bike-nerd said:
I've observed that when pedaling a bicycle, if the rider moves from seated to standing position while maintaining the exact same cadence (pedal revolutions per minute) and resistance, power output (as measured on a power meter) often decreases.
Do you have a strain gauge power meter or one that estimates from speed (and thus gives you the wrong answer)? If one's power really is decreasing it's because of personal reasons rather than physics which I'll explain below. For others including myself, we stand to increase power. However, the dynamics of pedaling while standing is slightly different as one loses a contact/balance point (i.e., the saddle) and as A.T. mentioned, engages upper body muscles which fatigue sooner. But for short periods such as attacking a climb or starting a sprint, this is actually desired, as rcgldr mentioned. If you watch professional bike racing you'll often see people standing for more power. This is more common among lighter riders as they have less mass to accelerate up off their saddles. Unless the upper body is a huge drain, human power should always increase while standing because standing increases the blood flow to the legs (by un-pinching the femoral artery) so one can deliver more energy to the working muscles.
But there are trade-offs to standing: energy lost to accelerating off the saddle, holding up one's body weight (as the body does internal work when standing due to dynamic balancing), as A.T. mentioned, energy lost to upper body muscles (engaged for pulling and balance), and
most importantly, the energy lost to aerodynamic drag from increasing frontal area.
bike-nerd said:
My theory is that you add mass when you stand, and that alters the way power is produced - kind of like adding mass to one side of a fulcrum…
...I'm actually debating this issue with someone else (neither of us are physicists...) His argument is that there is a certain amount of power required to move pedals around the axis at given revolutions per minute, and that that power requirement does not change regardless of whether the rider is seated or standing. My argument is that when you add MASS to the pedals by standing, you change the power requirement.
Which of us is right?
Sorry, your theory is wrong. Your friend is correct. Adding mass would change moment of inertia, but it would have an minuscule effect on the power to move the bike. And you're not really adding mass you're just moving it around. What happens when you stand is you actually throw the bike slightly backwards then later pull it back forwards due to conservation of momentum. This is in fact a common cause of crashes when drafting as people throw their back wheel into the front wheel of the rider behind them. Also, if one increases torque by leveraging their weight differently it will only slow their cadence (in RPM or pedal velocity) as ##\tau=power/cadence##, and the power delivered to the cranks will remain the same as it's determined by physiology rather than mechanics. The linkage has a negligible effect on the amount of energy one can put into the pedals because there is barely any loss through the cranks.
You are correct that ##power=Fv##. The power ##P## to move a bike at a steady pace can be summed roughly as the power to overcome each of the three major forces as
$$P=K + \underbrace{c_r cos\theta \,v}_{friction} + \underbrace{mg sin\theta \,v}_{gravity} + \underbrace{\frac{1}2 \rho c_dA \,v^3}_{aero drag}$$ where ##K## subsumes power to overcome bearing drag, chain friction, acceleration and other small effects because they are so small compared to the three emphasized. ##\theta## is the arctan of the hill grade. ##\rho## is air density. ##A## is area orthogonal to wind which is frontal area in this case. The other constants are the coefficient of rolling resistance (due to internal friction of tire deformation) and the coefficient of aerodynamic drag (due to shape of body and bike that affects airflow). And ##v## is the speed.
You can see the biggest term is aerodynamic drag which is cubic with speed whereas the other terms are linear. So beware of standing or sitting up too much into the wind. For a more detailed and precise model see [1] and [2] below. For further reading, Fajans has looked at some interesting bike physics in [3].
Now the question really is why does
someone in particular produce less power standing on the pedals? The answer is one or more of the following factors: too much body weight, poor position/weight distribution/balance, poor handlebar setup, poor front geometry/mechanics of the bike itself, or simply not being used to it.
[1]
Martin et al., Journal of Applied Biomechanics 1998, 14, 276-291
[2]
http://www.analyticcycling.com
[3]
http://socrates.berkeley.edu/~fajans/Teaching/bicycles.html