Panasonic System Power Delivery Explanation

[flecc]

I've often advised of the need to pedal slowly in order to get full power on these motor units, There's been a number of queries about this and I've seen comments posted that the hill climbing on the Kalkhoff Agattu was best around 9 mph, another that top gear only was needed and yet another comment that it's better on hills than the flat.

The reasons for all those on that bike with the standard rear sprocket is that 9.4 mph is the last speed in top gear at which full motor power is contributed, from then on up it reduces in four phased steps until it's zero at 15 mph.

EU law requires power to phase down as it approaches the 25 kph limit, but without the point specified and it certainly doesn't intend as early as 9 mph (14.4 kph). Also the zero point in EU law is 25 kph (15.62 mph), not 15 mph, so why those two discrepancies?

The reasons are both due to national laws.

First the easy one to explain. Where most EU countries use the electric pedal assist 25 kph limit, Germany has it's own 24 kph limit, so the German made Kalkhoff has it's 22 tooth rear sprocket chosen with that in mind so that power disappears by 24 kph (15 mph). To exactly match general EU law a 21 tooth sprocket is needed to give the slight increase to 25 kph (15.62 mph).

The explanation for the very early phase down is more complex, and it results from Japanese law on electric assist pedal cycles. The Japanese have determined that the maximum power allowable must not exceed the power the rider puts in (1 to 1), and that this should only be fully available within normal cycling speeds. Unfortunately for us, the Japanese have a very different view on cycling speeds to that of UK riders, They regard their common cycling speed as being 15 kph (9.4 mph), and for "sports" riders like our lycra brigade, 24 kph (15 mph), which would raise a laugh from UK club riders who can often average 20 mph for an hour in moderately hilly areas.

Since sports riders don't use electric assist bikes, only the "common" bike's speed is legislated for. Therefore in accordance with that, the Panasonic design has integral to it the phase down above full assist at 15 kph (9.4 mph) when the bike is in top gear.

But that's not the end of it, for Japanese law prescribes the power phase down slope as well. Since an analogue slope doesn't readily match digital electronic systems working, Panasonic have chosen to have four step downs giving a rough tail off of power corresponding with the legal requirement, which is expressed in Japanese law by this equation:

1 - ( [kph - 15] / 9 ) = assist factor

where kph is the road speed.

Quite simply what this means is the road speed in kph, minus 15 (the 1 to 1 power assist limit), then divided by 9 produces a result which is subtracted from 1.

In a practical example, at 20 kph (12.5 mph), taking 15 from that 20 kph gives us 5. Then that 5 divided by 9 gives 0.55 recurring. To complete the equation we take that 0.55 from 1 to give 0.45 or 45%, and that's the ratio of rider power that the motor is allowed to assist with at 12.5 mph.

At the lower speed of 11 mph (17.6 kph) using the same calculation, 17.6 minus 15 then divided by 9 and taken away from 1 gives 0.71 or 71% of the riders input given as motor assistance.

At the higher speed of 13 mph (20.8 kph), only 36% of rider input is given by the motor.

For the export markets Panasonic now have the High Power mode which gives 1.3 times assist, but this is not a blanket 1.3 times, it's 1.3 times full 1 to 1 assistance up to 9.4 mph, and then above that speed at 1.3 times the above equation percentage results. So the three examples given in declining order of assist with speed become 92% at 11 mph, 59% at 12.5 mph and 47% at 13 mph. You can see from that how speeding up from 11 mph to 13 mph by pedalling faster halves the help the motor gives you, whatever mode you are in, so making work for yourself.

Of course all these are for top gear, and since the motor drives through the gears, when you change down, the power phase down point and the power assist levels drop too. On the Agattu with the Shimano Nexus Inter-7 hub, dropping from 7th to 6th gear is a 13% drop, so that's what you take from the above. It means a maximum 1 to 1 power assist speed of 8.2 mph, down from 9.4 mph, but of course that is what makes these bikes such superb hill climbers, the ability to shift the maximum power down to a speed that copes with any hill, however steep.

For example, our 7 speed Agattu's bottom gear is 60% down on the top gear, so the maximum assist power is available from zero to 3.8 mph, about the slowest speed one could keep balance at. This means a moderately fit 75 kilo rider providing a reasonable 200 watts could climb a 1 in 3.7 (27% hill) at that speed in highpower mode, and one would have to search far and wide for a hill that steep, there being only a handful of them in Britain.

For those with lesser hills, the rear hub sprocket can be reduced to shift the phase down point and end point of power assistance upwards, the limit set by the steepest hill a rider needs to climb, and ultimately the limits of the motor's power to maintain a high road speed against wind resistance.

To adjust the above calculations after the rear sprocket is changed, divide the equation answer by the new sprockets number of teeth and multiply by the old number of teeth, which is 22.

Of course all this is on a "nice to know" basis, so there's no need to carry around a mathmetician with calculator on the carrier. In practice it's just a matter of slowing the pedal speed when more assistance is wanted, either by going slower or by changing up a gear The fastest cadence (pedalling rotations) for the maximum assist at 9.4 mph in top gear is a very leisurely 39 per minute, or 1.5 seconds per rotation.

You might feel that Panasonic should alter the internal power phase down system for the export markets, but there are very good reasons for not doing that. Most important is that not very much power is needed for riding on the flat at normal cycling speeds, so providing full power at those levels could waste battery current and reduce this system's excellent range. Another is that the quality of the pedelec system operation which this unit is so famed for could be impaired by sensing at higher pedal rotational speeds, the system used not suitable for that. Since the desired result can be achieved by changing the rear sprocket on the bike, gaining higher speeds without impairing the unit's operation, the design is best left as it is.

I've entered this on my Lafree / Kalkhoff website for future reference on this link:

Power levels
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[simonbarnett]

Cripes! All very knowledgable, but the bottom line is change up to ascend a hlll and slow the pedalling. The only difficulty is it's the opposite of what we expect to do!

[flecc]

Originally Posted by simonbarnett

Cripes! All very knowledgable, but the bottom line is change up to ascend a hlll and slow the pedalling. The only difficulty is it's the opposite of what we expect to do!

Yes, it can be confusing, and it's the cause of many who try these briefly thinking they are no good. When they pedal fairly fast and don't sense power, they pedal even harder to try and get it!

The system's logic is simple though. If you are spinning fairly fast it sees that as you getting on fine and not needing help. If you are pedalling slowly, it sees that as you struggling, so it comes to the rescue. Logical when you think about it.

The important thing is that it allows it to be just like a normal bike in every way, unlike any other e-bike system. Help is there when it's genuinely necessary, but at other times you can be almost unaware that it is an e-bike, especially when the power is turned off.
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[musicbooks]

Thank you very much Flecc. This is extremely helpful. I am going to post a report on my impressions after two weeks of commuting very soon. I find that I am now getting the hang of the motor now and what is really great about it is as I ascend and reache the steepest part of the hill, it can feel as though there is no power. But if I slow down, there is a surge of energy through the hub and the bike seems to be pushed by an extra pair of hands from behind, thus alleviating the pain in the legs and chest just in the nick of time.

I have been experimenting with gears and levels of effort during my climb up the twin peaks of Mount Kilimanjaro and I'll comment on that too asap.

Thanks again
BW
musicbooks

[sabretache]

As one of those waiting delivery of a Pro Connect, I'd just like to add my own thanks for the impressive technical information provided by Flecc. It is very much appreciated.

[Larkspur]

Originally Posted by sabretache

As one of those waiting delivery of a Pro Connect, I'd just like to add my own thanks for the impressive technical information provided by Flecc. It is very much appreciated.

Me too! Thanks for taking the time to write it all down for us Flecc.

If I've understood what you are saying, then I assume that bike manufacturers must use rear sprocket size to synchronise cadence to the assisted speed limit in whatever market they are selling the bike in, taking account of whatever top gear ratio they have fitted. Am I right?


Chris

[flecc]

Yes Chris, the sprocket size determines the final assist cutoff point corresponds with the legal limit, 25 kph in most of Europe and 24 in Germany. For Europe in general that leaves the highest point of maximum power at 9.4 mph and the phase down as described. If they were sold in Sweden it would be 30 kph and maximum power to 11.3 mph.

That's not Sweden suddenly getting all liberal, they have a higher minimum age limit of 15 years, and all riders have to wear helmets and have third party insurance.
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[Larkspur]

Originally Posted by flecc

Yes Chris, the sprocket size determines the final assist cutoff point corresponds with the legal limit, 25 kph in most of Europe and 24 in Germany. For Europe in general that leaves the highest point of maximum power at 9.4 mph and the phase down as described. If they were sold in Sweden it would be 30 kph and maximum power to 11.3 mph.

That's not Sweden suddenly getting all liberal, they have a higher minimum age limit of 15 years, and all riders have to wear helmets and have third party insurance.
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Oh good..as my wife is of Swedish descent, I reckon I must definitely qualify for a smaller sprocket when my Pro Connect arrives.

Chris

[nasatir]

Thank you Flecc, I found this very helpful, indeed.

However, I am not clear about what pedaling strategy to employ when attempting to maximize my range on a hilly ride.

I presume the maximum range is obtained by simply turning off the motor but I would like some assist up some of the hills. Should I drop into the lowest gear and pedal as slowly as I can (thus saving my bio mechanical energy) or should I shift into the highest gear and pedal as quickly as I can which would be quite slow, of course, but would this save my stored electromechanical energy?

Would my battery last longer if I pedaled slowly up hills in my lowest gear or pedaled slowly up hill in the highest gear I can manage?

Thanks.

[flecc]

Hi nasatir

With the Panasonic unit, the greatest saving of energy for hill climbing is to opt for a speed that allows you to climb on Standard power, rather than the slightly faster climb on high power. This is what I said in my Agattu review Extra section:

Reducing speed has a far greater effect than changing power modes. For example, at 7.5 mph on a 14% hill in Standard mode, changing to High Power saved me 32 watts of effort, but cost the motor and battery the same 32 watts extra. Alternatively, slowing very slightly to 6 mph and leaving it in Standard mode saved me 52 watts of effort, saved the motor 52 watts of effort as well and reduced the load on the battery.

So although going slower like that makes the motor run for a longer journey, the fact that it's only a little bit slower but saves so much power will increase the range, as well as being less demanding on you.

However, pedal at or just below the 39 cadence for maximum power, for although that uses a bit more than if you pedalled much faster, it starts to remove the point of having electric assist if you pedal fast just to save a minute bit of power. Much better is to switch off when the going is easy and save in that way without stress to yourself.

In that way I was able to achieve an over 50 mile range equivalent with average hills included at the age of 71, so many would at least equal that. I doubt if many would require such a range though.
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