**Forces**

Any object which is free of external
forces, or on which the sum of external forces is zero, will either be at rest
or will be moving with a constant velocity.

A bicycle seems to disobey this principle because when we stop pushing the
pedals we will slow down and ultimately come to rest. This simply means that
there are a number of external forces that we need to overcome in order to
maintain a constant velocity. These forces are caused by the resistance of the
air, by the resistance to rolling, and to the change in gravitational energy on
an inclined road.

The force on the pedals is transmitted to
the contact between the tire and the ground by means of the chain ring, the
chain and the cog.

The reaction of the ground generates the driving power. To say it the way of
Newton, the rider pushes the ground backwards, the ground pushes the bike
forwards!

In normal conditions the length of the cranks is much smaller than the radius of
the wheel, and the chain ring is bigger than the cogs, thus the driving force is
much smaller than the force applied to the pedals.

In physics a force is expressed in units
Newton (N). Sometimes the kilogram-force ( kgf) is used as a practical
indication of force. This is the force that is caused by gravity on a mass of 1
kilogram. The kgf equates to 9.8 Newton.

The force of the foot on the pedal is decomposed into a
radial force which is parallel to the crank and is directed towards the
centre of the bottom bracket, and a tangential force
which is perpendicular to the crank. The radial force is completely
useless and a good rider will rotate the pedals elegantly which means that this
radial force is minimized. When the rider has a bad technique or when he is
tired he will have an ugly and less efficient pedalling cycle.

The relation between the useful tangential force
on the pedals **F _{t} **and the driving force

Here **R ** is the radius of the
wheel, L is the length of the crank,
**n _{v} **is the number of teeth on the chain wheel
and

When using the big gear e.g. 54 x 11 the driving force may be 10 times smaller than the pedalling force, yet we are riding at high speed!

However when climbing and using a mini gear of 30 x 25 the force ratio is only 2.43

Luckily we do not need a high driving force in order to go fast on a flat road. A standard person (not too fat nor too slender) may need only 17 N to be riding at 32 km/h. With a gear ratio 52 x 16 this corresponds to a mean pedal force of 107 N which is approximately only 16 % of the weight of an adult person..

**Work
and
Energ****y**

Work is done
only when the force causes a displacement i.e. **Work = Force x Displacement
**The displacement has to be measured in the direction of the force which
means that when a displacement is perpendicular to the force, no work is done!

Sometimes even a very strong force does not deliver any work. No matter how hard you push against a wall, as long as the wall does not move you are not "working". For this reason bicycles should be as stiff as possible, the forces applied to the pedals are to be used to move the bicycles forward, not to deform the frame.

Energy is simply another word for work, work is transformed into energy and energy is transformed into work. We can distinguish 3 main forms of energy, Kinetic energy, potential energy and radiative energy such as heat and light. Let us illustrate the work-energy duality with help of a cyclist riding at constant speed on a flat road.

The work he does is used to displace the air, so the air gains some kinetic energy. Also the tires are deformed through the contact with the road. This deformation causes internal and external friction that is transformed into heat and causes the rolling resistance.

The physical unit of work and energy is the
Joule (J) but for practical reasons we frequently
use the secondary unit calorie (cal)

One calorie equates the amount of energy needed to increase the temperature of 1
gram of water by one degree centigrade.

One calorie is equal to 4.182 Joule. One
kilocalorie (kcal or Cal)
is equal to 1000 calorie. Please not that in the U.S.A the kilo cal is noted Cal
with capital C

An adult person will need a food intake of approximately 1600 kilocalorie per
day in order to stay alive without any extra effort or activity.

**Power**

Power is the amount of work done during one
second.

**Power = Force x
displacement per second = Force x
velocity
**The unit of power is Watt (W)

Suppose a person of 70 kg walks up the stairs of
2.70 meter. In order to do this he produces an amount of work70
x 9.81 x 2.70 = **1854 Joule. ** In order to walk this
steps in 5 seconds he needed a power of 1854/5 = **370 Watts** during the 5
seconds.

Professional cyclists typically produce 200 to 300 Watts on easy endurance
training, and between 350 to 450 Watts in long time trials, depending mainly on
the weight and talent of the cyclist.

It is not my purpose to go
deep into the many physiological aspects of power generation such as the the
rate of intake of oxygen (VO2), the blood concentration of lactate, the hart
rate. These are used as indicators of the "how good" the human machine is
running. We are more interested in the amount of work the human body can produce
in a steady state i.e. for an almost indefinitely long time. We can qualify the
best possible performance with the aid of 2 measurable parameters, the **
Critical Power** and the total **anaerobic work capacity**..

Het kritisch vermogen (KV) is het vermogen dat de fietser theoretisch oneindig lang
kan volhouden. Dit is dus het maximaal aėroob vermogen, waarvoor de type 1
spieren verantwoordelijk zijn. Wij aanzien kritisch vermogen P_{KV} en
maximaal aėroob vermogen P_{ae} als synoniemen.

Het
specifiek vermogen is het maximaal aėroob vermogen
gedeeld door de lichaamsmassa. Dit specifiek vermogen is allesbepalend voor **
klimmers.**

Het oppervlak-specifiek vermogen is het maximaal aėroob vermogen gedeeld door het frontaal oppervlak.

De anaėrobe capaciteit (AEWC = AnaErobic Work Capacity) wordt uitgedrukt in kJ of kcal en is de totale hoeveelheid werk dat de renner op anaėrobe manier kan leveren. Wanneer deze capaciteit wordt overschreden verzuren de spieren, gaat de renner door de muur, en valt stil.

Het oppervlak-specifiek vermogen
en de juiste dosering van kritisch
vermogen en AEWC
is zeer belangrijk voor ** tijdrijders**

Sommigen durven wel eens de begrippen Kracht en Vermogen (Power) door elkaar halen. Zo kunnen we horen dat Vinokourov met groot verzet en veel "power" klimt, daar waar in werkelijkheid een renner met een "klein molentje" sneller gaat en dus meer vermogen met minder kracht ontwikkelt.

Het totale vermogen (P) dat een fietser levert wordt gebruikt om de 3 weerstanden te overwinnen, m.a.w. de rolweerstand, de luchtweerstand en de klim- of zwaartekrachtsweerstand.

**P = P _{rol} + P_{lucht}_{ }+
P_{klim}**