I took the 50wh/km from
this guy's thesis here's an excerpt:
...
His calc was for a much faster kart, so I feel 50wh/km is very conservative in the case of this kiddie kart. I'd expect a Tesla to get near 100wh/km if it did slow laps of a go kart track
Without reading the whole paper for now...
And for a single lap on his göteborg race track not a km but a lap;
lap duration is 48s with about 12seconds in regenerative braking mode
and another 10-12 seconds of coasting along
(eyeballed from figure 3.4)
So maybe 25 seconds of load
Now, since you take ~ 3mins per km as per the calculatio above,
and we talk 56.6-ish Wh in 25 seconds of throttle down
(in case you want to stick with that example)
the multiplication factor would be 7.2 (180/25)
7.2*56.6 means 407Wh per km
Now, the gain from regenerative braking is already factored in in his 56.6Wh (w/o regen braking he used 67.9Wh per lap [figure 6.1])
And since I don't assume you have regen braking
that is what we would want to look at
7.2 * 67.9 -> 489Wh per km
Now, motor power is not necessarily a part of that equation mind you,
speed is, acceleration is, weight is, coefficients are..
but motor power is NOT..
it only affects how much acceleration you can achieve and what speed you're able to reach (and thus reduce time)
but since you converted that to distance travelled, speed is
effectively cancelled out.
You can run a 5kW motor and draw less than 800W mechanical from it easily.
So the difference between it and your 800W motor is just the weight and the efficiency difference between the two systems.
If you want to look at it the other way around...
his min calculated battery was 19.2Ah and in a 48V setup
(920Wh) to be drained in one race (13min)
putting the setup in the realms of 4246W of average powerdraw
And while you certainly cannot draw as much with your 800W motor,
that also means you cannot reach the 90km/h he peaked at, and certainly not accelerate as quickly.. sooo your total lap time would certainly increase,
but it's not totally impossible that your battery would have to be about the same size to finish the same race (in longer time at slower speeds but traveling the exact same distance on the exact same track)
Aaanyways...
NO you mess up a few minor things that will bite you later on.
first: 600W mechanical power out IS NOT 600Watt power drawn from the battery!
(system efficiency... 'he' gained an overall efficiency of 66.7% with his setup for example)
if we assume the same overall efficiency for your setup 600W of mechanical power on average on the rear wheels means 900 Watts of power drawn from the battery.
second: The Ah rating of your battery is NOT a fixed value,
it is what you can trickle from said battery at a much lower than 1C rating.
once you crank up the amperage the useable amount of stored energy is MUCH lower (as I said @4C I assume about 45% means ~3.2Ah in your battery not more)
that's only a guestimated value of course, if you have the proper battery documentation you can derive the actual values from there.
once you've drawn those 3.2Ah of energy, the battery is FULLY depleted
So DOD SOC and all that technical babble becomes 100% obsolete
since while nominally you only used 45% the battery still is in a 100% cycle (well actually -as I mentioned- it'll recover slightly.. so say 85-90%)
You will NOT stay above 55% SOC in fact you will drop below 10%,
once the cells are allowed to cool down it then again might rise back to 15% (in best case scenario) but that's it..
[Oh I think you got Depth of discharge and state of charge the wrong way around..
SOC 0% is an empty battery, and SOC 100% is a full battery.
DOD 0% is a FULL battery, and DOD 100% is an empty battery.
nevermind]
And these two things get you over and over again..
power draw (as stated above) might be as high as 900VA for your 600W estimate means 25Amps
and at peak power (pedal to the metal uphills) migth easily crack the 30Amp mark in drawn currents.
which again reduces the available [or rather useable] capacity of your battery.
that effect is also escalated by the low voltage cutoff of the controller btw..
(a 36V controller usually cuts power @32Volts at least to keep lead acid cells rechargeable.. and that means there's always a not too insignificant left over charge in your battery)
if you want a guaranteed 10min runtime..
all I can suggest is to scale up the batteries to 11Ah
that at a assumed max current of 33A would equate to 3C and an easier go on the battery.. a theoretical runtime of 20mins
and with a maybe 65% useable capacity @3c gives you 13mins;
the 3min overhead gives you a remaining SOC that should be enough to keep the cell at 10.5V and thus rechargeable.
And yes, going easier on the pedal increases ride time...
but that wouldn't be too bad, would it
Oh 75kg roughly.. good
let's check with
some math
64N @5.55 m/s means about 360watts mechanical
to keep the kart at speed on a slight incline.
less than 200 on level road
and maybe 300 to accelerate decently.
nice!
so the 800W motor never really needs to provide half it's nominal power; great.
Indeed the 7Ah batteries might do the trick then.
Sure one can accelerate quicker and climb steeper hills and all that to
reach it's limits, but ordinarily that's not exactly necessary in that setup on 'normal' western roads.
If you have 7Ah batteries alread.. it's worth a try I'd say
(with 14Amps peak current it might be able to peak at a 24min runtime then if I'm not mistaking)
'sid
- I hope it's wrong.