Sports Engineering

, 23:1

# Influence of mountain bike riding velocity, braking and rider action on pedal kickback

• Manuel Gerth
• Matthias Haecker
• Peter Kohmann
Original Article

## Abstract

When dealing with full suspension mountain bikes, pedal kickback is one of the main parameters used to assess the performance of rear wheel kinematics. According to the currently used theory of Kovács, pedal kickback is the backwards rotation of the crank during the compression of the rear suspension, which mainly occurs because of elongation between the bottom bracket and the rear axle. Most bike companies try to minimize pedal kickback during kinematic design, because this phenomenon creates unwanted harshness in the suspension and negatively influences rider stability due to the backwards rotation of the crank. When riding downhill above a certain velocity (i.e., the critical velocity) without pedaling or blocking the rear wheel, the cassette will complete a forward rotation instead of a backwards rotation of the crank, which is hereinafter referred to as freewheel theory. The cassette will perform this forward rotation without affecting the rider or creating suspension harshness. The paper discusses the analytical derivation for the calculation of the linearized critical velocity and presents a multibody simulation to calculate the exact critical velocity. The existence of the critical velocity is shown through measurements with an instrumented bike during a test ride on a downhill track and through an experiment performed under idealized conditions. The test ride demonstrated the influence of the rider on the critical velocity by moving the cranks in certain riding situations, such as landing on the front wheel first or hitting large obstacles. The crank movement leads to an increased (forward rotation) or decreased (backwards rotation) critical velocity. Both riding situations are reproduced with the multibody simulation.

## Keywords

Mountain bike MTB Downhill Pedal kickback Kinematics Multibody simulation

## List of symbols

$${ \omega }_{\text {c}}$$

Angular velocity of the crank in $$\frac{ \mathrm {rad} }{ \mathrm {s} }$$

$${ \omega }_{\text {rh}}$$

Angular velocity of the rear hub and rear wheel in $$\frac{ \mathrm {rad} }{ \mathrm {s} }$$

$${ \omega }_{\text {s}}$$

Angular velocity of the sprocket and cassette in $$\frac{ \mathrm {rad} }{ \mathrm {s} }$$

$${ \varphi }$$

Angle (pedal kickback) of the crank in rad

$${ \varphi }_{\text {s}}$$

Angle of the sprocket and cassette in rad

$${ \varphi }_{\text {rh}}$$

Angle of the rear hub and rear wheel in rad

t

Rear suspension compression time in s

$${ v }_{\text {c}}$$

Critical velocity in $$\frac{ \mathrm {m} }{ \mathrm {s} }$$

$${ v }_{\text {cl}}$$

Linearized critical velocity in $$\frac{ \mathrm {m} }{ \mathrm {s} }$$

$${ r }_{\text {w}}$$

Radius of the wheel in mm

v

Riding velocity in $$\frac{ \mathrm {m} }{ \mathrm {s} }$$

$${ l }_{\text {t}}$$

Thickness of the tire in mm

$${ z }_{\text {c}}$$

Number of teeth on the chainring

$${ z }_{\text {s}}$$

Number of teeth on the currently used sprocket

## References

1. 1.
IfD Allensbach, AWA (2017) Anzahl der Personen in Deutschland, die in der Freizeit Mountainbike fahren. Allensbacher Markt- und WerbetraegeranalyseGoogle Scholar
2. 2.
Software Racooz (2019) Bike suspension analysis and design software. https://www.bikechecker.com/. Accessed 27 May 2019
3. 3.
Canyon Bicycles GmbH: Canyon—this is why: the engineer at 1:26. youtube. https://www.youtube.com/watch?v=FgLQPabSNSQ. Accessed 27 May 2019
4. 4.
Großehagenbrock Giacomo, 77designz Develops a Bike Frame. https://www.pinkbike.com/news/developing-a-bike-frame-enduro.html/. Accessed 27 May 2019
5. 5.
Unno SL (2019) About us, kinematics development. https://www.unno.com/about-us/. Accessed 27 May 2019
6. 6.
Dave Trumpore on Pinkbike.com (2019) Testing with team specialized gravity. https://www.pinkbike.com/news/specialized-gravity-team-testing-winter-2016.html. Accessed 14 Apr 2019
7. 7.
Mike Levy on Pinkbike.com, Cannondale’s Split-Shock DH Bike Explained, https://www.pinkbike.com/news/cannondale-split-shock-dh-bike-explained-fort-william-dh-world-cup-2019.html Accessed 14 April 2019
8. 8.
Manuel G, Cornelius D (2016) Einfluss des Pedalrueckschlags auf das Fahrwerksverhalten von vollgefederten Mountainbikes. Pforzheim University, ForschungsberichtGoogle Scholar
9. 9.
Jens B (2013) Untersuchung des Einflusses geometrischer Parameter auf das Fahrverhalten von Einspurfahrzeugen. Master-Thesis, University of applied science AachenGoogle Scholar
10. 10.
Gergely K (2016) Pedal kickback calculation. Linkage bike suspension analysis and design software. https://www.bikechecker.com/linkagedoc/PedalKickbackCalculation.pdf. Accessed 9 Oct 2018
11. 11.
ADP Engineering GmbH, Kinematics Pedal kickback. https://www.rotwild.com/en/rot-wild/engineering/kinematics/pedal-kickback/. Accessed 30 Jul 2019
12. 12.
Cycling Sports Group Europe B.V. (Cannondale), Pedal Kickback in the Habit White Paper. Accessed 31 Jul 2019Google Scholar
13. 13.
Leo K (2019) Why speed doesn’t count on Leo’s Tech Blog. https://polebicycles.com/what-is-anti-squat-and-pedal-kickback/. Accessed 31 Jul 2019
14. 14.
Andy Wathis on Pinkbike.com (2019) Photo 11 of tech randoms: les gets World Cup DH 2019. https://www.pinkbike.com/photo/17449411/. Accessed 31 July 2019
15. 15.
Scheffer L, Thoma V, Lorenz L (2015) EP3133311A1. European Patent OfficeGoogle Scholar
16. 16.
Canyon Bicycles GmbH. Gravity Sender CF 8.0. https://www.canyon.com/gravity/sender/2018/sender-cf-8.html. Accessed 9 Oct 2018
17. 17.
Testbericht: Canyon Strive CF 8.0 Race on mountainbike-magazin.de. https://www.mountainbike-magazin.de/mtb/testbericht-canyon-strive-cf-8-0-race-modelljahr-2016/. Accessed 18 Sep 2019
18. 18.
Manuel G (2017) Aufbau eines parametrischen MKS-Modells als Grundlage fuer die Bewertung verschiedener MTB-Kinematiken. Master-Thesis, Pforzheim UniversityGoogle Scholar
19. 19.
Benedikt G (2015) Aufbau und Validierung eines erweiterten Fahrrad-Modells inklusive Fahrer in einer Mehrkoerpersimulationsumgebung. Bachelor-Thesis, Pforzheim UniversityGoogle Scholar
20. 20.
National Aeronautics and Space Administration (1999) International Space Station Flight Crew Integration Standard (NASA–STD–3000/T) Revision CGoogle Scholar
21. 21.

© International Sports Engineering Association 2019

## Authors and Affiliations

• Manuel Gerth
• 1
• Matthias Haecker
• 1
• Peter Kohmann
• 1
1. 1.Institute for Smart Bicycle TechnologyPforzheim UniversityPforzheimGermany