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Author Topic: a bit of math (1C charging)  (Read 683 times)

gyrocyclist

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a bit of math (1C charging)
« on: June 02, 2017, 10:53:44 PM »

I'm interested in the most efficient speed for touring, i.e,  the speed that gives the least total time. Equivalently, the largest average mph. I ended up writing a python script (attached, if anyone wants to play with it or check for errors in my math). One result I found surprising:
    if you can charge in four hours it's better to go slower;
    in two hours it doesn't matter;
    in one hour you should ride faster
I'm starting to understand why 1C is so great.

Simplifying assumptions: you ride at a constant speed until empty; you recharge to 100%; you get the following ranges at the following speeds (roughly what I think I get on my 2016 SR: 
    40mph, 145miles
    55mph, 100miles
    70mph, 80 miles

Statistics are for riding 400 miles (mpl is milage per leg) (see also attached plot)

charge time: 1 hour
mph: 45 legs: 3.1 mpl: 127 avg mph: 36 time: 11.0 rideTm:  8.9 chargeTm:  2.1
mph: 50 legs: 3.6 mpl: 112 avg mph: 38 time: 10.6 rideTm:  8.0 chargeTm:  2.6
mph: 55 legs: 4.0 mpl: 100 avg mph: 39 time: 10.3 rideTm:  7.3 chargeTm:  3.0
mph: 60 legs: 4.4 mpl:  91 avg mph: 40 time: 10.1 rideTm:  6.7 chargeTm:  3.4
mph: 65 legs: 4.8 mpl:  84 avg mph: 40 time:  9.9 rideTm:  6.2 chargeTm:  3.8
mph: 70 legs: 5.0 mpl:  80 avg mph: 41 time:  9.7 rideTm:  5.7 chargeTm:  4.0
mph: 75 legs: 5.1 mpl:  79 avg mph: 43 time:  9.4 rideTm:  5.3 chargeTm:  4.1

charge time: 2 hours
mph: 45 legs: 3.1 mpl: 127 avg mph: 30 time: 13.2 rideTm:  8.9 chargeTm:  4.3
mph: 50 legs: 3.6 mpl: 112 avg mph: 30 time: 13.1 rideTm:  8.0 chargeTm:  5.1
mph: 55 legs: 4.0 mpl: 100 avg mph: 30 time: 13.3 rideTm:  7.3 chargeTm:  6.0
mph: 60 legs: 4.4 mpl:  91 avg mph: 30 time: 13.5 rideTm:  6.7 chargeTm:  6.8
mph: 65 legs: 4.8 mpl:  84 avg mph: 29 time: 13.7 rideTm:  6.2 chargeTm:  7.5
mph: 70 legs: 5.0 mpl:  80 avg mph: 29 time: 13.7 rideTm:  5.7 chargeTm:  8.0
mph: 75 legs: 5.1 mpl:  79 avg mph: 30 time: 13.5 rideTm:  5.3 chargeTm:  8.1

charge time: 4 hours
mph: 45 legs: 3.1 mpl: 127 avg mph: 23 time: 17.5 rideTm:  8.9 chargeTm:  8.6
mph: 50 legs: 3.6 mpl: 112 avg mph: 22 time: 18.3 rideTm:  8.0 chargeTm: 10.3
mph: 55 legs: 4.0 mpl: 100 avg mph: 21 time: 19.3 rideTm:  7.3 chargeTm: 12.0
mph: 60 legs: 4.4 mpl:  91 avg mph: 20 time: 20.3 rideTm:  6.7 chargeTm: 13.7
mph: 65 legs: 4.8 mpl:  84 avg mph: 19 time: 21.2 rideTm:  6.2 chargeTm: 15.1
mph: 70 legs: 5.0 mpl:  80 avg mph: 18 time: 21.7 rideTm:  5.7 chargeTm: 16.0
mph: 75 legs: 5.1 mpl:  79 avg mph: 19 time: 21.6 rideTm:  5.3 chargeTm: 16.3
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BrianTRice

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Re: a bit of math (1C charging)
« Reply #1 on: June 02, 2017, 11:16:24 PM »

Nice! I've been tinkering on a worksheet for this, but naturally got carried away trying to justify my numbers with lots of drag etc modeling.

I think the one hour charge doesn't have that optimum speed because of drag onset raising charge consumption faster than the charge rate can compensate for, though, even at 1C.

I'll check your script to see whether I'm missing something or you are, though.
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BrianTRice

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Re: a bit of math (1C charging)
« Reply #2 on: June 02, 2017, 11:27:44 PM »

The calculus way to think about it is:

As long as drag increases more than linearly with speed...
Increasing speed uses more energy per distance covered.
You save time if your combined riding and charging time per that distance is lower.
So, for every increase in speed, the time saved eventually cannot be compensated for by the charge rate.

The worst part is that it's the charge limit of your destination that is often the determining factor for us with 1C / 11kW charging support!

And I still think you're underestimating drag at high speed. One thing to point out is that this speed is closer to airspeed than ground speed. Any headwind shifts the curve.
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hubert

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Re: a bit of math (1C charging)
« Reply #3 on: June 03, 2017, 03:21:54 AM »

Yes, that's the kind of calculation I made when I had to ride my newly purchased S 500km to home, but using only the internal charger. The calculations yielded that sad conclusion: to have a better average speed, ride so so so slowly, say 45km/h (30mph). Needed 1.5 days, and spent the best time of a day just waiting for the battery to charge sooo slowly.

Once or twice during the trip I could take advantage of the "vacuum" just behind a truck driving at somewhat higher speed. But that's uncomfortable and dangerous.

Have you calculated the instant power (in MW) you are "charging" when filling the ICE bike or car at the gas station? The main advantage of smoking vehicles is not so much the "range", but rather their very quick refill capability.
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42Cliffside

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Re: a bit of math (1C charging)
« Reply #4 on: June 03, 2017, 03:33:34 AM »

but at 33 kWh per gallon that gas is really inefficient.


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BrianTRice

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Re: a bit of math (1C charging)
« Reply #5 on: June 03, 2017, 04:14:31 AM »

Yes, that's the kind of calculation I made when I had to ride my newly purchased S 500km to home, but using only the internal charger. The calculations yielded that sad conclusion: to have a better average speed, ride so so so slowly, say 45km/h (30mph). Needed 1.5 days, and spent the best time of a day just waiting for the battery to charge sooo slowly.

Yes, but thankfully getting to a 4kW charging rate is now closer to being a commodity and that does mean you can travel at 45-55mph and not suffer for it.

Once or twice during the trip I could take advantage of the "vacuum" just behind a truck driving at somewhat higher speed. But that's uncomfortable and dangerous.

Yeah, it's much safer and more comfortable to duck behind a good windscreen or a basic fairing.

Have you calculated the instant power (in MW) you are "charging" when filling the ICE bike or car at the gas station? The main advantage of smoking vehicles is not so much the "range", but rather their very quick refill capability.

Yes, that's why we campaign to get better charging rate limits, stations, etc.

I'm not sure I have this right, but the charge rate to match a (looked up pump rate) 13gal/min is 13gal/min * 33.4kWh/gal = 434kWh/min.

And 434kWh/min * 60min/hr = 26000kW = 26MW.

but at 33 kWh per gallon that gas is really inefficient.

It's super-efficient! By a certain/usable interpretation, 100 miles on a 13kWh battery is 300mpg on an equivalent of ⅓ gallon of petroleum.

At that rate, we'd only need 26kWh to get a 200 mile range.

To achieve this realistically, let's say we want the break to be 15 minutes. At that rate we need: 26kWh * 60min/hr / 15min = 104kW.

But 1 hour break for 3 hours of riding is acceptable for most, and that means 26kW of charging, which is a 1C rate.

That's the sweet spot we need to aim for if we can get it. Right now, 1C charging with an aerodynamic boost is the way to get there.
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gyrocyclist

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Re: a bit of math (1C charging)
« Reply #6 on: June 03, 2017, 05:53:53 AM »

The calculus way to think about it is:

As long as drag increases more than linearly with speed...
Increasing speed uses more energy per distance covered.
You save time if your combined riding and charging time per that distance is lower.
So, for every increase in speed, the time saved eventually cannot be compensated for by the charge rate.

The worst part is that it's the charge limit of your destination that is often the determining factor for us with 1C / 11kW charging support!

And I still think you're underestimating drag at high speed. One thing to point out is that this speed is closer to airspeed than ground speed. Any headwind shifts the curve.

Attached is updated version of script. Changes: you can optionally input up to three data points (speed, range) if you don't like my defaults/they don't apply to the specs for your bike. Note that two of my default data points are from the Zero specs, the third (40mph, 145 range) is a guess on my part. Even if you don't want to run the script, you might want to take a quick look at the 'usage' to better understand what is does and doesn't do.

Also increased output to show stats up to 100mph, which I believe is approx. the top speed of any zero

Brian, I agree with most (all?) of your comments, with these caveats:

"for every increase in speed, the time saved eventually cannot be compensated for by the charge rate"
Hmm... mathematically correct -- but we only need to consider our fastest possible speed. More realistically, the top speed at which
we normally ride (mine is 85mph, for short stretches. I hit 90+ on a trial run on a flat, straight back-road when I was fooling around.
But I'm none too comfortable at those high speeds. At least until I get a full body-armor)
 
"I still think you're underestimating drag at high speed"
Um, I don't have any implicit factor for drag. It's implicit in the data points: mpg, range.

"Any headwind shifts the curve"
Yes! I should have  added "wind speed = zero" to my list of "ridiculous simplifying assumptions."
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42Cliffside

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Re: a bit of math (1C charging)
« Reply #7 on: June 03, 2017, 11:37:46 AM »

Quote
Quote from: 42Cliffside on Today at 02:33:34 PM
but at 33 kWh per gallon that gas is really inefficient.

It's super-efficient! By a certain/usable interpretation, 100 miles on a 13kWh battery is 300mpg on an equivalent of ⅓ gallon of petroleum.

At that rate, we'd only need 26kWh to get a 200 mile range.

whaa???

I was off by a bit, a gallon is 36 kWh Gas is super inefficient. I can go Far
Far Farther on electricity than on gas.
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grandpa

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Re: a bit of math (1C charging)
« Reply #8 on: June 03, 2017, 01:59:15 PM »

Simplifying assumptions: you ride at a constant speed until empty; you recharge to 100%; you get the following ranges at the following speeds (roughly what I think I get on my 2016 SR: 
    40mph, 145miles
    55mph, 100miles
    70mph, 80 miles

Seem very very very different of my personal feeling with my 2016 S

at a true constant 70mph during 100->0% batery, i think i cannot do 70 miles...

And the big missing of your graph is the famous max speed ! 80/83mph
I estimated that at a true constant 82mph during 100->0% battery, i cannot do 50 miles...
will change the aspect of your graph, higher speed is far from the way to do faster travel (even at 1C)
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Electric Terry

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Re: a bit of math (1C charging)
« Reply #9 on: June 03, 2017, 11:02:50 PM »

I love the concept of this graph, just run some real numbers and I think you will see the numbers across the board are optimistic for 2 reasons.

1) First is aerodynamics and drag.  I agree with everyone above, you can not maintain 85 mph for even an hour as drag is too high, and you will be hard pressed to ride at even 75 mph for an hour, its doable with a tailwind but not normally. 

2) But most important is a 1C 1 hour charge time is great, but effectively its really almost 1.5 hours.  To effectively measure charge time, you need to measure the total kWh added which say is 11.4 kWh on a 2017 13.0 SR at a charge stop from 0% to 100%.
You charge from 0-85% in 53 minutes at almost 12 kW (2 J plugs), but your charger tapers as voltage reaches 116 and it takes you 27 minutes until you are charging at less than 1000 watts and are full.  So that is 1 hour 20 minutes.

But wait, there is more.  You added 11.4 kWh in 1 hour 20 minutes, but the charging stop was 2 miles off the highway, and from the second you got off the exit, to the moment you got back on after charging is the time you need to use.  Say it was 5 minutes on both ends.  so your total charge time to add 11.4 kWh is actually 1 hour 30 min! or .75C not 1C

But wait, there is more.  You have to account for time it would take to replenish the 4 miles of total energy (at slower speeds) to get to the charge station and back from the highway as you may have left the highway at 3% and arrived back on the exit ramp at 97%
So subtract that from your energy added and you will see you're now like 0.75-0.7C

But wait, there is more.  You can't maintain 85 mph all the way down to 3% battery.  You can't even maintain 75 mph.  And unless you have a tailwind and are going down an incline, chances are it will be even slower.  So lets say you exit the highway between 10% and 20% SOC.  you are now charging less total at 1C (20% to 85%) but you still have to wait the same time for the taper charge, and it still takes you the same time to get on and off the highway and plug in.  And it still takes energy to do that.

Guess what?  You're 1C charge rate effectively becomes much closer to a 0.5C charge rate than it does 1C

And to calculate the best possible range, you want to match your ride rate to your charge rate.  If it takes 2 total hours to charge, you want to discharge in 2 total hours.  To ride for 2 total hours on the highway, you need to be around 55 mph or slower.

If you don't believe me, get some Diginow superchargers, and plan a single point about 50 miles away with dual J plugs.  Leave your house and top off at the closest dual J plugs to your house.  The second you are full and take off you start a timer.  Stop at the dual J plug location about 50 miles away and charge to full or as much or little as you want.  Turn around and go back to the first location and top off all the way to 100%.  I think you will find even with 1C charging, the slower you go down to perhaps 55 or 60 mph the total less time it takes.   As at 55 mph you perhaps don't even have to stop at the 2nd station, you can just bypass it and turn around and be able to make it back.  Think about how much time that saves, right?

This is the other factor.  You might have to stop early to charge because there are Dual J plugs 35 miles away, but not again for 80 miles.  In 60 miles there is a single j plug only.  You want to try to skip that  Since you don't want to try to ride 115 miles at highway speed, you stop at 35 miles to top off, but now you spent waiting for the full 100% taper charge, you spent the time getting on and off the highway, and the energy to get there just to add say 50% to your battery, and in this case your effective charge rate is well below 0.5C even though you charge at a 1C charge rate.  Does that makes sense?

Or you skip the dual J plugs in 35 miles and go to the single J plug but now your charge rate actually is 0.5C, you see?  There's a lot of strategy that is hard for a simple computer program to account for all factors. 

You want the numbers where it makes sense to ride 85 mph or faster?  Get a Vetter fairing.  My effective speed to travel for the least total time on a trip was over 100 mph, so the actual speed limit or about 10 mph over is what limited my the time of my trips.  This is the slightly modified 2012 Zero I went over 1000 miles on in less than 24 hours on in 2014.  And in 2015 went over 300 miles at Interstate speed on a single charge.  So you might say I have a little experience with estimating times and range.  With this little drag, the penalty for going faster is minimal, and the ability to choose to only stop where there are 4, 8 or 12 J plug or more at one location becomes easier to choose while skipping over the charge stations that are not multiple.

Add some more variables and your graph estimation will begin to get more accurate.  I'm excited to see it!  I hope this helps explain some things you might not have thought about.
« Last Edit: June 03, 2017, 11:22:39 PM by Electric Terry »
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gyrocyclist

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Re: a bit of math (1C charging)
« Reply #10 on: June 04, 2017, 05:46:34 AM »

I love the concept of this graph, just run some real numbers and I think you will see the numbers across the board are optimistic for [many]  reasons.

Thanks, Terry. I had thought about some, though not all, of the points you mention. Let me reiterate: my graph represents a non-realistic, best case scenario. It's only intended to give insight as to possible trade-offs between charge time and bike speed. It's in no way intended as an actual guide as to what anyone should expect in the real world.

I'll only comment on one of your points:   
  "And to calculate the best possible range ..."
True, but I'm not interested in the  best possible range. Rather, I'm interested in how quickly I can ride 400 miles. In other words, I'm interested in optimizing (reducing) time as opposed to optimizing (extending) range

Your mileage may vary. (Ouch;  bad pun. peace!)
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Re: a bit of math (1C charging)
« Reply #11 on: June 04, 2017, 09:16:11 AM »

I just want to go interstate speed (70-80mph) for a couple hours to get to mountain roads, or maybe just the dealer.
All I need is the new for 2030 ZF45 pack, complete with 6c charger.
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Re: a bit of math (1C charging)
« Reply #12 on: June 04, 2017, 10:17:00 PM »

Ok guys, i have something for you that it's now time to share. I made a tool in Excel to calculate AT WITCH SPEED IT IS BETTER TO RUN to get from point A to point B in the less time as possible. It take account of charging power, initial battery SOC, battery size, time to  install charging setup, etc... I made it about 3 years ago for my 2000km trip and it work PERFECT !!

At first i tought i could make an apps with it and make money but hey.. money is not what make me more happy.. it's youi all that discover the great benefit of EV transport guys and all great comments i receive from you for my various contributions..

so... time to pay it forward guys..! ;)

Here is OPTITRIP EV calculator v1.2

 

« Last Edit: June 04, 2017, 10:37:58 PM by Doctorbass »
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Re: a bit of math (1C charging)
« Reply #13 on: June 05, 2017, 01:05:18 AM »

Ok i see there is somem errors on the Wh/km since i modified few lines.. i'll correct these and repost it

Doc
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gyrocyclist

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Re: a bit of math (1C charging)
« Reply #14 on: June 05, 2017, 05:37:28 AM »

Ok guys, i have something for you that it's now time to share. I made a tool in Excel to calculate AT WITCH SPEED IT IS BETTER TO RUN to get from point A to point B in the less time as possible. It take account of charging power, initial battery SOC, battery size, time to  install charging setup, etc... I made it about 3 years ago for my 2000km trip and it work PERFECT !!

At first i tought i could make an apps with it and make money but hey.. money is not what make me more happy.. it's youi all that discover the great benefit of EV transport guys and all great comments i receive from you for my various contributions..

so... time to pay it forward guys..! ;)


 
Very nice. Could you explain your data sources, in particular, "measured efficiency?" I assume you made the measurements at each speed -- if so, over how many miles for each data point? Which data points are calculations, and which are real-world measurements?
(Um, if I knew more about excel am guessing I could took at the formulas in the spreadsheet)

I'm confused at to what the "range" column means. My first thought was kilometers per charge, but the numbers seem way to high for that.

I look forward to your revision.
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