0.29 * (climb_distance/time)^3 + 9.81*(time_rider_kg + time_bike_kg)*ascent/time
So basically it is potential energy plus a factor of speed due to wind resistance etc. The formula is very accurate on a steady climb with no flat spots on a wind free day, provided the ascent is known accurately.
For example a 70kg rider with a 10 kg bike riding at 20 km hour up a total ascent of 300m, distance is 5 km, in 15 minutes(15*60 sec) Power= 0.1315 * (5000/900)^3 + 9.81*(80)*300/900 Power= 22W from wind + 261 W from potential energy So as you can see, when climbing wind resistance doesn't count much, so if the ride has no flat sections (faster speed)and is a steady climb at 20km/hr or less the accuracy will be with in 5%, provided the ascent and weights are correct.
Previously the co-efficient we used was .1315 but we found this put Power on shallower climbs out.
We did extensive real life testing of the formula, using calibrated SRM cranks and several different climbs.