Inspired by earlier discussions here about air resistance and rolling resistance, I decided to do some tests and calculations. If you don't have access to a wind tunnel or a wheeltest laboratory machine, then you could instead do the following, as far as I have concluded:
1. Find two long slopes with the very same type of surface (same road perhaps). The angles need to be different  bigger difference is better. The angles must also be close to constant for such a long distance that you can find the equilibrium speed.
2. A day with no wind, find the equilibrium speed for rolling down each of the slopes. It will take some experimenting to find it, because you will need to enter the slope with a speed close to the equilibrium speed to get necessary time to make sure you are not accelerating or retarding any more. Take several readings and calculate the average value.
3. Measure the slope angles. I put one end of a 1 m steel rod to the road, held it horizontal with a waterlevel, and measured the distance from the other rod end to the road with a vernier caliper. Then I repeated at several places on the slope, and calculated the average. There may be easier ways for those with more appropriate tools.
4. Find the total mass for you, your gear, and your bike.
5. Put in all values in the formulas given in the Excel pic below.
Once you have calculated your air resistance coefficient CwA, then you "only" need to repeat the above procedure for one slope to find that terrain's rolling resistance coefficient. When you have both the air and rolling coefficients, you can calculate your power and where it goes at any given speed and slope for that terrain.
My tests were made with a hardtail with 29x2.1" IRC Mythos XC II  FK front and RK rear, a bit worn but not very much. Tire pressure was my normal  26 psi front and rear. I am 1.85 m (6'1) and have my handlebar 12 cm (4.7") under the saddle horizontal. My torso was at about 30 degrees angle from the horizontal.
The formulas were derived from the constant speed relationship Drive Power = Climb Power + Rolling power + Air Power: P = m*g*sin(x)*v + m*g*Cr*v + p*v^3*CwA/2.
Did I miss anything?
1. Find two long slopes with the very same type of surface (same road perhaps). The angles need to be different  bigger difference is better. The angles must also be close to constant for such a long distance that you can find the equilibrium speed.
2. A day with no wind, find the equilibrium speed for rolling down each of the slopes. It will take some experimenting to find it, because you will need to enter the slope with a speed close to the equilibrium speed to get necessary time to make sure you are not accelerating or retarding any more. Take several readings and calculate the average value.
3. Measure the slope angles. I put one end of a 1 m steel rod to the road, held it horizontal with a waterlevel, and measured the distance from the other rod end to the road with a vernier caliper. Then I repeated at several places on the slope, and calculated the average. There may be easier ways for those with more appropriate tools.
4. Find the total mass for you, your gear, and your bike.
5. Put in all values in the formulas given in the Excel pic below.
Once you have calculated your air resistance coefficient CwA, then you "only" need to repeat the above procedure for one slope to find that terrain's rolling resistance coefficient. When you have both the air and rolling coefficients, you can calculate your power and where it goes at any given speed and slope for that terrain.
My tests were made with a hardtail with 29x2.1" IRC Mythos XC II  FK front and RK rear, a bit worn but not very much. Tire pressure was my normal  26 psi front and rear. I am 1.85 m (6'1) and have my handlebar 12 cm (4.7") under the saddle horizontal. My torso was at about 30 degrees angle from the horizontal.
The formulas were derived from the constant speed relationship Drive Power = Climb Power + Rolling power + Air Power: P = m*g*sin(x)*v + m*g*Cr*v + p*v^3*CwA/2.
Did I miss anything?
Attachments

74.2 KB Views: 865