Alfred Ryder said:"Joe Pro" wrote
Quoted message said:Sure, quite simple. Not a physics major here, althought a few might be
lurking. The momentum of the wheels alone spinning at 40 mph is not
nearly
Quoted message said:enough to move a 155 lb rider on a 20lb bike forward.
Quoted message said:Interesting problem. Here is what I came up with:
Quoted message said:1884g Shimano R500 wheels without cassette or skewer
440 two Michelin Pro2 Race tires 23mm
200 two Continental tubes
50 two Zefal rim tapes
2574 TOTAL weight
Quoted message said:453.6 grams is one pound.
Quoted message said:5.67 pounds is total weight of wheels.
Kinetic energy for linear motion is (mv^2)/2. For rotational energy, as
in the wheels spinning, the energy is (Iw^2)/2, where I is the
rotational inertia and w is the angular velocity.
First I'll assume that the spokes and hub don't contribute much to the
rotational inertia. Then I'll estimate the distance from axis of
rotation to the center of mass for the rim/tire/tube/tape combination to
be 622 mm. Finally, I'll use 500g as an estimate of the rim mass. Then
I = m r^2
= (500 + 220 + 100 + 25) g * (622 mm)^2
= 0.33 kg m^2
The rotational speed (w) is 2 pi * linear velocity / circumference, or
w = 2 * pi * 40 mph / (2 * pi * (622+46) mm)
= 27 rad/sec
(note the mixed units; conversion factors required!)
So the kinetic energy of one rolling wheel is
KE = (I w^2)/2
= 0.33 kg m^2 * (27 rad/sec)^2 / 2
= 117 J
Now translate that into forward velocity of the rider. Assuming the 175
lb total for bike and rider, and assuming that all of the KE of the
wheels is conserved (none lost to skid marks, brakes, etc)...
KE = (m v^2)/2
v = sqrt(2 * KE / m)
= sqrt(2 * (2*117J) / 175 lb)
= 2.4 m/s (5.4 mph)
(note the extra 2 in the equation for the KE of two wheels, and the
mixed units requiring conversion factors that I have left out)
Summary: I disagree with your physics, but my conclusion is the same.
The rotational inertia of the wheels *alone* won't propel the rider very
far or very fast. A little energy lost to skidding wheels, maybe a
slight touch of the brakes, and the rider might move a few feet before
stopping.
By the way, I have tested this experimentally, but at less than 40 mph.
The experiment was unintended 🙂.
--
Dave
dvt at psu dot edu