9. Tour de France
The recumbent high racer is longer and 2 kg heavier than the regular racing bicycles of professional cyclists (table 1). This means a disadvantage in terms of speed, because it increases rolling and slope resistance (see the foregoing chapter). But an even greater disadvantage is the reduced pedaling power of the rider when cycling a recumbent bicycle (with the present construction of the handlebars). That reduction is yet to be objectively quantified. It is assumed here that the 1hour pedaling power of a cyclist on a recumbent high racer is 20% less than on a regular racing bicycle. However, when cycling recumbent, the air resistance is lower, thanks to a smaller front area, which is a big advantage for the high racer. The overall effect in terms of speed when cycling recumbent compared to regular cycling has not been clarified. Because as early as 1934 the UCI banned recumbent cyclists from competitions (5). That ban is in place up to the present day. So the question whether a professional cyclist could win, for example the Tour de France, on a recumbent bicycle has never been answered.
Model
In a model, we compare the performances of a professional cyclist on a regular racing bicycle and on a recumbent high racer in the Tour de France of 2013. That was the 100th edition of the Tour, won by Chris Froome. It consisted of 7 level stages (combined 1339 km), 2 individual time trials and a team time trial (combined 90 km), 5 hill stages (866 km) and 6 mountain stages (1108 km). Thus, the total route of that Tour was 3,403 km long (3). We compare the speed of Chris Froome on his regular racing bicycle in a model of this Tour with the speed he might have reached on a recumbent high racer. In doing so, each stage is considered a solo ride: so riding as a team and spills are not considered here. Flat tires and weather influences are also left out: in this comparison, the road is made of smooth, dry and clean asphalt and weather conditions are always calm.
Bicycles
Chris Froome’s regular racing bicycle (figure 1) has a ‘bare’ weight of 6.8 kg. It is equipped with a power and speed meter and a filled water bottle. The readytoride weight in our calculations is assumed to be 8 kg (table 1). Anything else that he may need on the road is taken along in a following car. The bicycle has tubes instead of tires. That brings the rolling resistance coefficient (Cr) down from 0.006 (equipped with tires) to 0.005 (table 1). Froome’s cycling position has been optimized in a wind tunnel so that his front surface (with his hands in the drop handlebars) is reduced from 0.4 to approx. 0.35 m² (figure 3). The air resistance coefficient (Cd) in his usual cycling clothing is approx. 0.9 (table 1).
Figure 1 The regular racing bicycle of Chris Froome, readytoride weight 8 kg
(photo Pinarello)
Figure 2 The recumbent high racer, readytoride weight 10 kg
(photo M5 Ligfietsen)
The recumbent high racer for comparison (figure 2) is longer than the racing bicycle and has a ‘bare’ weight of 9 kg. Including power meter and speedometer plus a full water bottle, its readytoride weight is 10 kg (table 1). Because the chain is three times longer, it must be guided in order to prevent swaying; which is why the intrinsic resistance is 7% for the high racer compared to 5% for the racing bicycle. Wheels and tubes, accounting for the Crvalue, are the same for both bicycles (table 1). Froome’s front surface (A) on the recumbent bicycle is 0.2 m². The Cdvalue (streamlining) is 0.9 on both bicycles (table 1).
Table 1 Specifications of Chris Froome’s regular and recumbent racing bicycle
racing bicycle  w kg  Pb % 
Cr
 A m²  Cd

regular  8  5  0.005  0.35  0.9 
recumbent  10  7  0.005  0.2  0.9 
Cyclist
Chris Froome is the rider of both bicycles. He has a length of 1.86 m and he weighs 67.5 kg (4). Equipped with cycling clothing, a helmet, glasses, gloves, chest band (part of the heart rate monitor), earphone plus transmitter/receiver and following a hearty breakfast, we put his readytoride weight at 70 kg. It is assumed here that his pedaling power during about one hour on the regular racing bicycle is 450 watt. However, stages in the Tour de France usually take 4 to 5 hours. And a pedaling power of 80% seems the max for a 5hours period, even for a welltrained champion like Chris Froome. Therefore we assume 0.8 × 450 = 360 watt to be the 5hours pedaling power (table 2).
Figure 3 Chris Froome, his front surface A = ± 0.35 m²
(photo The Telegraph)
Level stages
The average length of the 7 level stages is 191.3 km (1339/7). On the regular racing bicycle, his average speed in these stages at a 5hours pedaling power of 360 watt reaches 41.55 km/hour (11.541 m/s). Of this pedaling power (Ppe), 5% is lost to the intrinsic resistance of the bicycle: Pb = 0.05 × 360 = 18.0 watt (table 2). The power needed to overcome the rolling resistance is: Pr = m × g × Cr × v
Pr = (70 + 8) × 9.81 × 0.005 × 11.541 = 44.2 watt. The air resistance requires: Pd = 0.5 × ρ × A × Cd × v³
Pd = 0.5 × 1.23 × 0.35 × 0.9 × 11.541³ = 297.8 watt. Added up Ppe = Pb + Pr + Pd = 360 watt (table 2).
At an average speed of 41.55 km/hour, a stage of 191.3 km in length will take 4.604 hours (191.3/41.55).
Table 2 Pedaling power and speed in the level stages
racing bicycle  Ppe watt  Pb watt  Pr watt 
Pd watt  v km/h  r.time hours 
regular  360  18.0  44.2  297.8  41.55  4.604 
recumbent  288  20.2  49.2  218.6  45.16  4.236 
difference (%)      +8.7  
in the level stages, Chris Froome is 8.7% faster on the recumbent
compared to his regular racing bicycle
On the recumbent high racer, his 1hour pedaling power is an estimated 20% less than on the regular racing bicycle, so 0.8 × 450 = 360 watt. If we consider 80% of this value as his 5hours pedaling power on the recumbent bicycle, this comes to 288 watt (table 2). This brings Chris Froome’s average speed during the 7 level stages on the high racer to 45.16 km/hour (12.545 m/s). Overcoming the intrinsic resistance of the recumbent bicycle requires 7% of this 5hours pedaling power: Pb = 0.07 × 288 = 20.2 watt. The following applies to the rolling and air resistance:
Pr = (70 + 10) × 9.81 × 0.005 × 12.545 = 49.2 watt
Pd = 0.5 × 1.23 × 0.2 × 0.9 × 12.545³ = 218.6 watt
Added up Ppe = Pb + Pr + Pd = 288 watt (table 2).
At an average speed of 45.16 km/hour, a stage of 191.3 km in length takes 4.236 hours (191.3/45.16).
Time trials
The Tour of 2013 included two individual time trials and 1 team time trial. Altogether covering a 90 km distance. Professional cyclists use a special bicycle for these trials, which falls outside the scope of this comparison.
Hill stages
The 5 hill stages had a combined length of 866 km. So the average length was 173.2 km (866/5). Those stages included a total of 15 climbs in the 4th, 3rd and 2nd category, or an average of 3 hills per stage. Combined, the 15 hills accounted for 195.5 kilometers of climbing (2), or 39.1 km per stage (195.5/5). An average slope of 4% was observed for the hills, along with (rounded off) 13 km (39.1/3) for the distance of the uphill and the downhill section per slope. The sections between the hills are considered to be flat. And so each stage of 173.2 km in length includes 39 km of climbing (4% slope) and 39 km of descending, plus 95.2 km of flat road (173.2  78).
Uphill
On the regular racing bicycle, the 1hour pedaling power of Chris Froome is taken into account in the calculations for pedaling uphill. Because an uphill stroke takes less than 1 hour climbing and every uphill stroke is followed by a descent, being a period of relative rest for the cyclist. This 450 watt pedaling power brings his climbing speed to 31.34 km/hour (8.705 m/s) on the 4% slopes.
Pb = 0.05 × 450 = 22.5 watt
Pr = (70 + 8) × 9.81 × 0.005 × 8.705 = 33.3 watt
Pd = 0.5 × 1.23 × 0.35 × 0.9 × 8.705³ = 127.8 watt. The pedaling power required to overcome the slope resistance is: Psl = m × g × % × v
Psl = (70 + 8) × 9.81 × 0.04 × 8.705 = 266.4 watt
Added up Ppe = Pb + Pr + Pd + Psl = 450 watt (table 3).
At an average speed of 31.34 km/hour, the 3 climbs combined in each hill stage take 1.244 hours (39/31.34).
Table 3 Climbing speed on 4% slopes
racing bicycle  Ppe watt  Pb watt 
Pr watt  Pd watt  Psl watt 
v km/h  r.time hours 
regular  450  22.5  33.3  127.8  266.4  31.34  1.244 
recumbent  360  25.2  31.1  55.0  248.7  28.52  1.367 
difference (%)  20.0      9.0  
when climbing 4% slopes, Chris Froome is 9% slower on the recumbent
compared to his regular racing bicycle
On the recumbent high racer Froome’s 1hour pedaling power when riding uphill (less than 1 hour each time) is 360 watt. This brings his climbing speed on the 4% slopes to 28.52 km/hour (7.921 m/s).
Pb = 0.07 × 360 = 25.2 watt
Pr = (70 + 10) × 9.81 × 0.005 × 7.921 = 31.1 watt
Pd = 0.5 × 1.23 × 0.2 × 0.9 × 7.921³ = 55.0 watt
Psl = (70 + 10) × 9.81 × 0.04 × 7.921 = 248.7 watt
Ppe = Pb + Pr + Pd + Psl = 360 watt (table 3).
At an average speed of 28.52 km/hour, the 3 climbs combined on the high racer take 1.367 hours (39/28.52).
Downhill
If holding the legs still while descending, the pedaling power plays no role. The chain is not in motion and so the intrinsic resistance is limited to the friction in the axles, which requires 1% of the driving force (chapter Intrinsic resistance). The driving force stems from the slope resistance (Psl), which does not counteract, but rather generates drive. If the cyclist refrains from braking, his speed of descent will increase until the driving force and resistance (the sum of intrinsic, rolling and air resistance) balance one another.
In the descent on his regular racing bicycle, Chris Froome lies flat on the top tube (in ‘skiposition’); as a result, his front surface is reduced to ± 0.3 m². His speed of descent is then 45.46 km/hour (12.627 m/s).
Psl = (70 + 8 ) × 9.81 × 0.04 × 12.627 = 386.5 watt
Pb = 0.01× 386.5 = 3.9 watt
Pr = (70 + 8) × 9.81 × 0.005 × 12.627 = 48.3 watt
Pd = 0.5 × 1.23 × 0.3 × 0.9 × 12.627³ = 334.3 watt
Ppe = Pb + Pr + Pd = 386.5 watt (table 4).
At an average speed of 45.46 km/hour, descending the 3 slopes combined takes 0.858 hours (39/45.46).
Table 4 Descending speed on 4% slopes
racing bicycle  Psl watt  Pb watt 
Pr watt  Pd watt  v km/h  r.time hours 
regular  386.5  3.9  48.3  334.3  45.46  0.858 
recumbent  491.7  4.9  61.5  425.3  56.38  0.692 
difference (%)      +24.0  
when descending 4% slopes, Chris Froome is 24% faster on the recumbent
compared to his regular racing bicycle
On the recumbent high racer, his speed of descent on the 4% slopes, without pedaling or braking, is 56.38 km/hour (15.662 m/s).
Psl = (70 + 10) × 9.81 × 0.04 × 15.662 = 491.7 watt
Pb = 0.01 × 491.7 = 4.9 watt
Pr = (70 + 10) × 9.81 × 0.005 × 15.662 = 61.5 watt
Pd = 0.5 × 1.23 × 0.2 × 0.9 × 15.662³ = 425.3 watt
Psl = Pb + Pr + Pd = 491.7 watt (table 4).
At an average speed of 56.38 km/hour, descending the 3 slopes combined takes 0.692 hours (39/56.38).
Riding time per hill stage
Combined, the 3 climbs on the regular racing bicycle take 1.244 hours (table 3); the descents take 0.858 hours (table 4). On the level stages, his speed is 41.55 km/hour (table 2). At this speed, the flat sections between the hills (95.2 km combined) are covered in 2.291 hours (95.2/41.55). This brings the total riding time of a hill stage to: 1.244 (climbing) + 0.858 (descending) + 2.291 (flat) = 4.393 hours (table 8). And so the average speed in the 5 hill stages is 39.43 km/hour (173.2/4.393).
Combined, the 3 climbs on the recumbent high racer take 1.367 hours (table 3); descending takes 0.692 hours (table 4). The speed during the flat sections between the hills is 45.16 km/hour (table 2) and combined, they take 2.108 hours (95.2/45.16). This brings the total riding time of the average hill stage to: 1.367 (climbing) + 0.692 (descending) + 2.108 (flat) = 4.167 hours (table 8). With that, the average speed on the recumbent bicycle during the 5 hill stages is 41.56 km/hour (173.2/4.167).
On balance, during the hill stages Chris Froome is an average of 5.4% faster on the recumbent high racer compared to his regular racing bicycle (41.56/39.43). Indeed, he is 9% slower during the climbs on the recumbent bicycle, but he is 24% faster when descending, with an additional 8.7% on the flat sections.
Mountain stages
The 6 mountain stages of the Tour de France in 2013 had a combined length of 1108 km (5). Which is 184.7 km per stage. The stages altogether included 8 1st category mountains and 7 ‘hors catégorie’, or an average of 2.5 mountains per stage (15/6). Combined, the 15 mountains accounted for 209.7 kilometers of climbing (2) or 14 km per mountain (209.7/15) and 35 kilometers of climbing per stage (2.5 × 14). But the total number of descending kilometers was less than 209.7, because 4 of the 6 mountain stages finished on a mountain top. Thus the total number of climbs was 15, wheras the number of descents was only 11. And so the climbing involved a total of 210 km (15×14), but only 154 km of descending (11×14), or 25.7 km per stage (154/6). With that, each mountain stage of 184.7 km consists of 35 km of climbing, 25.7 km of descending and 124 km of flat adjoining sections (184.7–60.7). The average slope observed here is 8% for both uphill and downhill sections.
Uphill
On the regular racing bicycle, Chris Froome reaches a speed of 21.74 km/hour (6.040 m/s) when climbing the 8% slopes with his 1hour pedaling power of 450 watt.
Pb = 0.05 × 450 = 22.5 watt
Pr = (70 + 8) × 9.81 × 0.005 × 6.040 = 23.1 watt. In high mountains, we assume a value of 1 kg/m³ for the relative density of the air (ρ = 1), corresponding to a height of 1800 m (1).
Pd = 0.5 × 1.0 × 0.35 × 0.9 × 6.040³ = 34.7 watt
Psl = (70 + 8) × 9.81 × 0.08 × 6.040 = 369.7 watt
Ppe = Pb + Pr + Pd + Psl = 450 (tabel 5).
At an average speed of 21.74 km/hour, the 35 km of climbing take 1.610 hours (35/21.74).
Table 5 Climbing speed on 8% slopes
racing bicycle  Ppe watt  Pb watt 
Pr watt  Pd watt  Psl watt  v km/h 
r.time hours 
regular  450  22.5  23.1  34.7  369.7  21.74  1.610 
recumbent  360  25.2  19.1  10.4  305.4  17.51  1.999 
difference (%)  20.0      19.5  
when climbing 8% slopes, Chris Froome is 19.5% slower on the recumbent
compared to his regular racing bicycle
The 1hour pedaling power during climbs on the recumbent high racer is 360 watt and his climbing speed comes to 17.51 km/hour (4.864 m/s).
Pb = 0.07 × 360 = 25.2 watt
Pr = (70 + 10) × 9.81 × 0.005 × 4.864 = 19.1 watt
Pd = 0.5 × 1.0 × 0.2 × 0.9 × 4.864³ = 10.4 watt
Psl = (70 + 10) × 9.81 × 0.08 × 4.864 = 305.4 watt
Ppe = Pb + Pr + Pd + Psl = 360 watt (table 5).
At an average speed of 17.51 km/hour, the 35 kilometers of climbing take 1.999 hours (35/17.51).
Downhill
In the 8% descents on his regular racing bicycle (in skiposition, A = 0.3 m²), his speed (without braking) reaches 73.83 km/hour (20.508 m/s). The driving force is:
Psl = (70 + 8) × 9.81 × 0.08 × 20.508 = 1255.4 watt.
Pb = 0.01 × 1255.4 = 12.5 watt
Pr = (70 + 8) × 9.81 × 0.005 × 20.508 = 78.5 watt
Pd = 0.5 × 1.0 × 0.3 × 0.9 × 20.508³ = 1164.4 watt
Psl = Pb + Pr + Pd = 1255.4 (tabel 6).
At an average speed of 73.83 km/hour, descending 25.7 km of 8% slopes takes 0.348 hours (25.7/73.83).
Table 6 Descending speed on 8% slopes
racing bicycle  Psl watt  Pb watt 
Pr watt  Pd watt  v km/h  r.time hours 
regular  1255.4  12.6  78.5  1164.4  73.83  0.348 
recumbent  1596.9  16.0  99.8  1481.1  91.57  0.281 
difference (%)      +24.0  
when descending 8% slopes, Chris Froome is 24% faster on the recumbent
compared to his regular racing bicycle
On the recumbent high racer, his speed during the 8% descent reaches 91.57 km/hour (25.436 m/s). The driving force is:
Psl = (70 + 10) × 9.81 × 0.08 × 25.436 = 1597.0 watt.
Pb = 0.01 × 1597.0 = 16.0 watt
Pr = (70 + 10) × 9.81 × 0.005 × 25.436 = 99.8 watt
Pd = 0.5 × 1.0 × 0.2 × 0.9 × 25.436³ = 1481.1 watt
Psl = Pb + Pr + Pd = 1596.9 watt (table 6).
At an average speed of 91.57 km/hour, descending 25.7 km of 8% slopes takes 0.281 hours (25.7/91.57).
Riding time per mountain stage
Climbing the 35 km of 8% slopes on the regular racing bicycle takes 1.610 hours (table 5); descending 25.7 km takes 0.348 hours (table 6) The speed during the 124 km of flat sections between the mountains is 41.55 km/hour (table 2) and these are covered in 2.984 hours (124/41.55). This brings the riding time of a mountain stage on the regular racing bike to: 1.610 (climbing) + 0.348 (descending) + 2.984 (flat) = 4.942 hours (table 8). Which corresponds to an average speed of 37.37 km/hour (184.7/4.942).
On the recumbent high racer, the 35 km of climbing take 1.999 hours (table 5); descending 25.7 km takes 0.281 hours (table 6). The speed during the 124 km of flat sections is 45.16 km/hour (table 2). And so these are covered in 2.746 hours (124/45.16). Thus the riding time of a mountain stage on the high racer is: 1.999 (climbing) + 0.281 (descending) + 2.746 (flat) = 5.026 hours (table 8). It brings the average speed on the recumbent bicycle to 36.75 km/hour (184.7/5.026).
With that, Chris Froome is an average of 1.7% slower during the mountain stages on the recumbent compared to his regular racing bicycle (36.75/37.37). Due to the 4 finishes on the mountain top, he is missing 4 descents in which he would have been 24% faster on the recumbent high racer.
Summarized
The modeltour (not including the time trials) includes 1339 km flat kilometers in 7 level stages, 476 km between the hill stages (5×95.2) and 744 km in the mountain stages (6×124). Which makes a total of 2559 flat kilometers (table 7). The 4% climbs in the hill stages have a combined length of 195 km (5×39), as do the 4% descents. The 8% climbs make up a total of 210 km (6×35), the 8% descents come to (rounded off) 154 km (6×25.7). With that, the total length of the modelround is 3313 km (table 7).
On the recumbent high racer, Chris Froome is 8.7% faster during the flat kilometers compared to his regular racing bicycle, and he is 24% faster during the 4% and 8% descents. But when climbing the 4% and 8% slopes on the high racer, he is 9% and 19.5% slower, respectively (table 7).
Table 7 Distance and speed
 distance km  regular km/h 
recumbent km/h  difference % 
level stages  2559  41.55  45.16  +8.7 
4% uphill  195  31.34  28.52  9.0 
4% downhill  195  45.46  56.38  +24.0 
8% uphill  210  21.74  17.51  19.5 
8% downhill  154  73.83  91.57  +24.0 
Total  3313    
And the winner of the modeltour is …
Across the entire modeltour, Chris Froome is 3.202 hours faster on the recumbent high racer than on his regular racing bicycle (83.845 – 80.643) (table 8); that is to say, 3 hours, 12 minutes and 7 seconds. His average speed in the whole modeltour is 41.08 km/hour on the recumbent high racer (3313/80.643) versus 39.51 km/hour on his regular racing bicycle (3313/83.845). That is a difference of 3.8% (41.08/39.51).
Table 8 Riding time in various stages
 regular hours  recumbent hours 
level stages  7 × 4.604 = 32.228  7 × 4.236 = 29.652 
hill stages  5 × 4.393 = 21.965  5 × 4.167 = 20.835 
mountain stages  6 × 4.942 = 29.652  6 × 5.026 = 30.156 
total riding time  83.845  80.643 
difference  3.202 hour  3.8% 
on balance, Chris Froome is an average of 3.8% faster on the recumbent high racer
during the whole modeltour
Actual tour and modeltour
In the actual tour of 3403 km (3313 km plus 90 km time trials), Froome’s final time on his regular racing bicycle was 83.944 hours (83h 56' 40"), his average speed being 40.54 km/hour (3403/83.944). For the 3 time trials (90 km combined), he needed a total of 1.693 hours. If we subtract that from his final time, then he took 82.251 hours to cover the remaining actual 3313 km, bringing his average speed to 40.28 km/hour (3313/82.251). With that, he was 1.9% faster during the 3313 km of the actual tour compared to the modeltour on the same bicycle (40.28/39.51). How can this be explained?
In the actual tour, Chris Froome covered 3313 km as part of the pack. That is a serious advantage over the modeltour where he rode all 3313 km solo. This exceeds all other differences between the actual tour and the modeltour.
How significant is a difference of 3.8% to the final result?
In the actual tour of 2013, Chris Froome’s winning time was 83.944 hours (83h, 56' 40"). Svein Tuft was the 169th and last with a final time of 88.409 hours. A difference of 4.465 hours (4h 27' 55") (3). If Tuft had been the only one to ride a recumbent high racer at that time and if he had been 3.8% faster, then he would have arrived in Paris 3.360 hours earlier (0.038 × 88.409) and would have come in 32nd place (3).
If, on the other hand, all of the tour participants, except for Chris Froome, had rode high racers in 2013, and if each of them had been 3.8% faster, then Froome, with his final time of 83.944 hours, would have finished as number 112 with 3.120 hours (3h 7' 12") behind Nairo Quintana (who finished in second place in the actual tour of 2013).
Conclusions
1. In level stages, a professional cyclist like Chris Froome is almost 9% faster on a 10kg recumbent high racer than on a 8kg regular racing bicycle.
2. When climbing 4% and 8% slopes, he is 9% and 19.5% slower, respectively, on the recumbent compared to the regular racing bicycle.
3. When descending 4% and 8% slopes (without pedaling or braking), he is 24% faster on the recumbent high racer.
4. Across the entire route of the Tour de France of 2013 (with the exception of the time trials), he could have been 3.8% faster on a recumbent high racer, despite 2 kg of additional bike weight and ± 20% less pedaling power when riding recumbent.
5. If all of the participants of the Tour de France in 2013 had rode a recumbent high racer, with the exception of Chris Froome, then his winning final time on the regular racing bicycle would
have ranked him in 112th place of 169 participants.
Sources
1. Wiel van den Broek (2017): Technische artikelen over de fiets: Vermogen en krachten
2. Harmen Lustig (2017): De bergen in de tour van 2013
3. Wikipedia.nl (2017): 2013 Tour de France
4. Wikipedia.nl (2017): Chris Froome
5. Wikipedia.nl (2017): Werelduurrecord (wielrennen)
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© Leo Rogier Verberne
ISBN/EAN:9789082549515
www.recumbentcycling.org
