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Some Useful Energy Conversions
The energy stored in a capacitor is :
1/2 CV2 where C is the capacitance in farads and V is volts. The result is in
joules, which are the same as watt-seconds. So a 3000 farad capacitor
charged to 2.7 volts stores (3000 x 2.7 2) /2 =10935 joules. So if you could
extract all that energy with no losses, you could run a 1093.5 watt load for
10 seconds.
One horsepower of mechanical energy is defined as equivalent to 746 watts
of electrical energy. So this capacitor could theoretically run a perfect 1 HP
motor for 14.7 seconds. Of course, in real life, you can't get all the energy
out of the capacitor with no losses, and also a real motor will require more
than 746 watts input to make 1HP mechanical output.
And in between the capacitor and the motor you will likely also require
some power conversion to convert the capacitor voltage to whatever the
motor requires.
The kinetic energy in a moving object is given by 1/2 MV²_-, where M is the
mass in kilograms and V is velocity in meters per second. The result also
comes out in joules, so it is pretty easy to calculate the electrical equivalent
of kinetic energy. So if you have a 2 metric ton (2000KG) car moving 100
KM/hr (about 60MPH) its kinetic energy is 1/2 (2000)[(100 x 1000 /3600)]2
= 771604 joules. Since a 3000F cap charged to 2.7V contains 10935 joules,
it would take the energy of about 71 fully charged ucaps to accelerate it
from a standstill to 100 KM/H. This of course doesn't count the losses in the
motor, tire friction, wind resistance, inefficient power conversion, etc.
If you consider a 200 KG (440lb) motorcycle under the same circumstances,
it would require only about 7 ucaps to get it to 60 MPH.
The big advantage of ultracapacitors over batteries in such applications is
that they can be discharged almost instantaneously, so if you can turn the
stored electrical energy into speed as fast as the motor can use it. And
electric motors can be run for short periods at many times their nameplate
power rating as long as they don't overheat or mechanically come apart.
Google "electric drag race car" to see a ton of info and videos on this
subject. And most of them don't even use ucaps, just batteries.