Reflections on the potential of human power for transportation

Sunday, March 30, 2014

Why Hill Climbing is Hard or Efficiency and Pedal Power Production

Climbing steep hills on a bicycle is one of the joys and can be one of the most uncomfortable aspects of the sport. Above, two of the great climbers of the Tour de France make it look easy. Federico Bahamontes, the Eagle of Toledo and Charly Gaul, the Angel of the Mountains during the 1959 Tour. Gaul won the GC the previous year and 1959 would see Bahmontes’ as the overall winner. Bahmontes won the King of the Mountains title an unprecedented six times, possibly making him the greatest TdF climber of all time. Gaul was noted for love for inclement weather.

(TdF cognoscenti will quickly point out that after Bahamontes, Lucien Van Impe won six KOM titles plus one GC. Richard Virenque won seven KOM titles. Virenque's intimate association with performance enhancing substances taints his abilities and excludes him from the top climber title. So in all fairness it is between Bahamontes and Van Impe. Gaul, along with a host of others won two.) 

So when climbing steep hills, other than working against gravity, is there anything different about how a cyclist generates power, as compared to riding on the flats? The answer is yes. During hill climbing the rider’s efficiency in generating power is reduced. Why this is the case is one of the topics covered in this post.

When commercial recumbent bicycles (Avatar, Hypercycle, Easy Racer etc.) made their reappearance in the 1980’s, one of the reasons touted for their superiority over upright bicycles was that the bracing of the rider’s back allowed for much greater pedaling forces to be developed. The error here is that greater pedaling forces may lead to greater accelerations, but they alone do not lead to higher top-end speeds. In fact, the higher pedaling forces that could be achieved blew out more than a few recumbent cyclists’ knees. Forces that can be sustained for 10 reps using a leg-press machine quickly wear joints out over the duration of century rides.

So, it is appropriate to discuss force, work and power. The concept of force is simple, something that results in a pressure or a tension on objects to which it is applied. Units are often Newtons or pounds. A force moving through a distance is work or energy. Units are often Newton-meters, Joules or foot-pounds. For something to change, the force must move through a distance and do work.
The rate of doing work is power, work done per unit of time. Power is the product of force times velocity. Units are often Joules/sec, Watts, foot-pounds/sec or horsepower. For future conversations, one horsepower is about 748 Watts. When a cyclist increases elevation going up a hill, work is done. Riding up hill at a given velocity results in power being dissipated. Similarly, a cyclist pedaling against air pressure at a particular velocity is dissipating power. Power makes the bicycle move.

Peak power levels that are developed by elite athletes fall off with time. For short durations, on the order of less than a minute the power comes from the chemical stores within the muscles themselves. Since the duration is too short for oxygen to be adequately delivered to the muscles, this is anaerobic power. For durations of about six seconds, peak power levels 2hp. have been generated. Elite cyclists (Eddy Merckx for example) could generate .5hp. for about an hour. These aerobic levels are limited by the rate of oxygen consumption. For all-day activities, this level drops to about .25hp. due to toxic byproducts building up in the muscles.  Detailed graphs of power generation vs. duration can be found in books like the Third Edition (2004) of Bicycling Science by D.G. Wilson. Curiously, the unit of horsepower was supposedly the power level that could be sustained by a work horse all day. The peak power from a horse is about 12hp.


One factor that limits mechanical power produced aerobically is the rate of oxygen consumption, VO2. During the 1960s, when studies were being done on the feasibility of man-powered flight, a relation between VO2 and power production was empirically determined. 1 liter of oxygen consumed per minute would result in .1hp or 75W of mechanical power production.  What was overlooked was the fact that there are various efficiencies assumed in this relation. Some of the efficiencies are related to the bioenergetic processes going on in the muscle and some are related to the mechanical conditions of the activity used to generate the power. While it is difficult to modify the characteristics of the activity to improve the efficiency, it is rather easy to modify them to reduce the efficiency. This post will deal with three aspects that influence the efficiency of pedal-power generation, impedance matching, cyclically-varying-speed-crank speed systems and system kinetic energy.


The figure to the right is a plot of the force vs. velocity for the muscle group that flexes the elbow under maximum stimulation. This was empirically generated by D.R. Wilkie in 1950. The equation for the curve is to the right. Notice that if the load is above 48lb., the load cannot be moved and no useful work is done. At the other extreme, at zero load, a velocity of 21ft/sec can be developed but again, no useful work is done.

Now suppose we have the device pictured right, where the length “N” can be adjusted. The objective is to select an N that results in the highest velocity of the 48lb. weight, based on the graph of elbow-flexion performance shown above.

N, inches
P, pounds
V, ft./sec.
V of weight

The chart above shows the results for eight different values of N. Notice that for N of 3, the maximum power is generated and the weight moves the fastest. For this muscle group, the peak power is generated at 1/3 the maximum force and 1/3 the maximum velocity. Adjusting the length of N is analogous to a cyclist shifting gears on a bicycle to find the “sweet spot”. The “sweet spot” allows the cyclist to maximize the bicycle’s velocity for a given level of effort. The cyclist can pedal in a less-than-optimal gear, but the efficiency will be reduced and the oxygen consumption for a given power level will be elevated over the minimal optimum.


Cyclically-varying speed crank systems, CVSCS, for short, like fashions, seem to come and go. Attached to rotary cranks, they increase and decrease the crank speed (and inversely the gear ratio) in an attempt to improve aerobic efficiency. Recently some of the Tour de France racers have been using elliptical chainrings for the time-trial stages. The elliptical chainring is probably the oldest of the CVSCS, having been used on early safety bicycles over 100 years ago.  Archibald Sharp in his 1896 technical masterpiece, Bicycles & Tricycles, discussed the technical aspects of elliptical chainrings. More recent CVSCS are BioPace chainrings and the Powercam  crank mechanism. 
When I began my graduate research on optimization of human power production under Prof. Ali A. Seireg at the University of Wisconsin, the initial direction of the work was to focus on the effects of using non-circular-pedaling motions generated by an adjustable four-bar linkage. Since the curves generated by this linkage often had associated velocity patterns that were not optimal or even desirable, it was necessary to insert another mechanism between the linkage system and the load to produce adjustable velocity fluctuations that could modify those generated by the linkage. After some initial testing, it became clear that the velocity patterns were more important for power optimization than were the shapes of the pedal paths.

The photo, the table and the graphs that follow are from an article in the April 1986 issue of Soma: Engineering for the Human Body, published under the umbrella of the ASME. The graphs and photos were taken in turn from my doctoral thesis in mechanical engineering.

The research apparatus for my thesis is shown above. I was involved in designing all the components except the force-transducer pedal, which was developed for a previous research project. The use of a supine rider position was a result of directing the results along the lines of a commuter vehicle design. The novel feature of the apparatus was you could measure oxygen consumption, average and instantaneous force, velocity and power levels. The majority of tests were run at an average power of .15hp., with selective tests being run at .225hp.

The means of producing the velocity fluctuation was by using two universal joints. A single universal joint produces a velocity fluctuation when the input and output shafts are angled to each other. They were hooked together in phase so the velocity fluctuation was squared instead of the conventional orientation that cancels out that fluctuation. The cyclic angular fluctuation was

Output speed/Input Speed= ((1-sin^2(C)*sin^2(B))/cos(B))^2

where C is the crank angle and B is the offset angle. The maximum offset angle that was recommended for use was 45deg. and this resulted on a velocity fluctuation of +/-62%. This corresponds to an elliptical sprocket having a major/minor diameter ratio of 4.25/1. The velocity fluctuation of +/-25% corresponded to a major/minor diameter ratio of 1.66/1. Even the 25% setting would be considered extreme by current elliptical sprocket fashions.

The multiple compliances in the system deformed the fluctuation pattern in the manner shown below, shifting the velocity peak earlier in the cycle.

The phase relation between the pedal path and the fluctuation pattern could be changed over seven positions before repeating. The zero-phase position was when the pedals were mid-stroke moving forward and the fluctuation was at its lowest velocity point.

Since the readers may be more familiar with photos of current elliptical sprockets, for convenience, the various phase relations are represented as a crank arm that can be oriented in various positions on an elliptical sprocket. The chains that would connect to the rear derailleur extend horizontally to the left at the top and bottom of the chainring.

The powerful feature about the test apparatus is that by playing with the phase of the fluctuation, one could cause and measure changes in oxygen consumption while maintaining a constant average mechanical power level. The efficiency of the activity was being changed. And, while the 1liter VO2/.1hp. ratio was only improved on once, (.87 at 25% at a phase of 6 and .15hp.) many higher (less efficient) ratios were achieved. In the subsequent graphs, the velocities and forces plotted are in a normal direction moving away from the subject while the power values are the total values for the normal and tangential directions combined. A note about the selection of 50rpm as the standard pedaling speed. Since the high fluctuation of 62% caused very high peak pedal velocities, 50rpm was the highest average pedal velocity that could be sustained over all conditions.

 Above is a graph of VO2 vs. phase for .15hp., 50rpm and a 62% velocity fluctuation

 Here is the same test sequence along with other measurements. Addition cases of 25% fluctuation for power levels of .15hp. and .225hp. are listed.

  Above is the graphical data for 50rpm, a phase of 7 at 62% and .15hp.

Above is the graphical data for 50rpm, a phase of 3 at 62% and .15hp.

Lastly is data for 50rpm, a .225hp. power level with a phase of 6 at a 25% fluctuation. This is followed by a test at the same power level with no fluctuation. The VO2 for the 25%-fluctuation case was 17% lower than for the no-fluctuation case.

For use in subsequent discussions, it may be convenient to refer to a pedal cycle for an upright cyclist viewed from the crank side. For simplicity, divide it into four quadrants.  From 1:30 o’clock to 4:30 o’clock, the power stroke zone, this will be referred to as the downstroke. From 4:30 to 7:30, this will be the backstroke. From 7:30 to 10:30, this will be the upstroke and from 10:30 to 1:30, this will be the forwardstroke.

Looking at this data, one could observe that we reinvented the elliptical sprocket. Fluctuation phases that slowed the velocity (and increased the gear ratio) through the power stroke (1.5 to 4.5 o’clock for upright pedaling) produced significantly lower VO2s than those that increased the velocity through the power stroke.  Looking at the fluctuation phase crank sprocket diagram above, having the crank arm in positions 6 & 7 for lowest VO2 looks very similar to the orientation seen in actual bicycles.
It is interesting that even though the most efficient phase cases (6 & 7) tend to make the velocity profile more constant across the stroke, the actual power generated was over a narrower zone than a constant velocity system. We can consider this narrower power production zone as a pulsatile power pulse, P3. The power is more pulsatile than in the no fluctuation case.  Since both the Powercam and BioPace systems rely on producing P3, one may assume this is more efficient than the more uniform power distribution case.
One last observation on the research. Since it was clear over various fluctuations that VO2 was not proportional to average power, was there any measure to which VO2 was proportional? The average mechanical power was the average of the product of instantaneous force and the instantaneous velocity summed for both the normal and tangential directions. There is an arbitrary power calculation equal to the product of the average total force and the average total velocity. We christened this product physiological power. It appeared that VO2 was proportional to physiological power, high average forces times high average velocities require high oxygen consumptions.

I also have had experiences using a Durham elliptical sprocket, a Powercam and several variations of BioPace chainrings. No formal testing was done but I will share a few subjective observations.

I rode a 25mi. time trial with the Durham Elliptical. It made pushing big gears more comfortable than round chainrings. I purchased the 60T version. It worked very well standing up pedaling but its large size prevented it from being used on long steep hills.

The Powercam (a.k.a. the Biocam and Selectocam) has produced some impressive competition results. Scott Dickson finished second in the 1979 Paris Brest Paris cycling marathon, the first American to finish that well.  I used the Powercam briefly on an upright bike. The most noticeable performance feature was it was very difficult to stand up and pedal. When I bought an Avatar recumbent several years later, I mounted the Powercam on it. It had been suggested that it might work well for recumbent pedaling because you couldn’t stand up and pedal on a recumbent. It was good advice, and the Powercam improved on the notoriously poor hill climbing performance. 

The cam allows a more rapid change in pedal velocity than a non-circular chainring. The explanation for how the PC functions is that the gear is very high through the forwardstroke. As the downstroke is entered the gear drops rapidly and before the leg muscles can reduce the high force they needed previously, a large power pulse is generated. (Large force*high speed=large power pulse). When pedaling hard going up hill, you could feel the bike surging, speeding up and slowing down as the extra-instantaneous power from the pulse was put into the system. To absorb the excess power, the bicycle must speed up slightly and slow down after the pulse. To a much lesser degree, this speedup was also associated with the more extreme-shape versions of the BioPace chainrings. When used on mountain bikes, this power pulse could break the tire loose and the rider would loose traction. The tire breaking loose is often the kiss of death on steep climbs because it could end forward progress and cause the cyclist to put down a foot to prevent falling over. Hence the subsequent term of derision for suspension systems that bob during pedaling, “biopacing”.

I used the BioPace chainrings on both an upright and a recumbent. Correct phasing when used on a recumbent was questionable because the chainrings needed to be rotated ¼ of a revolution forward and the holes spacing only allowed for moves of 1/5 of a revolution. I thought that the increasing ovalarity from the large to small sprockets made sense, since the smaller ring would be used for hill climbing. Like the Powercam, but to a lesser degree, standing and pedaling in the smaller chainring didn’t seem to work as well as sitting. Using the small ring on a recumbent appeared to improve hill climbing speed.


The Powercam, BioPace chainrings and to a lesser extent elliptical and circular chainrings produce a P3 (pulsatile power pulse) interspersed with rest periods for the muscles. Since the external power demand is essentially constant, and the power production is intermittent, the excess energy (pulse energy less power demand energy) must be stored and recovered to accommodate the difference. The energy is stored in the kinetic energy of the bicycle/rider system. The excess energy storage is a function of the system mass and the square of the velocity change. 

KE= ½ M*(V2^2-V1^2)

Where V1 is the system velocity before the power pulse and V2 is the system velocity after the power pulse.
I have come up with a measure of the effectiveness of the energy storage capacity of the bicycle/rider system in relation to the power demand of the exercise. An activity with a lower power demand requires the storage of less kinetic energy to modulate the P3. My measure is a time constant, Tes (energy storage) equal to the kinetic energy of the system divided by the power required for the exercise.

As Tes decreases, it becomes more difficult to sustain P3. I inadvertently happened to determine what may be a minimum value of Tes for efficient power generation. I purchased a Monarch bicycle ergometer to use for off-season training. When I tried to pedal at a power level of about 200W it was very uncomfortable to sustain. I concluded that the system didn’t have enough inertia to modulate my power pulses. The ergometer had a 20” diameter aluminum flywheel and a gearing of 44/14. I decided to switch to 3/8” pitch industrial drive components because it allowed me to fit a 72T crank sprocket within the chain covers. I used a 10T cog on the flywheel, thus doubling the drive ratio. This resulted in the pedaling becoming reasonably comfortable. The kinetic energy of the system at a cadence of 70rpm was 538 Joules. Tes was therefore 538J/200W=2.7sec. So let us say a minimum value for Tes is 3sec.

Let’s compare this 3sec Tes to values for two on-the-road cases, a top athlete riding on the flats and climbing a steep hill.  Our cyclist has a system mass of 200lb. For the on-the-road case, our cyclist is riding at 25mph (36.7ft/sec) and is generating ½ hp. The Tes is 5671 Joules/375W or 15.2sec. For the 30% grade hill climb our cyclist is moving at 2.5mph (3.75ft/ sec). The Tes is 59.2J/375W or .16sec. So the Tes can vary by almost two orders of magnitude over the extremes of riding conditions.

When the Tes drops below a value of about 3sec, the rider must begin producing power during the forwardstroke, the backstroke and the upstroke of the pedal cycle. The power generation under these conditions is much less efficient than the power production during the downstroke. This is the reason that climbing steep hills becomes so difficult. The aerobic efficiency of power production has been significantly reduced. I have been passed by runners of lesser athletic ability while pedaling up steep hills.
So if anything, what can be done to improve the efficiency during climbing steep hills?

One approach that most riders uses is to stand up on the pedals. If you allow your body to sink when the pedal is passing through the downstroke, the center of gravity for the system with respect to the road sinks as well and the speed of the system moving vertically fluctuates. Since the power demand is now non-constant, if allows rest periods in power production and improves aerobic efficiency.

Clearly, P3 systems do not work because sufficient kinetic energy can not be stored in the moving mass of the system. A coworker has had some success with placing a spring in series between the pedals and the drive system to periodically store and release energy. 

A few years ago, I added a system that stored the energy in a long ½” diameter rubber cord to my EcoVia commuter trike. I could adjust the spring rate by adding or removing wraps of rubber. However, over a range from very soft to a very stiff rubber spring, my hill climbing performance was not as efficient as when using a round chainring. My only conclusion was that while my coworker used a metal spring, my rubber spring may have dissipated too much energy.

The hill drive system in the uncharged state. In the picture above, the bungee cord at the very right represents the energy storage medium and the sprocket at the very top has a one-way ratchet.

The same system is the charged state. Notice the displacement of the crank from the discharged to charged state. This shows the windup for the cyclic energy storage. The bungee has moved to the left, shortening the length of the drive side of the chain.

Lastly we come to that old favorite, the constant-torque treadle.

We know from the historical record that these systems can not be pedaled very quickly and consequently cannot produce high power levels. However, they do produce a constant torque throughout the stroke and this has to be more efficient than applying a large force through the forwardstroke, backstroke and upstroke of the pedal cycle. And there is some historical evidence that such systems excelled at hill climbing.

And what of Bahamontes and Gaul? Both used unorthodox climbing styles. Gaul used small gears and would spin up the hills. Bahamontes would alternate between sitting for 16 revolutions and standing for 16 revolutions. Their performances showed that each benefited from their preferred techniques.

Wow, did you really just read all that? You must almost be as big a bike-tech nerd as I am. On the upside, you will have plenty to think about as you slog up the next long hill!


Monday, December 30, 2013

The Technical History of the Bicycle: Part 3, The Safety Bicycle

This final installment of the “Technical History of the Bicycle” will take us from the Michaux velocipede to the modern safety bicycle. The modern bicycle owes it current configuration largely to the use of the chain-and -sprocket drive. The details of the evolution of the chain and sprocket drive and related multi-speed transmissions are covered in Frank Berto’s comprehensive book, “The Dancing Chain” so I refer those interested in the associated details to that source. Here we will discuss the evolution from a higher level and discuss some of the interesting dead ends that were developed along the way.

McMillan’s bicycle, discussed in Part 2, had almost all of the characteristics we associate with the modern bicycle.

To clarify that assertion, let me list five features of the bicycle. Of note, because of several record performances by Fran├žois Faure on a recumbent during the 1930’s, the Union Cycliste Internationale, UCI, came up with some very specific dimensions for a racing bicycle to prevent recumbents from being considered valid vehicles for competition. For the purposes of discussion I will keep things more general.

1       1. Two inline near-equal sized wheels 20 to 30 inches in diameter
2      2. Steering by rotating the front wheel about a semi-vertical axis
3      3. The rider seated between the wheels with the pedals below the rider
4     4. The pedals drive the rear wheel
5     5. The ratio between pedal rotation and wheel rotation can be something other than 1:1

The problems with McMillan’s design are a result of the crank-rocker mechanism he used. The ratio of pedal strokes to wheel revolutions is fixed at 1:1. The pedal cadence must be low due to kinetic energy fluctuations in the limbs (the fixed-gear nature of the drive helps with this). The drive has dead spots at the ends of travel. The direction of pedal motion does not point to the rider’s center of gravity, which would maximize the development of pedal force. This drive, also known as a harmonic treadle, is still found in children’s kiddie cars where performance is not an issue.

It appears that McMillan did increase the diameter of the drive wheel to get more vehicle speed per pedal stroke.

When Pierre Michaux added pedals to the Draisienne, the pedal location being in front of the rider necessitated that they attach to the front/steered wheel. The limitation that one crank revolution resulted in only one wheel revolution caused increasing drive wheel size to get more speed, a trend that was only limited by the necessity that the rider be able to straddle the wheel. These vehicles were known as Ordinaries, Penny Farthings, High Wheelers (I suspect the latter term came into use only after the safety bicycle became common) or just plain Bicycles. To minimize the coupling between pedal thrusts and steering inputs, the steering axis was nearly vertical and the direction of applied pedal force was vertical as well. This placed the rider directly over the front wheel where only the slightest obstruction to wheel motion caused the rider to pitch forward into a “header”.

Despite the header tendency, the ordinary became quite refined. Tangent spoking of the drive wheel, double-butted tubing, ball bearings, ergonomic saddles and handlebars were improvements on the basic design. And I must admit the simplicity of the Ordinary made it a beautiful machine. In fact, I saw a touring exhibit of bicycles from the Smithsonian during 1976 that featured a restored 1888 Columbia Light-Roadster Ordinary with its black frame and nickel plated accents. It was, and remains, the most beautiful bicycle I have ever seen.

Although Frank Berto points out that a front-steering, rear-chain drive safety precursor was built as early as 1869 by Meyer and Guilmet, the majority of attempts to remedy the “header problem” stayed closer to the Ordinary design. 

To reduce or eliminate headers, three approaches were taken in addition to the modern safety design. The rider was moved back from over the large front wheel by an intermediary-drive mechanism. The front wheel was reduced in size and some type of gearing was used to increase the wheel-pedal rotation ratio. The ordinary was turned around with the big wheel in the rear doing the driving and the little wheel up front doing the steering.

Several bicycles employed crank-rocker linkages. The rocker link oscillated back and forth, moving a connecting rod that caused a crank to rotate. Pedals could be attached to the rocker link or the connecting rod.

The Singer Xtraordinary from 1885 used a crank-rocker linkage to move the pedals back from the driving wheel and reposition the rider. The pedals were attached to the connecting rod (similar to point C, above) so the pedal path was egg-shaped but almost elliptical. The long axis of the path was oriented at an approximately 45deg. angle with the larger arc facing away from the rider. Unlike having the pedals attached to the rocker link, which stopped moving at its extremes of travel, the egg-shaped pedal path kept the feet in continuous motion, more like a circular-pedal path then a pseudo-linear pedal path.

The Facile and Geared Facile from 1887 (below) also used a crank-rocker linkage to move the rider rearward, but in this application the pedals were attached to the rocker link (point B, two pictures above).


With the regular Facile, the cranks were connected directly to the front wheel. With the Geared Facile, the cranks were interconnected by an axle that rotated freely in the front wheel hub. There was a gear attached to the connecting rod that drove a second gear attached to the wheel. If the tooth count on the crank gear was Nc and the tooth count on the wheel gear was Nw, then for each pedal revolution the wheel would move 1+Nc/Nw revolutions. This would allow a smaller wheel to be used and maintain the same vehicle-to-crank-speed ratio. I must confess that the Geared Facile is my favorite linkage-driven Ordinary bicycle because of the elegance of the drive mechanism.

The crank-rocker mechanism was used in numerous bicycles in the late 1800’s. As mentioned elsewhere, the problems associated with dead-spots of these linkages were reduced because whenever the wheel moved the linkage moved. The kinetic energy of the system kept the pedals from stalling at the ends of their travel. Many examples can be seen in Archibald Sharp’s xtraordinary book, “Bicycles and Tricycles: An Elementary Treatise on Their Design and Construction”, published in 1896 and republished by MIT Press in 1977. (Thank you D.G.W.!)

The Kangaroo Safety from 1884 employed a split-crank approach.  There were chain-sprockets on either side of the wheel hub and crank sprockets attached to each crank arm. Chains connected the crank sprockets to the wheel sprockets. This allowed the virtual center of the crankshaft to be located below the wheel center and the wheel to be geared-up and therefore made smaller in diameter. One wonders if the backlash between the two pedals through two chain drives was disconcerting to the novice rider.

The Crypto-Bantam Safety used an internal crank-hub planetary gearbox to increase the front wheel speed and allow a drastic reduction in wheel size.

The model above was an early version of the design from the 1890s. The clean lines and triangulated frame look very modern and the rider’s position could almost be called semi-recumbent. I suppose this should be no surprise since the planetary-hub drive located in the front wheel is a recurring favorite approach for recumbent designers.

One obvious solution to the Ordinary’s header problem would be to turn the design around, which is what was done with the Eagle from 1890. Unfortunately, since the conventional Ordinary’s saddle location was slightly behind the wheel hub, the Eagle may have had the tendency to tip backward. 

The American Star from 1884 took the Eagle concept and added a novel drive system to allow the saddle to be located in front of the wheel hub.

The Star was driven by what I will call a constant-torque treadle. Of the precursors to the modern safety bicycle, I saved the Star for last because of its transmission. After the chain and sprocket drive, the constant-torque treadle is probably the most popular alternative transmission. I tallied at least 16 uses of this approach, the last being a bicycle from the 1990’s.

Unlike the crank-rocker mechanism (or harmonic treadle) the constant-torque treadle has essentially a constant ratio between pedal speed and wheel speed. The average output torque over a pedal cycle is about 1.5 times that of a rotary-crank drive.

 The cable  is wrapped around a pulley that is connected to an output shaft by a one-way clutch or ratchet. Applying force to the pedal lever causes the cable to unwind and stretches the return spring. The rotation of the pulley causes the output shaft to rotate. Removing the force causes the cable to wind back up due to the force of the return spring. As the pulley rotates to wind the cable back up, the output shaft remains stationary.

The tensile member could be a cable, a belt or a chain. The cable mounting location on the crank lever can be varied to produce different gear ratios. The individual pedal levers are often coupled so as one moves forward the other moves back. The cable drums can be made non-circular to cause the gear ratio to increase from beginning to end-of-travel (Of course this makes the drive an increasing-torque treadle instead of a constant-torque treadle!). Prone to dead spots at the ends of travel like the crank-rocker, it nevertheless appears to have demonstrated outstanding performance in climbing very steep hills when low pedal cadences were used. I will go into more detail on the reasons for this performance in an upcoming post on human-power production.

That brings us to the Rover Safety of 1887, what historians consider to be the first true safety bicycle.

Let us agree that all of the bicycles we reviewed were safer that the conventional Ordinary in terms of addressing the header problem. Then way, among a consumer base that was very pro-Ordinary, did this design become the new standard? By moving the propelling function to the rear wheel and having the front wheel only do the steering, the problem of pedal forces causing unwanted steering inputs was eliminated. The gear ratios could be easily changed, originally off the bike but later while riding. However, I do not feel that either of these improvements were enough to supplant the modified-Ordinary approach. The most profound advantage was the modern safety bicycle was significantly more aerodynamic than the Ordinary. And given the lure of the bicycle is that one could travel faster than any other non-motorized vehicle at the time, greater speed was an improvement that could not be ignored. Traditional Ordinary riders initially said the safety bicycles, like tricycles, were for older individuals and people with families who could not risk injury, but when faced with being passed by riders on safety bicycles, they dropped taunt and changed horses.
The improvement in performance in an article of sporting equipment is difficult to ignore.

The 1930s saw a resurgence in horizontal, recumbent bicycles (the laid-back rider orientation had periodically surfaced previously, but this approach was not singled out for its improved speed potential) and they were beginning to show dominance over the modern safety bicycle in at least short-distance track competitions.

This might have been another step in bicycle evolution but the Union Cycliste Internationale decided to intervene and made the decision that these new designs were offering unfair advantages to their riders.  As mentioned in the beginning of this post, they came up with dimensional requirements for racing bicycles that would exclude recumbents from competition.

One might have been forced to wonder what the next stage in bicycle evolution would have been like, but due to the efforts of Prof. Chester Kyle at the University of California, Long Beach, bicycle evolution was resumed with the formation of the International Human Vehicle Association forty years later.
From a racing perspective, the bicycle may be near its performance limits. The flying 200m speed of 83mph and the hour-long speed of 56mph will no doubt be eclipsed, but not by great amounts. From a bicycle evolution standpoint the frontier is improving commuter vehicle performance to the point where, in first-world countries, the bicycle is more than just a commuter novelty for the enthusiast, it is a viable ecologically friendly alternative for the masses.