### B 2. Pedaling power

When cycling, your speed depends upon your pedaling power (Ppe) and the resistance that you must overcome using that power. At a constant speed, 4 components make up that resistance:
1. the intrinsic resistance of the bicycle (Rb)
2. the rolling resistance (Rr)
3. the air resistance or drag (Rd). And during a climb:
4. the slope resistance (Rsl).

The relationship between the pedaling power, the various resistances and the speed can be shown in a model (figure 1). We use this model to compare the speed of a regular racing bicycle with that of a recumbent high racer, on a level road and during a climb or descent. In the model, the pedaling power (Ppe) is the drive of the bicycle. This drive must overcome a number of resistances, resulting in speed or velocity (v). Pedaling power is measured in watt, speed in km/hour but in these calculations the speed is expressed in meters per second (m/s).

Figure 1 From pedaling power to cycling speed pedaling power (Ppe), intrinsic resistance (Rb), rolling resistance (Rr),
air resistance (Rd), slope resistance (Rsl) and speed (v)

Formulas
Approx. 5% of the pedaling power of a regular racing bicycle is needed to overcome the intrinsic resistance of the bicycle (Rb); this is approx. 7% for the recumbent high racer (next chapter). And so:
Pb = 0.05 × Ppe and Pb = 0.07 × Ppe, respectively. The portion of the pedaling power that is required to overcome the rolling resistance (Rr) is calculated as:
Pr = m × g × Cr × v (1) Overcoming the air resistance (Rd) requires:
Pd = 0.5 × ρ × A × Cd × v³ (1). When climbing, the pedaling power needed to overcome the slope resistance (Rsl) is:
Psl = m × g × % × v (1).

In these formulas, the mass (m) equals the ready-to-ride weight in kg of the bicycle plus the cyclist; the gravity (g) is 9.81 m/s²; the rolling resistance coefficient (Cr) has no dimension. The letter d (drag) stands for the air resistance, the Greek letter ρ (roo) for the relative density of the air; at sea level, it is 1.23 kg/m³, at a height of 1800 m, it is 1 kg/m³ (1). A (area) is the front surface of the cyclist plus bicycle in m²; Cd is the draft coefficient, which is a dimensionless number and a measure for streamlining. The slope is expressed as a percentage (%) during climbs and descents. The formulas are explained in more detail in the following chapters.

The bicycles
For speed comparison on a level road, during climbs and descents, we select a regular racing bicycle with a weight of 10 kg ready-to-ride (figure 2). It is compared to an equally heavy recumbent high racer (figure 3). Both bicycles have the same 28-inch wheels and the same tires, enforced with kevlar to prevent punctures. The rider on both bicycles is a non-competitive cyclist, with a ready-to-ride weight of 75 kg. The calculations are based on dry and smooth asphalt paving without bumps and cracks and weather conditions are always calm. All of the distances travelled on both bicycles are solo rides without crashes or punctures. The reported pedaling power and speed in the calculations are average values. Figure 2 Regular racing bicycle made of steel, ready-to-ride weight 10 kg
(Photographie L’Alpe d’Huez) Figure 3 Recumbent high racer made of carbon, ready-to-ride weight 10 kg
(photo M5 Recumbent Bicycles)

Power meters
Various power meters are available for measuring pedaling power (Ppe); but these are expensive and (in 2020) almost exclusively used by professional cyclists. In the SRM-system (Schoberer Rad Mess-system) (figure 4), strain gauges measure the pedaling power between the crank and the chainring (2). A small computer on the handlebars then calculates the pedaling power. Figure 4 SRM Wireless Training System

Garmin and Look Keo have also introduced power meters on the market (figure 5). These measure the pedaling power in the pedal spindles (3). This makes it easy to switch the meter over from one bicycle to another. And it is possible to compare the pedaling power between one leg and the other. Figure 5 Garmin Vector Power pedals

Pedaling power and speed
On a level and smooth asphalt road under calm weather conditions, the non-competitive cyclist on a regular racing bicycle, with his hands positioned in the drop handlebars, reaches a speed of 17.1 km/hour with a pedaling power of 50 watt (table 1). The speed on the recumbent high racer on that same road and with the same pedaling power reaches 19.9 km/hour. At 500 watt, the speed is 44.3 and 54.7 km/hour for the regular and recumbent racing bicycle, respectively. The calculations are explained in the chapters to come. Given the same pedaling power, the high racer is always faster than the racing bicycle on a level road. The difference increases from 16.4% at 50 watt to 23.5% at 500 watt (table 1 and figure 6).

Table 1 Pedaling power and speed (km/hour) on a level road

 racing bicycle 50watt 100watt 150watt 200watt 300watt 400watt 500watt regular 17.1 23.6 28.0 31.4 36.7 40.8 44.3 recumbent 19.9 28.3 33.9 38.3 45.0 50.3 54.7 difference (%) +16.4 +19.9 +21.2 +22.0 +22.6 +23.3 +23.5 Figure 6 The increase in speed in relation to an increasing pedaling power is non-linear

Pulling on the handlebars
Usually, the difference in speed between both bicycles will be less than calculated (table 1). Because the same cyclist can develop a higher pedaling power when riding in a sitting position than riding recumbent. Pulling on the handlebars of a regular racing bicycle is probably a more efficient way to transmit power to the pedals compared to pushing your back against the bucket seat of a recumbent bicycle. Pulling on the handlebars of a recumbent high racer might even diminish the pressure of your back against the backrest of the bucket seat. The only recumbent bike in which pulling the handlebars is an essential component of the drive concerns the so-called ‘rowing bicycle’. If the handlebars of an ‘ordinary’ recumbent bicycle can be adapted in such a way that pulling the handlebars increases the pressure on the pedals, has still to be demonstrated.

Pedaling power during one hour
How much pedaling power can the same cyclist develop in one hour on a regular racing bicycle, and how much on a recumbent high racer? No comparison of that kind has been made so far. It is estimated here that the 1-hour pedaling power of a recumbent cyclist is approx. 20% lower compared to the regular cycling position. Thus a non-competitive cyclist who can pedal a maximum of 225 watt on a regular racing bike for one hour will probably not exceed 180 watt on a recumbent high racer. Such a difference in pedaling power compensates in part the difference in speed between the two bicycles on a level road.

Conclusions
1. Pedaling power generates bicycle speed by overcoming the intrinsic resistance of the bicycle, rolling resistance, air resistance and (during a climb) slope resistance.
2. The recumbent high racer is faster than the regular racing bicycle at the same pedaling power on a level road; this difference exceeds 20% if the pedaling power exceeds 100 watt.
3. The 1-hour pedaling power of a cyclist is an estimated 20% lower on a recumbent compared to a regular racing bike because the recumbent cyclist cannot efficiently pull on the handlebars.

Sources
1. Wiel van den Broek: Technische artikelen over de fiets: Vermogen en Krachten. juni 2013
2. SRM Wireless Training System: Specialized Compact
3. Jeroen van Geelen: Garmin Vector Power pedalen: Power to the people