## Fanwheel Torque Drag Factor

In order accurately to model an ergometer the fanwheel torque drag factor asociated with each inlet damper setting should be known. The polar mass moment of inertia of the fanwheel, Io, must have been found by other means.

To find the drag factor, K, - for a given damper setting - the fanwheel must be free to spin in its housing. Determine its (small) constant bearing friction torque, Tf. Then, given an accurately measured initial angular velocity, w0 (rad/sec), note the time required, dT, for the wheel to come to a stop.

Then:
Dt *(K *Tf)0.5 /Io = tan-1[w0 *(K /Tf)0.5]

Where:
Dt = the elapsed time to stop; sec
Io = the polar mass moment of inertia of the wheel and its (small?) added mass; kg-m2
K = the torque drag factor; N-m-sec2
Tf = the bearing friction torque; N-m (may not be zero)
w0 = the initial wheel speed; rad/sec

Solving for K is then a trial and error process which converges rapidly. For the Concept-II Indoor Rower values of K are expected to fall somewhere in the range 0.001 - 0.0001. Concept-II publishes numbers in a range of about 90 to 220, presumably having applied a factor (1,000,000?) to put the figures into the more familiar range of the whole numbers.
The added mass (of air "laminated" to the wheel surfaces) increases the moment of inertia by some small and unknown amount and will introduce an error into the values determined for K.

If the bearing friction is too small, dT will be very large (theoretically infinite) and it would be better to take the time between an initial, w0, and a final, w1, wheel speed and use the more complicated relationship:

A = -Io /(K *Tf)0.5
B = (K /Tf)0.5
Dt = A *[tan-1 *w1 *B -tan-1 *w0 *B]

Where:
Dt = the elapsed time interval; sec
Io = the polar mass moment of inertia of the wheel and its (small?) added mass; kg-m2
K = the torque drag factor; N-m-sec2
Tf = the bearing friction torque; N-m (may not be zero)
w0 = the initial wheel speed; rad/sec
w1 = the final wheel speed; rad/sec