Motor Output Watts For MPH

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Motor Output Watts For MPH

Post by DrkAngel » Oct 21, 2013 10:15 pm

Some of my earlier graphs hinted at the watts-HP required to attain specific speeds.
I thought it might be handy to build a chart with specific watt requirements for various bike types to attain various speeds.

First graph limited in range to allow better visibility.
Watts = Speed.jpg
Watts = Speed.jpg (95.91 KiB) Viewed 3325 times
2nd charted to 50mph.
Watts = Speed 50mph.jpg
Watts = Speed 50mph.jpg (90.16 KiB) Viewed 3325 times
Mountain Bike 50MPH = 4280w
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Re: Motor Output Watts For MPH

Post by iovaykind » Oct 21, 2013 10:19 pm

Pretty accurate, I remember running 2.4kw to get about 42mph on my full suspension mountain bike. That's pretty much on the dot according to your graph.

It would be interesting to see where recumbent trikes would fall on that graph as well.

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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 21, 2013 10:54 pm

Recumbent trikes should fall somewhere between Race Bike and near to full recumbent.

Added HP labels for ease of identification.
Watts = Speed HP.jpg
Watts = Speed HP.jpg (92.95 KiB) Viewed 3325 times
Important to remember!
Watts are motor output watts ... not input watts!
Peak HP-output watts can require 200% the input watts.
Last edited by DrkAngel on Oct 22, 2013 9:33 am, edited 1 time in total.
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Re: Motor Output Watts For MPH

Post by Sunder » Oct 22, 2013 12:44 am

Interesting. I think this is fair proof that a very substantial amount of my energy is being wasted as heat. I'm pumping in over 1kw into a Q100 hybrid bike, but can only get it to low 40s (km/h), or about 26-27mph. I'm obviously running the motor well beyond design spec and so expect high losses. This is fairly good confirmation.

I did some research earlier, which compared 20 "road slicks" at 30km/h. The worst wasted 45W while the best wasted only 20W. I imagine that these numbers would scale exponentially, not linearly. I would be very keen to see a similar comparison for mountain bike tyres and commuter tyres.

In addition, there was an article that showed the difference between 30km/h with 10mm profile ultra light weight wheels, and 45mm aerodynamic wheels, and the difference was 11W. I imagine again that it would scale exponentially - probably cubicly as speed goes up.

Would also be interesting to see how different grades impact speed at fixed power. I guess that one is impossible without motor performance details.
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Re: Motor Output Watts For MPH

Post by heavymetalthunder » Oct 22, 2013 1:22 am

Thanks for the info. My test results are very similar to yours, but because my mountain bike have cargo racks and I tend to carry a bit more weight my power usage is a bit higher. Most riders don't realize how much more power they use once they pass the 20 MPH mark. That is why most ready to ride bikes with 20 MPH limit can go 15 miles or more using so little power.

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Re: Motor Output Watts For MPH

Post by dogman dan » Oct 22, 2013 7:18 am

Definitely panniers or a flapping coat can add 100w to what it takes to do 20 mph. I tend to use the 400w is 20 mph rule of thumb. I have done 20 mph on 300w at times, but generally there is a wind, or a slight incline that tweaks the real world number up and down 200w or so.

But overall, that's a great chart that is dead on for the mtb curve I have experience with.

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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 22, 2013 8:18 am

Noteworthy is that 20mph requires almost precisely 200% the watt output as 15mph.
1 hour at 20mph = 20 miles vs 2 hours at 15 mph = 30 miles, range ... from the same battery energy.
And the 15 mph speed "stresses" the battery less.
This does translate to double the cruising time, so limiting meandering speed, prolongs enjoyment while saving energy!

Of course, for commuting, time-speed considerations takes priority.

Pedal assist?
At lower speeds, pedal assist is a major factor.
For example cruising at 10mph requires 68w, adding 265w of pedal power will increase speed to 20mph.
Compare this to 30mph requiring 993w, adding the same 265w of pedal power will increase speed to only 32.6mph.
Lowering to a more aerodynamic position might add more speed than pedaling?
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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 22, 2013 8:52 am

DrkAngel wrote: Pedal assist?
At lower speeds, pedal assist is a major factor.
For example cruising at 10mph requires 68w, adding 265w of pedal power will increase speed to 20mph.
Compare this to 30mph requiring 993w, adding the same 265w of pedal power will increase speed to only 32.6mph.
Lowering to a more aerodynamic position might add more speed than pedaling?
A Mountain bike requires 255w of pedal effort to maintain 18mph.
I chose 18mph because most cyclists are familiar with the effort required to maintain this speed.

This graph demonstrates the additional speed available from adding the effort required to power a bicycle at 18mph.
Pedal assist.jpg
Pedal assist.jpg (91.83 KiB) Viewed 3272 times
From 10mph, assist will double speed to 20mph (10mph).
From 20mph, the same amount of pedal assist will increase speed 5mph.
From 30mph, the same amount of pedal assist will increase speed 2.5mph.
From 40mph, the same amount of pedal assist will increase speed <2mph.
However at 50mph, the same amount of pedal assist will increase speed ... barely ... 1mph!

On the other hand ...
This degree of pedal assist will more than triple range (300%) at 20mph and almost double range (200%), cruising at 25mph.
At 30mph assist increases range, possibly 33% (133% total).
Pedal assist contribution percentage declines quickly with speed.
Near 30mph, a more aerodynamic position outperforms even substantial pedal assist from a "proper" pedal seating position.

Even a race bike with cyclist in tuck position demonstrates the aerodynamic advantage clearly.
Aerodynamic.jpg
Aerodynamic.jpg (97.89 KiB) Viewed 3266 times
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Re: Motor Output Watts For MPH

Post by gogo » Oct 22, 2013 11:53 am

Subject: Does speed effect range?
Image
Image
DrkAngel wrote:Lowering to a more aerodynamic position might add more speed than pedaling?
This is the part of the equation that people have trouble grasping. Bicycles used to be pedal only. Now you are allowed 500% to 1000% of that pedal power. Power from pedaling is very optional now, and if aerodynamics are taken into consideration can even be a hinderance.

Headwinds can impose an exceptional load on the typical ebike. The starting power into a 30MPH headwind would be 500W and just 10MPH ground speed will take more than double that. It takes a special design to make >1000W at 10MPH (that's 100+ Wh per mile).
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Re: Motor Output Watts For MPH

Post by Samd » Oct 22, 2013 6:16 pm

I'm assuming the main difference between a road bike and mountain bike is tyres and seating profile against the oncoming wind/frontal drag?
http://ballaratebikes.com/

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Re: Motor Output Watts For MPH

Post by Sunder » Oct 23, 2013 1:57 am

That's awesome. You've just told me that the bike I was planning is still about 400w shy of what I need to keep 30mph up a 7% grade. I think you just saved me a lot of time and effort and future disappointment. I might regain some of that through lighter than cited weight and willingess to pedal, but also might lose some to the commuter hybrid upright seating position.

I think I will aim for 2kw instead of 1500w.
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Re: Motor Output Watts For MPH

Post by dogman dan » Oct 23, 2013 6:14 am

Depending on how poor your motor selection is, it might take even more due to wasted heat. To do 30 mph up 7%, you need more than a nine continent I think.


Good point earlier about 15 mph taking 200% less than 20 mph. I have often been amazed at how much further you can ride by slowing to just 18 mph vs 20 mph. At 15 mph, you can take a typical 700wh ebike battery a very long ways. If the route is hilly, as long as you get to ride back down the hills you can still get really good distance at 15 mph.

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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 23, 2013 7:18 am

Samd wrote:I'm assuming the main difference between a road bike and mountain bike is tyres and seating profile against the oncoming wind/frontal drag?
Tires-tyres is "a factor" while wind resistance is "the factor".
Tires effect road load which is a, relatively minor, linear factor while wind resistance is a geometrically progressive factor.

Frontal area is not as much a factor as the shape of the frontal area!
Image
See - Aerodynamic Factors


Sorry, had to "fix" this graph.
WeightvGrade1.jpg
WeightvGrade1.jpg (51.61 KiB) Viewed 3079 times
Last edited by DrkAngel on Oct 25, 2013 8:24 am, edited 3 times in total.
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Re: Motor Output Watts For MPH

Post by Sunder » Oct 23, 2013 4:20 pm

dogman wrote:Depending on how poor your motor selection is, it might take even more due to wasted heat. To do 30 mph up 7%, you need more than a nine continent I think.
This probably is a bit of a thread hijack, but I don't think it deserves its own thread... If I were to rewind a motor to my exact spec, should I be finding the maximum number of turns that can sustain 30mph no load speed at my LVC, then finding the thickest winding wire that will allow that many turns on the stator?

Is that the way to minimise heat inefficiency?
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Re: Motor Output Watts For MPH

Post by dogman dan » Oct 24, 2013 8:53 am

I just don't recall going that fast up 7% on less than 1500w. And for punishing use like going fast up hills, more than 1500w in a 9c or similar 28mm rotor motor can melt them fairly quick.

I don't know from experience what it takes to go that fast up 7%, I don't recall taking my race track bike to the hills ever. All my (9c) hill bikes max out at 30 on the flat, and go up the hills slower.

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Re: Motor Output Watts For MPH

Post by teklektik » Oct 24, 2013 12:04 pm

Ebikes.ca Simulator vs 'Motor Output Watts For MPH' Plots

The graphs above are essentially the familiar 'Load Line' curves drawn in Justin's Simulator which are independent of the motor/controller/battery configuration. By unselecting all but the black 'Load' radio button at the top of the simulator you can generate load lines two at a time for 'System A' and 'System B'. Using the two Custom Frame and Weight settings for each system, the load lines can be adjusted to match particular frame/weight configurations.
justinsimulator-2loadlines2.png
justinsimulator-2loadlines2.png (94.28 KiB) Viewed 2893 times
As mentioned on the simulator page, the load line represents the amount of power needed to propel the bike at a given speed. As shown in the image below, the intersection of the motor power curve with the load line shows the expected speed of the bike at the specified grade and throttle setting.
JustinSimulator-LoadLine+MotorPower.png
JustinSimulator-LoadLine+MotorPower.png (123.03 KiB) Viewed 2898 times
You can reverse engineer your proper CdA and Cr settings (Coefficient of drag x frontal Area, Coefficient of rolling resistance) by jiggling the custom Frame and Weight parameters with your particular build parameters to get a fair match with observed performance - this will make new 'What If' projections a bit more accurate. To guide your initial guesstimates, this table shows values that will yield the same results as the ebikes.ca Simulator built-in frame coefficients:
ebikes-ca_stdFrameCoefficients.png
(values determined empirically to match effects of built-in settings)
ebikes-ca_stdFrameCoefficients.png (5.21 KiB) Viewed 2883 times
Here are some typical bicycle Cr values for various surfaces from The Engineering Toolbox.
BicycleRollingResistanceValues.png
BicycleRollingResistanceValues.png (2.7 KiB) Viewed 2882 times
As a simple experiment, it's interesting to change the frame parameters to see the differences in expected speed between upright and tuck positions for a given power configuration.

Grade and Pedaling Effects
  • Increasing the Grade reshapes the Load Line causing it to rise more steeply.
    - This moves the intersection with the Motor Power curve to the left = lower expected speed
  • Decreasing the Grade reshapes the Load Line causing it to rise more slowly.
    - This moves the intersection with the Motor Power curve to the right = higher expected speed
  • Pedaling can be viewed as either affecting the Load Line or the Motor Power curve - viewing it as 'added motor power' may be more intuitive. This uniformly raises the entire Motor Power curve by the number of added Watts without changing the shape of the curve.
    - This moves the intersection with the Load Line to the right = higher expected speed
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Re: Motor Output Watts For MPH

Post by Sunder » Oct 24, 2013 5:26 pm

dogman wrote:I just don't recall going that fast up 7% on less than 1500w. And for punishing use like going fast up hills, more than 1500w in a 9c or similar 28mm rotor motor can melt them fairly quick.

I don't know from experience what it takes to go that fast up 7%, I don't recall taking my race track bike to the hills ever. All my (9c) hill bikes max out at 30 on the flat, and go up the hills slower.
Fair enough - but as I said, I'm now thinking closer to 2kw is more like what I need. That said, the 7% grade is only one hill for a short distance, so I guess if I lose speed there, I'm not going to be devastated. If I can't keep 30mph on the slight grades though - the places where I currently drop from low 40s (km/h) to high 30s on my 1kw bike, I would be pretty disappointed. (Sorry for the shift in measuring units - On my tablet and it's a hassle to convert).

The question though was less about what I needed to get there, but more about efficiency curves, and how to select number of turns and wire gauge. I think I've hijacked this thread enough. I think I should start my own one. Thanks though.
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Re: Motor Output Watts For MPH

Post by Samd » Oct 24, 2013 5:56 pm

DrkAngel wrote: Tires-tyres is "a factor" while wind resistance is "the factor".
Tires effect road load which is a reasonably constant factor while wind resistance is an algebraically progressive factor.
As a Degree Qualified Mech Eng I can see you're lumping Frontal Drag and Skin drag together into a lesson I really didn't need.

I was asking about rolling friction assumptions. I was trying to understand what your distinction was between each of the curves.
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Re: Motor Output Watts For MPH

Post by teklektik » Oct 24, 2013 6:58 pm

Samd wrote:
DrkAngel wrote: Tires-tyres is "a factor" while wind resistance is "the factor".
Tires effect road load which is a reasonably constant factor while wind resistance is an algebraically progressive factor.
I was asking about rolling friction assumptions. I was trying to understand what your distinction was between each of the curves.
The effect of rolling resistance is not constant but varies with velocity. Although the effect is small in comparison to the aero resistance, it plays a measurable role. This term is present in Justin's simulator and the effect can be seen by dropping the coefficient of rolling resistance to zero
JustinSimulator-CrEffectWithSpeed.png
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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 24, 2013 8:15 pm

Sorry, ...
As demonstrated in the following graph,
wind resistance is a geometric progression while
road load-rolling resistance is a simple linear progression.
Resistance.jpg
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"Speed" is in KPH.
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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 24, 2013 9:18 pm

Upgraded graph with a generic Rolling Resistance chart line.
Watts-Speed wRR.jpg
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At 50mph the rolling resistance is approximately 3.5% of the energy required from "Mountain Bike".
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Re: Motor Output Watts For MPH

Post by Samd » Oct 24, 2013 10:01 pm

Oh you guys have answered a question a second time that I didn't even ask. Wow.

I asked what the difference was in assumption between the bike curves. Ah hell. Getting kinda hilarious.
http://ballaratebikes.com/

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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 24, 2013 10:43 pm

Samd wrote:Oh you guys have answered a question a second time that I didn't even ask. Wow.

I asked what the difference was in assumption between the bike curves. Ah hell. Getting kinda hilarious.
Mountain Bike vs Race Bike w/tuck position vs Full Recumbent!
These are all listed in the legend.
Combination of wind and rolling resistance ...
I thought this was obvious and clear!
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Re: Motor Output Watts For MPH

Post by Samd » Oct 24, 2013 10:51 pm

No, I asked about tyres at the start. Good job on still dodging it though. World record.
Given that mountain bikes sometimes have mountain bike tyres, as to road bikes, and vice vera, it's assumed by this reader to be unclear as a representative sample of your average reader.

The riding position is clear. Hence not wanting or needing a lecture on drag components.
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Re: Motor Output Watts For MPH

Post by DrkAngel » Oct 24, 2013 11:16 pm

Samd wrote:No, I asked about tyres at the start. Good job on still dodging it though. World record.
Given that mountain bikes sometimes have mountain bike tyres, as to road bikes, and vice vera, it's assumed by this reader to be unclear as a representative sample of your average reader.

The riding position is clear. Hence not wanting or needing a lecture on drag components.
Mountain bike with standard mountain bike tyres vs
Race bike with standard race bike tyres vs
Recumbent with standard recumbent type tyres!

"Standard" as an average-representative of available in type.

What's with this fixation of yours with tyres?
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