Image from The Telegraph
John is right, Anto.
I haven't looked up the specs but that little battery above, which looks to have the mass of two 3.7V 2900mAh cells or 21.46W at 7.4V, would give 100W (200W used to be claimed for the Vivax motor) for 11 minutes max, and that's assuming the batteries can deliver the current that fast (about 5C; no presently available batteries which can do that are known to me), that you will fully drain the batteries (which will soon kill them beyond recharging) and that there is 100% efficiency in the entire system (in your dreams). In real life I reckon you'll be lucky to get 10W on the road for 20-30 minutes with that setup. Check my numbers and assumptions, if you please, George.
Of course, to a topclass racer, 5% extra power for the longest likely sprint could be worthwhile. To you, not so much. You're not a sprinter. Instead you're looking for endurance. The Vivax is not an endurance setup; even less is it a setup for a four-hour road extravaganza.
Okay, you want a four hour ride, and all you want is a little assistance on the hills and maybe a little help on the flat on the return journey to keep up with the young women. This is important. If you're going to run the motor all the time, you're talking about a battery that will double the weight of your bike. So we're looking for a compromise between reasonable assistance and dead weight to be pedalled home after the battery runs out. (My battery has never run out on the road because I look after it and know precisely what it can do.)
A battery assembly well known to forum members is a round bottle about 13 inches long and just under three inches diameter, containing enough high quality cells (Panasonic, Samsung) in series and parallel to make 8.8Ah at 36V nominal, but weighing around seven pounds with the cradle that fits it to the water bottle sockets. That's 316W of power, about 15 times as much as the little Vivax battery.
Now, you're never going to run this useful battery flat, you're never going to demand a faster current delivery than 1C, and you're going to run it only near the tops of steep hills for a short period of time, and for breakaways from standstill when you have full panniers on the bike (that last bit is not for carbon bikers but for the sensible people), and above all you will try to run it only at half throttle or, more precisely, you will try to control full throttle work to the absolutely necessary minimum. Actually, with a battery that powerful and a modest but efficiently torquey motor (250W) that becomes easy.
Under these circumstances, to include recharging the battery religiously after every ride, no matter how short, this battery, if a quality item to start with, will last for years (mine is four years old and still gives 98%). And you can expect bursts of 100W assistance for short periods for a full day on your average sort of Irish ride, lots of sweeping but not very large hills, some of them nastily steep towards the top, especially in the lanes. Or you could go into the real steepies for four hours. Or you could keep up with the young women on every hill, possibly for four hours. I've gone 22km on hilly roads with the throttle on almost all the time, taking it easy on the first ride after heart surgery, and according to the idiot lights I still had three-quarters of the battery capacity left when I arrived back home, which in my life-extending regime for the expensive battery means I could go double that distance without any trouble on the horizon, which is where I get the figure of 45km from that I usually quote when people ask me what distance the battery will do, because they think I'm being evasive when I tell them the truth, which is, "It depends on you much more than on the battery."
The big bottle battery looks like a thermos flask, if stealth is important to you. The front motor I had before (Bafang QSWXK) was often mistaken for a dynohub.
What I do is to control the battery/motor input by my heart rate monitor: if I'm approaching my permitted max heart rate, I open the throttle or switch in the pedelec assistance (a sort of automtic stepped throttle). Since I ride mostly on long-familiar roads, for an old chappie I look good storming up the hills, after not braking on the downhill before, without power and mostly nobody knows or cares that I switch in power when I run out of puff near the top.
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Yeah, I know, a lot to take in, and a bunch of complicated interrelationships. But a proper electric motor installation (the real stuff, not boutique gear for posers like the Vivax) doesn't leave a lot of change from a thousand Euro, and it's a technical subject, and a new technology to most cyclists who aren't nerds with electronics degrees, so it is worth a little time to get it right.
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I understand sleepers of all kinds. As a kid I fitted a mouse motor (Chevy small block V8, five litres) to a Fiat Topolino (which means Mouse!), which surprised a lot of fellows who looked down on the little "people's car", and later a 5.3L V12 Jaguar engine out on rails behind my BMW Isetta cabriolet (a bubble car) was less sleepy and even scarier when the power lifted the front, steering, wheels... The Vivax looks like too little, too late, too expensive, too much bother, too little return.