Real range vs. declared range?

To get just a little more mathy: squaring the speeds:

30^2 / 20 ^2 = 9/4, so it takes 2 &1/4 times as many watt-hours per unit time to go 30 mph vs 20 mph.

But i cover the same distance in 2/3rds the time when i go 30 vs 20.

So i multiply 9/4* 2/3 and i get 3/2. Put another way, compared to 20 mph, at 30 mph it takes 50% more energy to go a mile, so my watt-hours per mile will increase by 50%, and my range will decrease by 33%.

This affect continutes to be more dramatic at 35 mph, 40 mph, etc...
 
So here is my 'practical application test' from today before and after upgrades. These were replacing the 14-28T freewheel with 11-28T, plus changing OEM CST "knobby" All terrain 26x2.1" tires (55PSI) with puncture resistant CST 26x1.75" hybrid tires (65 PSI).

My usual city loop is 22miles with a very steep hill (15%) at the end. Last time I did an average of roughly 13.5 mph at PAS 4/5 with some pedaling but not too much because of ghost pedaling at higher speeds (20mph+). Afterwards the battery just went to 0 but then recovered to 1 (out of 5 levels) after stopping. I assume this is 15-20% capacity (48V 10.6Ah), depending on which V/% chart I trust ;-)

Today I did the same 22 miles loop at PAS 4/5, but average speed increased to 16.5 mph and battery went down to 1 bar and then recovered to 2 bars after the ride. I assume this is around 25-30% battery capacity.

I am just now measuring voltage every hour while charging in order to determine at what time the 80% charge level is reached for storage purposes and battery longevity.

It shows nicely that change of the freewheel easily gets rid of the annoying ghost pedaling. I went actually on a "no battery" 22mls ride yesterday, and honestly the bike rides now nicer and almost faster and shifts better than my old and trusted Trek FX (which might benefit finally from some maintenance). Using the battery I can now go to max 25mph on a flat, which is wicked fun, but only 22mph once battery drops to 50% charge. I think the hybrid tires add significantly to the range, saving roughly 10% capacity. Plus, if I tried to reduce average speed to 13.5 mph it probably be around at least 20% just for the change of tires, which probably adds a total of 5-6 miles in range. Way more if I reduce to PAS 2/3. Next upgrade definitely is a 14Ah battery so that will get me into a way more comfortable range.

I know, too many parameters changed to be described by math or to be a remotely scientific test, but, nevertheless, it provides some interesting insights for me and definitely shows the desired effects of the upgrades. The ebike is actually advertised as up to 40 miles range, and I am pretty confident that I can reach it at low PAS levels and after upgrades.

Btw, thanks for all the tips for upgrades and battery charging/measuring on here. I could not and would not have figured it out on my own. I am thankful to have found this great and knowledgeable community!
 

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So here is my 'practical application test' from today before and after upgrades. These were replacing the 14-28T freewheel with 11-28T, plus changing OEM CST "knobby" All terrain 26x2.1" tires (55PSI) with puncture resistant CST 26x1.75" hybrid tires (65 PSI).

My usual city loop is 22miles with a very steep hill (15%) at the end. Last time I did an average of roughly 13.5 mph at PAS 4/5 with some pedaling but not too much because of ghost pedaling at higher speeds (20mph+). Afterwards the battery just went to 0 but then recovered to 1 (out of 5 levels) after stopping. I assume this is 15-20% capacity (48V 10.6Ah), depending on which V/% chart I trust ;-)

Today I did the same 22 miles loop at PAS 4/5, but average speed increased to 16.5 mph and battery went down to 1 bar and then recovered to 2 bars after the ride. I assume this is around 25-30% battery capacity.

I am just now measuring voltage every hour while charging in order to determine at what time the 80% charge level is reached for storage purposes and battery longevity.

It shows nicely that change of the freewheel easily gets rid of the annoying ghost pedaling. I went actually on a "no battery" 22mls ride yesterday, and honestly the bike rides now nicer and almost faster and shifts better than my old and trusted Trek FX (which might benefit finally from some maintenance). Using the battery I can now go to max 25mph on a flat, which is wicked fun, but only 22mph once battery drops to 50% charge. I think the hybrid tires add significantly to the range, saving roughly 10% capacity. Plus, if I tried to reduce average speed to 13.5 mph it probably be around at least 20% just for the change of tires, which probably adds a total of 5-6 miles in range. Way more if I reduce to PAS 2/3. Next upgrade definitely is a 14Ah battery so that will get me into a way more comfortable range.

I know, too many parameters changed to be described by math or to be a remotely scientific test, but, nevertheless, it provides some interesting insights for me and definitely shows the desired effects of the upgrades.

Btw, thanks for all the tips for upgrades and battery charging/measuring on here. I could not and would not have figured it out on my own. I am thankful to have found this great and knowledgeable community!

Well Welcome to our little corner of the internet then :)
 
So here is my 'practical application test' from today before and after upgrades. These were replacing the 14-28T freewheel with 11-28T, plus changing OEM CST "knobby" All terrain 26x2.1" tires (55PSI) with puncture resistant CST 26x1.75" hybrid tires (65 PSI).

My usual city loop is 22miles with a very steep hill (15%) at the end. Last time I did an average of roughly 13.5 mph at PAS 4/5 with some pedaling but not too much because of ghost pedaling at higher speeds (20mph+). Afterwards the battery just went to 0 but then recovered to 1 (out of 5 levels) after stopping. I assume this is 15-20% capacity (48V 10.6Ah), depending on which V/% chart I trust ;-)

Today I did the same 22 miles loop at PAS 4/5, but average speed increased to 16.5 mph and battery went down to 1 bar and then recovered to 2 bars after the ride. I assume this is around 25-30% battery capacity.

I am just now measuring voltage every hour while charging in order to determine at what time the 80% charge level is reached for storage purposes and battery longevity.

It shows nicely that change of the freewheel easily gets rid of the annoying ghost pedaling. I went actually on a "no battery" 22mls ride yesterday, and honestly the bike rides now nicer and almost faster and shifts better than my old and trusted Trek FX (which might benefit finally from some maintenance). Using the battery I can now go to max 25mph on a flat, which is wicked fun, but only 22mph once battery drops to 50% charge. I think the hybrid tires add significantly to the range, saving roughly 10% capacity. Plus, if I tried to reduce average speed to 13.5 mph it probably be around at least 20% just for the change of tires, which probably adds a total of 5-6 miles in range. Way more if I reduce to PAS 2/3. Next upgrade definitely is a 14Ah battery so that will get me into a way more comfortable range.

I know, too many parameters changed to be described by math or to be a remotely scientific test, but, nevertheless, it provides some interesting insights for me and definitely shows the desired effects of the upgrades. The ebike is actually advertised as up to 40 miles range, and I am pretty confident that I can reach it at low PAS levels and after upgrades.

Btw, thanks for all the tips for upgrades and battery charging/measuring on here. I could not and would not have figured it out on my own. I am thankful to have found this great and knowledgeable community!

If ya can find some type of arms to go down from the rack to the frame on both sides it would help strengthen and solidify your rack there mate.

Nice lookin bike ya have there :)
 
If ya can find some type of arms to go down from the rack to the frame on both sides it would help strengthen and solidify your rack there mate.

Nice lookin bike ya have there :)
True, I actually have some arms that came with it that I could make fit. But for an extra battery or light stuff to bring along this one is more versatile with its quick release, plus rated 20lbs. For future heavy tools or groceries or camping or kayak hauls I have plan B in place :)
 

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To get just a little more mathy: squaring the speeds:

30^2 / 20 ^2 = 9/4, so it takes 2 &1/4 times as many watt-hours per unit time to go 30 mph vs 20 mph.

But i cover the same distance in 2/3rds the time when i go 30 vs 20.

So i multiply 9/4* 2/3 and i get 3/2. Put another way, compared to 20 mph, at 30 mph it takes 50% more energy to go a mile, so my watt-hours per mile will increase by 50%, and my range will decrease by 33%.

This affect continutes to be more dramatic at 35 mph, 40 mph, etc...
I don't want to lecture you :), but... from a physics point of view, the energy used is the "work" W = F * ds where F is the force and ds is the displacement. As you correctly said friction goes (approximately) with the square of velocity F = k*v^2, so W = k*v^2 ds, where k is the friction constant and v is the velocity. But v = ds / dt, which means ds = v dt. This again means W = k*v^2 * v dt. So the energy used is equal to k*v^3 dt, where dt is a (small) time interval.

Oooooook... I see some raised eyebrows here , but the point is that if you look at the energy used as a function of time, it goes as v^3, but if you look at it as a function of distance, - aka the range - it goes at v^2, as you correctly pointed out in your first comment. This means that to cover the same distance, energy goes like v^2.

So the difference in energy at 30 and 20 mph is actually (30/20)^2 = 2.25 times as you stated originally, not 1.5. And that means that if the range at 20 mph is 100 miles, for instance, at 30 will be only... 100/2.25 = 44 miles. Hard to believe but true (approximately).

That's also why increasing the bike hour record by a few miles needs a lot, really a lot of effort, that is mostly spent in reducing that friction coefficient k (mass doesn't really affect speed at constant velocity), because the energy goes linear with it, and not quadratically.

But... there is a but: the point is not even this because we do not know how the declared range has been calculated by every brand as, unlike for cars (cheating a part, right VW?...) there is no accepted standard.

That's why I created this thread, to assess more or less how much range we can expect in "realistic" conditions. We know that that "realistic" depends on a multitude of factors: overall weight, speed, gears, slope, acceleration, tyres, and even wind and air pressure (aka altitude)! But at least in this way we can understand how much to expect in "reasonable" conditions before buying an ebike.
 
True, I actually have some arms that came with it that I could make fit. But for an extra battery or light stuff to bring along this one is more versatile with its quick release, plus rated 20lbs. For future heavy tools or groceries or camping or kayak hauls I have plan B in place :)

I am saying this only because i had one and had 2 cans of beans and a pound of hamburger and a litre
of milk on mine and it broke at the weld on the seatpost collar.

Okie dokie, just sayin, be safe ;)
 
I am saying this only because i had one and had 2 cans of beans and a pound of hamburger and a litre
of milk on mine and it broke at the weld on the seatpost collar.

Okie dokie, just sayin, be safe ;)
Absolutely, I get it. It was $14.12 at the Walmart clearance rack so I won't even put milk on it, which I actually buy in gallon size :)
 
I don't want to lecture you :), but... from a physics point of view, the energy used is the "work" W = F * ds where F is the force and ds is the displacement. As you correctly said friction goes (approximately) with the square of velocity F = k*v^2, so W = k*v^2 ds, where k is the friction constant and v is the velocity. But v = ds / dt, which means ds = v dt. This again means W = k*v^2 * v dt. So the energy used is equal to k*v^3 dt, where dt is a (small) time interval.

Oooooook... I see some raised eyebrows here , but the point is that if you look at the energy used as a function of time, it goes as v^3, but if you look at it as a function of distance, - aka the range - it goes at v^2, as you correctly pointed out in your first comment. This means that to cover the same distance, energy goes like v^2.

So the difference in energy at 30 and 20 mph is actually (30/20)^2 = 2.25 times as you stated originally, not 1.5. And that means that if the range at 20 mph is 100 miles, for instance, at 30 will be only... 100/2.25 = 44 miles. Hard to believe but true (approximately).

That's also why increasing the bike hour record by a few miles needs a lot, really a lot of effort, that is mostly spent in reducing that friction coefficient k (mass doesn't really affect speed at constant velocity), because the energy goes linear with it, and not quadratically.

But... there is a but: the point is not even this because we do not know how the declared range has been calculated by every brand as, unlike for cars (cheating a part, right VW?...) there is no accepted standard.

That's why I created this thread, to assess more or less how much range we can expect in "realistic" conditions. We know that that "realistic" depends on a multitude of factors: overall weight, speed, gears, slope, acceleration, tyres, and even wind and air pressure (aka altitude)! But at least in this way we can understand how much to expect in "reasonable" conditions before buying an ebike.
No need to apologize. Your physics checks out. I should have slowed down and done the math all the way.
 
Since "real conditions" is still inherantly subjective, then perhaps the most honest thing for manufacturers to do is to list the watt-hours of the battery and let the customer understand that their range will vary greatly with conditions and rider usage.
 
Another consequence of what I was saying above concerns the maximum speed attainable on flat given a certain maximum power output.

In this case the energy delivered will be P*dt, but it is also F*ds (see my previous post), from which, since F=k*v^2, we have that P*dt = k*v^2*ds, or P = k*v^3 since v = ds/dt. Therefore, the velocity depends on the CUBIC root of the power.

This means that if, for example, you go from 250 W to 500 W, the increase in top speed will be only 25%, while with a 1000 W bike almost 60%, and with 2000 W you finally double your top speed, as (2000/250)^(1/3)=2.

Not bad, but not what many people would expect. It should also be considered that since in EU ebikes the motor assistance cuts off at 25 km/h (and is aided by the pedal), it's difficult to say what would be the maximum speed of a EU-compliant ebike at 250 W on the flat. It is possible to estimate it approximately, however, by reading on the display how much power P is delivered by, for example, pedaling at a constant 20 km/h, flat and windless, and calculating Vmax = 20*(250/P)^(1/3). If, for example, I consume 200 W at 20 km/h, I might expect a max speed of only... 21.5 km/h :confused: , with the same pedal assist (that is not true of course). I will try that as soon as possible, although it's always windy here.

I conclude by pointing out that much of this applies only to a certain approximation. And sorry for my nerdish posts! :geek:
 
I conclude by pointing out that much of this applies only to a certain approximation.
Next are aerodynamic considerations/calculations please. Completely underappreciated in the available range calculators, except maybe for weather/wind, which kinda goes in the same direction.

Wind and hills obviously are some of the worst enemies of regular cycling, and hence factors that likely influence power output of motors (hence batteries and range), significantly, and especially in the lower powered ebikes (250W-500W).

Since wind data is readily available in the weather forecast, probably something one can easily implement with some formula? The direction of wind is obviously important too.

 
We are straying off topic here, and i stand to be corrected, but it is my understanding that F=kv^2 is used for turbulent flow whereas aerodynamic shapes which can produce laminar flow encourage the friction force to approach v to the power of 1. This is how fully faired recumbents like the Varna Diablo reach speeds over 80 mph.

However, the best the daily cyclist can hope for is to reduce your frontal area by lowering your handle-bars or tucking in. This reduces the k factor but not the v^2 factor of F=kv^2.
 
We are straying off topic here, and i stand to be corrected, but it is my understanding that F=kv^2 is used for turbulent flow whereas aerodynamic shapes which can produce laminar flow encourage the friction force to approach v to the power of 1. This is how fully faired recumbents like the Varna Diablo reach speeds over 80 mph.

However, the best the daily cyclist can hope for is to reduce your frontal area by lowering your handle-bars or tucking in. This reduces the k factor but not the v^2 factor of F=kv^2.
Definitely an underappreciated consideration since air resistance seems to outweigh rolling resistance as well as weight individually, and even combined for faster riding.

Anecdotally, I only recently started noticing that while riding at ebike speed starting at 20-22mph wind gets significantly stronger/more noticeable than at acoustic bike speeds of 13-15 mph average. It's almost to a level I experience on a motorcycle but with full face helmet. Intuitively, the 57% air resistance described for faster/stronger riders seem to make a lot of sense (to me) even at these relatively low speeds.

1709479802572.png
 
We are straying off topic here, and i stand to be corrected, but it is my understanding that F=kv^2 is used for turbulent flow whereas aerodynamic shapes which can produce laminar flow encourage the friction force to approach v to the power of 1. This is how fully faired recumbents like the Varna Diablo reach speeds over 80 mph.

However, the best the daily cyclist can hope for is to reduce your frontal area by lowering your handle-bars or tucking in. This reduces the k factor but not the v^2 factor of F=kv^2.
I would love to find experimental power vs. speed data for bicycles, but it is not easy. I have only found not validated theoretical models around.

However, I was thinking that by taking advantage of the data measured and recorded by modern e-bikes and a constant slight descent, long enough to reach a decent speed, one could theoretically measure the friction coefficient of one's bicycle under realistic conditions quite easily.

The idea would be:
1) start stationary, in normal posture, on a day with negligible wind.
2) let the bike go downhill, without pedaling
3) download the data and see what the v(t) relationship is.
4) repeat several times, in slightly different positions of the pedals.

Basically, one could calculate the difference between potential energy Ep(t) = mgh(t) sin alpha, where alpha is the slope angle and kinetic energy E(t) = 1/2 m v(t)^2) at each speed v(t).

This difference would give a good evaluation of friction vs speed k(v) for YOUR bicycle with YOURSELF on top. No wind tunnel required... :cool:
 
I would love to find experimental power vs. speed data for bicycles, but it is not easy. I have only found not validated theoretical models around.

However, I was thinking that by taking advantage of the data measured and recorded by modern e-bikes and a constant slight descent, long enough to reach a decent speed, one could theoretically measure the friction coefficient of one's bicycle under realistic conditions quite easily.

The idea would be:
1) start stationary, in normal posture, on a day with negligible wind.
2) let the bike go downhill, without pedaling
3) download the data and see what the v(t) relationship is.
4) repeat several times, in slightly different positions of the pedals.

Basically, one could calculate the difference between potential energy Ep(t) = mgh(t) sin alpha, where alpha is the slope angle and kinetic energy E(t) = 1/2 m v(t)^2) at each speed v(t).

This difference would give a good evaluation of friction vs speed k(v) for YOUR bicycle with YOURSELF on top. No wind tunnel required... :cool:
For car racers there is a program (I can't remember the name), which is used to calculate the CDa (drag and loss coefficient) of their vehicles. They find a flat road, get the vehicle up to 60, and simply coast. They must put the mass of their vehicle and all contents for it to work. The formula is a simple derivation of F=MA, where F is the amount of drag slowing them down, M is the mass of the vehicle and A is the rate they are decelerating at. Keep in Mind that Acceleration/Deceleration is expressed as a change in velocity, and will still be called acceleration in physics. i.e. applying the brakes applies acceleration to your body to a physicist.

I used this program once to learn the CDa of a performance car I had, which had a body designed to produce large downforce figures. But to press a car downward requires "Work" and made the CDa of that vehicle as bad as a minivan. The roof of the car was only about 37 inches from the ground, and to the layman, it looked aerodynamically slick.

Then you can enter the CDa value into most formulas to figure out how much force/work is required to achieve a given steady-state speed. Once you know that figure, it can be converted to watts.

Keep in mind there are several eBikes which will tell you how many Watts are being fed to the motor at your current speed. If you have one of those bikes, you can cut to the chase.
 
Thank you for the information. Yes, it's more or less what I have in mind, only using the speed record downhill (and the phone GPS). High school physics, nothing more complicated.

It could be interesting trying with several bikes/riders. The slope should be not too much (to avoid too quick accelerations), but enough to reach a good terminal velocity (30 km/h or so) before the end. Then one could extrapolate for higher speed/powers. I will try as soon as I can and there is no wind, that is not easy here as we - thankfully - have a gentle, cool Trade Wind here most of the year (you should be especially generous with it, for it is what allowed Christopher Columbus to reach your untouched continent. :))
 
Dunno if there are any "grin" fanboys on this list here but the grin "cycle analyst" gives you a lot of quality info. I think i've only scratched the surface of what mine can do. In-the-moment speed and power read-outs, and it will tell you the watt-hours left, and calculate the honest watt-hours of the battery itself (nice way of testing manufacturer specs). I feel like a decent understanding of the drag coefficient could just be to cruise on flat and record watts at differrent velocities, and extrapolate the coefficient.
 
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