Watt-hours per mile needed to maintain various speeds

[xyster]

A major consideration has been overlooked in the many discussions concerning motor efficiency: wind resistance. The graph below is based on the efficiency of my hubmotor as calculated by ebikes.ca's hubmotor simulator:
http://endless-sphere.com/forums/files/hubmotor_sim_120.jpg
and the real-world power going certain speeds requires as calculated by the bicycle speed and power calculator:
http://www.kreuzotter.de/english/espeed.htm

As the graph shows, even though a motor "geared" for a top speed of over 40mph may have less than 50% efficiency when cruising at 10mph, the geometric progression of wind resistance at higher speeds easily trumps even a very significant, 48% --> 88% improvement in motor efficiency.

The break-even point where maximal total efficiently lies is around 10 mph. 5mph is about as efficient as 20mph. In other words, with this bike and motor as well as probably with most others, it is more efficient, and you can go farther, by riding at 10 mph rather than 5 mph. But anything above 10 mph is less efficient, and so you won't go as far on a charge.

Though the use of gears, as some nameless individuals here obsess endlessly on, can improve the situation somewhat, by far the most effective means of improving real-world range, efficiency, acceleration and top speed are to be found by focusing on aerodynamics, rather than comparatively miniscule motor, electrical, or drivetrain improvements.

The numbers used to construct the chart, and calculate Watt-Hours per mile, are included just above it.

 

[Matt Gruber]

moving to the MOON?
no atmosphere!
1/6 the weight!

 

[xyster]

moving to the MOON?

There are days I'd love to

Look Ma, no fairing!

 

[safe]

Acceleration and Hill Climbing are best dealt with by having a lower gear. Top speed demands a high gear, but without aerodynamic improvements most of the power you push into it gets wasted. All this "encourages" a riding style on a hub motor bike which maintains a fairly constant midrange speed... a sort of "cruise mode" type of riding experience. Any time you either go above or below the motors "sweet spot" you do what you can to get it back to where "it should be".

To "break free" of the "cruise mode" you need to solve the low end problem and the high end problem at the same time. Once you become tempted to go at higher speed you need to gear up for that and that weakens your low end performance. Go back down again and you can't hit the top speed. The "range" of top to bottom becomes too wide UNLESS... you go with more overall power and voltage. With more power you can still "cover" those low rpms and be able to reach the top rpms, but now you have a larger current drain problem and so you need to upgrade the battery supply. (however a low current limit with high voltage is very good,, the "ideal" motor has "peak power" and "peak efficiency" in alignment... which most people don't have) With Lithium being so light weight this is not a problem as far as weight, but it's not cheap to do.

Now let's say you do increase your raw power, unless you attack the aerodynamics problem your top speed will produce so much wasted energy that your budget will limit how fast you can go. My guess is that if you had an enormous battery... like 2000+ Watt Hours worth that you could get a decent ride and be able to pull high speeds too.

My feeling is that the ENTIRE bike needs to be looked at from all angles and really think hard about ways to solve these problems.

Raw power gets you very far... but at some point you have to think of creating more with a finite resource rather than just adding to the resource.

I'm the LAST guy who would say that aerodynamics are unimportant... my whole bike is DESIGNED around aerodynamics as its central focus. (the frontal area is almost half of a regular bike)

More speed always "costs" more than slow speed... the 10 mph is an artifact of a specific motor configuration. Aerodynamics start working against you from the start and never stops being a problem... it only gets worse at higher speeds... it's XXX rated... (the cube of speed)

 

[xyster]

All this "encourages" a riding style on a hub motor bike which maintains a fairly constant midrange speed... a sort of "cruise mode" type of riding experience. Any time you either go above or below the motors "sweet spot" you do what you can to get it back to where "it should be".

No different than any other motor as this statement from the initial post, predicated on the graph results, explains:

the geometric progression of wind resistance at higher speeds easily trumps even a very significant, 48% --> 88% improvement in motor efficiency.

Gears would have to improve motor/drivetrain efficiency by a lot more than 50% to outstrip the drag of the wind and remove that "sweet spot" you correctly note, but misattribute as a property of hubmotor-driven vehicles only. Charts you recently posted showed an efficiency improvement of far less than 50%. Hence, your geared homebrew bike has a sweet spot too, and I'd bet no matter what gear it is in, that sweet spot will be between 10 and 20 mph. We could know for sure if you had access to a dynometer.

 

[safe]

I'd bet no matter what gear it is in, that sweet spot will be between 10 and 20 mph. We could know for sure if you had access to a dynometer.

Actually it would be in first gear... probably near the efficiency peak since with that gearing the thing hits max rpms (no load) at around 32 mph. So the "sweet spot" for maximum mileage would probably be closer to 10 mph... very low that's for sure... booooring!

But the goal shouldn't be efficiency alone... the idea is to figure out how to get as much "bang for the buck" as you can. If with "less" you can do "more" then that's always better.

"Sport Riding" means wanting to get the most out of the bike in every way. Gearing helps. Aerodynamics helps. Weight distribution that is correct helps. Frame geometry and rigidity helps. Motors that approach the "ideal" for efficiency help. There's probably more, but you get the idea... every little bit adds up to be included in the "whole". Being able to "choose" to ride slow and boring and with long range or fast and exciting with as little losses as possible is also nice. 8)

I'll be looking forward to the fiberglass fairings I make this summer to see the improvements in top speed. It should add a few mph to the top end... maybe as much as 5 mph...

 

[jondoh]

I'm doing the math and I think your table (while nice) is a little optimistic.

For example, 20 mph and 21 watt hrs/mile.

From my experience on my last range test:

21 * 13.5 miles = 283.5 watt hrs
283.5 / 56 = 5.06 amp hours

I had 6 amp hours before pooping out. Maybe you should add a correction factor of 1.2 for real world conditions.

 

[xyster]

From my experience on my last range test:

21 * 13.5 miles = 283.5 watt hrs
283.5 / 56 = 5.06 amp hours

I had 6 amp hours before pooping out. Maybe you should add a correction factor of 1.2 for real world conditions.

The chart assumes no extra wind (completely calm day), and a completely level ride. It's also for the 5304 hubmotor running at 84 volts with .25 ohms of electrical resistance. Higher voltage of course means improved electrical/motor efficiency.

That your real-real-world results at 67% voltage were within 17% of predicted, I think speaks well of the chart's accuracy.