### C. Tour de France

The question whether or not a professional cyclist on a recumbent bicycle could win the Tour de France has never been answered. Because as early as 1934 the UCI banned recumbent cyclists from official competitions. And today, 86 years later, that ban is still in place (1). One can’t say in general that a regular racing bicycle is faster than a recumbent bicycle (or the other way round). The difference in speed between both bicycles varies with the circumstances: on a level road, during a climb or a descent. These varying differences are mainly based on:
- a greater pedaling power when cycling regular
- a smaller air resistance when cycling recumbent
That combination also explains the difference in speed under various circumstances. For example, headwind is relatively advantageous for the recumbent bicycle thanks to its smaller air resistance. But a rough road surface (greater rolling resistance) is relatively favorable for the regular racing bicycle because of the greater pedaling power of the same cyclist when riding regular. That’s why all of the circumstances are equal for both bicycles in the next chapters when calculating their speed in a Model Tour.

### C 1. Model Tour

We compare a professional racing bicycle with a recumbent high racer in a model Tour. The basis for that model is the 100th Tour de France in 2013. It consisted of 7 level stages (combined 1339 km), 2 individual time trials and 1 team time trial (combined 90 km), 5 hill stages (866 km) and 6 mountain stages (1108 km) (2). With that, the total route of the Tour de France in 2013 was 3,403 km long. But professional cyclists use a separate bicycle for time trials, which is outside the scope of our comparison. Therefore, we abstracted the 90 kilometers of the time trials from our model Tour and so its resulting total distance is 3313 km (3403-90). Each stage in the model Tour is considered a solo ride: so riding as a team is impossible. Spills don’t happen and flat tires are left out; all roads are smooth, dry and clean and the weather conditions are always calm.

Model stages
In this model Tour, all 7 flat stages are equal in length. The same goes for the 5 hill stages, in which all hills have the same 4% slopes of equal length to climb and to descend. The 6 mountain stages are also equal in length and the mountains have the same 8% slopes of equal length to climb and to descend. The sections between two hills or mountains are considered to be flat (table 1).

Tabel 1. Model Tour

 stages number length per stage flat km flat 7 1339 191.3 1339 hills 4% 5 866 173.2 475 mountains 8% 6 1108 184.7 744 total 18 3313 2558

Flat kilometers
The total length of the 7 level stages in the Tour de France 2013 was 1339 km (4). They have the same total length in the model Tour, so each flat stage is 191,3 km long (1339/7). The 5 hill stages have a total length of 866 km. So in the model Tour each hill stage is 173,2 km (866/5). The joint length of the 6 mountain stages is 1108 km and thus each stage is 184,7 km (1108/6). However, the sections in between the hills and the mountains are also considered as flat in this model Tour. So the number of flat kilometers is more than the level stages alone. This comes to about 5 x 95 = 475 km in the hill stages and about 6 x 124 = 744 km in the mountain stages (see below). Thus the model Tour has a total of 2558 flat kilometers (table 1).

Hill stages
The joint hill stages of the Tour de France 2013 had 15 ascents, representing a total of 195,5 km of climbing (4). So each hill stage in the model Tour becomes 39,1 km of 4% slopes (195,5/5) to be climbed, as well as 39,1 km to be descended; divided into 3 hills per stage. As a consequence, each hill stage has 95 km of flat sections between these hills (173,2-78,2) and the total number of flat kilometers in the hill stages is 5 x 95 = 475 km (table 1).

Mountain stages
The mountain stages in the Tour de France 2013 together comprised 15 mountains: 8 of 1st category and 7 ‘hors category’ with a total of 209,7 kilometers to be climbed (4). Therefore, each of 6 mountain stages in the model Tour has (rounded off) 35 km of 8% slopes (209,7/6) to be climbed, allocated to 2.5 mountains per stage. Thus, each separate slope is 14 km long (35/2.5). In the real Tour de France 2013, 4 stages finished on the top of a mountain. So, the total number of descents was only 11 (instead of 15). Therefore, in the joint mountain stages of the model Tour there is a total of 11 x 14 = 154 km of descending, meaning 25,7 km per stage (154/6). As a consequence, each mountain stage of the model Tour is 184,7 km long, consisting of 35 km of climbing and 25,7 km of descending, plus 124 km of flat sections in between the mountains (184,7-60,7). The resulting total number of flat kilometers in the mountain stages is 6 x 124 = 744 km (table 1).

Regular racing bicycle
Chris Froome’s racing bicycle (figure 1) has a bare weight of 6.8 kg. Equipped with a power and speed meter and a filled water bottle, its ready-to-ride weight in our calculations is assumed to be 8 kg. The bicycle has tubes instead of tires. That brings its rolling resistance coefficient (Cr) down from 0.006 (equipped with tires) to 0.005 (table 2). Froome’s cycling position (figure 3) has been optimized in a wind tunnel so that his front surface (hands in the drop handlebars) is reduced from 0.4 to ± 0.35 m². The air resistance coefficient (Cd) in his usual cycling clothing is approx. 0.9 (table 2).

Figure 1 The regular racing bicycle, ready-to-ride weight 8 kg
(photo Pinarello)

Figure 2 The recumbent racing bicycle, ready-to-ride weight 10 kg
(photo M5 Ligfietsen)

Recumbent racing bicycle
The recumbent high racer in the comparison (figure 2) is longer than the racing bicycle and has a bare weight of 9 kg. Including power and speed meter plus a full water bottle, its ready-to-ride weight is 10 kg (table 2). The extra 2 kg are a disadvantage for its speed because they increase the rolling resistance as well as the slope resistance. Moreover, its chain is three times longer and it must be guided in order to prevent swaying; which is why the intrinsic resistance is 7% for the recumbent high racer, compared to 5% for the regular racing bicycle. Wheels and tubes, accounting for the Cr-value, are the same for both bicycles. Froome’s front surface (A) on the recumbent bicycle is estimated as 0.2 m². The Cd-value (streamline) is 0.9 on both bicycles (table 2).

Table 2 Specifications of the regular and the recumbent racing bicycle

 racing bicycle wkg Pb% Cr Am² Cd regular 8 5 0.005 0.35 0.9 recumbent 10 7 0.005 0.2 0.9

Cyclist
In our model Tour Chris Froome is the rider of both bicycles. He has a length of 1.86 m and he weighs 67.5 kg (3). Equipped with cycling clothing, a helmet, glasses, gloves, heart rate monitor, earphone plus transmitter/receiver and following a hearty breakfast, we put his ready-to-ride weight at 70 kg. It is assumed here that his pedaling power during one hour on the regular racing bicycle is 450 watt. In speed calculations for the recumbent bicycle his 1-hour pedaling power is estimated 20% less, so 0,8 x 450 = 360 watt. These are the conditions for him to complete the model Tour on both bicycles.

Figure 3 Chris Froome, estimated front surface A = 0.35 m²
(photo The Telegraph)

Model Tour rider versus touring rider
The professional cyclist in the model Tour and his racing bicycle are significantly different from the touring cyclist and his bicycle in the foregoing chapters. The 1-hour pedaling power of Chris Froome (450 watt) is twice as high as the 1-hour performance of the touring cyclist (225 watt). And Froome’s front surface is smaller (0.35 m² versus 0.4 m²) thanks to a better cycling position. That reduces his air resistance. Moreover, Froome and his racing bicycle weigh respectively 5 and 2 kg less than the touring rider and his racing bike. Which reduces the rolling resistance and the slope resistance for the professional cyclist. All these things not only make the professional model Tour rider much faster than the touring rider, they also slightly change the speed differences between the racing bicycle and the recumbent high racer: with Froome as the rider of both bicycles these differences vary from the foregoing calculation results with the touring cyclist as the rider (chapters B2-7).

Conclusions
1. Because recumbent cyclists are banned from official cycling races, a direct confrontation between regular and recumbent racing bicycles in, for example, the Tour de France is impossible.
2. The varying differences in speed between both bicycles are mainly based on:
- a greater pedaling power when cycling regular
- a smaller air resistance when cycling recumbent
3. A comparative speed assessment of a regular and a recumbent bicycle needs the same competitive rider on both bikes, the same route and equal weather conditions: that’s to say a model Tour.
4. The 100th Tour de France of 2013 serves here as a model for the theoretical comparison of a regular and a recumbent racing bicycle with Chris Froome as the rider on both bikes.
5. The recumbent bicycle has 2 kg more weight and 2% more intrinsic resistance, both having an adverse effect on speed.

Sources
1. Wikipedia.nl (2017): Werelduurrecord (wielrennen)
2. Wikipedia.nl (2017): 2013 Tour de France
3. Wikipedia.nl (2017): Chris Froome
4. Harmen Lustig (2017): De bergen in de tour van 2013