Reflections on the potential of human power for transportation

Saturday, August 29, 2015

Transcending the Pedicar; The EcoVia, Epilog





Introduction:

So how did we get here? The goal was to produce an all-weather pedal-powered commuter vehicle that would be as high as an automobile, as narrow as a bicycle and be stable on slippery road surfaces. The solution that was chosen was a leaning tricycle, the EcoVia.



To date, the high-water mark in pedal-powered commuter vehicles is the Pedicar from 1973. The Pedicar was completely enclosed and obtained its stability from four wheels. The Pedicar only had a top speed of about 18mph because of the exposed wheels and the blocky body. Having a width of about 38”, it was somewhat limited as to where it could be ridden. Non-motorized vehicle barriers in my area can be as narrow as 36”.




Riding without the faring:

The EcoVia balances just like a recumbent bicycle. In fact, when the delta-trike layout was first assembled, the rider could not tell if they were riding a bicycle or a tricycle, unless they looked behind them. Subsequent modifications that required re-brazing on the areas holding that Igus bushings that allow the leaning have warped the bushing seats and increased the friction associated with leaning. Nevertheless, it still rides essentially like a bicycle.

Starting and stopping was done by lifting the support leg from the ground after thrusting the pedal forward with the other leg. Stopping was simply the reverse, putting down the support leg just prior to stopping. This process is typical of a recumbent having a mid-height (20”) bottom bracket and a seat height slightly higher.


Starting & stopping with the faring:

Problems with starting and stopping began when the faring was added. Once up to speed (several mph) it continued to ride like a recumbent bicycle. The problem arose because, since the faring pivots are part of structure that surrounds the front wheel, this structure got in the way of lifting the support leg when starting and putting the support leg down when stopping. It also restricted how far the foot could be placed away from the trike, severely limiting the ability to stop tipping.

The picture below shows the framework that supports the faring pivot at the bottom right.


As a result I sustained five low-speed crashes. Three were making tight turns where there was not enough speed to keep the trike upright and two were in attempting to start from a stop.

Lean locks:

Now the EcoVia has a lean lock that clamps a disk-brake rotor attached to the link that connects the pivoting wheel beams. It is activated by a lever next to the seat. The lever is an extension of a frame-mount gear-shift lever.




The logical approach when starting and stopping with the faring would be to engage the lean-lock lever for stopping and release it when the trike is moving. Unfortunately, with the faring in place, it was difficult to reach the lean-lock lever. As an alternative, I tried using a twist-grip shifter to pull on the caliper cable. It would not produce enough force to clamp the brake rotor hard enough to prevent tipping. Nothing is worse for stability than a partially engaged lean lock. It doesn’t prevent you from tipping but it does prevent you from balancing.

After three of the crashes, I went back to the seat-mounted lever. The faring did not sit straight on the frame and one side had more room next to the seat than the other. It was on this side that I reinstalled the lever. I also dropped the seat and faring height by about 4” to improve the static stability when the lean lock was engaged.

That didn’t solve the problem however. Since I had to release the steering to reach the lever, the trike would no longer being going straight by the time the lean lock was engaged and the trike ended up being tilted. To change the tilt one had to release the lean lock again, balance to get the trike upright and then reengage it before falling over. This was a problem.

I read that the Piaggio MP3 tilting-trike scooter had similar problems. It had a lean-lock that can only be engaged when the trike is going below several mph.


If the rider is not sufficiently upright when the lean-lock in engaged, there was a risk of falling over when the rider tried to stop.

It occurred to me that, if the trike was moved to an upright position when the lean lock was engaged, there would be no concern for falling over, within the limits of the static stability of the vehicle. I added two semi-vertical posts to the wheel beams. The pivoting of these beams allow the trike to lean. I also added a crosslink that would pivot and press against the wheel-beam posts. The crosslink was moved by a lever connected through a toggle that allowed a large force to be produced. The crosslink would prevent the wheel-beams from rotating and keep them parallel so the trike was held upright. I call this device the no-lean lock, NLL.

The NLL was never intended to center the trike from a fully leaned over position. At max lean of 27deg., the tipping moment is approx. 3000 in-lb. One would have to exert over 200 lb. on the 14” NLL lever to pick the trike up. Neither is it feasible to pull on the lever with this force or if it was the lever would bend before the trike moved. The intended range of operation is probably closer to 5deg. from being upright.

Below there are two pictures with the NLL on. Notice the toggle link is just slightly past horizontal.



Below is a picture of the NLL lever which is located outboard of the rider’s  left thigh.

Below are two pictures of the NLL off. The tike is tilted away from the viewer with the near wheel-beam down and the far wheel-beam up. The crossbeam is in contact with the far wheel-beam post. The trike is tilted to its limit and the lever is all the way forward.


The NLL reduced the tendency for falls and the problem with starting and stopping while the faring was installed was resolved.

Starting dynamically-stable vehicles:

So after building and riding a number of dynamically-stable vehicles, bicycles and recumbents, I can offer some observations on those factors that influence ease of starting. The two factors appear to be seat height and bottom bracket height. (This discussion assumes that the geometry of the vehicle produces a stable configuration when moving as opposed to vehicle like a rear-steering bicycle.)

The rider begins by sitting on the seat with one foot on the ground and the other foot on the pedal. The rider pushes down on the pedal. If the rider can obtain the minimum speed for balancing by the time the second foot lifts from the ground and presses on the pedal for the second stroke, balance is achieved. If the vehicle has not reached that speed when the rider lefts the ground foot, the foot must be quickly placed back on the ground and the procedure started again.

How quickly the vehicle tips is a strong function of how high the seat is off the ground. The higher the rider, the greater the inertia that must be rotated and the slower the tipping. This is why it is easier to start off on an upright bicycle than a recumbent. (It is easier to balance a meter ruler on your finger than a pencil.)  People who are very experienced riding upright bicycles still require a learning curve when learning to ride recumbents.

The time it takes for the rider to lift the foot from the ground to the second pedal is a function of how far the pedal is from the ground. The higher the bottom bracket, the longer it takes to lift the foot and the farther the vehicle will have tipped before the second pedal thrust. Recumbents with low seats and high bottom-brackets are hard to get started.

Current examples of leaning trikes:

My no-lean lock mechanism fixed my starting/stopping problems with the EcoVia, but how do other leaning trikes deal with the problem?

We will look at three other vehicles, the Drymer, the Varna Trike and the Velotilt.


Below is a picture of the Drymer

Below is a picture of the Varna Trike

And finally two pictures of the Velotilt.



The Drymer has a high seat height relative to the bottom bracket. As a result, it appears to start similar to a well-mannered recumbent like the Avatar 2000. Feet have clear access the ground with minimal obstructions. It does not appear that the Drymer has a lean lock nor does it probably need one for starting.

The Varna Trike should be considered a semi-leaning trike since only the rider and the front wheel lean. It uses a torsion bar type spring through the central frame tube to assist with balance.

I added strings to the wheel-beam posts on the EcoVia.

The springs were strong enough to develop about 50% of the tipping moment produced by the weight of the rider and the trike. Despite this high spring rate the friction associated with the leaning mechanism was great enough to prevent the springs from forcing the trike to become upright without a rider. While riding the trike with the springs, their presence was not apparent during low-g turns but appeared to resist proper leaning during higher-g turns. At this point I will assume that the torsion bar on the Varna trike merely serves to keep the trike upright without a rider. When the EcoVia was new and the leaning mechanism had lower friction, it would fall over without the lean-lock being engaged.

The Velotilt has a lean lock. Since its cover prevents any foot or hand contact with the ground while starting, the lean lock is required for operation. The lean lock is activated by a twist-grip shifter pulling on a cable for a disk brake caliper. Instead of a brake disk, a plate attached to the leaning mechanism is gripped by the caliper.

Faring performance with weather sealing:

In my previous post, I expressed disappointment that the faring did not increase the speed of the trike more than about 2-3mph, about 17mph without the faring and 20mph with the faring. It occurred to me later that, since the Spandura fabric had no moisture proof coating, much of the air was passing through the fabric instead of around. After adding several coats of moisture proofing, the cruse speed was raised to about 24mph. This speed was close to the original 40kph goal and is probably obtainable by reducing some of the mechanical frictions associated with the drive mechanism.

The road forward:

I believe the EcoVia needs to function in both statically stable and dynamically stable modes. Statically stable for low speeds, starting and stopping. Leaning would be employed for higher speeds. Better, quicker access to the lean-lock, for example a twist grip acting on a large radius plate to produce the necessary torque may eliminate the need for the no-lean lock. The left handlebar would have the lean-lock twist-grip and the right handlebar would have the gear-shift twist-grip.

The crashes painfully pointed out that I had designed no provisions for those possibilities. The nosecone can absorb frontal impacts, but the semi-rigid faring provides little protection when tipping over. The fabric gets shredded and the aluminum stringers get bent. The rider’s arm and ribs take the brunt of the impact with the ground. The next design will include three large diameter tubes spanning the width of the trike. One will be behind the rider’ shoulders, one will be beneath the seat and the third will be beneath the thighs. In the event of the vehicle tipping over, the three tubes will support the trike on the ground and take the impact. A provision will be provided to keep the rider constrained laterally in the seat.

One can trade off cruise speed for static stability. The EcoVia has a maximum faring width of 27.5” with a 20” wheel track. I plan to increase the track to 24” but keep the faring width at about 28-30” If I make the track wider the upper speed at which static stability is maintained increases, but the faring becomes wider and cruise speed is reduced.

As an asymptote for this approach, consider the Kettwiesel trike below. 

The Kettwiesel has about the same seat height and bottom bracket height as the EcoVia, but has a track about 32”. It does have the seat closer to the rear wheels than does the EcoVia, which can reduce tipping at the expense of a very-lightly loaded steering wheel. One can imagine that is the EcoVia’s dimensions were made similar to the Kettwiesel that leaning might become unnecessary. The EcoVia would be slower, less visible, but lower cost and lighter weight.

As a proof-of-concept the EcoVia has demonstrated that a leaning trike with lean locking can be high enough to be very visible in traffic (53” to the top of the helmet) and narrow enough (27.5”) to easily fit within roadside bike lanes. Using a semi-rigid faring with a nosecone, cruse speeds on the order of 25mph can be sustained by a reasonably fit rider. In addition, with drive to both rear wheels through what is essentially a positraction-type mechanism, the EcoVia offers outstanding performance for slippery road conditions.

Hephaestus

Saturday, March 14, 2015

Transcending the Pedicar: The EcoVia, Part 3


Let us review the human powered commuter vehicle criteria that were the requirements for the design of the EcoVia.

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



The completion of the faring essentially brings the EcoVia Mk1 project to a close. In this post, I will discuss the construction of the faring and reflect on how well the design criteria were met, comparing the EcoVia to the yardstick for commuter vehicles, the Pedicar.

 


The foundation of the faring was a lozenge shaped rectangle of ½” dia. cro-mo tubing. This rectangle is orientated parallel to the ground. The front of the rectangle screwed on both sides to a framework that attached to the trike chassis. Pivoting around the axis formed by the two screws allowed the faring to tilt forward for rider access. Attached at the front of the cro-mo rectangle was a smaller vertical rectangle of 3/8” dia. cro-mo tubing. This is where the nose cone attached
The nose cone was made from EPS insulation foam, five 2” sheets glued together and formed to the correct shape. The final shape was coated with Styrocoat to form a hard-protective shell. The back surface of the nose cone was glued to a 1/16” thick sheet of polycarb and the polycarb was in turn screwed the vertical portion of the cro-mo frame.
The skeleton of the faring was made from ½”x 1/8” soft aluminum strips screwed to the cro-mo frame and pop-riveted to each other. ¼” x 1/8” aluminum strips were used between the larger strips.

 

The two sagittal strips along the top of the framework are spaced about 10” apart. With the nose cone removed, a rectangle of double-stretch fabric wrapped around the cro-mo frame tube at its bottom and the aluminum strips at the front, back and top. The fabric was sewn in place with Kevlar thread. The fabric was Spandura, which in addition to being double-stretch that could be made water repellant with a spray like ScotchGuard.

Screwed to the framework along the faring top between the fabric strips and behind the nose cone was a polycarb strip. Behind the nose cone the strip was left clear. Around the rider’s head the strip stopped to allow for a polycarb windscreen. A second polycarb strip continued behind the riders head. A third polycarb strip enclosed the back of the faring and was hinged at the top to allow opening and access to the luggage compartment. This hatch was held closed by a magnet screwed to the framework.

 

Wireless turn signals were mounted behind the front window facing forward and at the top behind the rider’s head facing backward.

 

The front turn signal is shown above.
A wireless speedometer was attached to the inside of the windscreen along with the turn-signal controls.

 


Rear view mirrors, which really didn’t work very well were bolted to the framework through the fabric.

 

 
A handle was attached to the framework just behind the nose cone to allow the vehicle to be lifted and moved around.

 


The weight of the entire vehicle was 83#. The weight of the faring, without the front mounting bracketry and rear faring support, was 16#.
 
Of course, the nagging question was how would the faring improve cruise speed of the EcoVia? In an attempt to assess that objectively, I spent two weekends doing four test rides over a 6 mile stretch of road that, except for one gradual downhill, was essentially flat. Three of the rides were without the faring to familiarize myself with riding behavior and the fourth was with the faring in place.

I must say up front that I no longer ride recumbents but instead ride an upright mountain bike. I never could go as fast on a recumbent as an upright, despite 21 years of riding an Avatar 2000.

I noted two speeds from each run. One was a speed past a traffic monitor set up to advice motorists of their speed that I encountered early in the ride. I had routine readings on an upright of between 17 and 19 mph. The second speed was the average for the entire six mile run.

Without the faring the speed past the speed monitor was 17mph and the average over the six miles was 14mph.

With the faring the corresponding speeds were 20 and 16mph respectively.

Needless to say, the speed increase with the faring was unexpectedly low, despite the faring appearing relatively streamlined.

Three reasons for the low improvement come to mind. One is the added drag from the flow under the faring, since its bottom is open. The second is that mechanical losses from all the drive components dominated the aerodynamic losses. The last is that a vehicle as high as the EcoVia has a large cross-sectional area than typical streamlined vehicles, even though its width approximates that of a bicyce.

The day I used the faring was a chilly 40deg F and the space within the faring was comfortably warmer that the outside with only my face and neck feeling the chill.

So against the original design criteria and compared to the Pedicar (below), how did the EcoVia fare?

 


1.       Weather Protection: Assuming the fabric was sprayed with ScotchGuard, only the riders head is exposed to moisture. Internally the wheels were covered with fenders. So like the Pedicar the EV provides weather protection.

2.       Statically Stable: The EV has a lean-lock to make it statically stable and the Pedicar is naturally so.

3.       Reasonable Cruise Speed: I feel the EV fall short here, at least with me riding it. The 16mph average should be closer to 20mph. The Pedicar had a 15mph cruise speed.

4.        Cargo Carrying Capacity: Currently the EV has about a 2cu.ft. cargo capacity which could easily be increased to 3cu.ft. The Pedicar easily has twice that.

5.       No Wider than a Bicycle: The EV has a width of 28” and the Pedicar 38”.

6.       Same Height as an Auto: Both the EV and the Pedicar meet this criterion.

7.       Comfortable Posture and Ease of Entry: Again both vehicles satisfy this criterion.

8.       Two-wheel Drive: Both vehicles satisfy this criterion.

9.       Car Type Wheels: The EVs wheels can be removed with one screw. They are all the same and it carries a spare. It is not clear how the one would remove the Pedicar’s wheels.

10.   Electric Assist on Hills: Attempts to add electric assist to the EV have been put on hold indefinitely because the electrical engineer assisting me had more important obligations. Two attempts to develop a motor controller were unsuccessful. Only a small fraction of the motor’s 600 Watt potential were delivered by the batteries. The Pedicar has no electric assist.

I would say the EcoVia met seven of the 10 criteria. Bumping up the cargo capacity to 4cu.ft. should be straight forward. Bringing the cruise speed up to 20mph appears to be a lot more difficult.

 Some final thoughts:

 
1.       Starting and the lean lock: The procedure for starting on a recumbent bicycle requires supporting the bike with one foot and keeping the other foot on the pedal. The pedal is thrust forward and the bike needs to be moving fast enough to maintain balance until the second foot can thrust on the pedal. With the EV starts in this fashion were usually successful. If a start failed due to lack of speed, one foot could be put down to maintain support.
 
With the addition of the faring it was difficult to get the support foot back to the ground after unsuccessful launches. The presence of structure and the narrow width of the faring inhibited getting a foot back on the ground. Several painful crashes ensued during unsuccessful launches. 
 
So successful launches with the faring required the use of the lean lock. Below, the disk brake that acted as the lean-lock for the EV.

    


When the lean lock is engaged the vehicle is like any other statically-stable tricycle. The level of static stability is therefore a function of the c.g. height, the track width and the load distribution of the wheels.

Engaging the lean lock also makes climbing slow-steep hills much easier. You don’t have to waste energy and concentration on trying to balance the vehicle at very low speeds, which is where balance is poorest.  

So for the EcoVia Mk2 I will be lowering the seat height from 24” to 20” and increasing the track from 20” to 24” to improve static stability when the lean-lock is engaged. The other improvement will be pivoting the faring at the back instead of the front to eliminate the weight and the foot interference produced by the faring-support structure around the front wheel.

Below is the EV with the seat height reduced about 4”. Compare this to the second picture in the post.

 


 
2.       Aerodynamics and the Delta Trike layout. Despite the poor performance of the faring, I am still bullish on the rear-drive delta-trike layout. The drive to the rear wheels does prevent clean streamlining of the wheels, but the overall package is very compact and that should keep the wetted surface of the faring at a minimum. The most logical addition to the faring design in a panel under the vehicle to enclose the faring. It is in this area that the rear-wheel drive and pivoting-wheel beams presents problems.
 
I do take hope in the success of the Velotilt design. While the Velotilt drives the front wheel instead of both rear wheels it is the design that is most similar to the EV.

 
 Granted, the Velotilt is much lower than the EV and the streamlining much more sophisticated, but the 6okph speeds the vehicle is capable of obtaining indicate there is hope for the EV to sustain 35kph.
3.       Future weight reductions: I feel that is should be possible to pull about 20# out of the current weight of 83# for the EV. Most of this will be in a significant simplification of the chassis.

a.        An 11 x 1 drive will replace the two-stage 7 x 3 system with it twin bottom brackets.

b.      The structure for front faring pivoting will be eliminated.

c.       The Soft-Ride-type seat suspension will be eliminated in favor of a mountain-bike shock connected to a link that holds the linkage that synchronizes the pivoting wheel beams. This will remove one large frame tube

d.      Hydraulic disk brakes will eliminate the brake synchronization linkage that allows one lever to activate both rear brakes.

e.      Tube size and gauge will be optimized and not overdesigned as is currently the case.

So I consider the EcoVia Mk1 to be a successful proof-of-concept of a two-wheel-drive tilting trike, but much must be improved in production prototype.

Hephaestus

Saturday, July 12, 2014

Graeme Obree's Beastie: The Lure of the Linear Pedal Drive




This post was inspired by Graeme Obree, two time world hour record holder on modified upright bikes who, at the age of 48 rode his Beastie streamlined prone bicycle into the record books last September. Obree was attempting to break the flying 200m sprint for human-powered vehicles which stands near 83mph. At 56.6mph, Obree came up a bit short. Nonetheless, he did break the record for a streamlined vehicle using a prone rider position, and more significantly, in my opinion, he broke the record for a vehicle using a non-circular pedaling motion.

The two pictures below show a kinematic model of the Beastie's drive mechanism and an enlargement of the resulting pedal path. The path is an elongated ellipse whose major axis is tilted slightly downward front to back.




In the pictures above the cranks rotate in a clockwise direction and the pedals move in a counter-clockwise direction around the ellipse.

Obree bested the existing record for a linear-drive and prone-posture streamliner held by Richard Byrne on Steve Ball’s Dragonfly of 54.9mph. The Dragonfly used both arms and legs moving in straight paths for propulsion. The picture below is from Human Powered Vehicles by Abbott & Wilson.


For the purposes of the following discussion, I consider linear motion to include pedals moving in a straight  line, pedals moving in large arc over a small portion of a circle, and numerous curves generated by four-bar linkages having paths that are significantly longer (in the leg-extension direction) than they are wide. These coupler curves could be egg shaped, elliptical, figure-eight shaped among others. In the case of the Beastie, the pedal path is an elongated ellipse.
When someone of a technical bent takes a close look at the bicycle for the first time, they invariably comment that there has to be a more efficient means for the body to generate mechanical power than circular pedaling. Since a runner’s feet don’t go in circles, it makes no sense that feet going in circles on a bicycle are neither natural nor efficient. More often than not, the conclusion is that feet moving in a near-linear path would be a significant improvement.
The drive mechanisms that will be discussed here fall into two broad categories, oscillating treadles and constant-torque treadles

Oscillating treadles consist of an input link permanently connected to an output crank through an intermediate link. When the output crank moves continuously, the output link moves back and forth between its extreme positions or oscillates. For a constant crank speed, the speed of the input link varies over the cycle and often comes to a complete stop at the limits of travel. By its very nature, one important characteristic of the oscillating treadle is that one cycle of the input link results in only one rotation of the output crank. Some form of gearing is usually required between the crank and the wheel. These systems work best with fixed gearing so that the vehicle motion carries the pedals through their motion-dead spots
 The crank slider (the core of every IC engine) is an oscillating treadle. The mechanism used in the Beastie was a offset-crank slider where the slider track is not lined up with the crank pivot. In addition, the pedal is located above the connecting rod. This produces a relatively horizontal-flattened ellipse located above the crank center, which accommodated the rider being located above the crank center.


Because friction associated with the slider can waste energy, a rocker link often replaces the slider for mechanism used for human power generation. The connecting rod moves through a short segment of a large arc instead of a straight path.

When used by Kirkpatrick McMillan in the mid 1800’s the crank-rocker mechanism was the first bicycle drive.

Oscar Egg, a world-hour record holder on upright bikes, used a crank rocker for a streamlined recumbent design. Notice that this is a fixed-gear system where the vehicle motion prevents the pedals from stopping at their dead spots.

And the prolific Gary Hale produces his Glider which employs a crank-rocker.

And the crank rocker is still used to propel most children’s kiddie cars.
Referring to the crank-rocker diagram again, if the pedals are located at point A, they will travel in a circle. If they are located at point B, they will travel in a large arc. If the pedals are attached to the connecting rod, at point C, they will travel through a hybrid of the circle and the arc, an elongated teardrop. These coupler curves have the advantage that the pedal continues to move at the ends of the stroke conserving some of the kinetic energy of the moving limbs. The downside of locating pedals on the connecting rod is the pedals are connected to the frame through two pivotal joints instead of one. This can result in more flexible connection (read sloppy) than a connection through only one joint.
Another oscillating treadle mechanism is a rocking slider. The slider is attached directly to the crank instead of through a connecting rod. To compensate for the transverse motion of the crank, the slider must rotate about its sliding point.
 The K drive, nicknamed because Miles Kingsbury used it on one of his streamliners, is derived from an elliptical trammel. The mechanism can produce a straight pedal path but as configured here it produced a long-thin ellipse. The pedal path produced by this configuration is very similar to that employed in the Beastie.

The other drive mechanism that will be discussed is the constant-torque treadle.

Unlike the oscillating treadle, the ratio of input lever speed to output shaft speed is constant (and as a result, so is the torque). There is a one-way clutch located in the cable drum which allows the input lever to return to the beginning of stroke without reversing the motion of the output shaft. Additional stops must be inserted to limit the input link travel. The ratio of input link motion to output shaft motion can be adjusted by changing the position that the cable attaches to the input lever. This is one big advantage of the CTT; it can incorporate a very simple means to achieve multiple gearing. Some form of return device, usually a spring, must be used to reverse the input link motion at the end of travel.

The CTT is the mechanism most often reinvented by those who would improve the design of the bicycle propulsion mechanism. It is also has been the most prevalent drive system after the rotary crank. It was used on the American Star pre-safety bicycle in the late 1800’s and you can still find numerous prototypes today. Steve Ball’s Dragonfly used a modified version of the constant-torque treadle, as did the Pedicar.




There are several reasons why a person designing a human-powered vehicle (HPV) would use a pseudo-linear pedaling motion.

1.       There is interference between the pedals and the steered wheel with circular pedaling motion.

W. D. Lydiard used a rocking-slider mechanism to reduce pedal-steered wheel interference on his entry for D. G. Wilson’s 1968 Human-powered-vehicle design competition, the Bicar. The picture is from the first edition of Bicycling Science by Witt & Wilson.

I experimented with a crank-rocker mechanism in an attempt to reduce pedal-steered wheel interference in my EcoVia commuter trike design.


I employed a two sided pedal in this design. The outboard side of the pedal holds the rocker link that supports the pedal. In this location it is spaced wide enough to clear the turning wheel. The inboard side of the pedal holds the connecting rod which is located above the wheel and includes a bend to clear the wheel. This is my interpretation of D.G. Wilson’s crank-rocker concept sketch for a recumbent bicycle.

2.       The foot and knee moving through a pseudo-linear motion take up less volume than circular pedaling
A classic use of linear motion for this reason is in the Pressodyne streamliner form the late 1970’s. The article is from the Spring 1980 issue of Human Power.

Here are a few highlights relevant to the current discussion. The pedal motion was truly linear using rollers to support the pedal arms. The stilts-version of the Pressodyne used cables that connected the pedals to one-way clutches. This was a constant-torque treadle approach but no efficient means of limiting pedal travel was provided and the pedals crashed into the stops. The three-wheeled version used a crank-slider approach which was much smoother. The smoothness was also due to the fact that there was also no freewheel in the system (fixed gear). So, when the vehicle moved the pedals moved and there was no issue with dead spots in the motion.
The shape of the Pressodyne was not far of the mark for the optimal streamliner shape. Notice the similarity with probably the epitome of streamliner design, the Varna Tempest. The tempest required a bigger nose to house the circular pedaling but had a smaller canopy.


And reducing swept volume of the leg and foot is undoubted the reason Obree employed a teardrop-pedal path in his Beastie.
3.       The linear drive is simpler that a pair of cranks, a chain and two sprockets.
The Mergamobile was a pretty simple approach as was the 1921 J-Rad. One used the different pedal locations to obtain three different gear ratios. Both design use constant-torque treadles.

4.       The linear drive is more efficient than circular pedaling motion.

The constant-torque treadle is the most popular design proposed for improving the efficiency of bicycle propulsion
.
The most publicized use of a constant-torque treadle was in the 1973 Pedicar.



Trevor Harris, a race car designer and designer of the iconoclastic Can Am Shadow produced the Harris Vertical in the mid 1970’s.

The Alenax Trans-bar bicycle was commercially produced in the 1980’s.

The Alenax was an almost a direct copy of the Svea manufactured in Sweden in the late 1890’s. Paul de Vivie, Velocio, the pioneer cyclo touriste, supposedly experimented with the Svea in his quest to find the perfect touring bicycle.
Notice both the Harris and the Alenax have adjustable cable-attach positions on their pedal levers for variable gearing and both have synchronization mechanisms to move the pedals in opposition to each other. The Harris uses a rocker linkage and the Alenax uses a cable loop.
When discussing the reinvention of the constant-torque treadle, I can’t help but hear Santayana’s quote “Those that cannot remember the past are condemned to repeat it”. In this case “know the past” is more appropriate. The following optimistic declaration that the bicycle has been greatly improved is a fun foil to discuss the shortcomings of constant-torque treadles
.

It also may be useful for the reader to review the section on Power in the following post.


Let us begin with why the constant-torque treadle appears to be more efficient than the rotary crank. Assume the rider exerts a force of F in a straight line with each leg. With a rotary crank the torque that is transferred to the wheel is F*sin(theta) where theta is the crank angle. The average torque over a cycle is 2F/Pi or .64F. So from the start, from a torque standpoint the CTT is 57% more efficient.

Unfortunately there are two factors that prevent this increase in torque from being converted to an increase in power
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Our linear-motion bicycle salesman states that his drive develops full power from the beginning. That is not true. At the beginning of the pedal stroke, the foot is stopped but the output shaft is moving at full speed. It takes a portion of the pedal stroke for the pedals to catch up to the output shaft and during this catch-up phase no force is being produce and, as a result, no power is produced. Both the Dragonfly and the Harris Vertical incorporated cams to gear up the pedal stroke in the beginning to allow the pedal speed to more quickly match the speed of the output shaft. However the cam must be designed for a specific gear ratio. So on the Harris Vertical, the cam will only be effective for around one gear selection.

Another problem is the pedaling speeds that can be sustained with linear drives are significantly lower than those that can be sustained with a rotary crank. This is due to the kinetic-energy fluctuations of the moving limbs. With linear motion the foot stops at the pedal extremes and the kinetic energy drops to zero. With circular cranks, speeds of 300rpm have been achieved because the kinetic energy is relatively constant.  Since power moves the bike and since power is the product of torque times angular velocity, lower pedal speeds result in lower power levels.

The rider is very diplomatic when asked for his impressions riding the linear bicycle. He says it is much better than the first prototype but he doesn’t say it is better than a regular bicycle.

The linear bicycle riders comments that his leg muscles have gotten bigger riding the linear bicycle is an indication that things have become less efficient as opposed to more efficient. When Paul Dudley White, President Eisenhower’s personal physician and bike advocate, rode the Pedicar, he also noticed that it put more strain on the thigh muscles.

One factor that is inconsequential for light-weight vehicles like bicycles but becomes a problem for heavier commuter vehicles is that with the CTT drive, the vehicle cannot be rolled backward. The one-way clutches lock up going backward causing the input levers to jam against the motion stops. This is the reason the Pedicar incorporated a reverse gear at the cost of a significant increase in complexity of the transmission.
There appears to be a means of accelerating the foot at the beginning of the pedal stroke that remains effective throughout an adjustable gear range. When cams were used above, they were inserted in series with the drive cable. I advocate using springs in parallel with the drive cable.

Assume a synchronizing linkage is used to connect the pedals and move them in opposition.  Springs are located so each pedal compresses the spring as the pedal is pushed forward. The springs exert no force at the beginning of the stroke and exert maximum force at the ends of the stroke. Assume the force at the end of the stroke is 2*F.

The combination of the synchronizer mechanism and the springs results in the force vs. pedal position shown in the first graph. With no external load, the zero-force position for the pedals will be at midstroke. From the beginning of the stroke to midstroke, the springs act to move the pedal forward, accelerating the foot. From midstroke to end of stroke, the springs resist forward motion and add to the force required to propel the vehicle. If the average force required to drive the vehicle is equal to F, then each pedal sees a force vs. displacement curve shown in the second graph. The pedal encounters an increasing force from the beginning to the end of the stroke. Since the leg can exert more force as it extends, this matches the pedal force to the legs ability to generate force.

One approach to determining the spring rate for theses springs is to select them so a resonant condition occurs with the moving leg mass. Let us say the moving leg mass for each leg is ½ the mass of the thigh plus the mass of the shin and the foot. From anthropometric data, that comes to about 13.5% of body weight. With a 170lb. rider that gives a moving mass of 23lb. Let the resonance be at 75rpm or 1.25Hz. That requires a spring rate of approx. 4lb./in. Assume a pedal stroke of 180mm or 7in., then F is 28lb.

28lb at 75rpm and a 14” stroke corresponds to 110W. So at a power level of 110W, the pedal force is zero at the beginning of the stroke and 56lb. at the end of the stroke.  The spring rate could be increased so negative to low forces are encountered at the beginning of the stroke for power levels higher than 110W.
After thinking so much about the Pedicar, I couldn’t resist speculating about a drive-system redesign that would address its shortcomings. I also assumed it would be a banking-three wheeler with front steering. As a result the pedal levers are two-piece with the support link outboard of a two-sided pedal and the input link inboard of the pedal. ( See my crank-rocker design for the EcoVia, above.)

 I have included a synchronizer linkage and accelerator springs to smooth out the pedaling. Instead of the Pedicar’s five speeds covering a range of 6:1, I use a shifting quadrant on the input link that can be rotated over an 8:1 ratio, but a range divided into 21 steps. The 8:1 ratio using 16t freewheels as the one-way clutches required a gear-up mechanism. I incorporated a forward and reverse gear set into that mechanism. Recall that, since the one-way clutches prevent the vehicle from being pushed backward, some means of disengaging the drive or having a reverse gear is necessary to move the vehicle backwards
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When I stood back and looked at the design, I realized that although it addressed the Pedicar’s design deficiencies, it is probably no-less complicated than the Pedicar’s drive, and no lighter in weight. Since the cost of all-weather human-powered commuter vehicles seems to be the greatest factor preventing their popularity, this would not be a good design approach. An ultra-wide range cassette with a single chainring is cheaper, lighter weight and allows the vehicle to be pushed backwards.

So the next iteration of the EcoVia will pass on the constant-velocity treadle.

There is one circumstance where the constant-torque treadle performs significantly better than conventional circular pedaling is when climbing the very steep hills typically encountered in mountain biking. Outstanding hill climbing performance is mentioned in regard to the American Star of the late 1890s and the Pedicar.
A more detailed explanation of hill-climbing problems associated with conventional circular pedaling can be found in the Kinetic Energy and Cyclic Energy Storage section of the Why Hill Climbing is Hard post.

From the standpoint of power generation efficiency (mechanical power out/oxygen in) producing power in pulses interspaced with rest periods is better that producing power continuously. The extra energy produced during the pulses is used up during the rest periods and this energy is stored in changes in the kinetic energy of the vehicle. If the vehicle speed drops below a certain level, the power cannot remain pulsatile and the rider must produce power around the complete pedal cycle instead of the usual pulses produced from 1 to 5 o’clock in the pedal cycle.

The constant-torque treadle is cadence limited but this is not a problem because the low cadences associated with steep hill climbing are low. The dead spots in the pedal cycle are only momentary with the CTT and torque is produced for almost all of the cycle while the foot only moves through its normal force generating range. Adding acceleration springs just improves the performance assisting foot motion at the beginning of the pedal stroke.

Come to think of it, a few of the restored Alenax Trans-bar bikes were sporting mountain-bike tires.
If Graeme Obree had propelled his streamliner with convention circular pedaling, he probably would have gone faster, but he would only have a prone-rider record. I believe the linear-drive speed record is technically more interesting.

Hephaestus