Mono Posted August 10, 2017 Share Posted August 10, 2017 EDIT: you may want to check out these links http://forum.electricunicycle.org/topic/7549-current-demand-versus-battery-voltage/?page=3#comment-106384http://forum.electricunicycle.org/topic/7855-anatomy-of-an-overlean/http://www.ebikes.ca/tools/simulator.html as they provide similar and IHMO even more informative graphs. I collected a few graphs based on a relatively simple common motor model and calculations of drag and rolling resistance from these sources: https://evmc2.wordpress.com/2014/07/21/electric-motor-power-really-simple-and-hp-ratings/http://lancet.mit.edu/motors/motors3.htmlhttp://www.me.mtu.edu/~wjendres/ProductRealization1Course/DC_Motor_Calculations.pdfhttps://www.gribble.org/cycling/power_v_speed.htmlhttp://www.engineeringtoolbox.com/drag-coefficient-d_627.htmlhttps://en.wikipedia.org/wiki/Body_surface_area All errors are mine and bound to be corrected after a good nights sleep. The parameters I have set are: overall weight: 100kg rolling coeffient: 0.01 drag coefficient: 1.0 frontal area: 0.8m^2 max motor speed: 50-60km/h motor power: 500-1200W For a basic orientation, these are power versus speed graphs for an 800W motor: According to the motor model, the maximally available torque decreases linearly with increasing speed and becomes zero at max speed (as shown in the below figure, and like the shown estimated input power graph). Max speed is 60km/h here. From this, the shown mechanical power computes straight forward to be proportional to speed times torque. The mechanical power graph (orange line) has therefore a parabolic shape, where the maximal power output of the motor occurs at 1/2 of its limit speed, here at 30km/h. At 1/2 of the max speed, the electric input power is 1600W, the output power is 800W, the efficiency is 50%. The necessary electric input power to produce maximal torque grows to 4 times the nominal motor power at zero speed, here 3200W. The motor efficiency (all at max load) becomes the smaller the smaller the speed. Therefore, battery limitation may limit the shown electrical input and the mechanical output power to smaller values than displayed. (Not easily applicable to BLCD motors). The practical (very unsafe) limit speed is around 39km/h, where the power needed to keep up the speed (red line) crosses the motor power. Above 20km/h, the power needed to keep up speed is dominated by drag. More interesting is the forward thrust (force) of the same 800W motor due to its torque. (The torque is determined by its max speed and power specs): The nominal torque/forward thrust is just a straight line from its maximal value down to zero at max speed. The used unit for the y-axis is the downward force of one kg (i.e. 9.81 N). This is a rather tangible unit, as we have a feeling for the downforce, that is the weight, of a kg. At 30km/h, almost half of the torque is needed to keep up the speed. An equivalent of 5kg additional "freely available" surplus thrust remains to accelerate or balance the wheel, to get over bumps or out of potholes etc. A little scary, but OK-ish. Even more interesting (in light of http://forum.electricunicycle.org/topic/7654-story-of-me-learning-riding-and-falling-off-an-inmotion-v8) is investigating the "free" remaining surplus forward thrust (force) to accelerate and balance the wheel as a function of speed for different slopes. The surplus thrust is shown for three different motor specs and three different slopes. The vertical distance between the graphs of the same color is pretty much proportional to overall weight (here 100kg). This shows that riding into a slope with high speed is crazy dangerous. Driving at 20km/h into a 10% = 5.7º incline, an 800W 55km/h motor drops from 11kg to 1.1kg surplus-thrust to just about still balance the rider. (A 800W 40km/h motor has 2.2kg left, which is only little better). For a slope of 0% the graphs are almost independent of weight (only rolling resistance depends on weight). At 30km/h, any rider of a 500/800/1200W wheel has <2/5/10kg to play with, whether they weigh 60kg or 120kg. The only difference is that 2/5/10kg feels less to play with for a 120kg rider. The critical lean angle depends of course on the weight, as much at 30km/h as it does at 0km/h. Finally the same graphs assuming a limiter restricts the current to three times the nominal motor power, e.g. to 30A = 3 * 800W / 80V. (Limiting to four times the nominal motor power doesn't change the above graphs.) I can do these graphs easily for any parameter configuration, if you ask I may give it a shot... Link to comment Share on other sites More sharing options...
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