Reflections on the potential of human power for transportation

Tuesday, February 21, 2012

Raptors Revisited

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 20th 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 19th 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.

Tuesday, February 7, 2012

The Drymer and Varna Lean Forward

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.

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. 

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.