robocam said:
What do you mean by "using the RPMs?" Are you saying he should use a higher or lower overall gear ratio?
gman1971 said:
...In order to take advantage of the three speed/power modes you need a high revving driveline; again, I am topping out at 45 in 13T downhill (at 43.9 volts); and cruising in 6th gear at 30-32 mph with 44 volts on the tank... so in order to take advantage of the switches you need to use the RPMs this motor has to offer, and IMO a 13T-44T-44T-11T doesn't lend itself to that.
G.
The final result is exactly the same, but internally it makes a world of difference, and here is why:
Lets assume the motor puts out 1000 watts, (POWER = 1000W), very simple, any combination of RPM multiplied by a Torque that results in 1000 WATTS will be a valid number, so 100RPM and 10Torque would be a valid motor output. So lets assume our motor is spinning at 500 RPM, so b/c of that the motor has very little torque of just 2 TQ units. (whatever, NM, FtLbs... etc)
So, at the motor you have the freewheel sprocket that connects to the crank. This is (n my case) a 13T motor sprocket and a 44T chainring. B/c the smaller is driving the bigger we have torque multiplication, so our motor puts 2 TQ x ( 44T / 13T ) = ~6.76 TQ at the crank; but WAIT!! we can't just count torque alone, b/c the power would be ZERO, so in order for POWER to conserve throughout the entire drivetrain we also need to divide the RPM by the reduction ratio, which yields a total 147 RPM at the crank. Now at our crank we have a cadence of ~147 RPM and a torque of 6.76 TQ, which effectively yields 1000 Watts of power. So far so good; we haven't invented a perpetual motion machine... yet...
Anyhow... now we have the two chainrings exchange, and this is the real tricky part, b/c you can't solve this use RPM alone, you have to use another interpretation of POWER for solving this; so we know that Power = Torque x RPM, but Power is also Force x Linear Velocity (kph, mph etc) And the reason why we can't use POWER = RPM x TORQUE is because both chainrings are spinning around the same axis and torque is the "rotational force" which is independent of the diameter of the rotating disk, which will be identical for both chainrings but not the force at each point of contact with the chains. So we must convert our RPM into LINEAR VELOCITY and then use our power formula to determine the force because of power conservation.
So a 44T is ~182mm chainring and is spinning at 147 RPM which means the input drive chain is moving at of 2.8 meters/second. Now we plug 2.8 meters/second into the POWER equation and we get 1000W = 2.8 m/s x FORCE, and we solve for force and we get 357 UNITS OF FORCE.
So while 44T chainring is receiving 357 Force units at 2.8 m/s the 48T chainring with 199mm is also spinning at 147 RPM so that speeds the cassette chain up to 3.06 meters/second and now we plug the speed 3.06 into the POWER equation and we get 1000W = 3.06 m/s x FORCE, we solve for force and we get total 326 FORCE UNITS going through the chain. So we reduced the amount of force from 357 to 326, a 10% decrease in force means longer lasting drivetrain.
So now we have 1000 watts of power in the form of 326 Units of Force and 3.06 meters/second going through the chain down to the cassette... So now our input force is constant, and when we change the cassette sprocket we are changing the lever point, the further from the axle the more torque it has, but it also spins slower, all governed by the equation POWER = TORQUE x RPM.
But now, lets run the numbers with a 48T-44T chainring instead of a 44T-48T
We know our first reduction is 13T/48T, so we have 7.3 Torque, a 10% increase on the crank, and crank is now spinning slower at 135 RPM... so far so good. Power still 1000 watts.... But now the second chainring is smaller, 44T, so that is going to slow down the output chain speed compared to the input chain. So at 135 RPM the input drivechain is moving at 2.81 m/s, so therefore the 44T chainring is making the cassette chain move at 2.57 m/s, we plug this velocity figure into our power equation and we have 1000W = 2.57 m/s x FORCE, we solve for FORCE and we get 390 UNITS OF FORCE, vs the 326 UNITS OF FORCE on our previous example of 44-48T a whopping 20% increase in frame flexing, sprocket bending, chain stretching force. And 20% is not something to be taken lightly...
This is the secret to keeping your drivetrain alive when running several kW (this is how real high power bikes do it too, they have a huge rear sprocket so they can run a shitton of RPM through the chain and let the final sprocket do the lever (torque multiplication) using the wheel axle as fulcrum)
Hope this helps,
The moral of the story is if your motor has the RPM capabilities, then you should always aim for higher RPM and not for more torque (unless you like fixing bent stuff)
G.