EUC Math - Question #1

[The Fat Unicyclist]

Okay, here is a question for all of you EUC math geeks...

A road runs up the side of a hill. The road is 2.5km long, with a (fairly) consistent gradient of 0.1 (10%).

If a hypothetically fat unicyclist (120kg - including lunch) lived 1km (40%) up that hill and had a fully charged EUC (IPS191 - 1000W / 340Wh), how far would he have to ride UP the hill (from his home), to allow him to ride DOWN the hill to the bottom without overcharging his battery?

[Chriull]

There is not enough known about the regenerative breaking efficiency, charging characteristic of the wheel going down and specific overvoltage threshold including delay of your BMS to give any rough estimate. Imho - if anyone knows - please share!

In some other threads regarding other wheels was stated, that a little bit going up is more than enough to go down safely (to be on the safe side, one could go up a little bit every couple of 100m's going down...), if i remember correctly...

edit: bms characteristics should be known enough, but overcharge characteristics of the battery pack could also be a unknown...

[Hunka Hunka Burning Love]

Let me take a stab at this one, but I'm no math geek by any means.

Okay, say you ride uphill 1 km and use up 1 unit of battery power.  If coming downhill 1 km recharges the battery by 33% or 1/3 of a unit the next two kilometres downhill would recharge the other 2/3 leaving you at 100% charge.  The remaining 0.5 km would overcharge the battery 16.5% so it is best to travel uphill 1.5 km.

 Maybe.

[The Fat Unicyclist]

2 minutes ago, HunkaHunkaBurningLove said:

Okay, say you ride uphill 1 km and use up 1 unit of battery power.  If coming downhill 1 km recharges the battery by 33% or 1/3 of a unit the next two kilometres downhill would recharge the other 2/3 leaving you at 100% charge.  The remaining 0.5 km would overcharge the battery 16.5% so it is best to travel uphill 1.5 km.

 Maybe.

So if the downhill run gives back 1/3 of a unit, then (as I'm starting 1km up) I need to ride uphill 500m, allowing me to then go downhill 1500m.

This is of course assuming that the "1/3 recharge" rule is valid. But is this something that we know about EUC? 

[Chriull]

Imho efficiency is much worse. And also imho the battery voltage while charging(downhill)/discharging(uphill&partly downhill) is very "dynamic" and not directly proportinal to the capacity.

so imho (again?) that is something to be solved empirical. Start i.e. with going up 10m every 500m. Maybe the first time go up 30-50m.. Or the mentioned 500m up and then 1500m down - you will see if it works out ?.

Or you take something like the Charge Doctor V2.0 ( http://forum.electricunicycle.org/topic/346-charge-doctor/) and recharge your wheel just to 80-90% while staying uphill..

 

[Hunka Hunka Burning Love]

Whoops forgot to take into account the house is 1 km up the hill.  I thought the house was 2.5 km at the top of the hill.  I was watching Game of Thrones while replying.  So if riding uphill 1 km uses up 1 unit of battery power and coming back down recharges 1/3 or 33% then travelling down 2 km would recharge 2/3 or 66% of that unit of power used up.  So travelling 0.5 km up and coming down 1.5 km would recharge 33%% plus 16.6% or 49.5 % of the unit used up.    If you go up 0.25 km that 16.6% gets cut in half so even less is recharged.

Does that make any sense?  Sorry it's been a long day and I'm watching Preacher now which is super violent.  So it looks like you might not need to ride up that far?  As long as you ride up a little you should be okay?

I'm just guessing on that 1/3 regeneration estimate.  I did read someone measured like around 30% battery recovery coming downhill after a trip uphill.  So  my sample size to base this estimate on is one which isn't that great.  I've also likely over simplified a few things.  Actually I could be totally wrong with my calculations so take what I've writen with a grain of salt.  A big grain!  

EDIT:. Let me look at it a different way.  Say you travel uphill X kms draining 33% battery power.   Coming down the same distance you recharge 1/3 of the 33% you used up.  You would have to continue travelling downhill 2 times X kms to recharge the total 33% of battery power consumed.  Going downhill over 3 times X would over charge the battery.  So if you travel 500 m uphill you should be able to go downhill 1.5 km if regeneration efficiency is 30%.

If regen is 25% going uphill 500 m would allow you to go down 4 times 500 m  or 2 kms.  So the worse the regen the further you can go downhill or less you have to go uphill to go down the same distance.

I wonder theoretically whether a rider could go forever down an infinite hill if they could tune the regeneration to not over-charge the battery but to only charge what is lost... assuming the battery can last forever....

[HEC]

In general if your trip's start point is regularly at top (or middle) of longer downward hill / slope then charging under maximum battery capacity is the best practise. Either use (modify) charger to have two end voltages or use timer or separate cut-off device base on the battery voltage.

[johrhoj]

The amount of energy you can recover depends on how and where you drive. From the powertrain point of view it looks pretty good. The energy conversion efficiencies from chemical to electrical (battery), DC current to AC current (inverter), electrical to mechanical (motor), and torque to force (transmission and wheels) are all quite high and work just as efficiently returning energy into the battery.  ...  We must also remember that, even though the battery-to-wheel conversion efficiency is pretty good (up to 80% or so), the energy makes a full circle back into the battery and it gets converted twice for a net efficiency of at most 80% * 80% = 64%

The text above comes from a piece of documentation on electric car regenerative breaking. I think it applies to EUC also. It seems to me that the theoretically maximum regeneration then is 64%. That would translate to going up hill all the way, before going down again.

However, any energy used to overcome friction with air and road, cannot be regenerated, and that is why you will never make the maximum. Road conditions and wheather conditions play a role, as well as the speed with which you will go.

If you know how far you can go on a full charge, then you know how many of the energy is used per km, and you can sort of calculate the amount of energy spent that you cannot regenerate.

Hope this helps  

 

[HEC]

There are no transmissions in EUCs but even then the best (claimed) recuperation is 70%, usually between 50 - 60% at most. 

[johrhoj]

Suppose you and your wheel together weigh 135kg.
You have 340WH batteries. This equals to 1.224.000 Joules of energy.
Suppose you get a distance of 20km per charge on flat conditions. This is 61200 J per km.
1 meter up (pure potential energy) = 135 * N = 1350 J. This is the energy you can regain.
Your hill (10%) goes up 100m for every km.
Then:

1km uphill = 1km flat + 100m up equals to 61200 + 135000 = 216200J of energy spent.
1km downhill = 1km flat - 100m down * 66% equals 61200 - 90000 = -28800J of energy regained.

Conclusion is that for every kilometer you go up (your specific hill), you need to go 7.5 kilometers down again to regain all energy, with a regeneration efficiency of 66%. I would say that going 200 meter up should do the trick.

According to these calculations, if you would continually go up or down, in stead of flat, your range would go from 20 km to around 15 kilometer. 

@HEC

The lack of transmission will decrease the energy needed to go flat (less mechanical friction), but not much. In the calculation above i use 66% in stead of 64%. That might make up for the difference.

[dpong]

How fast are you willing to ride down the hill?  Seems that how much braking you are doing on the way down will wildly effect the results. 

[Skara]

12 hours ago, HunkaHunkaBurningLove said:

I wonder theoretically whether a rider could go forever down an infinite hill if they could tune the regeneration to not over-charge the battery but to only charge what is lost... assuming the battery can last forever....

You would need some way to lose the energy. Traditional brakes lose it as heat, so maybe the easiest way to design an EUC which can go downhill indefinitely would be to add disk brakes. A huge heat sink with a fan could work, especially if re-gen efficiency is as low as 30%, in which case 70% is already being converted to heat by the current EUCs. In fact, this makes me think that the efficiency must be better, since otherwise why would the EUCs have trouble with downhill - bad design of course being one possible explanation. 

How you go downhill is important - if you go really slow, the potential energy is reclaimed slowly also, so a heat sink would be sufficient. If you go really fast, air drag will consume the energy, again making it easy on the wheel. So the difficult cases are with moderate speeds, exact worst speed depends on your air drag coefficient, i.e. shape. Trailing an umbrella as an air brake would be a low tech solution, or just keeping your jacket spread wide open with hands. (Now that would grab people's attention!  )

[Jurgen]

Did my change in picture inspire you to answer this question?

Maybe you could ask the manufacturer what the % efficiency is when discharging and when charging.

I don't know the exact efficiency figure of the EUCs but don't count them to be fantastic, especially not going uphill.

F.ex. if going up the efficiency would be 40% (60% loss), and going down it would be 80%; this means going down you regain 80% of the 60% lost going up, which is around 1/3.

This means you will have to drive down 3x the distance you drove up, before you reach 100% charge again.

For a 1000m hill in this example you would have to ride uphill for 500m.

[Mono]

5 hours ago, Skara said:

You would need some way to lose the energy. Traditional brakes lose it as heat, so maybe the easiest way to design an EUC which can go downhill indefinitely would be to add disk brakes.

If an EUC brakes fiercely it actually drains energy. So not going at constant speed should do the job already with a conventional EUC.  

[Skara]

17 hours ago, Niko said:

If an EUC brakes fiercely it actually drains energy. So not going at constant speed should do the job already with a conventional EUC.  

Interesting, I wonder what's happening then? Maybe firmware simply does not allow quick switching between charge and drain of battery. 

Anyway, that situation would be firmly in the "heat sink required" category: both the potential energy and whatever it drains from the battery would need to be dissipated as heat. 

[Mono]

22 hours ago, Skara said:

Interesting, I wonder what's happening then? Maybe firmware simply does not allow quick switching between charge and drain of battery.

I think the reason is that recuperative braking has a limited torque compared to active (battery draining) braking. Or, in other words, the max current for draining is much larger than for charging (I forgot the specific numbers, but I think they are available). 

22 hours ago, Skara said:

Anyway, that situation would be firmly in the "heat sink required" category: both the potential energy and whatever it drains from the battery would need to be dissipated as heat. 

Its pretty similar to the situation where one would continuously switch between max acceleration and max braking. I didn't try it for that long, but I wouldn't be surprised if the wheel would get into its over-heat regime within less than ten or even five minutes.

[The Fat Unicyclist]

Okay, so I've been trying out different "hill things," but I think I've ended up with more questions than before. Particularly after a short ride today up and down and up the hill...

Looking at the attached images, I started at the green dot (with 100% charge), went up the hill a way, down to the bottom, along the flat and back up to where I started from. 

From this (and other rides), I think I have identified the following; 

• Going uphill faster pulls energy from the battery faster. 
• Over a period of time the batteries can't sustain too much draw. 

So the faster I go, the sooner I have to stop, at which time the battery "recovers" and I can continue again. 

But can someone confirm that this is correct for me please (with technical words)?

More confusing is the downhill... particularly on the route I have shown here. During the less-steep parts of the downhill I do indeed notice the battery charge increasing. To the point that it is very close to being 100% again. 

But on the particularly step parts (which are almost to the point that I couldn't brake to a stop if I wanted to), it seems that I am actually using power rather than regenerating it. 

So it occurs to me that there are two extremes here;

1. If I were to free-wheel down the hill - ie. at a neutral speed - I wouldn't generate any charge or use any power (but would probably die).
2. If I stopped on the hill and used the motor to hold my position, it would use power and eventually drain the battery. 

So does that mean that everything in between (speedwise) is in between (chargewise)?

Or to put it another way, is there a point where braking (hard) changes from generating power to using power? 

I would appreciate any physictisical comments on this...

[thefork]

I don't know much about electronics, but it seems to me that for any given down-hill gradient g, with unicycle U and rider weight M, there is a particular speed s that will yield maximum regeneration. There would also be a faster speed s' and a slower speed s'' where the battery will be neither drained nor recharged. Going faster than s' or slower than s'' would drain energy from the batteries.

Please someone correct me if I'm wrong (I would also like to know since I too live near the top of a hill). 

[Chriull]

58 minutes ago, The Fat Unicyclist said:

Okay, so I've been trying out different "hill things," but I think I've ended up with more questions than before. Particularly after a short ride today up and down and up the hill...

Looking at the attached images, I started at the green dot (with 100% charge), went up the hill a way, down to the bottom, along the flat and back up to where I started from. 

From this (and other rides), I think I have identified the following; 

• Going uphill faster pulls energy from the battery faster. 
• Over a period of time the batteries can't sustain too much draw. 

Quote

So the faster I go, the sooner I have to stop, at which time the battery "recovers" and I can continue again. 

But can someone confirm that this is correct for me please (with technical words)?

About this phenomenom was a discussion in this post and before:

Some more information you can finde i.e. here: https://en.wikipedia.org/wiki/Peukert's_law

Also you'd have with most wheels the overheating problematic while going up. Slowly (because the wheel can't go faster) going uphill is one of the most demanding situations for a wheel. 

Your battery pack configurations (how many cells there are in parallel) is the important thing detemining how long how much current the cells can provide. And of course the cooling of the mosfets/motherboard determines how long they can controll/switch the current before they overheat.

Quote

More confusing is the downhill... particularly on the route I have shown here. During the less-steep parts of the downhill I do indeed notice the battery charge increasing. To the point that it is very close to being 100% again. 

Which does not necessarilcy mean that the batteries are charged to 100% again. Once the regenerative breaking happens, the voltage provided by the motor could push up the battery cell voltages so much, that the measurement from the mainboard shows that they are full - but they are just in process of charging and once the motor voltage drops the battery voltage drops again too. (caused by the internal resistance of the cells - this is also discussed in the postings before the link above - but in the "other direction", while discharging).

Also one thing i noticed from my Ninebot One E+: The procent battery charge shown is "induced" from the battery voltage. For absolutely max battery voltage to a little drop always 100% battery charge are shown, and only after a certain threshold of the battery pack voltage a reduced charge is shown. (Like with the tank gauge in most cars - a certain amount of gas has to be used up, before one sees the gauge showing less than full)

Quote

But on the particularly step parts (which are almost to the point that I couldn't brake to a stop if I wanted to), it seems that I am actually using power rather than regenerating it. 

So it occurs to me that there are two extremes here;

1. If I were to free-wheel down the hill - ie. at a neutral speed - I wouldn't generate any charge or use any power (but would probably die).
2. If I stopped on the hill and used the motor to hold my position, it would use power and eventually drain the battery. 

So does that mean that everything in between (speedwise) is in between (chargewise)?

Or to put it another way, is there a point where braking (hard) changes from generating power to using power? 

I would appreciate any physictisical comments on this...

 

As far as i understood till now, there are three types of breaking possible with BLDC motors:

1) shorting the motor coils/putting a load on the motor coils: If the mosfets shorten the coils the motor breaks, like with burned mosfets the wheel is stuck. By PWM the breaking force could be regulated. But imho these shortening induces too much current/stress on the mosfets and the coils! So could be that this is of no practical use in our wheels. Maybe also just for some deceleration/speed cases. In this case energy is just burned by the mosfets and motor coils - no charging or discharging of the batteries.

2) Just like with accelerating the controller board keeps the magnetic field in "front" of the magnets for breaking the controller can keep the magnetic field "behind" the magnets to break the wheel. This way of breaking consumes power from the battery like normal driving.

3) regnerative breaking: The voltage induced by the motor is big enough so that current can flow to the battery -> energy is consumed by the battery (battery is charged) and the motor has a load (the battery) which decelerates the motor. @esajhas also found some links, which show imho also some king of using the controller in combination with the motor coils to act as step up converter for the motor voltage, so that also with lower motor voltages the batteries could be charged?

Edit: Depending on speed/deceleration the firmware is "free to choose" between the different breaking modes - or there are just some breaking modes to be choosen for different use cases...

[Mono]

On 6/7/2016 at 9:08 PM, Skara said:

Interesting, I wonder what's happening then? Maybe firmware simply does not allow quick switching between charge and drain of battery. 

I believe we can see the switch in the graphs @esaj was showing and I also think I can feel it sometimes when breaking as a very short hick-up in the behavior of the wheel. 

On 6/7/2016 at 9:08 PM, Skara said:

Anyway, that situation would be firmly in the "heat sink required" category: both the potential energy and whatever it drains from the battery would need to be dissipated as heat. 

Right, I am pretty sure that you will not be able to power-break for a minute, probably not even for more than 20 seconds. I guess that the motor will heat up pretty quickly and the controller will cease to sustain power breaking.

[Hunka Hunka Burning Love]

I'll have to check my motor temperature the next time I roll down a hill, but does the controller actually heat up?  I'm sure others have tackled longer and steeper hills than I ever have, yet we don't hear any stories of braking failure except when starting with a fully charged battery pack.  I would think the battery would heat up, but what would make the MOSFETs heat up if the speed is within normal operating range and there are no directional changes occuring?

Wouldn't the current just be flowing in the opposite direction making the wheel act like an alternator in a car?  It would just generate electricity rather than consume it as in motor drive mode.  I'm no MOSFET expert so I'm posing this more out of curiosity.

[esaj]

10 hours ago, HunkaHunkaBurningLove said:

I'll have to check my motor temperature the next time I roll down a hill, but does the controller actually heat up?  I'm sure others have tackled longer and steeper hills than I ever have, yet we don't hear any stories of braking failure except when starting with a fully charged battery pack.  I would think the battery would heat up, but what would make the MOSFETs heat up if the speed is within normal operating range and there are no directional changes occuring?

Wouldn't the current just be flowing in the opposite direction making the wheel act like an alternator in a car?  It would just generate electricity rather than consume it as in motor drive mode.  I'm no MOSFET expert so I'm posing this more out of curiosity.

From what I know, during regenerative braking, the bridges needs to be "pulsed" on and off, so the cycle seems to be more like "short through low-side mosfet to build up magnetic field in coil" (also brakes the motor) and then close the low-side, open high-side so the energy stored in motor coils can be discharged to the battery pack and repeat, fast. Not sure if the highs-ide mosfets are actually "open" (conducting) when the battery is being charged or whether they just rely on the internal body diodes to conduct. Then it would probably be enough just to keep the low-side shorted and when the voltage raises high enough to overcome the body diode voltage drop, (some) current will flow to batteries. If using only the diodes, they have a (relatively) high voltage drop (for a typical diode, around 0.6-0.7V, but can go above 1V on the mosfets with higher current), so if the motor was producing, say, 5A (I don't know how much current the braking produces), the power dissipation on the mosfet when that current flows through the body diode could be around

0.6V * 5A = 3W

1V * 5A = 5W

On the other hand, on 75NF75 (for example), the maximum junction-to-case -thermal resistance is around 0.5 degrees Celsius per watt, so assuming good thermal connection to heatsink and large enough heatsink, that shouldn't be a problem. On the other hand, if the connection is not good, it can go way up  (62.5 degrees per watt junction-to-ambient, ie. totally without heatsinking or mosfet thermally disconnected from the heatsink). Different manufacturers cite somewhat different maximum junction temperatures, and may use different dopings, but it's usually somewhere between 125-175 degrees celsius (150 degrees seems a good rule of thumb?) where the doped N/P -regions start to break. Bear in mind that that's the internal junction temperature, which is always higher than ambient temperature (ie. temperature inside the mainboard compartment) during use.

[zlymex]

I've installed an precision current sensor(LEM LTS-25NP) last year to my IPS T260(quite similar to IPS Lhotz) to measure the current between the battery and control board.
The data was sampled by Graphtec GL220 with 100ms interval both for current and voltage signal at the same time.

The hill I tested is 931 meters long and 111 meters high(slope of 12%),  the total weight was 89.7kg and the potential energy 27.1Wh.
The ascend consumed 35.87Wh so the efficiency is 68.1%.
The descend charged 12.69Wh so the efficiency is 52.0%.
Therefore, the overall efficiency is 35.4%
If I lived 1km on the hill, then I have to climb 548 meters up before I can go down to the bottom on a fully charged T260.
The upward distance is calculated by 1/(1/35.4%-1)

I did the similar thing to my MSuper V3 last month and rode the same hill again a bit faster this time and the total weight is 95.6kg.
The ascending efficiency is 55.4%, descending efficiency is 53.8% and the overall efficiency is 29.8%.
It can also be seen from the temperature curve that it rises very fast, but begins to fall when downhill.

As far as I know, there is only one type of braking for an EUC, that is regenerative braking.

It is a lovely place of OP to ride an EUC.

[The Fat Unicyclist]

23 minutes ago, zlymex said:

It is a lovely place of OP to ride an EUC.

I can still see my house from there! 

[Hunka Hunka Burning Love]

46 minutes ago, zlymex said:

As far as I know, there is only one type of braking for an EUC, that is regenerative braking.

Correct me if I'm wrong, but doesn't the current have to be negative in order for charging to occur?  It looks like most of the downhill current is initially hovering around -5A then goes positive to around +8A.  Is there still charging potential when the current is positive?  I wonder if you were to go faster downhill whether that would drop the average downhill current towards a greater negative value resulting in greater regeneration.  

Regarding temperature I can see that going uphill draws some spikey current peaks around the 22:13 mark around +20A which would makes sense making the temperature rise as more current is drawn.  When descending it looks like the majority of the current spikes are from -5A to +8A which is moving a lot less electrons around so it cools down.  I wonder though if you were to go faster downhill whether things would heat up again say if you could create -20A to recharge.  Your speed going up looks pretty well mirrored with the speed going down.  I wonder what a speed going down of 35-40 kph would look like on the graph (not that I recommend doing it unless there is enough reserve speed available from the wheel!).