If you keep your legs still during a descent, then the pedaling power plays no role. The driving power then depends upon the slope: the steeper the slope, the higher the speed of descent. That driving power equals the pedaling power that is required to overcome the slope resistance during the climb (1). So Psl = m × g × % × v also applies during the descent. If you refrain from pedaling, the chain is not in motion. Only the wheels spin around the axles. As a result, the power needed to overcome the intrinsic resistance of the bicycle is limited to 1% of the driving force (see Intrinsic resistance). This applies to both the regular and the recumbent racing bicycle. And so during the descent (without pedaling): Pb = 0.01 × Psl.
If you refrain from braking, your speed will increase until the power required to overcome the total resistance (intrinsic resistance, rolling- and air resistance) equals the driving force. So: Pb + Pr + Pd = Psl
During a descent on the regular racing bicycle with the hands in the curves of the handlebars, a front surface A of 0.4 m² is assumed for a non-competitive cyclist. His speed of descent on a 3% slope, without pedaling or braking, reaches 34.01 km/hour (9,446 m/s). The driving force in this descent is: Psl = m × g × % × v
Psl = (75 + 10) × 9.81 × 0.03 × 9.446 = 236.3 watt. The intrinsic resistance costs 1%: Pb = 0.01 × 236.3 = 2.4 watt. The pedaling power needed to overcome the rolling resistance: Pr = m × g × Cr × v
Pr = (75 + 10) × 9.81 × 0.006 × 9.446 = 47.3 watt. The air resistance requires: Pd = 0.5 × ρ × A × Cd × v³
Pd = 0.5 × 1.23 × 0.4 × 0.9 × 9.446³ = 186.6 watt
Added up Pb + Pr + Pd = 236.3 watt (table 1).
Table 1 Speed of descent on a 3% slope
|0.4 ||236.3 ||2.4 ||47.3 ||186.6 ||34.01|
|0.2 ||334.3 ||3.3 ||66.9 ||264.1 ||48.10|
His speed of descent on a 3% slope on the recumbent high racer (without pedaling or braking) reaches 48.10 km/hour (13,362 m/s):
Psl = (75 + 10) × 9.81 × 0.03 × 13.362 = 334.3 watt
Pb = 0.01 × 334.3 = 3.3 watt
Pr = (75 + 10) × 9.81 × 0.006 × 13.362 = 66.9 watt
With a front surface A of 0.2 m², the air resistance requires:
Pd = 0.5 × 1.23 × 0.2 × 0.9 × 13.362³ = 264.1 watt
Added up Pb + Pr + Pd = 334.3 watt (table 1).
So in the descent of a 3% slope, the speed of this non-competitive cyclist is 48.10 km/hour on the recumbent high racer, which is 41.4% faster than on the regular racing bicycle (48.10/34.01).
Slope and speed of descent
Steep slopes usually have hairpin bends so that the descent requires braking. That limits the speed in the intermediate strokes. But in (almost) straight descents, if braking is unnecessary, high descending speeds can be reached. The difference in speed between the recumbent and the regular racing bicycle is ever growing with increasing steepness of the slopes (table 2). Thus, our non-competitive cyclist reaches a speed of 59.77 km/hour on a 8% slope with the regular racing bike, holding his hands in the curves of the handlebars (table 2). This is 84.53 km/hour on the recumbent high racer. However, the relative difference between the bikes (with the same rider) remains 41.4% on all slopes (table 2).
Table 2 Slope and speed of descent (km/hour)
|0.4 ||34.01 ||46.08 ||55.59 ||59.77 ||67.38|
|0.2 ||48.10 ||65.16 ||78.62 ||84.53 ||95.28|
|-50||+41.4 ||+41.4 ||+41.4 ||+41.4 ||+41.4|
As the steepness of the slope increases, the relative difference in speed
between the two bicycles remains constant
Figure 1 As the steepness of the slope increases, the absolute difference in speed
between the two bicycles increases
The major difference in the speed of descent between the recumbent and the regular racing bicycle is caused by the difference in front surface of the rider. Which is why professional cyclists lie on the top tube of their regular racing bike during a descent in order to make their front surface as small as possible. This ‘ski-position’ enables a rider with an average build to reduce his front surface from 0.4 m² to approx. 0.3 m². That is a reduction of 25%. In that way, he can achieve a speed of 69.02 km/hour with the 10-kg regular racing bicycle on a 8% slope (without braking). That is 15.5% more than with the hands in the drop handlebars (69.02/59.77) but still 22.5% less than on the recumbent high racer (84.53/69.02). In descents of this kind, skiers can reach a speed that exceeds 100 km/hour. Their ‘rolling resistance’ on the piste is most likely lower than that of a racing bicycle on asphalt.
1. During a descent (without pedaling and/or braking) you are more than 40% faster on every slope when riding a recumbent high racer compared to a regular racing bicycle (with your hands in the handlebars).
2. By making a descent on a regular racing bike in a ‘ski-position’, the front surface is reduced by approx. 25% compared to positioning your hands in the drop handlebars; this ‘ski-position’
increases the speed of descent on a 8% slope by about 15%.
1. Wiel van den Broek: Technische artikelen over de fiets; Vermogen en Krachten, juni 2013. http://www.velofilie.nl/vermogen.htm
© Leo Rogier Verberne