I am working with ultacapacitors in my company, developing alternative power sources for automobiles. Ultracapacitors are great for storing energy for short high-power bursts, such as zapping people or accelerating from a stop light. They are also good for storing energy recovered during braking. If you look, you will note that the stun guns take a certain amount of time to recharge (like a camera flash), and the discharge is very short (less than a millisecond). It is this ratio between charge and discharge times that multiplies the battery power up to the needed stun power.
Driving off capacitors continuously is another matter. The charge q held by a capacitor is equal to the capacitance C times the voltage V. The current I drawn from a capacitor is equal to C times the change in voltage deltaV divided by the time deltaT needed to make that change in voltage. This is very different from a battery, which tends to hold a relatively constant voltage until most of its charge has been extracted.
Maxwell Technologies sells ultracapacitors designed for automotive use. For example, they sell a 3000 Farad capacitor rated for 2.7 Volts that has a mass of 0.55 kG and is 0.475 liters in volume. In volumes of 100+, they sell for about $100 each. Some electric motor controllers will operate nominally over a factor of two range of input voltage from the batteries. Let us assume a motor controller that will take the voltage range of 135 Volts to 75 Volts. In this situation, deltaV is 60 Volts. Since 50 ultracapacitors are needed to support the peak voltage of 135 volts, the initial series string will cost $5,000. The capacitance of two identical capacitors in series is half the capacitance of each unit. Therefore, our series capacitance is 60 Farads. So 60 Volts times 60 Farads yields 360 Amp-seconds of charge. Not Ah (Amp-hours), but Amp-seconds. Let us say that you want to accelerate real fast, like a Tesla. Assume 720 Amps for 5 seconds. You will need 10 stings in parallel to store enough energy for that kind of acceleration. So now the total cost is $50,000 and you have 1 Ah of charge. The weight of the 500 ultracapacitors is 275 kg, or 600 lbs. The volume of the 500 ultracapacitors is roughly 200 gallons, or the volume of two 55 gallon drums. Alternatively, you can drives calmly at 70 Amps for about one minute.
No editorial comments, just the facts.
Gerry
