**Science**

**PowerCurve – Premium non-circular chainrings based on Science**

- Analysis of the pedalling process.

The moments (“torques”) which are generated in the joints through the muscles are needed on the one hand to generate the force on the pedal (**non-kinetic **driving force) and on the other hand these moments have to accelerate and to decelerate the masses of the lower limbs (**dynamic or kinetic** force/moments).

In other words, the **total driving moment** in each of the joints of the lower limbs can be decomposed into a **kinetic moment **(intersegmental moment due only to the dynamic action of the leg links) and **a non-kinetic moment** (moment only due to pedal forces).

*M _{total} = M _{non-kinetic} + M _{kinetic}* equation (1)

This moments-equation is valid for ankle-, knee- and hip joint respectively.

Kinetic forces/moments **do not generate “external” ****crank power**. They do not contribute to the propulsion but are only needed to move the legs. The kinetic force/moment component is due to gravitational effects acting on the masses of the moving legs and due to inertial effects (acceleration and deceleration of the legs) during pedalling.

- Kinetic forces/moments.

The **non-kinetic** moment is only a consequence of the applied pedal forces and does not depend on the masses nor on the accelerations of the lower limbs.

The **kinetic** forces / moments are a function of the masses, the moments of inertia, the angular accelerations and linear accelerations (of the centre of gravity) of the foot, leg and thigh and also of the gravity acting on foot, leg and thigh.

These kinetic forces / moments acting on the joints at a given pedaling rate, **can **be **modified** by a **change** of the angular accelerations and the linear accelerations of the lower limbs. **However the non-kinetic moments remain unchanged.**

- Non-circular chainrings.

When cycling at constant speed with a **non-circular chainring**, the pressure point of the foot is describing a circular motion but the **crank angular velocity is varying **through one revolution (what is not the case with a circular chainring). This means there are angular accelerations and linear accelerations.

These angular accelerations, but also the linear accelerations of the lower limbs, **can be changed** by modifying the ovality and the shape of the chainring, the orientation of the crank relative to the major axis of the chainring and by varying the pedaling frequency.

- Modification of the kinetic forces/moments in the joints.

By modifying the geometry (ovality, shape and position of the crank) and the rotation frequency of the oval chainring, other angular- and linear accelerations occur and cause **altered kinetic forces**** / moments in the joints.**

- Optimization

Through simulations with different ovalities, shapes and crank positions versus the major axis of the chainring, **an optimal**** non-circular chainring** can be found.

This **optimal** non-circular chainring **minimizes** the kinetic force-moment in the joints.

See also the equation (1).

When the total driving torque (total moment) remains the same, the muscles which have to generate the same total driving torque, will deliver **more**** non-kinetic moment** **with the same effort** (indeed, because they have to generate less kinetic moment) and consequently more pedal force and thus **finally more pedal power.**

That optimal non-circular chainring **(criteria for the optimization)**

–**minimizes** the peak-load (kinetic joint moment and -joint power) in the extensor muscles of the joints compared to a circular chain wheel.

-and thereby **maximizes** a kinetic crank power gain compared with a circular chain wheel,

at a given pedalling rate.

Both the unloading in the extensor muscles of the joints and the crank power gain increase more than proportionally with increasing pedalling cadences.

In cycling the extensor muscles are predominantly recruited and provide most of the forward drive (external crank power) for the bicycle movement.

Any “unloading” of the extensors is favourable regarding extensor muscle fatigue and allows the cyclist to keep a given level of crank power longer.

**PowerCurve**non-circular chainring.

The **PowerCurve** chainring is the result of the optimization study.

That optimal non-circular chain wheel is the best performing non-circular chainring selected from multiple (36) simulated and investigated geometries and crank orientations.

See “Performances”.

The **PowerCurve** has the following “optimal” features:

ovality 30 %, four shape segments (round, a transition section to flat, a flat segment and a spiral of Archimedes for transition from flat to round) and the crank arm positioned at 68°, measured clockwise from major axis of the oval for the standard racing bike (seat tube angle about 73°).

However, the optimal crank offset is depending on the bike geometry and the seating position of the rider. Therefore the **PowerCurve** has also two additional mounting options: one at 76° for TT-bikes (seat tube angle about 80°) and one mounting possibility at 84° for extreme forward seating position.

For practical reasons (see “Product Description”) the ovality is limited to 25%. This does not give a noticeable loss of performance.

- References

- DIAMOND, N.D., BATH, B.S., HOLSCHER, R.B., ELMER, S.J., and MARTIN, J.C., Effects of noncircular chainrings on maximal cycling power
*. Neuromuscular Function Lab, Department of Exercise and Sport Science, College of Health, University of Utah, Salt Lake City, UT, USA,*2010 - GROSJEAN, P., et GRAPPE, F., Effets du plateau non circulaire Ogival comparé au plateau circulaire classique sur le pattern de pédalage et lors de différents exercices maximaux et en endurance.
*Departement Sport-Santé, Université de Franche-Comté, Besançon*. 2013 - HORVAIS, N., SAMOZINO, P., ZAMEZIATI, K., HAUTIER, C., HINTZY, F., Effects of a non-circular chainring on muscular, mechanical and physiological parameters during cycle ergometer tests
*Isokinetics and Exercise Science*15, Number 4, 2007.

- HULL, M.L. and JORGE, M., A method for biomechanical analysis of bicycle pedalling.
*Biomechanics*18: 631-644, 1985.- JONES, A.D., and PETERS-FUTRE, E.M., Physiological response to incremental stationary cycling using conventional circular and variable-geared elliptical Q-chain rings
*. School of Medical Sciences, Faculty of Health Sciences, University of KwaZulu-Natal,*2008. - KAUTZ, S.A. and HULL M.L., A theoretical basis for interpreting the force applied to the pedal in cycling.
*J. Biomechanics*26, No 2, 155-165, 1993 - MALFAIT, L., STORME, G., and DERDEYN, M., Comparative biomechanical study of circular and non-circular chainrings for endurance cycling at constant speed
*.**www.noncircularchainring.be*, 2006-2010

- MALFAIT, L., STORME, G., and DERDEYN, M., Why do appropriate non-circular chainrings yield more crank power compared to conventional circular systems during isokinetic pedalling?
*www.noncircularchainring.be*, 2012

- MATEO, M., BLASCO-LAFARGA, C., FERNANDEZ-PENA, E., and ZABALA,M., Efectos del sistema de pedalo no circular Q-Ring sobre el rendimiento en el sprint de la disciplina ciclista BMX.
*European Journal of Human Movement*25, 31-50, 2010. - MILLER, N.R., ROSS, D., The design of variable ratio chain drives for bicycles and ergometers-application to a maximum power bicycle drive.
*Journal of Mechanical Design*102, 711-717*,*1980.

- PEIFFER, J.J., and ABBISS, C.R., The influence of elliptical chainrings on 10 km cycling time trial performance.
*International Journal of Sports Physiology and Performance, 2010, 5, 459-468.* - RAMBIER, N. et GRAPPE,F., Effet de l’utilisation du plateau O’symetric sur la performance du cycliste.
*Departement Sport-Santé, Université de Franche-Comté, Besançon*. 2013

- RANKIN, J.F., and NEPTUNE, R.R., A theoretical analysis of an optimal chainring shape to maximize crank power during isokinetic pedalling.
*Journal of biomechanics*41, 1494-1502, 2008.

- RATEL, S., DUCHE, P., HAUTIER, C., WILLIAMS, C., and BEDU, M,. Physiological responses during cycling with noncircular “Harmonic” and circular chain rings.
*Eur J Appl Physiol*; 91(1): 100-104, 2004. - REDFIELD, R., and HULL, M.L., On the relation between joint moments and pedalling rates at constant power in bicycling.
*J. Biomechanics*19: 317-329, 1986.

- STRUTZENBERGER, G., WUNSCH, T., KROELL, J., DASTL, J., SCHWAMEDER, H., Effect of chainring ovality on joint power during cycling at different workloads and cadences.
*Sports Biomechanics*, 12 pages, 2014. - VAN HOOVELS, K., KONINCKX, E., and HESPEL, P., Study of the effect of non-circular chainwheels in cycling. Department of Kinesiology, Exercise Physiology Research Group, K.U. Leuven. Unpublished, 2010.