How much miles per hour required to generate electricity calculations?
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Distance:
Speed, Pack KWh rating, driving conditions, aerodynamics, vehicle weight, hills, temperature, driving styles and several other factors
play into the distance question.
The basic formula for determining distance is: ( KWh of pack / wh/m ) = Distance
*note: there are adjustments that have to be made to this formula, see usable pack size below*
Watt-Hour per Mile (Wh/m):
The basic rule of thumb for vehicle is:
Small Vehicle 250-300wh/m
Small Pickup 350-400wh/m
The calculation is: Volts x (Amp Draw / MPH ) = Wh/m
Battery Pack Size (KWH):
Pack Voltage x Amp-Hour rating of battery = KWH
Usable Pack size: KWh x 0.80 x Peukerts = Usable KWh
Peukerts:
Lead-Acid = 0.55
LiFePO4 = 1.0
Yes, you get a BIG hit on your available power when using Lead-Acid. However, they are generally cheaper than LiFePO4 batteries.
Putting all this together - Example:
Vehicle: Miata
Batteries: 12 - 12V Lead-Acid, rated at 100 ah
Pack Voltage: 144V (12 batteries x 12V each = 144V)
Pack Size: 14.4 Kwh (144V x 100 ah = 14.4 Kwh - Remember, we can not use all this)
Usable Pack: 6.336Kwh (14.4 x 0.8 x 0.55 = 6.336 Kwh usable)
From experience, we know that a Miata using a 144V system will draw around 90amps at 50MPH.
Therefore, the Wh/m usage = 144V x ( 90Amps / 50MPH ) = 259Wh/m
The distance our Miata will travel on this setup is: 6.336kwh / 259wh/mi = 24 Miles (at 50MPH)
If we had a lithium pack of equal voltage and ah, the range would be 44 miles (because Peukerts effect does not play a role)
14.4 x 0.8 = 11.52 kwh usable / 259 = 44
On a side note, 144 volt pack of lithium ( LifePO4) cells would consist of 45 of the lithium cells (they are nominal 3.2 volts each)
To CALCULATE this in reverse, (using LifePO4 cells)
say you need to go 44 miles per charge at 50 mph and want to know what size batteries you need......
we will use the 259 wh/mi avg.
wh per mile / pack voltage = ah per mile
So in our "car" 259/144= 1.8ah per mile
so you would need ah per mile x miles per charge needed x 1.2 (so you still had 20% charge left after the drive)
in our "car" 1.8 x 44 = 79.2 x 1.2 = 95 ah batteries at 144 volts needed to go the 44 miles.
A lot of people wish to go close to 100 miles in our experience. To make it simple, for this car to go say 88 miles (double the 44 it is
capable of now) the total Kwh of the pack has to be doubled. This can be done in a few different ways, most common would be to double
the ah rating of the batteries used or double the voltage by using double the amount of the same 100 ah batteries.
In our above case, that would be 45 of the 200 ah cells, or 90 of the 100 ah cells.
Keep in mind the components used must be rated for the voltage and amperage
B
battery would be 100amp draw, and 3C is 300 amps. So if you limited your controller to draw the max of 300 amps from the batteries at
144 volts, the acceleration would be Ok. With a 300 amp limit at 288 volts the acceleration would be impressive.
The usual recommendation is to use larger ah batteries, from 160-200 ah and adjust your voltage to get your needed KWh pack, so that
3C is between 480 - 600 amps.
Performance
Now we get to the fun part, calculating HP
V x A = watts, and watts/746 = HP so V x A / 746 = HP
If we had a 144 volt pack of 200ah batteries, and a 1000 amp controller, using the above formula we could have 193 HP, (at a 5C draw)
and if we had 288 volt pack of 100ah batteries we could have potentially 386 HP ! (these are calculated without efficiency included,
figure about 85% efficient)
Only one problem, that much electrical power put into the motor could easily destroy it rather quickly ! The common "in the field"
estimate of KW power a 9" motor can handle (for short periods) is 100 KW. So using the above formulas, 144 volt system should be
limited to about 700 amps, and the 288 volt system to 350 amps. Still, 135 hp is pretty good for a small car. NOTE: use high power levels
at your own risk for motor damage.
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