Hello. Using the helpful information at http://www.crystalyte.com/->"motor specs->"Hub motor simulator", I finally pulled up the data for a Golden Motor engine, 36 v, 35 amp controller for a 26 inch wheel and 115 kg(253 pounds) and did some fancy schmancy physics to set up a differential equation to describe the velocity of this bike over time, assuming it starts from a dead stop on entirely flat ground(I basically accounted for the air-drag and the torque curve over the velocity range). The acceleration seemed slow(7 mph at 5 seconds and 11 mph at 10 seconds) but the top speed seemed to be reasonable(23 mph) so I assumed my mathematics weren't off. Are these reasonable values?
After this, I started doing the calculations for going up a 10 degree hill(It seems to be the usual "near-maximum" steepness of hills around my neighborhood) and found that at no point would the bicycle accelerate! It'd basically just start rolling backwards at a dead stop and, if you were initially approaching the hill at some speed, you'd quickly decelerate and then start rolling backwards! Is this usual behavior for a 500 watt engine for a torque between 40-50 NM at a stop? Being able to climb hills is a pretty important factor for my decision to acquire an electric bicycle, and the hub motors seem more elegant than exterior motors, so any experiences countering my calculations would be nice. Thanks! Perhaps I'm not considering something.
I'll post the math/physics if anyone's interested.
Post the physics. That seems a little off. It should be able to climb that hill, albeit kinda slowly. Taking 5 seconds to get to 7mph also seems off. Even my BD36 in a 26" 36V 30A with really saggy batteries were able to do better than that.
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Also, how do you edit a comment?
Edited:
Or, erm, I mean the original post?
http://www.ebikes.ca/simulator/
That's the actual address of the Hub Motor Simulator. Plugging in the appropriate values for the simulator(26 in, 35 amp controller, Golden Motor motor, etc.), you see a near linear curve that seems like it could be approximated with a line(Basically a line connecting the intercepts for the torque on the vertical and horizontal axes.). Converting the NM into force using N(newtons) by plugging in the 26 inch value(I got 74.1 Newtons), I seem to come up with the force equation
F_motor = 74.1 - 5.928*v where v is velocity(in meters/second).
Using the air friction equation from http://hyperphysics.phy-astr.gsu.edu/Hbase/airfri.html and a reasonable value of .6 m^2 for the frontal surface area, an air density of about 1.1 kg/m^3 and a coefficient of drag of .5(I actually borrowed these values from http://www.analyticcycling.com/ForcesPower_Page.html ), I found the air drag to be .17*v^2. So the net force equation is
F_net = F_motor-Drag = 74.1 - 5.928*v - .17*v^2
Since F = ma, where m is mass and a is acceleration, and a = dv/dt, where v and t is velocity and time respectively(in seconds),
you'd get
m*dv/dt = 74.1 - 5.928*v - .17*v^2
or using the 115 kg value for the m,
dv/dt = (74.1 - 5.928*v - .17*v^2)/115.
Using maple and Dfield 6, I was able to construct the differential equation and initial condition of not moving at time=0 and the resulting velocity curve showed up.
Modifying the above equation to account for being on a hill, I basically found that
F_net = F_motor-Drag-m*g*sin(angle) where g is the gravitational acceleration(9.8 m/s^2), m the mass and the angle being the angle the hill makes to a flat piece of land, in degrees. Plugging in the numbers, I found that
dv/dt = [(74.1 - 5.928*v - .17*v^2)/115] - g*sin(angle). You'll notice that if g*sin(angle)>74.1/115, then the acceleration is negative, and you start accelerating backwards. For you to actually be able to accelerate up the hill, these calculations show about a 3.7 degree angle and less being necessary. Maybe there's something I'm missing: I've read that the motor might use "Pulse width modulation" which just sounds like short intermittent bursts of high current that make the "motor current" 'higher' than the battery's current and this might be activated under a high load but I don't know if this would be particularly advantageous for climbing hills. There's like nobody offering electric bicycles in my area(Besides Walmart) and practically no one owns one in my area, so I really have to ask here.
Once someone has posted a follow-up you can't. Threads get too confusing if people can rewrite history at any time. You can ask a friendly and helpful moderator (like me) to do it for you. What do you want to do?
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Your calculation is fine, but you may be overestimating the steepness of the slopes you need to climb.
A 10 degree sloping street (18 percent) is a San-Francisco-style steep street. Only a few of the hillier cities in the US/Canada have more than a few streets that steep or steeper.
And 74 n-M turning a 26-inch (incl tire?) wheel isn't very much hill climbing force - that's why e-bikes have pedals!
I climb a really steep hill on my daily commute, and while I do not have to peadle to help, it will be very slow and hard on the battery and motor if I don't peadle a lot. I run a wilderness brushed motor at 36 volts. If you have a really hilly area, you should get up your hills fine at 48 volts, or more if its really steep. A brushed hub at 48 volts will get you up hills in most cities.
Be the pack leader.
36 volt sla schwinn beach cruiser
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I just inquired the local city for the grade data and it appears the really steep hill is about 10 degrees, but the lanes on that road are too thin to safely accommodate a bicycle(and it doesn't have any sidewalks) so the other "serious" hilly-road is about 5 degrees. If only I weighed 50 pounds lighter, I wouldn't have to pedal! XD Oh, perhaps that's just the incentive.
I'm thinking about a 48v motor which should increase the torque by 4/3 so hills shouldn't be an issue. Possibly a smaller bike wheel would help, but that'd also decrease the top speed but I'm really looking for a bicycle with near-optimum electrical efficiency around 20mph and a possible speed of 30 mph with reasonable electrical efficiency so I guess that won't be an issue at 48V.
Oh, no, it's really nothing. There are just things I say sometimes that I almost feel compelled to word more carefully, but it's really trivial for practical purposes.