Why oval?

The basic principle

Production models

Simulation pedal movement

Asymmetric oval

Theoretical computations

Adjustment of muscle coordination

Measurements

Personal experience

Links

Appendix 1- Simple computing model

With oval chain wheels there are many alternative settings possible. In addition to the optimum shape also the optimum ovality (= ratio between largest and smallest diameter) and the optimum angle between the crank and the largest diameter of chain wheel must be chosen. This has led to numerous variants since 1890 (see History), which almost all have failed.

Also market leader Shimano did a great effort around 1980 with the Biopace chainwheel. Here the chainwheel has the greatest size at the top and bottom dead center (0 and 180 degrees), which was the maximal wrong choice. The Biopace failed completely, giving oval chainwheels a very bad id. This has also meant that the major manufacturers do not support this type of chain wheel and oppose its use.

Despite of this, impressive results are achieved recently. So Chris Froome has won the latest Giro of Italy and the Vuelta of Spain. The Tour de France of 2017, 2016, 2015 and 2013 are also won by Froome and the Tour of 2012 by Bradley Wiggins. Both used the oval Osymetric chainwheel. At the ladies the Dutch Marianne Vos has won almost everything with the elliptical Q-ring. And with an unfaired recumbent Aurélien Bonneteau rode a world 1 hour-record using an Osymetric.

This has led to renewed interest in the oval chain wheel and to new production models.

Modern bikes are equipped with a large number of gears, which must ensure that the pedals can be kicked around with optimal cadence at every bike speed. In this cadence the muscles deliver work at optimum muscle speed for the purpose of maximum power.

If we examine the pedaling motion, we see that the foot neatly rotates at a constant speed. But if we look at the muscle speed within one pedal movement, we see that this varies widely and therefore certainly is not optimal at every pedal angle. Improvement is possible by using an oval chain wheel, which has to ensure, that the muscle velocity varies less, and thus is more optimal.

Mounting an oval chain wheel does not change the path of knee and foot. If the legs at each position of the crank deliver exactly the same force as at a round chain wheel, then exactly the same work will be performed by the legs (force and traveled distance are the same) as at a round chain wheel.

What does change is the speed at which knee and foot move. This also changes the speed at which muscles are contracted (muscle velocity.) At an enlarged diameter of the chain wheel the pedal moves slower and muscle speed decreases. Muscles have the property that they can deliver more force at lower muscle speeds and work more efficiently then.

On the other hand at a smaller diameter, the muscle speed increases, so that the muscle can deliver less force at a lower efficiency.

At the successful Osymetric and Q-rings chainwheels the chainwheel should preferably have the greatest size at the angle where the leg gives the most power, the most muscles are active and have the highest muscle velocity. According to measurements below from The Pedaling Technique of Elite Endurance Cyclists this happens, when the angle between the crank and the line through hip joint and crank axle is about 110 degrees (crank 110 degrees past the upper dead center). At this angle also the muscle speed is almost maximal.

The best way to mount the oval chain wheel is dependent on the chain position! This means a totally different position at a recumbent (chain almost parallel to pedaling) than at an ordinary road bikes (chain nearly perpendicular to pedaling). An optimally mounted chain wheel is at a road bike therefore greatest at 90 - 110 degrees before the crank, at a recumbent at 40 - 60 degrees before the crank. This positioning of the oval chain wheel ensures that many muscles benefit from the reduced muscle speed and deliver more strength and that a small number of muscles have to contract faster and hence lose stength. The net result is a gain in strength and power at the same pedaling cadence.

So at equal cadence an oval chain wheel gives greater power at higher efficiency. But this is not all. We have seen that with proper positioning of an oval chain wheel average muscle speed is less than at a round chain wheel being pedalled around with the same cadence. To get the optimum speed for maximum muscle power an oval chain wheel should be pedalled around faster. Because then the average muscle speed is similar to that of a round gear, also the muscle force per revolution is almost equal. Because of the larger number of revolutions at higher cadence the oval chain wheel delivers even higher maximum power.

Conclusion. On the one hand the oval chain wheel provides at the same cadence greater efficiency and output due to a lower average speed muscle. On the other hand it makes sure that a larger maximum power can be delivered at a higher optimum cadence.

To illustrate this principle a simplified mathematical model is created to show the profit of an oval chain wheel (see Appendix 1- Simple computing model).

Thanks to success the number of production models increases:

The elliptical Q-rings are available with ovalities 1.1 and 1.16. These chain wheels can be mounted in any position and thus are easily applicable to any recumbent. In addition, the manufacturer claims that the chain wheel for each individual can be ideally placed based on Spin Scan Analysis. Changing gears is more easy than at the Osymetric.

Probably based upon the Q-ring also a 56-teeth or bigger oval chain wheel can be ordered for recumbents (with small wheels) at Peter de Rond. The 62teeth-130BCD is also for sale at Velomobiel.

The Osymetric has a greater ovality 1.215. Unfortunately, this chain wheel can be attached to the crank with only one set of holes and can thus at a five-arm crankset be shifted relative to the crank only in steps of 72 degrees. Due to the 180 degrees symmetry of the chain wheel this yields an effective adjustability in steps of 36 degrees. A shift of 72 ° or three times 72 degrees gives a reasonable setting at a recumbent.

The new Dutch PrOval has an even greater ovality of 1.25 or 1.3. This chainwheel is adjustable via three set of holes, which are right next to each other. In addition, the chainwheel can be displaced in a multiple of 72 degrees (as in Osymetric), which due to the symmetry of 180 degrees also here produces an effective adjustability in steps of 36 degrees. Changing gears is more easy than at the Osymetric. Is out of production at this moment.

The less known Ogival even has an ovality of 1.428, has three sets of holes for adjusting and therefore is a bit better adjustable than the Osymetric.

Besides there also is the Korean Doval and the Ridea from Singapore.

At Comparative biomechanical study of circular and non-circular chainrings for endurance cycling at constant speed several oval chain wheels are described in great detail.

At a graphical model of the pedal movement it is shown, how nowadays produced oval chain wheels influence the angular velocities and therefore also the muscle velocities of leg muscles.

At the simulation of the recumbent the angle between chain and the line through hip and crank axle is 20 degrees. At a "normal" bike this angle is 75 degrees. Therefore 55 degrees mus be added to an optimal "OvalCrankAngle" for a recumbent, to get the same optimal setting for a normal bike. If at te simulation the "NormalBike" option is chosen, this addition is automatically made and also the presentation of the pedal movement is 75 degrees rotated. The field "OvalCrankAngle" can be adjusted.

The field "Ovality" shows the ratio between largest and smallest diameter. The field "Teeth" shows the number of teeth difference, that is pedalled at the largest and smallest diameter, compared to a round chain wheel with equal (52) total nuber of teeth.

The shape of the displayed oval chain wheels is determined based on pictures on the internet. For the "Qring", "Osymetric", "Ogival" and "Proval" the calculated ovality is consistent with the specification of the manufacturer. At the two shown chain wheels of "Ridea" the calculated ovalities are considerably larger than according to the inscription, probably because of distorted pictures.

The "Quoval_1.3" is a theoretical chain wheel with large ovality of 30% and still good characteristics.

The "red" line inside the chain wheel indicates, where the simulation situates the largest diameter of the chain wheel. The position is not entirely obvious. There are chain wheels, that are circular at the largest diameter. In that case the line is positioned at the point, where the diameter decreases sharp suddenly (after the circular area). This position is important, because it is expected that this point should more or less have to coincide with the point, where the angular velocity of the knee and hip reduces suddenly.

If the shown angular velocities of the hip and knee for the "Osymetric" are compared with that of the round "Circle", then it is clear to see that the maximum angular velocities have decreased and that at the beginning of the "pushing" kick motion, the speed is higher.

Some remarks:

- For larger ovality, the maximum angular velocities is more reduced and an increasing gain in efficiency or power is expected.
- At the "Ogival" it seems the ovality of 1.42 is too large. There arises even a dent in the angular velocities when the chain is on the maximum diameter of the chain wheel. If one changes from locked ankles to moving ankles, it seems that the "Ogival" still shows excellent angular velocities.
- The "Proval_1.3" shows a sharp peak in the angular velocity of the crank. It is doubtful whether this acceleration can be really delivered and the chain remains sufficiently tight.
- The optimal "Oval Crank Angle" seems to be for all oval chain wheels at 60 degrees for a recumbent and at 115 for a normal bike. An exception is the narrow "Ogival". Here a little smaller "Oval Crank Angle" of 40 degrees (95 degrees for a normal bike) seems to be better.

There are two kinds of oval chain wheels, symmetric and asymmetric.

Examples of symmetric chain wheels are the Q-ring and the Ogival. Characteristic is that the largest and the smallest diameter are perpendicular to each other. To both diameters applies that they divide the oval in planes, which are each other's mirror.

Examples of asymmetric chain wheels are Osymetric, Doval, Ridea and PrOval. Here the smallest and largest diameter are not perpendicular to each other and the partial surfaces are not mirror images. Problem with Osymetric and Proval is also that the chain wheel is circular at the largest diameter, which makes it that the position can not be determined unequivocally.

For this reason at the graphical simulation the chain wheels are not positioned using the largest diameter, but the smallest diameter is positioned 15 degrees beyond the "top dead center for the knee". (As explained at the paragraph concerning the dead center in fact there are 2 dead centers). This positioning ensures that symmetrical and asymmetrical chain wheels somewhat useful can be compared with each other.

Differencies between symmetrical and asymmetrical chain wheels are clarified if one shows both the graphics of Q-ring-QXL and Osymetric at the graphical model. Despite the higher ovality of the Osymetric the maximum diameter of the two chain wheels is the same. The Osymetric maintains this maximum ovality much longer, which should result in a lower average muscle speed and more power.

There is no known reason why an oval chain wheel should have to be symmetrical. It seems that an asymmetrical chain wheel can be better adapted to the irregular graphics of the muscle speeds and will ultimately lead to better results. What shape / ovality / positioning is the most optimal, is still unknown.

Many theoretical calculations of optimal oval chain wheels contain mistakes or are based upon incorrect optimization criteria. In a number of cases, these calculations are revoked, but are still used in these calculations new publications.

The more accurate calculations are based on muscle groups and therefore are very complex. These calculations and results are unfortunately not fully documentated and difficult to verify.

Especially Hull has published a lot and is often cited.

In his early work he relies on "inverse dynamic based optimization". At cyclists measurements are made of the size and direction of pedal force and the angular velocities and positions of hip, knee and ankle joint during a whole pedaling movement. Using this measurements joint torques at hip, knee and ankle are computted. Based on these computed joint torques, the influence of changes to the bike or the kind of riding is predicted, to determine what adjustment gives the best result.

This method was elaborated very far by Hull and Gonzalez at the publication MULTIVARIABLE OPTIMIZATION OF CYCLING BIOMECHANICS from 1988. From measurements on a regular cyclist optimizations are calculated for a large, normal and small cyclist, to determine the ideal combination of cadence, crank length, hip angle, distance between hip and crank, and position of the foot on the pedal.

In 1985 Hull publishes together with Jorge A method for biomechanical analysis of bicycle pedalling. In this article, they calculate per joint kinematic and static moment forces as independent moment forces. The kinematic forces would ensure the acceleration and deceleration of the legs, the static moment forces would ensure the forces on the pedal.

In 1991 Hull publishes together with Kautz and Beard An angular velocity profile in cycling derived from mechanical energy analysis. Herein, the acceleration and deceleration of the legs is seen as inefficient. At each position of the pedal the ideal angle velocity from the crank is calculated , so that the internal energy (sum of kinetic and potential energy) varies minimally and all muscle power is transmitted to the pedals.

In 1993 Hull and Kautz publish A theoretical basis for interpreting the force applied to the pedal in cycling. Here, in the calculation of the forces due to the moving leg they take account of the forced circular path of the pedaling movement. The calculations are inconsistent with the calculations of kinematic moment forces from 1985, that therefore are **rectified** by means of this publication.

In 1995 Hull and Kautz publish Dynamic optimization analysis for equipment setup problems in endurance cycling. A MCF (Moment Cost Function) is used to determine the optimal oval chain wheel. According to this calculation the shape of this chaint wheel depends on the cadence.

In 1996 Hull and Kautz evaluate the state of affairs in Cycling optimization analysis. Herein, a large part of the earlier work is **rectified**:

- optimizations, which take no account of muscle characteristics, (e.g., muscle force that depends on the speed with which muscles contract), do not give a correct result.
- optimizations, which minimize internal work (due to gravity and acceleration / deceleration of the legs) do not give a correct result.
- cost functions (such as MCF, Moment Cost Function), which take no account of muscle characteristics, do not give a correct result.

Neptune and Kautz evaluate in 2002 the state of affairs in Biomechanical Determinants of Pedaling Energetics: Internal and External Work Are Not Independent. Here again is explained, why optimization based on minimal internal work can not work. Also is explained that optimization by minimizing the index of force effectiveness.

While much of the early work of Hull is rectified, we see newer publishing, relying on his methods. So Kaandorp 2006 publishes Optimaliseren van cranklengte en trapfrequentie bij fietsen (Dutch). Optimizations are made without taking into account muscle properties. Also the Moment Cost Function does not take into account muscle properties

In Comparative biomechanical study of circular and non-circular chainrings for endurance cycling at constant speed from 2010 and Appropriate non-circular chainrings from 2012 Malfait, Storme and Derdeyn various oval chain wheels are described in detail. Also these calculations are based on the early work of Hull. The optimizations do not take into account muscle characteristics. The calculation of the internal energy is obsolete and is wrongly used for optimization. The classification of the various oval chain wheels and determination of the optimal angle between the crank and the largest diameter of the chain wheel is therefore incorrect.

Concerning oval chain wheels only A theoretical analysis of an optimal chainring shape from 2007 by Rankin and Neptune satisfies. On the basis of theoretical muscle properties they come to an improvement of 3% at optimal positioning and optimal eccentricity of 1.29. The gain is attributed to the fact, that in the pushing phase the muscles are active for longer, but a real explanation is not given.

We conclude, that optimizations based on moment forces from the joints are not able to predict the ideal oval chain wheels. Optimizations based on muscle characteristics in theory have this possibility. However, they are so complex that it is hardly to prove that the predictions with oval chain wheels are correct and where the profit is caused by.

A strange mistake within the scientific cycling world is the idea that a cyclist hardly needs time to adapt to a modified bicycle configuration and to perform optimally on this configuration. E.g. James C. Martin comes in Crank length pedaling technique (2008) based on from measurements from 2000 to the statement that it costs ** a maximum of only 3 days of exercise (36 seconds!) to learn to produce the maximum power **.

This makes scientific research on the pedal movement very cheap, but unfortunately this statement does not correspond with reality.

A remarkable survey THE INFLUENCE OR NONCIRCULAR CHAINRINGS ON MAXIMAL AND SUBMAXIMAL CYCLING PERFORMANCE was performed in 2014 by CHee Li Leong and the same James C. Martin.

Explicitly it is stated that the test persons ** are experienced cyclists who have no experience with oval chain wheels **. The subjects are randomly fitted with a circular chain wheel(C), a Q-ring of Rotor (R) with eccentricity 1.13 or an Osymetric (O) with eccentricity 1.24. The chain wheel is hidden so that the test persons can not see it themselves.

The mounted chain wheel drives a flywheel. The test subjects must speed up this flywheel as fast as possible within a period of no less than 4 seconds. The maximum delivered power and the corresponding cadence are determined. With each chain wheel, such a measurement is performed 3 times.

As can be expected with this type of measurement, no extra power is measured when using the oval chain wheels.

Fortunately, the researcher is looking for an explanation and a second experiment is being carried out.

During an interval of no less than 3 seconds, the maximum power is measured for the 3 previously mentioned sprockets, with the cadence fixed at 60, 90 or 120 revolutions per minute.
It can be expected that the measured angular velocities of the hip and knee are lower at the moment that the oval chain wheel has the largest radius. This does not appear to be the case. ** The angular velocities of hip and knee are equal to those of a round chain wheel, but the angular velocity of the ankle is different**.
The subjects are apparently unable to adjust the coordination of hip and knee muscles to the oval chain wheels in such a short time and compensate for this by adjusting the rotation of the ankle. This inadequate way of pedaling can not possibly lead to power gains!

Although the researcher finds that research into possible learning behavior when adjusting muscle coordination for oval chain wheels is necessary, the final conclusion is drawn, that oval sprockets do not provide a power advantage.

The final conclusion of this research should have been that research on oval gears has no meaning whatsoever when measured on subjects, that are untrained on oval chain wheels. Conclusions, which are based on a research with untrained subject at a bicycle configuration with major changes, can go into the trash

In 1992, Hull M. Williams, K. Williams and SA Kautz publish Physiological response to cycling with both circular and non-circular chainrings. This was followed by A COMPARISON OF MUSCULAR MECHANICAL ENERGY EXPENDITURE AND INTERNAL WORK IN CYCLING in 1994 from Hull, SA Kautz and Richard R. Neptune, and in 2000 by Adaptation of muscle coordination to altered task mechanics during steady-state cycling from Richard R. Neptune and W. Herzog. in these tree publications measurements on a round chain wheel compared with measurements on an oval chain wheel, which is mounted in two different positions: the largest dimension of chain wheel parallel resp. perpendicular to the crank. The conclusion of these measurements is that oval chain wheels gain nothing but cost extra energy. In fact, this is not surprising because the subjects got far too little time for adaptation to the oval chain wheel. In some experiments one even tried to avoid that subjects got experience with oval chain wheels. Would this kind of measurement be done at the introduction of clap skates, they would never have broken through!

The publication Effect of chainring ovality on joint power during cycling at different workloads and cadences 2014 from G. Strutzenberger et al for this reason measure no profits at the Q-ring and Osymetric.

At an investigation from O'Hara e.o. trained subjects were given a week to get used to the mounted chainwheel. Again, the Q-ring with ovality 1.1 is compared to a circular chain wheel with the same number of teeth.

The test was done at a maximum power at a 1 km. trial with standing start and a solid, self-selected gear. The total power delivered by the Q-ring showed an astonishing 6.2% higher and the average speed 1.6% higher.

This unexpectedly high result may be due to the type of experiment. Because only one gear may be used, one must choose between a low gear, which makes tarting very easy and a high gear, which is optimal at top speed. This leads to a too low gear, which must be pedaled around so quickly at top speed, that the power supplied is less than the maximum because of the too high muscle speed.

Because of the lower average muscle velocity, this decline in power is less intense at oval chainwheels As a result, the power advantage of oval chainwheels increases at higher cadence (see the Appendix 1- Simple computing model).

Measurements of O'Hara, while pedaling around with less than maximum (submaximal) power, showed at the oval chainwheel a 2% lower heart rate and oxygen consumption, indicating a higher efficiency, but the results are statistically not proven.

We conclude that comparative measurements only provide relevant results, if sufficient time is practiced with the oval chain wheel. A protocol as from O'Hara seems to produce the most pure results. At an ovality of 1.1 after one week already relevant differences can be measured, which are not greater after further training. It is expected that at a greater ovality the period of habituation will be much greater.

If you claim that oval chain wheels yield a performance gain, you can not escape also mounting oval chain wheels, although this is nonsensical due to the (lack of) physical condition.

Because I ride in the flat northern Netherlands only with the large front chain wheel, only the largest chain wheel needs to be replaced.

On my Nazca recumbent that was 52-tooth. Because in my opinion, the biggest diameter should be equal to the diameter of the circular chain wheel and to avoid problems with the front derailleur, I wanted a 50-tooth oval with sufficient ovality.

Unfortunately then the choice is limited and only the Osymetric BCD 130/50 turned out to meet.

Then immediately there is a second problem: the Osymetric has only one set of holes. The adjustability is therefore only in increments of 36 degrees.

A setting is chosen where the recumbent largest diameter is kicked a little later than in the standard Osymetric-setting for a normal bike. The angle between the crank and the starting point of the reduction of the diameter of the chain wheel is about 75 degrees. The installation gave no problem. The chain is slightly noisier, but does not have a tendency to run off of the chain wheel.

Initially you will have trouble getting decent kicking around. The feet should move so fast through the lower dead point, that they can barely keep up the circular movement. You get quickly used to it and after two rides you do not notice it anymore.

What is especially striking is that acceleration seems to be much easier. It also seems as if the oval gear invites to draw by far in gear. Pedaling feels much smoother, which you would not expect because of the varation in rotation speed of the pedals.

All in all the chain wheel works so well, that I also bought one for the Quest. Theoretically one should be able to cycle faster, but I could not measure this because of the lack of a stable condition.

To explain the advantage of an oval chainwheel, we use a strongly simplified model of leg muscle power.

Look at measurements below from The Pedaling Technique of Elite Endurance Cyclists.

According to the figure a cyclist delivers **by far the most power** while stretching the leg. This stretching phase is mostly responsible for the delivered power and therefore we restrict ourselves to the stretching phase. Because pedaling is done with constant speed, the graph of output power as a function of crank angle exactly has the same course. This also applies to the graph of the power supplied as a function of the time.

We simplify the delivered power to a block-shaped form, with the leg in the second and third quarter of the linear phase delivering three times as much power than in the first and fourth quarter. This is the green line at the next figure.

To compare round and oval, we use a strongly simplified (not manufacturable) oval cahin wheel. The chainwheel has the same number of teeth as the round one and an ovality of 1.5 . Also the chainwheel is block-shaped. The half of the chainwheel has a small diameter equal to 4/5 of the round chainwheel. The other half has a large diameter equal to 6/5 of the round chainwheel. The chainwheel is mounted so that the large diameter exactly matches the phase of great power from the leg muscles.

The delivered power is the magenta line at the above fugure. In the phase of high power the pedaling speed becomes 5/6-th smaller and hence the delivered power. But this phase now takes a factor 6/5 longer, so the total delivered power at this phase does not change. In the phases of low-power the power increases by a factor of 5/4, takes the duration of the phase a factor 4/5 shorter and also at this phases the total delivered power remains the same.

Mounting an oval chainwheel thus seems to have no effect.

However, we assumed, muscle forces do not change, when using oval chainwheels. But muscle speed changes. And, as shown in next figure, muscle force will decrease, as the muscle contracts faster and muscle speed increases.

In order to replicate this muscle behavior in the calculation model, we use the formule from Hill to compute muscle force as a function of muscle speed :

force = force_{0} * (1.0 - speed) / (1.0 + speed / 0.25) .

At the model we assume that muscle force in the phase of high power (green) is a factor 2 greater than muscle force at the phase of low power (magenta).

This Hill formule leads to next powers at the phase of high (green) and low (magenta) power according to the formule:

power = power_{0} * speed * (0.25 - 0.25 * speed) / (speed + 0.25)

At the phase of low power it is not only the force that is less, but is also the muscle speed is smaller than in the phase with high power. The ratio between the two speeds we setassume to be 4/9. This ratio is independent of the cadence, which is pedaled.

At the figure below the brown line shows the power, if account is taken of power change due to changes in muscle speed. At the phase of high-power the muscle speed is lower than at a round chainwheel, causing the muscle force to increase so much, that the power is almost equal to that of a round chainwheel. But at an oval chainwheel this phase lasts much longer!

At the phase of low power delivered power decreases but is still higher than at a round chainwheel. Clearly is shown that the oval chainwheel eventually yields a power profit.

In http://www.cornant.uk/info/ovals03.html a power graph for a more realistic oval chainwheel shows a similar shape with lower peak power during a longer time.

The muscle speed depends on the speed of pedaling. Based on the muscle model described here, the muscle force can be determined for the phase of low and high power and ultimately the delivered power at the stretching phase as a function of cadence. The green line in the figure below applies to the round chainwheel, the magenta line applies to the oval chainwheel.

The ovality can be changed. An ovality smaller than 1.0 (greater than 0.0) shows the power loss of a chainwheel like the Biopace with large diameter at the dead points.

We can conclude the following:

- The same muscles produce at an oval chainwheel at each cadence more power than at a round chainwheel.
- The difference increases with higher cadence.
- The percentage difference increases stronger with higher cadence.
- The maximum power is significant higher at an oval chainwheel and is delivered at a higher optimal cadence.