 (See “Back to the Future” below), was one of these insightful designs.

The Pedicar was beautifully executed and at $550 was a bargain when you consider that a custom bicycle cost about that at the time. It embodied many of the characteristics I consider necessary in a commuter vehicle. Even the industrial designers at Chrysler took notice of it if only to poke fun. Notice the mention of rotary-action to counter the touted benefits of the Pedicar’s linear pedaling system.

Mr. Bundschuh must have had a lot of industrial resources at his disposal to produce it.

Unfortunately the Pedicar was far ahead of its time and had one flaw that may have prevented its success. More on this later.

And there was the widespread media coverage in 1980, when the vector tricycles broke the 60mph speed barrier.

What was more captivating than the Vector single covering the flying 200m at 63mph was the Vector tandem being ridden in traffic on the freeway and covering over 50 miles in less than an hour. At last the media got the idea that pedal powered commuter vehicles were fast enough to be taken seriously. The New York Times did a piece on future bikes with the Vector as the central theme and the Reader’s Digest reprinted the article. Three years later Scientific American did an article on human-powered land vehicles and a painting of the Vector graced the cover.

One vehicle to come out of the post-Vector optimism was the Cyclodyne. At first glance, the Cyclodyne looked like someone finally got the design of a human- powered commuter vehicle, HPCV for short, right. It was fast. During a road test by David Kennedy for Popular Science, as he pulled into traffic he was shocked to see he was doing 30mph. With a cruise speed advertised between 20 and 45mph, front wheel drive and steering, rear suspension and reasonable cargo carrying capacity, the Cyclodyne looked to have covered all the bases. At $3800 plus $120 shipping, however, it was not cheap. (At the time, Early Winters Outfitters in Seattle was selling a Vector for the outlandish price of $10,000. No one ever bought it and it was donated to the local HPV club as a tax write-off. The Cyclodyne people claimed their vehicle was cheap by comparison but it was still much too expensive.)

So, if we build it, will they buy? After a considerable amount of thought and a considerable amount of time perusing the literature, these are my criteria for a HPCV. Granted a lot of creative designing and building of HPCVs has taken place all over the world and it is not my intention to undervalue these contributions to the state of the art. However, IMO, a single vehicle with most of the necessary criteria does not yet exist. The list is roughly in descending order of importance. The focus will be on a single-rider vehicle.

It might be informative to measure the Pedicar and the Cyclodyne against these criteria, since I consider both vehicles good examples of HPCVs.

1. Weather Protection: The HPCV needs to be usable when using a bicycle is prohibitive. By providing protection from rain and snow the driver is kept warm and dry. The body of the HPCV must also provide adequate ventilation, since three times the mechanical work required to propel the vehicle is produced as waste heat. Remember that the hour-record for streamlined recumbents was more an issue of cooling than raw power production. (See “Back to the Future” below).

With the exception of the open side windows, the Pedicar appears to provide excellent inclement weather protection. The windshield wiper is also a practical addition. The Cyclodyne is also completely enclosed with the exception of the rider’s head protruding from the faring.

2. Statically Stable: I am assuming the HPCV will be used in snow and icy-road conditions. When the wheels of a bicycle slip laterally, the cyclist falls over. The value of static stability was made very clear to me on an icy bike trail with a tight curve. I watched a cyclist fall over into the grass when he hit the ice. I was on three-wheeled roller skis for Nordic training. I didn’t fall when I hit the ice but only slid laterally. So the HPCV must have three or four wheels.

A bit here about three-wheel layouts and I will exclude rear steerers. (See “Bucky and the Urbee” below). The symmetric layouts are one-wheel forward, OWF and two-wheels forward, or TWF. Each has advantages and disadvantages when it comes to occupant packaging. If all three tires on the vehicle are the same, there are advantages to having each tire equally loaded. For a triangle this occurs when the center-of-gravity is located one-third of the wheelbase distance from the twin wheels or two-thirds of the wheel base distance from the single wheel. Consider the riders c.g. to be located at approximately his belt buckle and assume the major mass component of the system is the rider.

For the OWF layout, this locates the rider within the wheels resulting in a very compact package. In addition, all three wheels fit within the body without requiring any openings for the steered wheel. The downside of this layout is there is no volume left over for cargo carrying and the rider’s legs are located in the same volume as the steered wheel.

For the TWF layout, the rider’s legs protrude in front of the two front wheels causing the overall vehicle length to be significantly longer than the OWF layout. Openings in the body are also required to allow for the steering of the front wheels. On the upside, the rider’s legs do not interfere with the steered front wheels and the volume around the rear wheel and be used for cargo carrying.

The Pedicar’s four wheels would make it very stable in slippery conditions as do the Cyclodyne’s three.

3. Reasonable Cruise Speed: The body that provides the weather protection should also be aerodynamic and therefore increase cruising speed. An average cyclist can cruise between 12 and 15mph. If the rider in the HPCV can cruise between 20 and 25mph this would allow for short to moderate (up to 10mi?) commutes to be conducted in acceptable times. This speed target is very arbitrary.

The exposed wheels of the Pedicar gave it excessive aero drag and this detracted from any gains provided by the body. Cruise speed estimates were between 13 and 18mph which is little better than the bicycle. The Cyclodyne, on the other hand, boasted a very impressive cruise speed.

4. Cargo Carrying Capacity: The traditional measure for minimal cargo capacity has been two bags of groceries. An alternative could be a briefcase and a lunchbox. (The 17”-wheeled Moulton bicycles were designed for increased cargo-carrying capacity. I met a math Prof. in Milwaukee who broke his Moulton’s frame trying to carry a 65lb. filing cabinet.)

It looks like you could fit a filing cabinet into the back of the Pedicar and the cargo capacity of the Cyclodyne appeared to be more than adequate.

5. No Wider than a Bicycle: The HPCV may be significantly faster than a bicycle but in many situations it won’t be as fast a car. As a result, it should be able to fit within bike lanes and bike paths and should protrude minimally into traffic.

The Cyclodyne fell down on this point. The problem with this was brought to light by someone who bought a used version. While pedaling down a two lane road, he noticed there was a long line of cars backed up behind him. He wasn’t going at the posted speed, but the cars nevertheless were unwilling to pass him. Apparently, the drivers didn’t know what to make of the vehicle. This occurrence was nerve-racking for the rider and happened frequently enough that he removed the faring so the car drivers could see he was only riding a pedaled tricycle. Thus, the Cyclodyne’s impressive cruise speed was reduced to that of a bicycle.

The Pedicar, while not as wide as the Cyclodyne, was significantly wider than a bicycle.

6. Same Height as an Auto: I am fortunate that in over 45 years of riding derailleur bicycles I have never been hurt by being hit by a car. I have been hit three times however, and each time the driver claimed that he/she didn’t see me. I believe that HPCVs should be more visible than bicycles, not less, and to me, that means keeping the rider’s head height at least equal to that of a driver sitting in a sports car.

The Pedicar has good rider height and the Cyclodyne has adequate rider height.

Now, a statically stable vehicle (three of four wheels) prevents rollovers by maintaining a certain ratio (determined by the Gees the vehicle is designed to resist) of vehicle width to vehicle height. Narrow vehicles must be kept low while higher vehicles must get wider. So the prudent observer will see the apparent conflict between point 5 and point 6.

The solution is to allow the vehicle to lean into corners like a bicycle at regular speeds, but to lock out the leaning at low speeds and when riding during slippery road conditions. This can be accomplished by articulating the paired wheels. One goes up, the other goes down and the vehicle leans. The lean-lock can be manually engaged or automatically engaged during braking. I will spend more time discussing leaning tricycles in my next post.

7. Comfortable posture and ease of entry: Someone said that getting on an upright bicycle was like performing a stunt. Your leg must be lifted high over the top tube during mounting. This requirement resulted in the concave curved top tube of older women’s bikes and some modern bikes. At best, I believe that a HPCV should require a low step-over height for entry and that the pedal bottom bracket (I have assumed rotary crank drive here, more about alternatives in a future post) should be at least 10” below the seat. Seat height should be about 24”

I formed this opinion after riding an Avatar 2000 for almost 22 years. (That’s the great Prof. David Gordon Wilson in the picture, the co-developer of the Avatar, lifelong cycle commuter and HPV guru par excel lance). I have ridden a number of other recumbent layouts (most my own creations) but none were as easy to mount and as comfortable to ride as the Avatar. People who test rode Avatars were unanimous in how easy it was for them to master. With a seat height of 24” and a bottom bracket height of 13” it had good visibility on the road and, as I told an inquisitive bystander, if someone would steer it, I could pedal and sleep at the same time. The under-seat steering also contributed to ease of mounting and provided a very comfortable hand position.

8. Two-wheel drive: If a tricycle layout is used that equally loads all the tires, then a two-wheel drive vehicle will have twice the tractive force of a one-wheel drive vehicle. Maybe it’s because I live in an area where almost everyone has a least one four-wheel-drive car that makes me think this would be a nice feature. That being said, if you are designing a OWF vehicle, than all you need is the addition of some type of differential between the back wheels. A TWF configuration is more complicated. It needs two constant-velocity couplings to drive and steer in addition to a differential.

The Pedicar drove both rear wheels and the Cyclodyne drove both front wheels. The Cyclodyne people did make an Ecodyne tricycle with rear-wheel drive for $2500, so we can deduce that the front-wheel drive and differential added $1300 to the cost of the vehicle.

9. Car-type Wheels: Since the thought process here is to give a HPCV some of the conveniences of a car, why not be able to change a wheel when a tire goes flat instead of having to fix the tire. Make all the wheels interchangeable, mount them on only one side (cantilevered) so they are easy to remove and attach them with only a few bolts. Even if not easy to remove, cantilevered wheels allow one to remove the tire without removing the wheel.

During the 1960’s the Italian bicycle company Cinelli produced some bivalent hubs that allowed the front and rear wheels of a derailleur bike to be interchanged. Quite ingenious. (By the way, Cinelli also had clipless pedals in the 60’s as well!)

So instead of carrying a patch kit or a spare tube, just carry a spare wheel. Extra weight, but added convenience.

It appears that since the Pedicar’s wheels are cantilevered that they may be interchangeable. The Cyclodyne’s front wheels appear cantilevered but the rear is supported on both sides. I suspect they are not interchangeable nor are the front wheels, being driven, easy to remove.

10. Electric Assist for Hills: Adding electric drive assist to all types of commuter vehicles is the current trend. Should a HPCV also have an electric assist for hills? Reasonable streamlining should insure that pedaling alone can produce adequate cruise speeds. However, since the vehicles are much heavier than a bicycle, the Pedicar being about 100lb. and the Cyclodyne being over 70lb., electric assist could make hill climbing more acceptable.

Another issue for electric assist is a legal. In Seattle, a vehicle classified as an electric-bicycle cannot exceed 20mph with both pedaling and the electric assist. So, exceeding 20mph with electric assist would make the HPVC a motorized vehicle and thereby deny the rider access to bike paths and trails. If the electric assist is only used for hill climbing and the motor is geared so 20mph cannot be exceeded, the HPVC is still legally be an electric bicycle.

Whew! That was one long windy rant! So what’s the bottom line here? Both the Pedicar and Cyclodyne were well thought out HPCVs, but they didn’t meet all my criteria. The vehicle width issue is a serious one, but to address it and keep the rider sitting high requires the added complexity of leaning the vehicle. In my next post I will discuss two current HPCV products that lean. And we haven’t discussed cost. What is an acceptable cost when a Tata Nano is selling for $3000 in Asia?

Hephaestus

Bucky and the Urbee

2012-01-15T12:41:00.000-08:00

The Urbee hybrid two-seater car has had a lot of media hype lately, largely because its body is manufactured using 3D printing (rapid prototyping). But its claims of high efficiency are due to the compactness and low aerodynamic drag of its body and its light weight. What is of interest here is the car uses a three-wheel chassis. The two front wheels are driven and the single-rear wheel does the steering.

This layout has some significant advantages that allow for a car with a narrow cross-section. Since the two front wheels do not turn, the width of the vehicle can be minimized. It is only made up of the width of the two passengers and the two narrow wheels. The extra volume required for steering the rear wheel easily fits within the frontal width and allows the vehicle to be tapered for better aerodynamics. Contrast this layout with the wheels-on-pontoons approach of the Very Light Car (see “Back to the Future” below). If the steering allows the rear wheel to turn perpendicular to the front wheels, the vehicle can make extremely tight turns, having a turning radius little more than the vehicle’s wheelbase.

Of course the most famous use of this wheel configuration was Richard Buckminster (Bucky) Fuller’s Dymaxion car of 1933.

Fuller didn’t arrive at this layout arbitrarily. He was trying to design an omnidirectional transport that could be used on land, in the water and in the air. As a result the wheel layout was identical to the tail-dragger approach common in aircraft of the day. Fuller envisioned that at high speed the rear wheel would lift off the ground and steering would be controlled by means other than the rear wheel. The body was intended to be essentially horizontal in this state and, as a result, the body has an upward-forward slant in its layout.

The Dymaxion car was much more aerodynamic and had much more internal space than contemporary cars. The Dymaxion car was quite revolutionary for its time but suffered from several traffic accidents that undermined the design. The accidents were blamed on driver error, but I suspect the rear-wheel-steering system.

You see, rear-steering tricycles are inherently unstable. If the rear wheel is given positive castor (see “The New Balance” below) then during turns, the radial acceleration forces will cause the turn to tighten. This positive-feedback effect will cause a “ground loop” which will eventually cause the vehicle to overturn. This is the reason that there are no longer any pivoting tailwheel aircraft. Contrast this with a front steerer where taking ones hands off the wheel causes the turn to be reduced. If the wheel is given negative castor, the ground loop problem is eliminated but the vehicle won’t run straight will hands off the steering.

The typical design approach to remedy these problems is to make the steering kinematically neutral and provide a secondary means to cause the steered wheel to straighten when hands are off the steering.

The Urbee’s rear wheel is located in the center of a horizontal bearing with the rolling elements located outboard of the wheel. This approach is kinematically neutral but the mechanism to cause the wheel to self-center is unclear. The Urbee engineers feel that they have eliminated any stability issues with this design. Their approach appears to allow for 90 degrees of steering angle.

The Dymaxion car used a near-vertical single-bladed steering fork whose axis intersected the ground within the contact patch of the tire, essentially resulting in near-zero castor. Notice between the two versions shown, the side the fork was on has been reversed and notice the fork is raked from side-to-side in addition to front-to-back.

Of course this three-wheel configuration has been used numerous times. I have used it twice. The first time was for the University of Wisconsin’s entry to the 1979 SCORE (Student Competition on Relevant Engineer) Energy Efficient Vehicle Competition. The entry of a pedal-assist small-gas engine three-wheeler into a field of automobile-type vehicles was the brain-child of the late-great Prof. Ali A. Seireg. Prof. Seireg was a bit of a showman and he realized that to get the media to notice our entry, we needed to present an unconventional approach. Prof. Seireg did make the right call. Time Magazine’s coverage of the event had pictures of only two vehicles, and the UW runabout was one of them.

Despite how technically tantalizing this vehicle layout is, I have to question the wisdom of using it for mass-produced consumer vehicles, thought it may be acceptable for experimental vehicles, record-setting vehicles and military vehicles. Even though the stability problem may be addressed, any litigation involving a crash of the vehicle is bound to raise the issue of its unconventional steering. How do you counter the prosecution’s expert-witness’s first utterance that “Everyone knows a rear-wheel-steered vehicle is unstable”?

The New Balance

2012-01-02T17:12:00.000-08:00

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 Draisine.

The fascinating thing is that there were no precursors to the Draisine. 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 Draisine 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 Draisine 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 Draisine 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 Draisine 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.

Hephaestus

Back to the Future

2011-12-27T17:10:00.000-08:00

"Those who cannot remember the past are condemned to repeat it." George Santayana, 1905

In September of 2010, the Progressive Automotive X-Prize concluded with the announcement that the Very Light Car from Edison2 had won 5 million dollars for best performance in its mainstream vehicle class. The class was a four passenger car with four wheels arranged in the traditional rectangular layout. It was the only vehicle in the class to achieve over 100 MPGe. What is interesting about the VLC was it was powered by a 40hp. 250cc I.C. engine and weighed only 830lb. The efficiency was attributed to the light weight and very low aerodynamic drag, (a CD of 0.160 in a later version.

Now cyclists, probably more than any other group of commuters, know the significance of both aerodynamic draw and vehicle weight on efficiency. The efficiency of chemical to mechanical work in muscle is about 25% and mechanical power generated by the human body is fixed at about ½ Hp or less for periods of about an hour. So it is not unreasonable to use top speed as an indicator of vehicle efficiency.

Since the vehicle weight is usually a small component of the system weight (vehicle & rider), and then is only noticeable in acceleration/deceleration and hill climbing, its influence on vehicle velocity is significantly less than air drag. (Yes, weight will affect rolling resistance as well)

George Georgiev and his Varna team have probably achieved about the lowest aerodynamic drag of a human powered vehicle. In 2009 his Varna Tempest, with Sam Wittingham as the motor, covered a flying 200m. averaging 82.8mph. That same vehicle covered 56.3 miles in an hour on a GM test track. From an aerodynamic standpoint, it takes 3.2X the power to go 82.8mph than it does to go 56.2mph, but oddly enough the later record was harder to break. Exercising in an enclosed space for an hour requires adequate rider cooling and supplying fresh air to breathe without compromising the aerodynamics.

Now the Tempest could not have competed for the X Prize. There were two alternative vehicle categories. One consisted of a two-side-by-side- passenger layout and the other two-passenger-tandem layout. There was a motorcycle with outriggers in the tandem category as well as a side-by-side pedal-assisted electric tricycle in the side-by-side category. But there was no single occupant category, which is unfortunate, since so many short trips are made by vehicles with only one occupant.

The idea of a single-occupant, all-weather, high-efficiency commuter vehicle is by no means new. Pedal-powered velomobiles such as four-wheel Velocars and three-wheel Phantoms were used in Europe during WW2, when conventional cars were not available. Several design surfaced during the bike-boom in the USA during the early seventies. The human-powered-vehicle movement which began in the mid seventies has spawned numerous novel designs. And of course, there is the Sinclair C5 pedal-assisted electric tricycle from the early eighties.

My favorite is Bob Bundschuh’s marvelous Pedicar from 1973. While its use of four wheels and its linear-pedal motion may not have been optimal, it definitely captures the potential utility of such a vehicle. I believe the Pedicar is the template for a future commuter vehicle.

http://www.youtube.com/watch?v=zvh44wzhw9c

As of yet, these vehicles have not caught on as a serious transportation alternative. The designs may not have been adequate and energy concerns weren’t as important as they are now.

But maybe now the world is finally ready for them.

Hephaestus