Efficient pedaling
Simulation of pedaling
Leg muscles
Hip muscle strength
Knee muscle strength
Total muscle strength
Dead center
Muscles passing one joint
Muscles passing two joints
Pedaling power per joint
Ankle muscle strength
Pedal pressure by leg weight
Energy costs of speed changes leg
Cadence and efficiency
Changing pedaling movement
Oval chainwheel
Seat angle
Crank length
Distance hip crank axle
Pedaling standing
Climbing with a recumbent
Graphical model
Graphical model for older browsers
Links
This page gives a closer look at efficient pedaling on a recumbent. The page was constructed because of a number of articles in Ligfiets& 20085 on climbing with a recumbent. Specially the experiments in the article "Kracht zetten" of Kees de Rooy were interesting. His measurements suggest that the maximum pedal pressure depends considerably on the recumbent or upright position of the cyclist. This would lead to the conclusion that a recumbent rider can use his muscle less efficiently than an upright cyclist.
Here we conclude:
In a graphical model the reader can experiment with the geometry of the pedal movement. The geometry can be adjusted by using the mouse, dragging the pedal circle or by filling in the sizes (in mm.).
In this way plots of different geometries can be compared. The plots can be removed by clicking on "ClearGraph". The pedal movement can be temporarily stopped and restarted by clicking on "Stop" or "Start".
The color "red" shows the angular velocity of the thigh around the hip at a constant angular velocity of the pedals; the color "purple" shows the angular velocity around the knee.
The color "orange" gives the sum of kinetic and potential (="total") energy of one leg of an uprightcyclist and the color "green" of a recumbentrider. Through the "Cadence" field, the number of revolutions can be adjusted, which affects the kinetic energy per minute.
By clicking on "BothLegs", plots are shown, which sum the "total" energy for both legs. By clicking on " Kinetic ", only the kinetic energy is shown; by clicking on "Potential", only the potential energy is shown.
The fields "PowerRec" and "PowerNor" show the power that respectively a Recumbent or an upright (Normal) cyclist should deliver to a leg to turn around the crank at a constant speed. Where the energy of a leg decreases, this power again is delivered to the pedal.
At the pedal an arrow is drawn for a recumbent or upright bike, which shows the force that should be delivered by leg muscles or is delivered to the pedals beacuse of the movement of the leg and foot.
For a further explanation, see paragraphs Pedal pressure by leg weight and Energy costs of speed changes leg.
By means of the field "Chainwheel" one can choose one of the popular oval chain wheels of this moment and compare the pedaling behavior. With the field "OvalCrankAngle" the angle between crank and maximal chain wheel diameter can be adjusted. At oval chain wheels the relative angular velocity of the pedal is shown with the color "blue".
See paragraph Oval chainwheel.
Also in a primitive way the ankle movement can be adjusted.
Field "FootanglePush" contains the angle between foot and shin while pushing the pedals. This angle is assumed fixed between pedal angle "PushAngBeg" and PushAngEnd". Notice this angel is measured at the anke joint, not at the bottom of the foot.
Field "FootanglePull" contains the angle between foot and shin while pulling the pedals. This angle is assumed fixed between pedal angle "PullAngBeg" en PullAngEnd".
Between these "fixed areas" the foot is gradually moving (the Cosinusfunction is used) from a constant angle to the next constant angle (e.g. from "pushing" angle to "pulling" angle). If the leg is getting too short, the angle of the ankle is automatically adjusted (enlarged).
With the button "Lockankle" the angle of the ankle can be locked.
Field "KneeAngleLimit" reduces the maximal angle between thigh and shin (to avoid muscle damage around the knees).
See paragraph Changing pedaling movement.
The graphics is written in JavaScript with "Canvas", which makes it possible to the user to change the coding or calculation. At older browsers the JavaScriptlibraries "wz_jsgraphics.js" and "wz_dragdrop.js" are used, which can be downloaded from the Javascriptwebsite of Walter Zorn. If this link does not work anymore, there still is the Javascriptarchive of Walter Zorn.
The next pages will contain a more detailed explanation of the graphical model. We first look at the pedal movement with locked ankles.
The next mechanical model of leg muscles (left) comes from Forces in bicycle pedaling by Jim Papadopoulos. Notice that some muscles span two joints like e.g. the Rectus Femoris, which spans the hip and the knee. This makes it very complicated to create a model for computation of leg muscle power. In the simplified model of leg forces (right), it is assumed, that only muscles are used, which span one joint.
We also assume the cyclist is riding with constant speed and also the pedals are rotating with (almost) constant speed. The upright cyclist is sitting on the seat and the sitting position of both the upright and the recumbent cyclist do not change. The shoes are fixed to the pedals, therefore not only pushing but also pulling forces from the leg can be passed to the pedals. The ankle joint is locked at a fixed angle; the muscles spanning the ankle do not contribute to the pedal movement.
A+B=Quadriceps D+E=Hamstrings G+H=Triceps Surae 

Model leg muscles  Model leg forces 
Here we examine, how muscle force which stretches or bends the thigh at the hip, is transferred to the crank.
The "red" chart of the the graphical simulation with locked ankles, shows the angular velocity of the hip at a constant angular velocity of the pedals.
This chart looks very weird. At the stretching phase of the leg we see the angular velocity of the hip joint is constantly increasing. When the thigh is almost fully extended, the angular velocity decreases very quickly, and both the thigh and knee abruptly stop the movement and change direction of motion. The greater the distance between hip and pedals, the more abrupt this changing of direction will be.
The figure above displays how the "hip force" is transmitted to the crank. The thigh moves around the hip and pushes at the shin with a force (red), perpendicular to the thigh. The shin freely rotates at the knee and at the pedal and is only able to transfer forces, that coincide with the shin (brown).
This shin force is transferred to the pedal and causes there the effective pedal force (green), perpendicular to the crank.
At the hip in fact there are 2 transfer rates which partially compensate each other. During stretching of the hip with constant angular velocity and torque, the speed of the foot would decrease to zero and the force would become very large. But because the foot is attached to the pedal and moves circularly instead of linear its speed will decrease less and also the force will grow less fast.
Looking closer to the the graphical simulation with locked ankles, then we conclude:
Often there is the statement, that muscle foirce from the leg is only efficiently transferred to the crank if the direction of this force is perpendicular to the crank. One can easily see this is not true for the muscles around the hip by looking at a simulation with thigh and crank of equal length and a fully stretched foot. At the stretching pedal stroke thigh and crank rotate exactly parallel and synchronous. The force from thigh on the shin is exactly equal to the force from foot on the pedal: it has the same direction and the same size. This is not only true when shin and resulting force are perpendicular to the pedal, but at any angle of the stretching pedal stroke.
The figure above displays how the "knee force" is transmitted to the crank. If only the muscles around the knee are activated, the leg can freely rotate around the hip and also around the pedal. This means that muscle forces around the knee can not cause any force perpendicular to the (dotted) line between hip and pedal. The direction of the forces at hip and pedal, caused by knee muscles, will coincide with the (dotted) line through hip and pedal (brown).
Note that at constant muscle force and constant muscle torque, the force increases (torque = force * distance) if the leg is stretched more, because the distance between force line and knee decreases.
This force is transferred to the pedal and causes there the pedal force, perpendicular to the crank (green).
The "purper" chart at the simulation with locked ankles shows the angular velocity of the shin relative to the thigh at a constant angular velocity of the pedals.
Just as at the forces around the hip also at the knee there are in fact 2 transfer rates which partially compensate each other. During stretching of the knee with constant angular velocity and torque, the speed of the foot would decrease to zero and the force would become very large. But because the foot is attached to the pedal and moves circularly instead of linear its speed will decrease less and also the force will grow less fast.
Looking at the simulation with locked ankles, we conclude:
Also at the knee it is not necessary, that the resulting force at the pedal is perpendicular to the crank. It is difficult to make this visible, but it follows from the law of conservation of energy. The energy delivered by knee muscle force can only be delivered to the crank.
The figure below combines hip muscle strength and knee muscle strength.
Both forces are independent of each other and can be summed (by vector). This sum of forces (red) is passed to the pedal and causes there the effective pedal force (green), perpendicular to the crank.
The stretching and bending phases around hip and knee mostly coincide, but not always. Between 0 and 45 degrees the hip is bending and the knee is stretching. And immediately after 180 degrees the knee must bend, while the hip still is stretching.
At literature about upright bicycles one usually measures pedal angles relatively to the "top dead center" and shows these measurements at graphics. Unfortunately the name is totally wrong, because one simply uses the "top center" of the crank (see Considerations about Dead Centre in cycling).
At upright bikes an angle shift occurs in the charts when cycled with a different angle of the seat tube, so that the angle of the pedal stroke with the dead point changes and graphs can not be compared because of this angle shift.
Graphs of upright and recumbentmeasurements, which are based on this definition of the top dead center, have a much greater angle shift and can impossibly be compared with each other.
At bicycles in fact two different top dead centers (tdc) are possible:
The next step is to determine when the leg muscles are activated. We first look at muscles that rotate only one joint.
We use measurements below (electromyogram or EMG), from the book Road cycling, Robert J. Gregor and Francesco Conconi.
These measurements are relative to the dead center for the hip (see Dead center). Compared to angles relative to the dead center for the knee the angles at these graphs are 20 degrees smaller!
Besides there is some relay between electrical activation (shown at an EMG) and the resulting force. This gives yet another difference of about 22 degrees!
Graphs should be shifted about 67 degrees to the right to show correct forces relative to top dead center for the knee.
The measured activation is as expected:
It is getting complicated e.g. at the rectus femoris, which is on top of the thigh, passing hip and knee. At activation this muscle will bend the hip and stretch the knee.
At first sight the the graphical simulation shows that the rectus femoris only can give positive power between 0 and 45 degrees, bacause only at this area the hip bends and the knee stretches.
But the EMG of the rectus femoris shows, this muscle is activated a lot more early and also stays activated for a longer period. Already at 320 degrees the muscle is active. At the graph of the graphical simulation we see, that from that angle the angular velocity of the knee is much smaller than the one of the hip. Therefore the muscle length of the rectus femoris will decrease. If the muscle delivers force here, this will have a positive power effect on the pedal movement. On the one hand negative power is supplied to the knee rotation, because the muscle tries to stretch the knee, while it is still bending. On the other hand more positive power is supplied to the hip rotation. The sum of both powers is positive.
At the EMG after 45 degrees the muscle still is activated. At the graph of the graphical simulation we now see, the angular velocity of the knee is much larger than the one of the hip. Therefore also here the muscle length of the rectus femoris still will decrease. On the the one hand negative power is supplied to the hip rotation, because the muscle tries to bend the knee, while it is still stretching. On the other hand more positive power is supplied to the knee rotation. The sum of both powers is positive.
Conclusion: the rectus femoris is able to deliver force and power between 320 (40) and 135 degrees.
The same reasoning is possible for the biceps femoris (long head), the semimembranosus and the semitendinosus(together called hamstrings), which are below the thigh, passing hip and knee. These muscles stretch the hip and bend the knee. This happens between 180 and 200 degrees. But also here we see at the graph of the graphical simulation, that based on the angular velocities of hip and knee, these muscles arre able to deliver positive force and power between 170 degrees and 320 degrees.
The EMG of the semitendinosus more or less agree with the graphical simulation but the EMG's from the semimenbranosus and specially the biceps femoris (long head) differ considerably.
This can be explained with Lombard's Paradox which describes a paradoxical muscular contraction in humans. When rising to stand from a sitting or squatting position, both the hamstrings and quadriceps contract at the same time, despite their being antagonists to each other.
The rectus femoris biarticular muscle acting over the hip has a smaller hip moment arm than the hamstrings. However, the rectus femoris moment arm is greater over the knee than the hamstring knee moment. This means that contraction from both rectus femoris and hamstrings will result in hip and knee extension. Hip extension also adds a passive stretch component to rectus femoris, which results in a knee extension force. This paradox allows for efficient movement, especially during gait.
Because of the asymmetric fixation to hip and knee the biceps femoris behaves more like the gluteus maximus. The muscle will already be activated as soon as the stretching of the hip starts, because the torque at the hip is much larger than at the knee.
Muscles like biceps femoris and rectus femoris are asymmetrically fixed to hip and knee. This fixation influences the torque at the joints. Also this makes it incorrect to assume that angular velocity and muscle velocity are proportional.
If one wants to know how much power is generated at a joint, then it is not sufficient to measure the size and direction of the force on the pedal, but also the exact movement of the leg must be captured ( e,g, by means of video). The delivered power per joint can then be computed, after eliminating the gravitation and forces to change speed and direction of movement of the legs (kinetic energy). At the illustration below fromf High Tech Cycling the principle is shown.
Different sources give varying results concerning the power per joint.
So there is the nice pedaling model concept for computation of pedaling force and power for an upright bike. The next graphs shows forces for different joint as a function of the bending angle.
Torque hip  Torque knee 
Stretching hip.  75%  
Bending hip.  10%  
Stretching knee.  9%  
Bending knee.  6% 
Graphs below are copied from Exercise and sport science .
The graphs shown here for torque and power are from different sources.
In 1986 M. O. Ericson et al, measure at 6 healthy people, pedaling 120 Watt at 60 revolutions per minute the following power rates:
Stretching hip.  27%  
Bending hip.  4%  
Stretching knee.  39%  
Bending knee.  10%  
Stretching ankle.  20% 
We assumed before that the ankle was locked. This assumption makes the model more easy, but is not obvious.
E.g. there is the statement that a cyclist should try to activate all possible leg muscles to deliver maximal power. This would mean also the muscles around the ankle should be mobilised.
The forces around hip and around knee support independently of each other (parallel) the pedal movement. The force around the ankle plays quite another role and is working in serie with forces from the other joints.
This means that the ankle joint has to transport the power from both the hip and the knee to the pedal.
To deliver positive work, the activated ankle muscles should shorten. At the pushing phase of the leg this means the ankle should stretch. The traveled distance is at the expense of the working distance for thigh and shin. This means these (stronger) muscles can deliver less power. Also the distance between hip and crank axle should be a little bit enlarged, to support this ankling.
At H. H. C. M. Savelberg, 2003 it is stated that the hip angle influences the optimal angle at the ankle. At a recumbent with a large hip angle, the ankle should be more stretched to get optimal efficiency.
Ken Roberts, 2006 argues, that rotation at the ankle ("ankling") is not productive. He refers to the pedaling technique of Lance Armstrong, who even let his ankle bend at the bottom dead center, and to an extensive study of Kautz and Coyle, 1991.If ankling is used, it can be done in several different ways.
At THE INFLUENCE OF NONCIRCULAR CHAINRINGS ON MAXIMAL AND SUBMAXIMAL CYCLING PERFORMANCE by Chee Li Leong (2014) considerable power is measured ath the ankle joint. The experienced test subjects have to pedal the maximum power at 60, 90 or 120 revolutions per minute for a short time. Absolutely the contribution of the ankle increases with higher cadence to 90 rpm, the contribution to the total power decreases from 15% at 60 rpm to 12% at 120 rpm. This contribution from the ankle indicates that it is certainly useful to use the ankle muscles for pedaling power.
The graphs in this study indicate that the ankle stretches gradually during the stretching phase of the hip. The ankle bends again in a short time at the top dead center.
At the graphical model with varying ankle angles this "ankling" principle is clearly shown.
At https://cyclingtips.com/2009/05/efficiencyofpedalstrokeankling/ and at https://cyclingtips.com/2009/11/ankling/ (with videoimages) "ankling" is only done at the top and bottom dead center:
At the graphical model with varying ankle angles the "ankling" principle is clearly shown.
Until a pedal angle of 130 degrees the ankle stays bend with a constant angle of 110 degrees. At 130 degrees the leg is almost maximally stretched. Thigh and pedal axle are almost on the same line. Close to pedal angle of 130 degrees, angular velocity of hip and knee grow fast and a lot of power can be developed.
From about a pedal angle of 130 degrees the ankle stretches to an angle of 140 degrees. The knee angle almost stays constant while the hip angle still decreases to almost 0 degrees.
Next the ankle remains stretched at an angle of 140 degrees. Both the knee and hip get bending.
The graphical model tries to show this mechanism clearly and therefore the graphs look rather "peaky". In reality the angle velocities will change more smoothly.
To apply "ankling" optimally, a right adjustment of the distance between hip and crank axle is required. If we lock the ankle at 140 degrees, this distance maximally is 807 mm. at the graphical model (with field "KneeAngLimit" at 150 degrees). If we lock the ankle at 110 degrees, this distance maximally is 774 mm.. The difference is only 3 cm.. Somewhere between these limits the distance must be adjusted; the graphical model uses the maximal distance of 807 mm..
If the ankle really is bent to 110 degrees during stretching the leg, then "ankling" is automaticlly applied, because the distance between hip and crank axle is too large for a locked ankle at 110 degrees.
This way of "ankling" is useful, especially at a low cadense using much muscle strength. This particularly is true for recumbent cyclists, because they cannot pedal standing on the pedals while accelerating or climbing. Unnecessary active contraction of the muscles around the ankle at the stretching phase of the leg, while doing no work, is minimized and muscle force of other leg muscles can be used maximally.
At several places it is stated, that pedal pressure caused by the weight of the legs of upright cyclists, sitting at the saddle, is larger than pedal pressure of recumbent cyclists. This should give upright cyclist more power; some estimate this advantage at 10% or even more.
This advantage for upright cyclists is just fancy and in fact is totally absent. The pedal pressure of the leg that is pushed downwards (upright bike) is more or less compensated by the pressure at the other pedal, that must be pushed upwards at the same time. And when a leg is back again at its starting position after a full 360 degrees pedal rotation, the weight of the leg has not given any power contribution to the pedal movement.
To get an impression of the effective pedal pressure, we compute the change of potential energy of the legs during a complete rotating pedal movement and also compute kinetic energy. We do this for a recumbent with hip and crank axle horizontally on the same line and for an upright bike with the line through hip and crank axle at 75 degrees from horizontal.
For the computation of potential energy we estimate the upper thigh at 5 kg, the under thigh at 4 kg, and the upper and under shin at 3 kg each. We assume the these weights are concentrated at the ends of thigh and shin. This gives a weight of 7 kg at the knee and 3 kg at the pedal.
At the graph of "total" energy also the kinetic energy of a leg is computed, to show the energy needed for decrassing/increasing the mass of the leg. This is done for 90 revolutions/minute, but the cadence can be adjusted.
If the energygraph rises this means a part of the pedalforce is needed for the "internal total" energy and wil not be used for driving speed. If the graph declines, the energy is freed again and will then be used for pedal force and driving speed.
The graph for potental energy (click on button "Potential") shows, the maximal potential energy at an upright bike is larger than at a recumbent! Between 60 and 180 degrees at recumbents there is more effective pedal force caused by the weight of the leg than at upright bikes.
The potential energy of both recumbent end upright bike depend on the distance between hip and crank axle.If we enlarge the distance the difference is growing. If we lower the distance the difference get smaller and finally the potential energy at an upright bike is greater.
If we sum the potential energy for left and right leg (click on "BothLegs"), then we see, the maxima for both recumbent and upright bike are considerably lower. As predicted the movement of left and right compensate each other almost completely.
At the pedal movement speeds of thigh, shin and foot continuously change. Energy is needed to change these speeds. There are publications, that try to improve the edfficiency of the pedal movement by minimizing these speed changes, e.g. by applying oval chainwheels, see Appropriate noncircular chainrings.
But the pedal movement has magical properties.
If we bind a pair of cut feet at the pedals of a chainless crankset and give the cranks a push, the pedals will turn around endlessly (apart from friction losses), although the direction of movement of the feet continuously is changing.
If we couple a pair of legs to the feet, fix the ankles, so they do not bend, also fix the position of the hip joint and again give a push at the pedals, also this construction will turn around endlessly (apart from friction losses). No muscle forces are needed! The movement of legs and feet is completely determinated by circular movement of the pedals.
At the dead centers (with respect to the hip) the speed of the knees is nil and all (kinetic) energy is present at the speed of the circular moving feet. Next the knees and legs are accelerated which will slow down the feet. At the next dead center the knees again will come to a standstill and is the (kinetic) energy againg going to the feet, that get the same speed as at the previous passage of the dead center.
At the pedal movement of a real bike, pedals are turning around with an almost constant speed and the energy , needed for acceleration of the knees, cannot come from the slowdown of the feet. Therefore muscle force is needed now to accelerate the knees. But the energy, that is freed by the slowdown of the knees, can completely be used as pedal power.
This meachnism makes the pedal movement of a bike very efficient! E.g. at running or skating continuously energy is needed to move the legs to the right position for the next takeoff; at bicycles this all works automatically, controlled by the magic of the pedaling circle.
We conclude that both the gravitation force (see previous paragraph) and the speed changes of the legs do not have to cost any energy!
Nowadays it is assumed that the performance of a cyclist is not limited by the oxygen, received via heart and lungs (V02 max), but by the acidification of the muscle by lactic acid that occurs during heavy muscular work. Through careful addressing the available muscle cells, the formation of lactic acid should be minimized.
Look at some basic properties of muscles.
Important is the socalled resting length of a muscle. The graph below from The Biomechanics of Force and Power Production in Human Powered Vehicles shows, that the active muscle strength decreases at an increasing difference between current muscle length and resting length. The maximal active muscle strength occurs, if the muscle is stretched a little bit.
The explanation: the active muscle strength is proportional to the number of active (they supply force) actin/myosin bindings. This number is dependent of the muscle length. As the muscle shortens, the increasing overlap of actin and myosin chains leaves relatively few additional binding sites. As the muscle is elongated, decreasing overlap of actin and myosin chains provides relatively few binding sites (see Development of active force (or tension)).
Figure below from The Influence of Muscle Physiology and Advanced Technology on Sports Performance shows the relation between velocity of the muscle movement and the maximal muscle strength. At a motionless muscle the force is maximal; at greater velocity the maximal force decreases, finally to zero.
The same figure also shows the relation between velocity and the delivered power. We see there is an optimal velocity where delivered power is maximal. The figure also shows the efficiency, which has a similar course, but is maximal at a 50% lower velocity.
Similar graphs for force and power (here for 2 cyclists) are found if maximal force and torque is shown as function of pedal frequency (see Optimal cadence selection during cycling ). For both cyclists the maximal power is found at 100 revolutions per minute.
The figure below from The Influence of Muscle Physiology and Advanced Technology on Sports Performance shows force and power as function of muscle speed from both the slow and fast muscle cells.
The above three figures together suggest for slow muscle cells a maximal power at about 90 rev./min. and a maximal efficiency at a about 60 rev./min.. Fast muscle cells should have a maximal power at about 210 rev./min. and a maximal efficiency at a about 140 rev.
To measure the basic effects of pedal frequency on leg muscle cells, researchers of the universities of Wisconsin and Wyoming asked eight cyclists to do a test (seee The effect on pedaling frequency... ). The experienced cyclists should cycle for 30 minutes at 2 different pedal frequencies at 85% of their VO2 max (= maximal volume of oxygen that can be burnt).
In the one case the cyclists had to pedal with 50 revolutions per minute, in the other case with 100 revolutions per minute. The research showed that for both cases the heart beat, the breathing frequency and the lactic acid grade were almost identical.
But cycling with low frequency caused more glycogen depletion at the muscle cells.
More force must be generated when pedaling with low frequency. To generate this force both the slow (type I) muscles as the fast muscles ( type II) must be used.
Less force needs to be genereted when pedaling with high frequencies and the slow muscles can deliver this force by their own, although the total power is the same.
The research shows that force development as opposed to velocity of contraction determines the degree of type II fiber recruitment when the metabolic cost of exercise is held constant.
An experimental proof of the higher efficiency of slow muscle fibers can be found at High Efficiency of Type I Muscle Fibers Improves Performance .
At Cadence, power, and muscle activation in cycle ergometry the muscle activation (EMG)) is measured for a number of pedaling powers (100, 200, 300 en 400 W) at different pedaling frequencies. The results are at the graph below.
We see, a higher level of power generation causes the minimal muscle activation (maximal efficiency) to occur at a higher cadance. At a power level of 400 W the minimum activation occurs at 90 rev/min.. At this higher pedaling frequency the power of the slow muscle fibers is optimally used, causing a lower than maximal efficiency for the slow muscle fibers. The maximized power of the slow muscle fibers causes a minimized usage of the fast fibers.
This all leads to the conclusion one should pedal fast to get an optimal power from the slow muscle fibers and to spare the fast muscle fibers. The faster movement of the legs takes some energy, which adversely affects efficiency.
Conversely, slow muscle fibers are more efficient than fast muscle fibers. Besides slow muscle cells are capable, not only to burn the valuable and limited glycogen, but also to burn fat which is present plenty. This gives leg muscles the possibility to deliver power for a longer time. This results in greater endurance and / or larger (final) sprint power.
During training and competition riders should preferably use a high pedal frquency, both on the flats and the climbs. Slow muscle fibers give a maximum output at about 90 revolutions per minute. For inexperienced athletes, this means a cadence of 80 to 85, but for the trained cyclists a cadence of around 100.
An additional advantage is that a high cadence saves the knee joints.
At the simulation we found that the transmission of force moments around the knee and hip to the crank certainly is not linear. It is therefore highly unlikely that the muscle forces optimally support the pedal movement. So there have been numerous attempts, to construct a more optimal drive.
One approach is to change the pedal movement of the leg. This category includes the linear drive where the foot does not follow a circle, but goes back and forth. Another recent design is the SDV DRIVE WITH OVAL PEDAL MOTION. This gives the foot the opportunity, to move as long as possible in the direction of the force, which should increase the work done. Earlier we have shown that an angle between direction of the force and direction of the pedal movement is not the big problem and does not give significant loss of power.
A very long existing approach is to move the foot still in circles, but to construct a non linear transmission from pedal axle to the pedal powered wheel.
A relatively recent variant of this is shown at rotorcranks. Here the pedal is moved faster at the pulling motion, than at the powerful pushing motion. The aim is that the leg stays as long as possible in a position where much force can be put. Unfortunately the rotor crank is quite expensive and heavy.
The simplest variant is the oval front chainwheel that is treated at a separate chapter, see Oval chainwheel.
The end conclusion of this chapter: at all circumstances oval chainwheels have advantages. At submaximal pedaling at long distances the oval chainwheel increases efficiency, which benefits endurance. In force explosions it contributes to a higher pedaling power. Unfortunately the expected profit is no more than 3%.
The seat angle is defined here as the angle between the upper body and the line through hip joint and pedal axle.
Just this seat angle is a major difference between an upright bike and a recumbent. At an upright (racing) bike this angle is not larger than 80 degrees. At a recumbent it depends upon the type of the recumbent and varies from 105 to 150 degrees (for a (racing) lowrider).This influences the torque of all muscles that are attached at the hip, because:
Already at 1990 Danny Too has done an extensive investigation to the optimal seat position for maximal pedaling power. At a review of 2008 he has illustrated the experiment with photos.
Interpretation of the measurements of Too is rather difficult because of his rather curious definition of the seat angle, that does not coincide with his definition of the mean hip angle. We use the definition as shown at the beginning of this paragraph.
Too measures the maximal pedaling power at 16 different cyclists and 5 different seat angles: 180, 155, 130, 105 and 80 degrees.
At every seat angle he determines the minimal hip angle (shown at the photos above), the maximal hip angle and the mean hip angle.
His measurements show that at a seat angle of 105 degrees (photo 4) with a mean hip angle of 77 degrees the maximal power is generated, which differs considerably from measured power at other seat angles.
Too's explanation states, that at a mean hip angle of 77 degrees the thigh muscles are contracting at a length equal to the resting length, where they can deliver maximal power (see Cadence and efficiency).
We see both the seat angle of the racing upright cyclist (80 degrees, photo 5) and the seat angle of the recumbent lowrider (155 degrees, photo 2) are not optimal for maximal power.
According to these measurements the racing upright cyclist can generate considerably more power (mountain upwards or at a sprint), than sitting on the seat.
It is unclear how much Too's experiments are influenced by the seat angle the cyclists normally use.
It would be obvious, that the optimal seat angle changes due to long and intensive training, depending on the type of sport (e.g. running, cycling, skating). Indeed measurements are known, where the optimal hip angle/knee angle/ muscle length for maximal depends on the the types of sport (zie H. H. C. M. Savelberg, 2002 or W. Herzog,1991).
But there are also measurements, which deny this dependency (see e.g. Momentknee angle relation in well trained athletes, 2008).
For the average recumbent rider the standard crank length of about 173 mm. is excellent. But for riders with very long or short legs some power profit can be acquainted by using other lengths.
First we show two tables for upright bikes (see fietsafstelling (bicycle adjustment)) which show the relation between body length an optimal crank length:
Estimated inner leg length:

Advised crank length:

As expected the optimal crank length increases at larger legs, but the increment is rather small. There is no argumentation for this increment.
Chris Brands concludes at trapfrequentie (pedal frequency) that the optimal muscle speed is dependent of the ratio between slow and fast muscle fibers.
Next he suggests that a long and a short leg have the same optimal angular velocity (at the same ration between slow and fast fibers).
This last statement is unlikely. Look e.g. at the thigh muscles, that deliver force to rotate the thigh at the hip. At a long leg these muscle will also be long and the muscles are fixed to the leg far from the rotation axle. It seems to be realistic to assume the lebgth of the muscle and the distance of the fixationpoints to the rotation axle are increasing proportional to the length of the leg.
In that case the muscle speed is not proportional to the angular velocity but is proportional to the displacement of the knee or knee velocity. The consequence is that the ratio between muscle force and knee force is about the same for short and long legs
At a complete pedal movement the displacement by the knee is more or less proportional to the crank length and is hardly dependent of the (thigh) leg length. This also is true for for the muscle velocity. So, if a leg has the optimal muscle velocity for maximal powerat a given cadence and crank length, this also will be true at a leg with any other length.
Still there is, specially at short legs, a good reason to choose shorter cranks. At short legs and some fixed crank length the rotation angle of the thigh is larger than at longer legsm with loner. This can be easily verified at the graphical simulatiom with locked ankles.
If we decrease the thigh and shin length with 10% from 450 to 405 mm., then the rotation angle of the thigh increasesdwith 7% from 60 to 64 degrees. Notice, that at the simulation the distance between hip and crank axle automatically (optimally) is changed.
Because of this increased rotation also an increasing part of the maximal elasticity is used. At paragraph Cadence and efficiency we saw, the maximal muscle force is not constant, but depends on how far the muscle is stretched. At the minimal and maximal length of the muscle, the muscle delivers less force. Somewhere between at the resting length the maximal force can be delivered. At paragraph Oval chainwheel the total leg force shows the same behavior.
Maximal or minimal stretch caused by too long cranks costs power, because the muscles cannot deliver force in that situation. Therefore at short cranks should be used at short legs.
A shorter crank results into a lower muscle velocity. To get the optimal muscle velocity at shorter cranks a lower gear must be used together with a higher cadence.
Also mounting a longer crank at long legs can enlarge efficency, but the expected profit is not spectacular.
At a too short crank only a small part of the muscle cells are used. Enlarging the crank will not increase the short term delivered power, but it will increase the continuous power.
Long cranks have some disadvantages:
James C. Martin has done measurements at optimal crank length in 2001 measurements for optimal crank length in 2001 and has explained this in 2007.
He measures an optimal crank length of 145 mm., almost the same result at 170 mm. and significant lower power at 120, 195 and 220 mm..
He notices that optimal velocity of the pedal at a long crank is significant higher than at shorter cranks. Because of the high values of the optimal cadence this is not a miracle.
Also Danny Too reports at his review of 2008 a lot of measurements. Unfortunately the measurement conditions are not fully described.
At 1 of the measurements (more detailed described at EFFECT OF PEDAL CRANKARM LENGTH ON CYCLING DURATION IN A RECUMBENT) he tries to find the optimal crank length for an uprightbike or recumbentlowrider (seat angle 155 degrees) and for a "recumbent" (seat angle 105 degrees), see paragraph Seat angle photo 2 and 4. The cyclist should pedal at 60 revolutions/minute. Every minute he enlarges the pedal resistance with 0.5kg. The time is stopped, as soon as the cyclist can not pedal the 60 revolutions/minute anymore.
At the "recumbent" he measures an optimal crank length of 145 mm. with elapsed time 737 sec.; at 230 mm. he measures 694 sec..
At the uprightbike he measures an optimal crank length of 230 mm. with elapsed time 565 sec..; at 145 mm. he measures 541 sec..
At these measurements the larger crank is totally not compensated by a higher gear.The measurements at a large crank show the effect of both the larger hip rotation angle and lower transmission ratio between muscles and "wheel resistance".
The measured optimal crank length of 230 mm. could only be reached because the measurement is done at a low pedal frequency ( 60 rev/min). At this frequency the muscle velocity is about the same as with a crank length of 170 mm. and an optimal pedal frequency of 90 rev/min.
It is difficult to measure the effect of changing the crank length. Therefore we could not find measurements, that proof the optimal crank length.
At website Kirby Palm comes to the statement the optimal crank length increases linear to the inner leg length:
 crank length = 0.216 * inner leg length.
At this page we come to the statement that there is an optimal rotation angle for the thigh (=difference between minimal and maximal thigh angle). This optimal angle is dependent of the seat angle and independent of the leg length. For a bicycle with a small seat angle (racing upright) a small rotation angle is optimal, because then at the powerfull pushingphase the muscles function the nearest to the optimal thigh angle. At a large seat angle (recumbent lowrider) for the same reason a large rotation angle is optimal.
The optimal rotation angle can be adjusted by choosing the right carank length at a given leg length. At the graphical model we have determined at different leg lengths (upper an lower leg same size) and maximal(optimal) distance between hip and crank axle the crank length, that gives a rotation angle (HipAngDiff) of 53 degerees.
The results are shown at the table below:
Inner leg length  Crank length 
75 cm  146 mm 
80 cm  157 mm 
85 cm  164 mm 
90 cm  173 mm 
95 cm  184 mm 
100 cm  195 mm 
Very important is the right distance between hip and crank axle. Both a too short and a too long distance may easily hurt the knee, which often occurs at recumbent riders.
At a too short distance shin and thigh are too much perpendicular to each other which causes the knee joint to be overtaxed. Besides, if the distance is only a little bit too short, the cyclist can generate a lot of force at he bottom dead center. The force is perpendicular too the pedal movement, is therefore useless, but can easily cause injuries.
At a too long distance the knee will easily bend too far at a fully stretched in case of roughness at the road.
Too establishes at his review, that morre power can be delivere a larger distance between hip and crank axle.
At http://www.bikefitting.com/English/Theory/SaddleHeight.aspx some methods are explained to find the optimal distance for upright cyclists.
A good method starts from the angle of the knee. When the pedal is in its lowest possible position, the knee should be able to bend 25 to 30 degrees.
But according to this webpage Gonzales and Hull (1989) showed that an optimal adjustment of the bicycle depends on more than one variable, and that these variables are correlated and interrelated. They are in favor of a multivariable measuring method because the singlefocus approaches described above are too limited and do not lead to individual optimization.
None of the methods pay attention to "ankling" and consequencies of this way of pedaling for the optimal distance between hip and crank axle.
The graphical model shows that the optimal distance increases, if more "ankling" is applied, and the rotaion angle of the ankle increases.
It also shows that the optimal distance is getting critical at more "ankling". If we decrease at th graphical model the value "footangpull" to 130 degrees (ankle rotates 20 degrees), then the distance between hip and crank axle only decrease 10 mm. Increasing "footangpull" to 150 degrees (ankle rotates 40 degrees) causes the optimal distance to increase only 10 mm. The fine tuning is mm.work!
A good tuning can be achieved if at a maximal bent ankle and fully stretched leg (thigh is pointing to the pedal axle) the pedal is positioned 20 to 45 degrees before bottom dead center.
Some paragraphs above we saw a standing cyclist has the advantage that the "seat angle"" is more optimal, because the thigh muscles can be better used.
A second advantage concerns th possibility to use the gravitation force. The company MetriGear (adopted by Garmin) has compared pedal forces from sitting and standing cyclists. Clearly can be seen, that at the botttom dead center the sitting force is much smaller than the standing force.
If a cyclist is not sitting at the saddle the vertical forces on the pedals (average during a full 360 degree pedal movement) must be equal to the gravitation force. Otherwise the body would fall or rise to heaven.
If one sums the downward forces of the left and right leg, one can easily see, these are not constant. This means the body must be moving up and down during a full pedaling circle.
At bottom dead center the downwards force is maximal and the body is moved upwards (by muscle force).
At 90 degrees total downward leg forces are smaller and the body is moving down. Therefore hip angle and knee angle change more slowly and the muscles have to do less work, because the body weight helps a little bit.
This mechanism in fact gives the standing cyclist the possibility to generate power at bottom dead center by means of tangential forces, which effectively can be used at 90 degrees to generate radial forces at the pedals.
The advantage even is increased because slower contracting muscles at 90 degrees can generate more force.
In this way a standing upright cyclist can effectively use leg power near the bottom dead center.
Unfortunately this trick is not possible for a recumbent.
A beloved subject at the flat Holland. It was treated exhaustively at the Dutch recumbent magazine Ligfiets& 20085 and 20091. Some explanations given here for bad climbing with a recumbent:
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