Hill climbing

[hoppy]

Have just acquired an inclinometer to measure my local hills.There are four steep ones within four miles. Without pedalling my 17 month old Tonaro Compy will climb 1 in 7 in 2nd gear at 7mph,1 in 6 in bottom at 5mph,1 in 5 at 4 mph,but 1 in 4 needs light pedalling to maintain 4mph. The total weight is 115kg.Can anyome calculate the power output at the wheel?

 

[Orraman]

Perhaps?

4 mph = 4 * 5280 fpm /60 /60 = 5.8666 fps horizontal

1 in 5 = 5.8666 / 5 = 1.17333 fps vertical

115 kg = 253 lbs * 1.17333 = 296.85-ft.lbs/sec

conversion
foot-pound per second to watt (ft-lb/sec to w):

w = 1.35581794833 × 296.85-ft.lbs/sec ~ 403 W

Dave

foot-pound per second to watt - power conversion table (mobile)

 

[hoppy]

Many thanks,Orraman: an interesting and believable result that shows the value of variable gear ratios for efficiency.

 

[Woosh]

One of our engineers said that is more than 500W at the wheel (if sustained), probably drawing in excess of 17A from the battery to account for heat loss.

 

[flecc]

There is some inconsistency between the three figures given, which is normal since there are slight variations an any hill and parts of miles per hour involved between each division. Using the standard climb/power equation often employed in e-bike design circles, the respective outcomes for the three gradients you've supplied are, 504 watts, 419 watts and 403 watts. The latter two figures are the more believable for this type of system and what is known elsewhere about this system's performance.

P.S. Using some lesser gradients like 1 in 8 and 1 in 10 at higher road speeds will produce a more accurate calculated result.
.

 

[Deleted member 4366]

One of our engineers said that is more than 500W at the wheel (if sustained), probably drawing in excess of 17A from the battery to account for heat loss.

He's partially right, but it depends on which bike and motor you have. The 250w Bafang, like in your bikes would have a maximum efficiency of about 80%, so going up a slight hill at 15mph producing 400w of power, it would be drawing 400/40v *100/80 amps. (power/volts =amps), which would be 12.5 amps from the battery. When it goes up a steeper hill and slows down to 8 mph, the efficiency drops to about 60%, so the current from the battery would be 400/40 *100/60 = 17 amps (if the controller allows it). For 500w, it would be about 20 amps.

The OP has a Tonaro with crank drive so that the motor speed can be increased to a more efficient RPM at low speed, so current drawn might be back to 12.5 amps, but it depends on the exact speed that the motor is spinning. More torque is produced at lower RPM, which gives more climbing power, but is not so efficient in it's use of battery power.

These calculations don't take into consideration the controller efficiency, so actual currents from the battery would be a bit highr.