We all know that riding a bicycle a certain distance is less tiring
and faster than running that same distance. One could conclude (and
through scientific method we know) that less calories are expended,
even though more mass is moved that same distance when cycling (human
+ bicycle) than when running (human only). So why is bicycling so much
more efficient than running?

im guessing wheels are a lot more efficient at carrying forward
momentum from previous pushes than our feet are. Especially downhill,
but htat is obvious. HEaring and actually clever person answer would
be cool.
Good question

It's all in bicycle aerodynamics energy and power use breakdown.

If I build a powerful, well-tuned engine that can run at redline RPMs
for hours, and then drop it into a big Ford monster truck chassis, the
truck might go 120 mph. But if I drop it into a thin fiberglass
Lambhorigini chassis, I might hit 200 mph.  That is a big difference. 
Engine performance didn't change, but performance velocity did. To
some extent, the same efficiency effect is observed in every endurance
sport. Efficiency is critical to maximizing performance velocity.  You
are maximizing physiological efficiency on a bike (well, I guess
"maximizing" it would be in cruising behind the wheel of a car and
using only your right foot for the gas and the brake.)

Physiological Efficiency Defined

In an exercise setting, efficiency is defined as the percentage of
energy expended by the body that is converted to mechnical work
(another form of energy).

Work Efficiency = Mechanical work  / Chemical energy expended.  The
sprocket wheels are set up so that you have to pump your legs and move
your body no more than at a light jog's pace to travel faster than a
sprinter.

Galactic Polyglot

A large portion of the energy expended when running goes to raising
and lowering the body rather than propelling it forward.

The first portion of Wikipedia's entry on "Wheel" gives you a good
idea of how efficient a wheel is in avoiding friction.  Though
Wikipedia's offline right now, you can find it's entry at this page:
http://www.answers.com/wheel

Simply the frictional comparisons between a runner and a bicycle make
large differences, given the Wikipedia data and large foot surface vs.
small bicycle surface.  In addition, as others have pointed out, the
human machine wastes lots of energy to accomplish its forward motion
(including the generation of excess body heat), energy that's
converted efficiently by a bicycle, with many estimates being that
bicycles convert greater than 95% of the human energy:
http://www.papimi.gr/zeromuscleefficiency1.htm

You may also find this page on bicycle power generation interesting:
http://users.frii.com/katana/biketext.html

Google search strategy:
"bicycle efficiency"

Best regards,

Omnivorous-GA

Inertia.

Newton's First Law of Motion states that "An object at rest tends to
stay at rest and an object in motion tends to stay in motion with the
same speed and in the same direction unless acted upon by an
unbalanced force."

The wheel recycles the energy your body exerts by using your momentum
to propell itself (and you) until all of the energy has been exhausted
by friction from the earth, bearings & wind. Without the wheel, your
body is forced to re-create nearly all of the energy that the bicycle
was recycling, with every step.

This is a classic college physics type question.


While the decrease in friction has been mentioned - this is not why
the wheel is more "efficient" - consider the fact that a wheel on
asphalt has more friction than one on ice - yet it's harder to bike on
ice than on asphalt becuase the wheel would begin to slip on ice - in
fact you need the road to wheel friction to convert the rotation of
the wheel into forward motion.

A bike is a simple machine that uses gears.

The primary reason that biking is more efficient than running has to
do with speed advantage.

Consider a bike with 'F' teeth on the front gear (the one you pedal)
and 'R' teeth on the rear gear (the one connected to the bike wheel)
the distance 'd' the bike travels per each rotation of the front gear is: 

d=(F/R)*C

where 'C' is the circumference of the rear wheel.

The ratio F/R is the speed advantage - incidentally, the inverse of
this ratio would be the mechanical advantage of the gear set.

Think of it this way - on a multi-speed bike the bigger rear cogs make
it easier to pedal (less force) but you go slower - the smaller cogs
make it harder to pedal but you go faster.

The human body has a narrow band of power output and bike gear ratios
are chosen to maximize performance within this band.

Suppose for argument's sake that you chose a gear ratio of 1:100 i.e.
R has 100 times as many teeth as F - then each rotation of the front
gear would only make the bike go 0.01C forward - in this case, the
runner would be faster than the biker and reach the finish line
expending less energy. The biker would have to pedal furiously to
maintain enough forward momentum to keep the bike balanced. - This
would never happen in real life because this gearing is not
appropriate for a human on a bike.

You can also make the following rough analogy - consider a human with
roller blades - although the leg motions in roller balding are a bit
different than in running - they are *almost* the same - so the speed
(or calorie consumption)difference between the blader and the runner
would be due to the efficeincy of the wheel versus the foot in
converting human power output into forward motion.

Clearly a biker can go faster than a roller balder (given a long
enough track that the biker can reach top speed etc.) - then the speed
difference (or calorie consumption difference) between the biker and
the roller blader would be due to the greater speed advantage of the
bike versus the roller blades. - clearly the speed advantage of the
bike is the major effect.