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extended abstract

Improvement of Cycling Efficiency for Drivetrains with Elasticity

25/02/2023| By
Willem Willem den Boer

Test and modeling results are presented on a bicycle crankset with limited elasticity. They show cycling efficiency improvements of around 2 %.

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Type of the Paper: Extended Abstract

Improvement of Cycling Efficiency for Drivetrains with Elasticity

W. den Boer

Huron Cycling LLC;

Name of Editor: Jason Moore

Submitted: 28/02/2023

Accepted: 13/04/2023

Published: 26/04/2023

Citation: den Boer, W. (2023). Improvement of Cycling Efficiency for Drivetrains with Elasticity. The Evolving Scholar - BMD 2023, 5th Edition.

This work is licensed under a Creative Commons Attribution License (CC-BY).


Test and modeling results are presented on a bicycle crankset with limited elasticity. Figure 1 depicts the operation principle and photograph of the cranksets. Like record-breaking running shoes, the crankset has spring action, which mitigates the effect of the dead zone during the pedal stroke. Fiber composite leaf springs are inserted inside the hollow carbon crank arms. The crank arms are not directly attached to the crank axle. Instead, sleeve bearings allow the crank arms to rotate by up to about five degrees relative to the crank axle. The rotation is counteracted by the springs and is proportional to applied torque at the pedals.

Figure 1. Solidworks drawing and photograph of cranksets with elasticity.

The angle of rotation θ at the crank arms relative to the crank axle is given by:

\(\theta = \frac{\tau}{k} = \frac{P}{\omega k}\) (1)

where τ  is the torque from the tangential force F applied at the pedals (τ = F*r with r the crank length of 175 mm). P is the applied power and ω is the angular velocity of the crank arms. k is a constant representing the degree of elasticity by bending of the leaf spring. For conventional cranksets without intentional elasticity the k value is high (Fairwheel Bikes, 2021), typically > 5000 Nm, so that θ is small. In our novel crankset k = 1000 Nm, resulting in θ = 0.07 rad (4 degrees) and a deflection at the pedals D = θ *r = 12.25 mm (0.48 inch) for a tangential force of 400 N (90 pounds). Leaf springs with different k values can be used depending on the power and skill of the cyclist.

The novel crankset was installed on a carbon frame bicycle and compared with a conventional crankset with forged aluminum crank arms, while keeping the gear ratio constant at 36/17. To eliminate wind drag factors and changing conditions the testing was performed indoors on a Tacx Neo smart trainer with a slope setting of 3 %. Two power meters were used:

  1. A Powertap P1 pedal power meter at left and right pedals to measure input power

  2. The internal power meter of the Tacx Neo to measure effective speed

The ratio of effective speed to input power is used as a measure of cycling efficiency. Depending on the maximum torque during the downstroke this ratio is typically a few percent higher than for the conventional crankset (Bastianelli et al., 2019, Den Boer, 2019-1). Details of multiple tests which show consistently improvement of around 2 % at constant power levels of 200 W and cadence of 71 rpm will be presented. Other implementations of elastic drivetrains have also demonstrated improvements in cycling efficiency (Hamamoto, 2019).

To understand the test results computer modeling of bicycle speed and crank arm angular velocity vs. time was performed for different values of k, input power and cadence. The power P applied to the crank arms was assumed to vary sinusoidally from a maximum during the downstroke to a minimum close to zero in the dead spot, in agreement with our measurements of the rotation angle θ  vs. time for left and right crank arms.

It is difficult to explain the observed improvement in cycling efficiency from just the dependence of force and angular velocity profiles on k. The improvement is attributed instead to the conversion of irreversible energy losses from twisting in conventional crank arms (Fairwheel Bikes, 2021, ACT Lab 2016) and flexing of the frame (ACT Lab, 2017) under load to reversible energy losses (energy return) with the leaf springs in our crankset. The strain energy losses in the crank arms of conventional cranksets can be 1.6 % at a cadence of 100 rpm (Fairwheel Bikes, 2021) and even higher at lower rpm for the same power input. Energy return from the elastic leaf springs, contributing to torque, provides a qualitative explanation of the observed improvement in efficiency. It depends not only on the k value of the novel crankset, but also on the stiffness of the frame and the conventional crankset used in the comparison. The modeling shows that the expected efficiency improvement with the novel crankset is proportional to τ0/k, where τ0 is the maximum torque applied to the pedals during the downstroke. According to equation (1) the improvement is therefore also proportional to P and inversely proportional to ω (i.e. cadence).

In addition to energy return there is another potential benefit of a degree of elasticity in the crank arms: It may reduce the onset of muscle fatigue (Hamamoto, 2019) by reducing the force on the pedals during the first part of the downstroke.

Our measurement of deflection angle θ with rotation sensors has been used to determine the torque profile vs. time. In combination with angular velocity measurement it is therefore a method to measure power at left and right pedals (Den Boer, 2019-2) without relying on strain gauges.


  1. ACT Lab (2016), Crank Fatigue Test,

  2. ACT Lab (2017), Frame Fatigue with Pedalling Forces Test,

    1. Bastianelli, B. M., Workman, A. & McGregor, S. (2019, June), Novel Crank with Elastomer Spring Improves Effective Power in Trained Cyclists and Triathletes, Medicine & Science in Sports & Exercise, Chicago, 2019,   51(6S):p 942-943, June 2019.

  3. Den Boer, W. (2019-1), US Patent 11,142,281, Cycle Crank Assembly,

  4. Den Boer, W. (2019-2),White Paper IMPACT power meter August 2019:

  5. Fairwheel Bikes (2021),

  6. Hamamoto, Y. (2019), US Patent 10,450,030, Rotational Apparatus and Bicycle provided with same,

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Submitted by25 Feb 2023
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Willem Den Boer
Huron Cycling LLC
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