How many Nm with these variables?
- Thread starter pwbset
- Start date
mcstar
100 W
You still need to know wind resistance and rolling friction. These can be calculated by getting up to speed on the flats and then measuring how far you go before stopping with no further power applied.
Force_needed=(rho/2.0)*C_d*Area*(v_try+v_wind)^2+Math.sin((tan^-1)(grade/100.0))*m*g+C_r*m*g
Force_wheel = torque/radius; Since Force_needed=Force_wheel where v stabilizes, you'd solve for
torque = radius*[(rho/2.0)*C_d*Area*(v_try+v_wind)^2+Math.sin((tan^-1)(grade/100.0))*m*g+C_r*m*g]
Enjoy! Remember, all of these are in standard SI units(meters, NM, m/s, kg, m/s^2, etc.) EXCEPT for the grade. That's just a simple "tangent definition"(distance-forward divided by the distance going up) in percentage.
C_r is the coefficient of rolling friction(Since you're on gravel, it's going to be higher than .01 that's usually assumed for rubber on pavement) and C_d is the drag coefficient(usually around .9), and rho is the air density(assume around 1.2 for convenience). Also, this equation assumes that wind resistance is a headwind. If it were a tail wind, you'd have to calculate it differently where v_try<v_wind(stick a negative on the first additive term). Also, v_try is the velocity the bike is going. g is the gravitational constant(assume 9.8 m/s^2, and Area is the frontal area(assume around .6), and radius is the bicycle's wheel radius(1/2 the diameter).
Force_wheel = torque/radius; Since Force_needed=Force_wheel where v stabilizes, you'd solve for
torque = radius*[(rho/2.0)*C_d*Area*(v_try+v_wind)^2+Math.sin((tan^-1)(grade/100.0))*m*g+C_r*m*g]
Enjoy! Remember, all of these are in standard SI units(meters, NM, m/s, kg, m/s^2, etc.) EXCEPT for the grade. That's just a simple "tangent definition"(distance-forward divided by the distance going up) in percentage.
C_r is the coefficient of rolling friction(Since you're on gravel, it's going to be higher than .01 that's usually assumed for rubber on pavement) and C_d is the drag coefficient(usually around .9), and rho is the air density(assume around 1.2 for convenience). Also, this equation assumes that wind resistance is a headwind. If it were a tail wind, you'd have to calculate it differently where v_try<v_wind(stick a negative on the first additive term). Also, v_try is the velocity the bike is going. g is the gravitational constant(assume 9.8 m/s^2, and Area is the frontal area(assume around .6), and radius is the bicycle's wheel radius(1/2 the diameter).
pwbset said:
To get up that hill you need at least 122 * 15/100 kg of thrust ie 18.3 kg or 179 Newtons. In at 24" wheel, that equates to 55 N-m of torque ( that's at 0 kph :lol: )
With a little more torque you can overcome some rolling and air resistance and go up faster.
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